Keywords: Process Control
Abstract: Advanced motion systems like pick-and-place machine used in the semiconductor industry challenge the frontiers of systems and control theory and practice. Since experimentation is fast, a machine in the loop procedure can be explored to close the design loop from experiment, experimental model building, model-based control design, implementation and performance evaluation. Nevertheless, reliable numerical tools are required to meet the challenges posed with respect to dimensionality and model complexity, including the open problem of determining disturbance models and suitable specification models. Extension of linear modelling techniques towards some classes of nonlinear systems is relevant for improved control of specific motion systems, such as with friction. Other challenging applications in need for advanced modelling and control are fuel efficient vehicles, including ultra-clean engines, and vehicle electric and hybrid power trains. Another area where a lot of development for identification and control is necessary, is the control of unstable phenomena in plasma’s for nuclear fusion reactors.

Keywords: Nonlinear System Identification, Multivariable System Identification
Abstract: Hammerstein and Wiener models are nonlinear representations of systems composed by the coupling of a static nonlinearity N and a linear system L in the form N-L and L-N respectively. These models can represent real processes which made them popular in the last decades. The problem of identifying the static nonlinearity and linear system is not a trivial task, and has attracted a lot of research interest. It has been studied in the available literature either for Hammerstein or Wiener systems, and either in a discrete-time or continuous-time setting. The objective of this paper is to present a unied framework for the identication of these systems that is valid for SISO and MIMO systems, discrete and continuous-time setting, and with the only a priori knowledge that the system is either Wiener or Hammerstein.

Keywords: Nonlinear System Identification, Mechanical and Aerospace
Abstract: This paper considers the identification of linear systems based on binary measurements of the output. In contrast to existing techniques with strict requirements on the excitation signals, the identification is performed based on a sequence of short and independent measurements. The linear systems are represented using Finite Impulse Response (FIR) models, whose parameters are estimated by exploiting the known characteristics of the binary measurement. Two different methods are derived, both yielding convex parameter estimation problems that can be solved with standard software. The first achieves a high prediction accuracy but yields constrained optimization problems. A second alternative is therefore derived with a slightly worse performance but without constraints, such that solutions can be found more quickly. The identification procedure for both is illustrated on a simulation model.

Keywords: Nonlinear System Identification, Multivariable System Identification, Grey Box Modelling
Abstract: In this paper, a novel method is proposed for the identification of a fairly general nonlinear structure called Linear Fractional Representation (LFR), also related to Lur'e type systems. It consists of one static nonlinearity (SNL) connected to the input and the output via a multiple-input-multiple-output (MIMO) linear time-invariant (LTI) block. The nonlinear LFR structure encompasses, e.g., Wiener-Hammerstein and nonlinear feedback models. The procedure starts from 2 state-space models corresponding to the best linear approximation at 2 input variance levels. The MIMO LTI block is estimated by exploiting the approximate structural relationships, taking the state transformations carefully into account. Using the measured input and output, the input and the output of the SNL block are then reconstructed, yielding a nonparametric estimate of the SNL, which is finally converted into a parametric estimate. In the whole procedure, the internal signals, the linear and the nonlinear part need not be known. No stability requirement was imposed on the linear models used. The functional form of the SNL is not needed to find the MIMO LTI block and the nonparametric SNL estimate. The simulation results, supporting the theory, show the superior quality of the obtained initial estimate of the LFR nonlinear model compared to both linear models. This shows that the method is a very promising approach in the field of block-oriented nonlinear modelling.

Keywords: Nonlinear System Identification, Nonparametric Methods, Other
Abstract: Model identification is addressed for nonparametric Hammerstein-Wiener systems with static input nonlinearity and backlash output nonlinearity. Interestingly, both input and output nonlinearities are allowed to be nonparametric and nonsmooth. A frequency identification method is developed that involves the application of conveniently designed pulse width modulated (PWM) input signals. PWM inputs feature frequency-decoupling of the underlying Wiener subsystem, making possible its accurate frequency identification whatever the input nonlinearity. Then, a set of points on the input nonlinearity are in turn estimated applying PWM input signals repeatedly with fixed frequency but different amplitudes.

Keywords: Closed Loop Identification, Nonlinear System Identification, Identification for Control
Abstract: The continuous-time model identification problem of closed-loop Hammerstein-Wiener system with unknown controller and different noise situations is studied. A two-stage approach is proposed, based on the refined instrumental variable method. With the assumption of monotonic nonlinear function, the closed-loop non linear model is iteratively estimated as an over-parameterized MISO LTI model. To obtain an accurate model in the closed-loop case, the identification is implemented in two stages: 1) identification between the input and the reference signal, which produces estimate of the noise-free input, 2) identification between the output and estimated noise-free input signal. Monte Carlo simulation analysis is carried out to illustrate the effectiveness of the proposed method, in both output and process noise circumstances.

Keywords: Nonlinear System Identification
Abstract: In this paper, we investigate the identification of the class of block-oriented nonlinear systems presented by Li et al. [2011] by using an iterative method. Firstly, a common model is proposed to represent such block-oriented systems. Then identifying the common model is formulated as a biconvex optimization problem. Based on this, a normalized alterative convex search (NACS) algorithm is proposed under a given arbitrary nonzero initial condition. It is shown that we only need to find the unique partial optimum point of a biconvex cost function in the formulated optimization problem in order to obtain its global minimum point. Thus, the convergence property of the proposed algorithm is established under arbitrary nonzero initial conditions. The approach presented in this paper provides a unified framework for the identification of block-oriented systems.

Keywords: Nonparametric Methods, Frequency Domain Identification
Abstract: Most research on system identification is focused on the identification of parametric models, for example a transfer function or a state space model where the information is condensed in a few parameters. In the daily practice, nonparametric methods, like frequency response function measurements, are intensively used. Recently, it was indicated that nonparametric identification methods could be used to robustify the parametric identification framework. A nonparametric preprocessing step can also be used to reduce or even eliminate the required user interaction, making system identification accessible for a much wider user group. For that reason, there is an increasing interest in nonparametric identification. In order to choose, compare, and to benchmark these nonparametric methods, it is very important to select the proper criteria. In this paper we identify and discuss the important choices that should be considered. It will be shown that these strongly depend on the intended use of the nonparametric model.

Keywords: Nonparametric Methods, Frequency Domain Identification
Abstract: Recently, Hägg, Hjalmarsson and Wahlberg proposed a novel non-parametric method that directly estimates the frequency response at N equidistant frequencies when N measurements are available. The specific feature of the method is that together with these estimates, the transient, or, equivalently, the leakage, is explicitly estimated. The estimates are obtained by solving a least-squares problem. The method involves three design variables, the number of estimated transient terms, a number of auxiliary impulse response coefficients (that also are estimated), and the size of a frequency window. At present there is no analysis of how these design variables affect the properties of the method, which we will call TRIMM (TRansient Impulse response Modeling Method). In this contribution we provide bias and variance analysis for two extreme cases of the window size. We show that at one extreme value, the method coincides with the Empirical Transfer Function Estimate, and at the other extreme it is close to directly estimating a FIR model. This indicates that TRIMM provides an intermediate between non-parametric and parametric estimation. The results allows us to quantify bias and variance errors at the two extreme cases under study, and gives insight into how to choose the design variables in a systematic way.

Keywords: Frequency Domain Identification, Nonparametric Methods, Vibration and Modal Analysis
Abstract: A review of the relationship between the frequency response function of linear system and the DFT of the input and output signals show that the output DFT is a sum of two terms. The first term contain the FRF multiplied with the input DFT and the second term capture the effect when the system is not operating in a periodic fashion. The utilization of these two terms when performing non-parametric frequency response function estimation has led to the previously developed Local Polynomial Method. This paper acknowledge that the two terms can better be approximated by local rational functions with a common denominator polynomial and a new method called Local Rational Method has been developed. Numerical simulations illustrate the performance of the new rational method in comparison with the polynomial one. The results suggest that the new rational method gives better performance when the system has a resonant behavior.

Keywords: Nonparametric Methods, Frequency Domain Identification
Abstract: This paper analyzes two recent methods for the nonparametric estimation of the Frequency Response Function (FRF) from input-output data using Prediction Error identification. Such FRF estimate can be the main goal of the identification exercise, or it can be a tool for the computation of a nonparametric estimate of the noise spectrum. We show that the choice of the method depends on the signal to noise ratio and on the objective. The method that delivers the best FRF estimate may not deliver the best estimate of the noise spectrum. Our theoretical analysis is illustrated by simulations.

Keywords: Frequency Domain Identification, Nonparametric Methods
Abstract: This paper extends the Local Polynomial Method (LPM) for linear and time invariant systems excited by periodic signals. LPM is a robust and fast method for finding a non- parametric Frequency Response Function (FRF) estimate. A good FRF estimate is important in designing a good controller. Since both the system FRF and the transient behave smooth as a function of the frequency, LPM assumes that these functions can be approximated locally by a low degree polynomial. However, if the FRF varies strongly as a function of the frequency this assumption results in bias errors due to under-modeling. That is why this paper presents a transient LPM. This transient LPM suppresses the transients as well as the original LPM but does not introduce bias errors due to under-modeling. The variance of the FRF estimate via the transient LPM will be slightly larger than the variance of the FRF estimate via LPM. However, when these non-parametric FRF estimates are used to find a parametric estimate, this variance difference will not affect the result. Thus, the reduced bias of the FRF estimate via the transient LPM will lead to a better parametric FRF estimate. A disadvantage is that the transient LPM cannot estimate the level of the nonlinear distortions.

Keywords: Frequency Domain Identification, Continuous Time System Estimation, Identification for Control
Abstract: A method of finite-frequency identification for stable plants with time-delay in the presence of unknown-but-bounded disturbance and measurement noise is proposed. This method uses test signal which is a sum of harmonics. Quantity of harmonics does not exceed count of plant coefficients. Conditions of convergence of identification process are also given.

Keywords: Subspace Methods, Time Series, Machine Learning and Data Mining
Abstract: In recent years there has been growing interest in convex optimization techniques for system identification and time series modeling. This interest is motivated by the success of convex methods for sparse optimization and rank minimization in signal processing, statistics, and machine learning, and by the development of new classes of algorithms for large-scale nondifferentiable convex optimization.

Keywords: Fault Detection and Diagnosis, Hybrid and Distributed System Identification
Abstract: Change detection has traditionally been seen as a centralized problem. Many change detection problems are however distributed in nature and the need for distributed change detection algorithms is therefore significant. In this paper a distributed change detection algorithm is proposed. The change detection problem is first formulated as a convex optimization problem and then solved distributively with the alternating direction method of multipliers (ADMM). To further reduce the computational burden on each sensor, a homotopy solution is also derived. The proposed method have interesting connections with Lasso and compressed sensing and the theory developed for these methods are therefore directly applicable.

Keywords: Machine Learning and Data Mining, Maximum Likelihood Methods, Time Series
Abstract: We present an alternating augmented Lagrangian method for convex optimization problems where the cost function is the sum of two terms, one that is separable in the variable blocks, and a second that is separable in the difference between consecutive variable blocks. Examples of such problems include Fused Lasso estimation, total variation denoising, and multi-period portfolio optimization with transaction costs. In each iteration of our method, the first step involves separately optimizing over each variable block, which can be carried out in parallel. The second step is not separable in the variables, but can be carried out very efficiently. We apply the algorithm to segmentation of data based on changes in mean (l_1 mean filtering) or changes in variance (l_1 variance filtering). In a numerical example, we show that our implementation is around 10000 times faster compared with the generic optimization solver SDPT3.

Keywords: Basis Functions, Machine Learning and Data Mining, Other
Abstract: Given a linear system in a real or complex domain, linear regression aims to recover the model parameters from a set of observations. Recent studies in compressive sensing have successfully shown that under certain conditions, a linear program, namely, l1-minimization, guarantees recovery of sparse parameter signals even when the system is underdetermined. In this paper, we consider a more challenging problem: when the phase of the output measurements from a linear system is omitted. Using a lifting technique, we show that even though the phase information is missing, the sparse signal can be recovered exactly by solving a semidefinite program when the sampling rate is sufficiently high. This is an interesting finding since the exact solutions to both sparse signal recovery and phase retrieval are combinatorial. The results extend the type of applications that compressive sensing can be applied to those where only output magnitudes can be observed. We demonstrate the accuracy of the algorithms through extensive simulation and a practical experiment.

Keywords: Time Series, Multivariable System Identification, Machine Learning and Data Mining
Abstract: Cointegrated Vector AutoRegressive (VAR) processes arise in the study of long run equilibrium relations of stochastic dynamical systems. In this paper we introduce a novel convex approach for the analysis of these type of processes. The idea relies on an error correction representation and amounts at solving a penalized empirical risk minimization problem. The latter finds a model from data by minimizing a trade-off between a quadratic error function and a nuclear norm penalty used as a proxy for the cointegrating rank. We elaborate on properties of the proposed convex program; we then propose an easily implementable and provably convergent algorithm based on FISTA. This algorithm can be conveniently used for computing the regularization path, i.e., the entire set of solutions associated to the trade-off parameter. We show how such path can be used to build an estimator for the cointegrating rank and illustrate the proposed ideas with experiments. 

Keywords: Nonlinear System Identification, Nonparametric Methods, Bayesian Methods
Abstract: A variant of Gaussian Process is proposed in this study for nonlinear non-parametric system identification. Only local data is used to construct the estimate. Moreover, the hyper- parameters are adjusted to minimize the local weighted prediction errors. The proposed scheme seems to have semi-global modeling properties of Gaussian Process for limited data sets and also possess local convergence properties if the data set is sufficient rich.

Keywords: Nonparametric Methods, Nonlinear System Identification, Machine Learning and Data Mining
Abstract: Multi-step ahead prediction is a common approach for the simulation of dynamic system behavior. Recently, Gaussian Processes combined with an autoregressive model structure gathered much attention for this task. In order to overcome the computational burden of standard Gaussian Processes at large data sets and to provide a reliable variance prediction for time-dependent use cases, we introduce in the present paper the combination of several sparse Gaussian Process approximations with the framework of uncertainty propagation. We show the results of the proposed approaches at an artificial, chaotic time series and a real world example stemming from an engine air system. The real world example also contains a comparison of the modeling performance to other data-based methods, in particular ordinary least squares and multi-layer perceptrons.

Keywords: Nonparametric Methods, Bayesian Methods
Abstract: FIR (finite impulse response) model is widely used in tackling the problem of the impulse response estimation with quantized measurements. Its use is, however, limited, in the case when a high order FIR model is required to capture a slowly decaying impulse response. This is because the high variance for high order FIR models would override the low bias and thus lead to large MSE (mean square error). In this contribution, we apply the recently introduced regularized FIR model approach to the problem of the impulse response estimation with binary measurements. We show by Monte Carlo simulations that the proposed approach can yield both better accuracy and better robustness than a recently introduced FIR model based approach.

Keywords: Nonparametric Methods, Bayesian Methods
Abstract: A new nonparametric approach for system identification has been recently proposed where, in place of postulating parametric classes of impulse responses, the estimation process starts from an infinite-dimensional space. In particular, the impulse response is seen as the realization of a zero-mean Gaussian process. Its covariance, the so called stable spline kernel, encodes information on system stability and depends on few hyperparameters estimated from data via marginal likelihood optimization. This approach has been proved to compare much favorably with classical parametric methods but, in data rich situations, a possible drawback may be represented by its computational complexity which scales with the cube of the number of available samples. In this work we design a new computational strategy which may reduce significantly the computational load required by the stable spline estimator, thus extending its practical applicability also to large-scale scenarios.

Keywords: Bayesian Methods, Maximum Likelihood Methods, Nonparametric Methods
Abstract: It has been argued in the recent literature that linear system identification can be tackled in a Bayesian framework provided a suitable class of priors is considered. These priors essentially encode stability of the system but have to be flexible enough to adapt to a wide range of situations. Part of this flexibility is achieved introducing hyperparameters in the prior distribution which have to be estimated from data. In this paper we study the properties of a class of empirical Bayes estimators in terms of their Mean Squared Error. We do so in a simplified scenario which however captures some of the essential features arising in system identification.

Keywords: Particle Filtering/Monte Carlo Methods, Bayesian Methods
Abstract: Gaussian innovations are the typical choice in most ARX models but using other distributions such as the Student's t could be useful. We demonstrate that this choice of distribution for the innovations provides an increased robustness to data anomalies, such as outliers and missing observations. We consider these models in a Bayesian setting and perform inference using numerical procedures based on Markov Chain Monte Carlo methods. These models include automatic order determination by two alternative methods, based on a parametric model order and a sparseness prior, respectively. The methods and the advantage of our choice of innovations are illustrated in three numerical studies using both simulated data and real EEG data.

Keywords: Multivariable System Identification, Continuous Time System Estimation
Abstract: This paper is about the identification of a MIMO continuous-time (CT) transfer function model with different denominators. A new algorithm is proposed with two main steps. The first step consists of the estimation of an overparameterized MIMO CT reinitialized partial moment model and the second one performs a moment-based transfer function model reduction. For the unknown structure case, a system structure estimation procedure is given.

Keywords: Continuous Time System Estimation, Filtering and Smoothing, Subspace Methods
Abstract: This paper presents a generalization of the minimax state estimation approach for singular linear Differential-Algebraic Equations (DAE) with uncertain but bounded input and observation's noise. We apply generalized Kalman Duality principle to DAE in order to represent the minimax estimate as a solution of a dual control problem for adjoint DAE. The latter is then solved converting the adjoint DAE into ODE by means of a projection algorithm. Finally, we represent the minimax estimate in the form of a linear recursive filter.

Keywords: Continuous Time System Estimation, Closed Loop Identification, Nonlinear System Identification
Abstract: This paper presents two off-line output error identification algorithms for linear continuous-time systems with unknown time delay from sampled data. The proposed methods (for open and closed loop systems) use a Nonlinear Programming algorithm and need an initialization step that is also proposed from a modification of the Yang algorithm. Simulations, as illustrated by Monte-Carlo runs, show that the obtained parameters are unbiased and very accurate.

Keywords: Continuous Time System Estimation, Basis Functions
Abstract: The topic of time-delay estimation from Laguerre spectra of the input and output signal is re-approached. A formal proof of the relationship underlying an earlier suggested subspace continuous time-delay estimation method is given. Further, it is shown that a class of Laguerre polynomials plays a key role in the mathematical modeling of time delays in Laguerre domain. The robustness of the time-delay estimation algorithm is also investigated. It turns out that there is always a certain choice of the Laguerre parameter that renders an exact estimate of the time delay in the face of a finite-dimensional multiplicative dynamical perturbation, provided that the input is a single Laguerre function of any order.

Keywords: Continuous Time System Estimation
Abstract: An algebraic approach to the identification of parameters for a heavy rope model is proposed. It is based on operational calculus. The parameters are calculated solely from the measurements of the lower and the upper deflection of the rope. Two different sets of boundary conditions are discussed.

Keywords: Continuous Time System Estimation
Abstract: The amplitude, frequency and phase of a biased and noisy sum of two complex exponential sinusoidal signals are estimated via new algebraic techniques providing a robust estimation within a fraction of the signal period. The methods that are popular today do not seem able to achieve such performances. The efficiency of our approach is illustrated by several computer simulations.

Keywords: Hybrid and Distributed System Identification, Multivariable System Identification
Abstract: In this paper, a new identification method for large interconnected systems is presented. A string of systems which all have a full state-space parametrization is considered. The proposed method optimizes the Output-Error of the lifted system by using a structure exploiting Steepest-Descent method. It is shown that the computational drawback inherent to large interconnected systems can be efficiently managed by using Sequentially Semi-Separable (SSS) matrix operations. Finally, a numerical example is presented in order to show the effectiveness of the proposed algorithm.

Keywords: Maximum Likelihood Methods, Frequency Domain Identification, Multivariable System Identification
Abstract: In this paper, a multivariable frequency-domain maximum likelihood estimator based on a modal model formulation is proposed. The proposed approach is mainly introduced to improve the accuracy of the modal parameters estimated by the poly-reference least squares complex frequency-domain (i.e. pLSCF) estimator and to have their confidence intervals as well. In that approach, a 3-step procedure is introduced to improve the estimates accuracy while taking the advantage of the very clear stabilization diagram of pLSCF estimator. The proposed approach has been optimized to reduce the computation time as well as the memory requirements. The algorithm is evaluated and compared with two other published algorithms by means of Monte-Carlo simulations.

Keywords: Multivariable System Identification, Nonlinear System Identification, Nonparametric Methods
Abstract: The paper analyzes some problems appearing under identification of stochastic systems and concerned with applying measures of non-linear dependence of random processes (values). An approach utilizing such a measure based on the quadratic Rényi entropy is considered. A constructive procedure of deriving a linear input/output model that is a statistical equivalent of a multivariable stochastic system driven by a Gaussian white-noise process. A key issue of such a procedure is applying the condition of the component-wise coincidence of the mentioned measure based on the Rényi entropy of the order 2 of the input and output processes of the system and the input and output processes of the linearized model as the statistical linearization criterion. The approach enables one to obtain explicit analytical expressions determining elements of the weight matrices of the linearized model. The paper has been supported by a grant of the Russian Foundation for Basic Researches (RFBR): project 12-08-01205-a.

Keywords: Grey Box Modelling, Multivariable System Identification, Identifiability
Abstract: Estimating the order as well as the matrices of a linear state-space model is now an easy problem to solve. However, it is well-known that the state-space matrices are unique modulo a non-singular similarity transformation matrix. This could have serious consequences if the system being identified is a real physical system. Indeed, if the true model contains physical parameters, then the identified system could no longer have the physical parameters in a form that can be extracted easily. The question addressed in this paper then is, how to recover the physical parameters once the system has been identified in a fully-parameterized form. The novelty of our approach is on transforming the bilinear equations arising from the similarity transformation equations as a null-space problem. We show that the null-space of a certain matrix contains the physical parameters. Extracting the physical parameters then requires the solution of a non-convex optimization problem in a reduced dimensional space. By assuming that the physical state-space form is identifiable and the initial fully-parameterized model is consistent, the solution of this optimization problem is unique. The proposed algorithm is presented, along with an example of a physical system.

Keywords: Other
Abstract: This paper proposes a method of estimating the HRTF (head-related transfer function) to shorten its measurement time by applying a system identification method. Since each directional HRTF has conventionally had to be measured one by one, a larger number of directions results in a longer HRTF measurement time. Since multidirectional HRTFs can also be treated as an MISO (multiple-input single-output) system, the proposed method estimates them simultaneously by a PEM (prediction error method). Experimental results indicated that the proposed method shortens the measurement time for HRTFs of 61 directions by a factor of 280.

Keywords: Bayesian Methods, Multivariable System Identification
Abstract: This paper considers a Bayesian approach to linear system identification. One motivation is the advantage of the minimum mean square error of the associated conditional mean estimate. A further motivation is the error quantifications afforded by the posterior density which are not reliant on asymptotic in data length derivations. To compute these posterior quantities, this paper derives and illustrates a Gibbs sampling approach, which is a randomized algorithm in the family of Markov chain Monte Carlo methods. We provide details on a numerically robust implementation of the Gibbs sampler. In a numerical example, the proposed method is illustrated to give good convergence properties without requiring any user tuning.

Keywords: Identifiability
Abstract: We address the interconnection of stochastic systems. A stochastic system is defined as a probability triple. The specification of the set of events is an essential part of a stochastic model. Models often require a coarse event sigma-algebra. A stochastic system is linear if the events are cylinders with fibers parallel to a linear subspace of a vector space. Two stochastic systems can be interconnected if they are complementary. We discuss aspects of the identification problem from this vantage point.

Keywords: Maximum Likelihood Methods, Nonparametric Methods, Input and Excitation Design
Abstract: Prediction error methods (PEM) are often used to identify a dynamic system starting from input-output samples. In particular, in the classical parametric scenario models of different order are identified from data and compared using the cross validation (CV) paradigm where measurements are split into a training and a validation data set. However, some inefficiencies related to this popular approach to system identification have been recently pointed out. This paper provides some insights on the reasons of such pitfalls, clarifying why PEM equipped with CV may lead to estimators with large variance and a poor predictive capability on new data.

Keywords: Others
Abstract: This article explores the link between prediction error methods, nonlinear polynomial systems and generalized eigenvalue problems. It is shown how the global minimum of the sum of squared prediction errors can be found from solving a nonlinear polynomial system. An algorithm is provided that effectively counts the number of affine solutions of the nonlinear polynomial system and determines these solutions by solving a generalized eigenvalue problem. The proposed method is illustrated by means of an example.

Keywords: Multivariable System Identification
Abstract: We propose a new finite sample system identification method, called Sign-Perturbed Sums (SPS), to estimate the parameters of dynamical systems under mild statistical assumptions. The proposed method constructs non-asymptotic confidence regions that include the least-squares (LS) estimate and are guaranteed to contain the true parameters with a user-chosen exact probability. Our method builds on ideas imported from the "Leave-out Sign-dominant Correlation Regions" (LSCR) approach, but, unlike LSCR, also guarantees the inclusion of the LS estimate and provides confidence regions for multiple parameters with exact probabilities. This paper presents the SPS method for FIR and ARX systems together with its main theoretical properties, as well as demonstrates the approach through simple examples and experiments.

Keywords: Model Validation, Identification for Control
Abstract: This paper deals with the problem of the estimation/validation of pseudo-linear models structure when outliers are present in the residuals. These corrupted data lead to unbounded modeling errors, involve long tail of the probability density function, and damage the model order estimation. Thus, from a ω-corrupted distribution model of these data, a parameterized robust estimation criterion (PREC) with an extended scaling factor in the Huber’s norm and a robust final prediction error criterion (RFPE) based on M-estimates are proposed. Simulation results are given and the estimated orders of the robust models are derived from the new model validation criterion.

Keywords: Continuous Time System Estimation, Nonparametric Methods, Process Control
Abstract: This paper demonstrates a novel method for identifying the higher moments of an arbitrary linear-time-invariant system. By combining the method introduced in this paper and current available methods for reconstructing a function from its moments, it is possible to reconstruct a system from its input and output data. As a result, the paper introduces a new approach in system identification. Moreover, a relationship between the upper and lower limits for the time delay and the first two moments of a specific class of linear systems is derived.

Keywords: Identifiability
Abstract: System identification is the science of constructing models from data. A model is never an exact description of reality, and it is desirable that the identified model comes accompanied by certificates of quality able to describe the level of precision of the model and its domain of validity. This paper is about certified system identification. Our contention is that data contains more information than traditional identification methods can exploit, and, by looking at classical identification problems with new eyes, methods can be developed carrying precise quality guarantees that are valid under general assumptions. Taking the challenge of developing these methods may lead to a paradigm shift in many contexts in which identification is applied.

Keywords: Bounded Error Identification, Nonlinear System Identification
Abstract: In this paper we present a single-stage procedure for computing bounds on the parameters of linear systems with input and output backlash from output data corrupted by bounded measurement noise. By properly selecting a sequence of input/output measurements, the problem of evaluating parameter bounds is formulated as a collection of sparse nonconvex optimization problems. Convex-relation techniques are exploited to efficiently compute guaranteed bounds on system parameters by means of semidefinite programming.

Keywords: Nonlinear System Identification, Recursive Identification
Abstract: This paper deals with the identification of Wiener models that involve backlash operators bordered by possibly noninvertible parametric lines. The latter are also allowed to cross each other making possible to account for general-shape static nonlinearities. The linear dynamic subsystem is not-necessarily parametric but is BIBO stable. A frequency identification method is developed that provides estimates of the nonlinear operator parameters as well as estimates of the linear subsystem frequency gain. The method involves standard and separable least squares estimators that all are shown to be consistent. Backlash operators and memoryless nonlinearities are handled within a unified framework.

Keywords: Nonlinear System Identification, Closed Loop Identification
Abstract: The study in this paper is motivated by the modeling of control valves with significant stiction. By assuming linear dynamics of the controlled process, the joint characterization of the control valve and of the controlled process is formulated as the identification of an extended Hammerstein system. A point-slope-based hysteresis model is used to describe the input hysteresis nonlinearity of the control valve. An iterative algorithm is proposed to solve the identification problem. The basic idea is to separate the ascent and descent paths of the input hysteresis nonlinearity subject to oscillatory excitations. Some identifiability analysis is performed: the proposed extended Hammerstein model structure is identifiable, and given the true input nonlinearity, the oscillatory signals in feedback control loops are shown to be informative by exploiting the cyclo-stationarity of these oscillatory signals. Industrial examples are provided to verify the effectiveness of the proposed identification algorithm in characterizing complicated characteristics of control valve stiction in practice.

Keywords: Nonlinear System Identification
Abstract: This work introduces a new formulation of the Hammerstein-Wiener system for identification purpose. Two methods to calculate the estimates are implemented: the overparametrization approach, and the iterative approach. The good performance obtained by both methods is shown with a simulation example.

Keywords: Frequency Domain Identification, Nonlinear System Identification
Abstract: The notion of frequency response functions has been generalized to nonlinear systems in several ways. However, a relation between different approaches has not yet been established. In this paper, frequency domain representations for nonlinear systems are uniquely connected. Specifically, by means of novel analytical results, the generalized frequency response function (GFRF) and the higher order sinusoidal input describing function (HOSIDF) for polynomial Wiener-Hammerstein systems are explicitly related. Necessary and sufficient conditions for this relation to exist and results on uniqueness and equivalence of the HOSIDF and GFRF are provided. Finally, a numerically efficient computational procedure is presented that allows to compute the GFRF from the HOSIDF and vice versa.

Keywords: Maximum Likelihood Methods, Nonlinear System Identification, Fault Detection and Diagnosis
Abstract: The paper is devoted to the estimation of a nonlinear parametric model of the heteroscedasticity. The heteroscedasticity occurs in regression when the measurement noise variance is non-constant. Sometimes, the noise variance can be represented as a parameterized function of independent variables, so-called variance function. The maximum likelihood estimation (MLE) of variance function parameters leads to a system of nonlinear equations. The iterative solution of these nonlinear equations is based entirely on a successful choice of initial conditions. Hence, in the practice, the nonlinear MLE is intractable. To overcome this difficulty, another linear quasi-MLE estimator is proposed. It is strongly consistent, asymptotically Gaussian and only slightly less efficient than the Cramer-Rao lower bound. By using this estimator as an initial condition, an asymptotically efficient estimation is obtained by using one-step non-iterative Newton method. This approach has been applied to the GPS navigation in the constrained (urban) environment.

Keywords: Maximum Likelihood Methods, Nonparametric Methods, Vibration and Modal Analysis
Abstract: In this paper, modeling of the pavement as a wave propagation medium and estimation of the corresponding model parameters is approached from a system identification perspective. A model based on the physical background is proposed and the corresponding parameters are then estimated from measurement data. In order to achieve the latter, two estimators are proposed, their performance evaluated, and then applied to the measurement data. It is found that the proposed methods are applicable and the results show that different eigenmodes of the structure are excited.

Keywords: Maximum Likelihood Methods, Time Series
Abstract: Stochastic processes with long-range dependence are found in many applications. ARFIMA models can be used to characterise both their short-term correlations and the phenomenon of long-range dependence. Maximum likelihood estimates of the model parameters have nice statistical properties but are ill-conditioned and hard to compute. Whittle's approximation has the same asymptotic properties and yet is easier to compute. We propose a regularisation of Whittle's approximation that overcomes the problem of ill-conditioning. Good results are demonstrated in numerical simulations.

Keywords: Maximum Likelihood Methods
Abstract: In this paper, we consider a number of technical problems associated with identification of linear systems using quantized and intermittent information. More specifically, we study asymptotic properties for identification of such systems, including strong consistency, asymptotic normality and asymptotic efficiency, and determine their relationship with quantization errors and the packet losses. Furthermore, we discuss how to design quantizers to improve these asymptotic properties. Some open problems will also be proposed.

Keywords: Time Series, Basis Functions, Mechanical and Aerospace
Abstract: The identication of stochastic systems operating under multiple conditions is addressed based on data records obtained under a sample of these conditions. The problem is important in many practical applications and is tackled within a recently introduced Functional Pooling framework. The study focuses on the case of operating conditions characterized by several parameters. Global Vector-dependent Functionally Pooled models of the ARX type are postulated, proper estimators based on the Least Squares and Maximum Likelihood principles are formulated, and their strong consistency and asymptotic normality are established. For model structure selection a Genetic Algorithm based procedure is formulated. The performance characteristics of the methods are assessed via a Monte Carlo study.

Keywords: Others, Subspace Methods, Toolboxes
Abstract: The question in the title is answered empirically by solving instances of three classical problems: fitting a straight line to data, fitting a real exponent to data, and system identification in the errors-in-variables setting. The results show that the nuclear norm heuristic performs worse than alternative problem dependant methods---ordinary and total least squares, Kung's method, and subspace identification. In the line fitting and exponential fitting problems, the globally optimal solution is known analytically, so that the suboptimality of the heuristic methods is quantified.

Keywords: Maximum Likelihood Methods
Abstract: In this contribution we present a method to estimate structured high order ARX models. By this we mean that the estimated model, despite its high order is close to a low order model. This is achieved by adding two terms to the least-squares cost function. These two terms correspond to nuclear norms of two Hankel matrices. These Hankel matrices are constructed from the impulse response coefficients of the inverse noise model, and the numerator polynomial of the model dynamics, respectively. In a simulation study the method is shown to be competitive as compared to the prediction error method. In particular, in the study the performance degrades more gracefully than for the Prediction Error Method when the signal to noise ratio decreases.

Keywords: Nonlinear System Identification, Multivariable System Identification, Identifiability
Abstract: Recently a new approach to black-box nonlinear system identification has been introduced which searches over a convex set of stable nonlinear models for the one which minimizes a convex upper bound of long-term simulation error. In this paper, we further study the properties of the proposed model set and identification algorithm and provide two theoretical results: (a) we show that the proposed model set includes all quadratically stable nonlinear systems, as well as some more complex systems; (b) we study the statistical consistency of the proposed identification method applied to a linear system with noisy measurements. It is shown a modification related to instrumental variables gives consistent parameter estimates.

Keywords: Nonlinear System Identification, Nonparametric Methods
Abstract: This paper gives a primal-dual derivation of the Least Squares Support Vector Machine (LS-SVM) using Instrumental Variables (IVs), denoted simply as the Primal-dual Instrumental Variable Estimator. Then we propose a convex optimization approach for learning the optimal instruments. Besides the traditional argumentation for the use of IVs, the primal-dual derivation gives an interesting other advantage, namely that the complexity of the system to be solved is expressed in the number of instruments, rather than in the number of samples as typically the case for SVM and LS-SVM formulations. This note explores some exciting issues in the design and analysis of such estimator.

Keywords: Multivariable System Identification, Hybrid and Distributed System Identification, Vibration and Modal Analysis
Abstract: In this paper, we propose a novel approach to the identification of multiple-input multiple-output (MIMO) wave propagation models having a common-denominator pole-zero parametrization. We show how the traditional, purely data-based identification approach can be improved by incorporating a physical wave propagation model, in the form of a spatiotemporally discretized version of the wave equation. If the wave equation is discretized by means of the finite element method (FEM), a high-dimensional yet highly sparse linear set of equations is obtained that can be imposed at those frequencies where a high-resolution model estimate is desired. The proposed identification approach then consists in sequentially solving two large-scale convex optimization problems: a sparse approximation problem for estimating the point source positions required in the FEM, and an equality-constrained quadratic program (QP) for estimating the common-denominator pole-zero model parameters. A simulation example for the case of indoor acoustic wave propagation is provided to illustrate the benefits of the proposed approach.

Keywords: Nonlinear System Identification, Hybrid and Distributed System Identification
Abstract: Recent years have witnessed a growing interest on system identification techniques for switched and piecewise affine models. These model classes have become popular not only due to the universal approximation properties of piecewise affine functions, but also because the proposed identification procedures have proven to be effective in problems involving complex nonlinear systems with large data sets. This paper presents a review of recent advances in this research field, including theoretical results, algorithms and applications.

Keywords: Hybrid and Distributed System Identification, Nonlinear System Identification, Quantum Systems
Abstract: Piecewise Affine maps (PWA) constitute an attractive modeling abstraction for nonlinear dynamic systems. An important feature of PWA model structures is that they carry the quite natural intuition according to which the operating space of a complex physical system can be decomposed into an appropriate number of pieces on which the system can be viewed as being affine. The paper presents a new method for the recovery of piecewise affine systems from observed samples of data. This problem is usually addressed through data clustering procedures which, unfortunately, are rarely guaranteed to be optimal. The ambition of this work is to overcome the need of resorting to a systematic clustering. To this end, some ideas of sparse optimization are used in combination with the local linearity property of PWA maps.

Keywords: Input and Excitation Design, Subspace Methods, Multivariable System Identification
Abstract: A basic class of multivariate system identification input design methods is proposed. Only reliable numerical linear algebra is used. The underlying idea is to inject energy into the invariant eigenspace for a subset of preestimated plant eigenvalues. Standard Schur pseudotriangular factorisation is used to pretarget a subsequent singular value decomposition. Explicit state-space formulas are given. Examples indicate that the approach may be useful in some practical applications. The approach may be considered user-friendly.

Keywords: Nonlinear System Identification, Nonparametric Methods, Hybrid and Distributed System Identification
Abstract: In this paper, a new identification method for non-parametric piecewise affine (PWA) models is introduced. The method is based on the non-parametric data-based representation of PWA maps and the data compression with l1 optimization technique, which enable the method to deal with large data sets. In the proposed scheme, the prior knowledge about partitioning of the PWA map is not required, and the trade-off between complexity and accuracy of the model is easily adjusted by one parameter, which can be determined by holdout validation technique in practical situations. These features of the proposed method provide the high usability in practical problems, which is demonstrated through numerical and experimental examples.

Keywords: Fault Detection and Diagnosis, Mechanical and Aerospace
Abstract: In this paper a method to detect asymmetric faults in a wind turbine rotor is presented. The paper describes how fault diagnosis using an observer-based residual generator approach is able to distinguish between the nominal and faulty case by the injection of e.g. a sinusoidal excitation signal into the system. In the case of a wind turbine, an excitation signal is automatically generated by the rotation of the rotor in a turbulent wind eld. Using the multi-blade coordinate transformation, the detection of asymmetries in the rotor of the wind turbine is greatly improved.

Keywords: Fault Detection and Diagnosis, Subspace Methods, Mechanical and Aerospace
Abstract: Most subspace-based methods enabling instability monitoring are restricted to the linear time-invariant (LTI) systems. In this paper, a new subspace method of instability monitoring is proposed for the linear periodically time-varying (LPTV) case. For some LPTV systems, the system transition matrices may depend on some parameter and are also periodic in time. A certain range of values for the parameter leads to an unstable transition matrix. Early warning should be given when the system gets close to that region, taking into account the time variation of the system. Using the theory of Floquet, some symptom parameter of stability- or residual- is defined. Then, the parameter variation is tracked by performing a set of parallel cumulative sum (CUSUM) tests. Finally, the method is tested on a simulated model of a helicopter with hinged blades, for monitoring the ground resonance phenomenon.

Keywords: Maximum Likelihood Methods, Fault Detection and Diagnosis, Mechanical and Aerospace
Abstract: Aircraft and spacecraft electrical power distribution systems are critical to overall system operation, but these systems may experience faults. Early fault detection makes it easier for system operators to respond and avoid catastrophic failures. This paper discusses a fault detection scheme based on a tunable generalized likelihood algorithm. We discuss the detector algorithm, and then demonstrate its performance on test data generated from a spacecraft power distribution testbed at NASA Ames. Our results show high detection accuracy and low false alarm rates.

Keywords: Fault Detection and Diagnosis, Biological Systems, Process Control
Abstract: Monitoring drinking water is a public health problem because water is essential for human life. A typical modern drinking water distribution system includes a water purification plant, water towers, water tanks, pumps and pipes. Many procedures are developed for monitoring water quality in water treatment plants. Monitoring of water distribution systems has received less attention.

The goal of this paper is to study the problem of drinking water safety by ensuring the monitoring of the distribution network from water tower to private residences. The proposed approach is based on the observation of residual chlorine concentrations which are provided by sensors network. By using the hydraulic model, it is possible to compute the nominal residuals chlorine concentrations under assumption that quality of the water at the water tower output is known. If a significant reduction of the residual chlorine concentrations is observed then it can be interpreted as presence of a dangerous water contamination. This event should be detected as reliable as possible provided an acceptable detection delay and false alarm rate. The traditional abrupt change detection theory is well developed in the case when the duration of the post-change mode is infinite. Unfortunately, in the discussed case the transient signal duration is short. Hence, the usage of traditional change detection algorithm is compromised.

A criterion based on the minimization of the missed detection probability provided that the false alarm rate is upper bounded is used in the paper. A suboptimal detection algorithm is designed. The theoretical analysis and the results of simulation are provided.

Keywords: Fault Detection and Diagnosis, Grey Box Modelling, Mechanical and Aerospace
Abstract: The robust tuning methodology developed in this paper aims at adjusting automatically the hyperparameters of fault-diagnosis procedures for complex case studies. The strategy should make an efficient use of computer simulations of these case studies, which will usually be computationally expensive. To this end, Kriging-based optimization is called upon. Robustness to environmental disturbances is achieved by continuous minimax optimization, and handled through an iterative relaxation procedure. This strategy is applied to the automatic tuning of a model-based fault-diagnosis scheme for a realistic aerospace application.

Keywords: Nonlinear System Identification, Other
Abstract: In the context of parametric identification, the study presented in this communication is based on the implementation of an iterative regularization method (conjugate gradient algorithm) in order to identify coordinates of several heating fixed sources in a three dimensional geometry. Such an inverse heat conduction problem (described by a set of partial differential equations) is ill-posed (in Hadamard’s sense). The robustness of the proposed identification method is illustrated considering temperature measurements (observations are performed using three sensors) and realistic disturbances.

Keywords: Hybrid and Distributed System Identification, Multivariable System Identification
Abstract: In this paper we propose a computationally efficient algorithm for identifying spatially distributed discrete-time state-space models. In the case of identifying spatially invariant distributed systems, the computational complexity of the proposed algorithm scales linearly with the number of local subsystems. In the case of identifying spatially varying distributed systems the computational complexity of the proposed algorithm scales quadratically with the number of local subsystems. We demonstrate the effectiveness of the proposed identification algorithm by performing numerical tests.

Keywords: Vibration and Modal Analysis, Mechanical and Aerospace
Abstract: The purpose of the study is to illustrate the possibility of boundary conditions identication in case of beams. The problem is understood as a determination of various spatial derivatives of transverse displacements. Using the assumption that displacements can be approximated by Taylor expansions on a domain near its boundaries, the spatial derivatives are estimated using particular pointwise derivatives estimators. This approach enables the extraction of these quantities using a weighted spatial integration of the displacement eld. Numerical simulation using exact and noisy data are shown in order to clarify the link between the size of the integration domain and the wavelengths of the vibrations.

Keywords: Bayesian Methods, Neural Networks, Vibration and Modal Analysis
Abstract: This paper addresses an inverse approach to characterize the frequency-dependent elastic modulus of the polymer layer in laminated structures. Represented by fractional derivative models, the modulus is identified based on a finite element model of the laminated structure from the experimental frequency response functions. An efficient Markov Chain Monte Carlo method is implemented to learn the identification parameters from a Bayesian perspective. A surrogate model is applied to alleviate Bayesian computation through the use of artificial neutral network. The proposed approach is experimentally validated on a laminated glass.

Keywords: Continuous Time System Estimation, Frequency Domain Identification, Model Validation
Abstract: Fractional order dynamic models (e.g., systems of ordinary and partial differential equations of non-integer order in time and space) are becoming more popular for characterizing the behavior of complex systems. Justification for such models is typically based on improved fits to experimental data or a reduced mean squared error for models with the same number of fitting parameters. This rationale, however, is relative to the form of the selected fitting function, and is dependent on the order of the derivatives. Nevertheless, there seems to be a recognition that fractional order models work better than integer order models in describing the electrical and mechanical properties of multi-scale, heterogeneous materials. In order to address this issue and to offer a new approach for establishing the utility of fractional order models, we calculate the total Shannon spectral entropy for the case of anomalous diffusion governed by a fractional order diffusion equation generalized in space and in time. This fractional order representation of the continuous time, random walk model of diffusion gives a spectral entropy minimum for normal (i.e., Gaussian) diffusion with surrounding values leading to greater values of spectral entropy.

Keywords: Identifiability, Nonlinear System Identification, Biological Systems
Abstract: Definitions of identifiability and methods for checking this property for linear and nonlinear systems are now well established. Recently, some works have provided identifiability definitions for set-membership models in a bounded-error context and established links with classical identifiability definitions. These works are summarized in the first part of the paper, recalling the two complementary definitions: set-membership identifiability that is conceptual and mu-set-membership identifiability that can be put in correspondence with existing set-membership parameter estimation methods. In the second part, two methods for checking set-membership identifiability and mu-set-membership identifiability are proposed. The first one is an extension of a method proposed by Pohjanpalo based on the power series expansion of the solution that accounts for the initial conditions of the system. It generalizes to nonlinear systems the initial extension provided in one of our previous paper. The second method is based on differential algebra and makes use of relations linking the observations, the inputs and the unknown parameters of the system. Classically, when using this method, initial conditions are not considered but it has been shown recently that they can change the identifiability results. In this paper, an extension using initial conditions is proposed. In the third part of the paper, a numerical parameter estimation method is deduced from the differential algebra method and an example is presented.

Keywords: Hybrid and Distributed System Identification, Bounded Error Identification
Abstract: Set membership estimation (SME) of nonlinear hybrid systems is still a challenging issue. Although SME of nonlinear continuous systems has made significant progress recently, the direct extension of these methods to the hybrid case is not easy. Meanwhile, satisfiability (SAT) checkers for Boolean combinations of arithmetic constraints over real- and integer-valued variables have made significant progress, as they can effectively deal with algebraic constraints between variables and non-linear ODEs, what is denoted as SAT Modulo ODE. Finally, the corresponding solvers solve in a natural way the hybrid differential and algebraic constraints satisfaction problems that underlie SME of hybrid systems. This paper presents the application of such a SAT Modulo ODE solver to SME of hybrid dynamical systems.

Keywords: Nonlinear System Identification, Identification for Control, Model Validation
Abstract: Solid oxide fuel cells (SOFCs) can be used as decentralized energy supply devices for providing electricity and heat directly by converting chemical energy. In such applications of SOFCs, the electric power demand is commonly varying over time. Therefore, all processes in fuel cell systems are typically instationary. For example, the heating and cooling phases for starting up and shutting down the fuel cell system as well as the response to varying electrical load demands characterize the instationarity of the operating conditions for the thermal subprocess. In contrast to most existing control approaches, which only cover stationary operating strategies, our work aims at controlling SOFC systems in instationary operating regions. This means that a mathematical system model for these regions is necessary. Such control-oriented models for the temperature distribution in a fuel cell stack module can be obtained by the method of finite volume discretization. On the basis of the first law of thermodynamics, local energy balances are derived for each volume element, which leads to a system of coupled nonlinear ordinary differential equations. In this paper, parameter identification routines are compared which are based both on classical floating point techniques and on verified interval arithmetic approaches. In particular, interval techniques are employed to deal with imperfect system knowledge expressed by bounded parameter uncertainties and to search for globally instead of locally optimal system parameterizations.

Keywords: Nonlinear System Identification, Continuous Time System Estimation, Other
Abstract: In this paper online verified state and parameter estimation for a tank system on real time hardware is presented. The Taylor Model based estimator determines guaranteed enclosures of the state and parameters in the presence of uncertainty in the intial state, the sensor and in the system parameters. The structure of the implementation on the real time hardware is shown. The properties of the estimator and its optimization for the real time application are discussed. Experimental results are presented. This is a break through for verified state and parameter estimation for continuous time systems.

Keywords: Mechanical and Aerospace, Model Validation, Frequency Domain Identification
Abstract: Dielectric spectra of materials are often difficult to analyze since the common software algorithms and line shape functions do not always provide unambiguous data for the fitted parameters. In particular, this article deals with epoxy/ceramics nano-prepolymers studied by dielectric spectroscopy. In this situation, both system (the prepolymer with nanofillers) and method (the dielectric spectroscopy) are complex. Taking into account the experimental error of each data point in the measured dielectric spectrum, the sofware based on a global optimization algorithm which uses interval analysis, provides a confidence interval for every parameter of the dielectric function implemented in the software. Then, this software is able to deliver and guarantee the number of relaxation processes even if they are in part masked by other phenomena like conductivity or electrode polarization.

Keywords: Nonparametric Methods, Nonlinear System Identification, Recursive Identification
Abstract: The paper surveys the ideas of cooperation between parametric and nonparametric (kernel-based) algorithms of nonlinear block-oriented system identification. Various strategies are proposed, dependently on the system structure, number of data and the prior knowledge. The estimates are consistent and their rates of convergence are presented. The aim of the paper is to show some recent results in the field in a systematic, ordered way.

Keywords: Nonlinear System Identification, Frequency Domain Identification
Abstract: The parameters of a Wiener-Hammerstein model, a nonlinear block structure comprising two linear filters separated by a memoryless nonlinearity, may be identified using an iterative nonlinear least squares optimization, however avoiding suboptimal local minima in the error surface requires a good initial estimate of the parameter vector. The Best Linear Approximation (BLA) of a Wiener-Hammerstein model will contain all the poles and zeros of both linear elements, but does not provide any information regarding which poles and/or zeros should be assigned to either of the linear elements. This information is contained in the nonlinear terms in the system response. One such nonlinear term is the BLA fitted between a suitably chosen nonlinear transformation of the input, and the output residuals remaining after all linear terms have been removed. The poles and zeros present in this nonlinear transfer function are used to classify the poles and zeros in the initial linear fit as belonging to either the first or second linear element in the Wiener-Hammerstein model. The procedure is illustrated by applying it to experimental data from a Wiener-Hammerstein benchmark system.

Keywords: Nonlinear System Identification, Nonparametric Methods
Abstract: The concept of inverse regression has turned out to be quite useful for dimension reduction in regression analysis problems. Using methods like sliced inverse regression (SIR) and directional regression (DR), some high-dimensional nonlinear regression problems can be turned into more tractable low-dimensional problems. Here, the usefulness of inverse regression for identification of nonlinear dynamical systems will be discussed. In particular, it will be shown that the inverse regression methods can be used for identification of systems of the Wiener class, that is, systems consisting of a number of parallel linear subsystems followed by a static multiple-input single-output nonlinearity. For a particular class of input signals, including Gaussian signals, the inverse regression approach makes it possible to estimate the linear subsystems without knowing or estimating the nonlinearity.

Keywords: Nonlinear System Identification, Nonparametric Methods, Identifiability
Abstract: Abstract: This paper discusses convergence properties of the recently introduced MINimal LIPschitz (MINLIP) estimator for the identication of a monotone Wiener model from noiseless input-output measurements. This estimator is entirely build around the notion of complexity control, making the approach conceptual quite dierent from traditional identication schemes based on least squares, prediction error methods, maximum likelihood or numerical projections. Sucient conditions from which the result follows are given in terms of `rotational complete inputs', a generalization of the notion of Persistency of Excitation. Finally, we will extend results towards dynamical systems and give examples where this phenomenon occurs.

Keywords: Particle Filtering/Monte Carlo Methods, Hybrid and Distributed System Identification
Abstract: Particle methods are a category of Monte Carlo algorithms that have become popular for performing inference in non-linear non-Gaussian state-space models. The class of “Rao-Blackwellised” particle filters exploits the analytic marginalisation that is possible for some state-space models to reduce the variance of the Monte Carlo estimates. Despite being applicable to only a restricted class of state-space models, such as conditionally linear Gaussian models, these algorithms have found numerous applications. In scenarios where no such analytical integration is possible, it has recently been proposed in Chen et al. [2011] to use “local” particle filters to carry out this integration numerically. We propose here an alternative approach also relying on “local” particle filters which is more broadly applicable and has attractive theoretical properties. Proof-of-concept simulation results are presented.

Keywords: Maximum Likelihood Methods, Recursive Identification, Time Series
Abstract: In this paper we formulate the nonnegative matrix factorisation (NMF) problem as a maximum likelihood estimation problem for hidden Markov models and propose online expectation-maximisation (EM) algorithms to estimate the NMF and the other unknown static parameters. We also propose a sequential Monte Carlo approximation of our online EM algorithm. We show the performance of the proposed method with two numerical examples.

Keywords: Maximum Likelihood Methods, Particle Filtering/Monte Carlo Methods, Nonlinear System Identification
Abstract: State-space models are a very general class of time series capable of modeling dependent observations in a natural and interpretable way. While optimal state estimation can now be routinely performed using SMC (sequential Monte Carlo) methods, on-line static parameter estimation largely remains an unsolved problem. In Andrieu and Doucet (2003) it was proposed to use a pseudo-likelihood approach. This pseudo-likelihood can be optimised directly using a stochastic gradient algorithm, but we focus on an on-line Expectation-Maximization (EM). We present here novel simple recursions that allow us to estimate confidence intervals on-line and develope new theoretical results concerning the pseudo-likelihood estimate. More precisely we characterise the loss of efficiency compared to that of the maximum likelihood estimate, and also quantify the bias of the estimate in cases where the pseudo-likelihood needs to be approximated. We show in a tractable situation requiring no Monte Carlo simulation that these theoretical results accurately predict performance, pointing to their practical relevance.

Keywords: Particle Filtering/Monte Carlo Methods, Filtering and Smoothing, Time Series
Abstract: In this article, we develop a new Rao-Blackwellized Monte Carlo smoothing algorithm for conditionally linear Gaussian models. The algorithm is based on the forward-filtering backward-simulation Monte Carlo smoother concept and performs the backward simulation directly in the marginal space of the non-Gaussian state component while treating the linear part analytically. Unlike the previously proposed backward-simulation based Rao-Blackwellized smoothing approaches, it does not require sampling of the Gaussian state component and is also able to overcome certain normalization problems of two-filter smoother based approaches. The performance of the algorithm is illustrated in a simulated application.

Keywords: Mechanical and Aerospace, Vibration and Modal Analysis, Input and Excitation Design
Abstract: In this paper, the use of advanced, flexible shaker excitation signals will be investigated with the aim (1) to obtain improved Frequency Response Function (FRF) estimations and (2) to assess the non-linearities of the excited system / structure. Pseudo-random and more general multisine signals, rather than the more traditional pure or burst random signals, will be used to increase the accuracy of the FRF estimate. Moreover, special multisine data acquisition and processing methods to identify the level of non-linearity will be illustrated by means of Ground Vibration Testing data of an F-16 aircraft. The presented methods allow assessing the non-linearities at a single excitation level, which is in contrast to the more traditional method of repeating the test at multiple excitation levels and observing the FRF differences.

Keywords: Vibration and Modal Analysis, Multivariable System Identification, Frequency Domain Identification
Abstract: This paper presents an identification algorithm dedicated to the Modal Analysis of physical objects. This algorithm was specifically designed to process cases where short duration tests with multiple-input excitations are used to identify the system. To conform to these particular conditions, an iterative identification method was developed. It makes use of an appropriate parametrization of multivariable transfer functions based on structured matrix fractions. The identification problem is solved in the frequency domain using an output-error formulation. This paper details this algorithm which is evaluated on an example illustrative of the in-flight modal analysis of an aircraft.

Keywords: Vibration and Modal Analysis, Identification for Control, Mechanical and Aerospace
Abstract: This paper describes the development of a decoupling vibration control system for a multi-axis hydraulic shaker facility. The control system is based on the Internal Model Control (IMC) architecture. While an accurate model of the hydraulic subsystem should only be identified once, there is a strong need for a systematic procedure for identifying the mechanical subsystem. Based on the PolyMAX identification method, an accurate mechanical model can be obtained through experimental modal analysis. In a simulation analysis, the resulting PolyMAX-IMC control system has proven to achieve an improved performance regarding reference tracking, limited time harmonic distortion and cross-talk reduction.

Keywords: Process Control, Identification for Control, Nonlinear System Identification
Abstract: Distillation columns are one of the first unit processes to which MPC (Modelbased Predictive Control) was successfully applied in an industrial context. The methodology that is used to execute such APC (Advanced Process Control) projects has not fundamentally changed in the decades that have passed since its inception. Linear black-box models are still the most commonly used type of models in such applications. However, obtaining black-box models by performing dedicated plant tests is often prohibitively time-consuming (and hence costly), which limits the cost-efficient application of APC. On the other hand, in several applications non-linear models offer significant benefits when combined with a high-performance non-linear APC controller. INCA MPC4Distillation employs a novel modeling approach, by combining physical knowledge and historical data in order to identify dynamic models that can be used for APC. This new technology results in accurate non-linear models and does not rely on dedicated step tests, which results in increased benefits to the customer and at a lower cost than existing methods. Experience shows that INCA MPC4Distillation models can typically be obtained in a matter of days, as opposed to several weeks when one would use the classical modeling approaches. The results are illustrated using results obtained on a high-purity binary distillation column.

Keywords: Nonlinear System Identification, Basis Functions
Abstract: A continuous piecewise linear (CPWL) function equals an affine function in each of the subregions which tessellate the domain. By CPWL identification, one nonlinear system can be approached by a set of linear systems and then linear techniques are applicable. For the convenience of further application, the number of subregions should be moderate. However, because the relation between the subregions and parameters of a CPWL model is very complicated, existing identification methods usually lead to a lot of unexpected subregions, when training the parameters of traditional CPWL models. In this paper, domain partition based CPWL neural network, which is recently proposed, is utilized to solve the problem above. The relation between parameters and subregion structure of such model is analyzed. Then an algorithm of adjusting vertices is proposed to improve approximation precision with moderate number of subregions. Compared with some prior identification methods, the proposed algorithm uses much less subregions and achieves satisfactory precision in numerical study.

Keywords: Hybrid and Distributed System Identification, Identifiability
Abstract: The paper addresses the problem of minimality and identifiablity of Switched ARX (abbreviated by SARX) models. An SARX system is a finite collection of ARX systems such that each ARX system is associated with a discrete mode. We consider systems in discrete time and we assume that the switching is externally generated.

We propose definitions of identifiability and minimality for SARX models which depend only on the paratemers of the model, not on data. We formulate conditions for minimality and identifiability of SARX systems. In particular, we show that SARX systems are generically identifiable.

In order to prove these results, we convert SARX systems to a state-space form, using the regressor as a state-variable, as in [2]. We then analyze minimality and identifiability of the resulting state-space representation by applying [1]. One striking conclusion is that the state-space representation of [2] appears to be generically minimal and identifiable for SARX systems with more than one discrete mode. This is in stark constrast with the linear case (one discrete mode), where the naive state-space representation of [2] is never minimal.

The above results represent a formal justification of the conjecture that switching can help identification. That is, by switching between non-identifiable linear systems, it might still be possible to identify them.

[1] M. Petreczky, L. Bako, J.H. van Schuppen. Identifiability of discrete-time linear switched systems, In Hybrid Systems: Computation and Control 2010.

[2] S. Weiland A. Lj. Juloski, B. Vet. On the equivalence of switched affine models and switched {ARX} models. In 45th IEEE Conf. on Decision and Control, 2006.

Keywords: Hybrid and Distributed System Identification, Identification for Control, Other
Abstract: Joint estimation of states and events in linear regime-switching systems is studied under irregular sampling schemes which stem from improved sampling and quantization methods for efficient utility of communication resources. Joint observability and sampling complexity are established. Observer design and convergence analysis are developed for systems under noisy observations. It is shown that our algorithms converge strongly and guarantee a convergence rate of magnitude O(1/N).

Keywords: Maximum Likelihood Methods, Nonlinear System Identification, Bayesian Methods
Abstract: In this paper, we explore the identification of sparse FIR systems having quantized output data. Our approach is based on the use of regularization. We explore several aspects concerning the implementation of the Expectation-Maximization (EM) algorithm, including: i) a general framework, based on mean-variance Gaussian mixtures, for incorporating a regularization term that forces sparsity, ii) utilization of Markov Chain Monte Carlo techniques (namely a Gibbs sampler) and scenarios to implement the EM algorithm for multiple input multiple output systems. We show that for single input single output systems, it is possible to obtain closed form expressions for solving the EM algorithm.

Keywords: Biological Systems, Bounded Error Identification
Abstract: In this paper we address the problem of identifying a linear parameter varying (LPV) model of the glucose-insulin dynamics in Type I diabetic patients. First, the identification problem is formulated in the framework of bounded-error identification, then an algorithm for parameter bounds computation, based on semidefinite programming, is presented. The effectiveness of the proposed approach is tested in simulation by means of the widely adopted nonlinear Sorensen patient model.

Keywords: Subspace Methods, Biological Systems, Fault Detection and Diagnosis
Abstract: This paper addresses the detection and classification of low amplitude signals within the QRS complex of the signal-averaged electrocardiogram. Linear and bilinear Kalman filter models are fitted using the subspace system identification family of algorithms. If the residuals from the models are a white noise process, then anything that cannot be modeled with the state-space models will show up in the residuals as low amplitude signal + noise. Diagnostic tests and analysis on the residuals will then lead to detection and classification of abnormalities in the intra-QRS complex. The end result is a diagnostic tool to aid the physician.

Keywords: Other, Closed Loop Identification, Identification for Control
Abstract: A closed-loop controller for rocuronium-induced neuromuscular blockade using the first twitch of a train-of-four electromyographic stimulation as the measured signal is presented. Central to this development is the use of a two-parameters Wiener model, previously proposed to atracurium. The controller includes recursive parameters identification by an EKF, inversion of the nonlinearity using the current nonlinear parameter estimate and a pole placement controller for the exactly linearized system. Numerical tests on the performance of this adaptive structure were carried out on a bank of 500 simulated standard PK/PD models. The developed controller steers the neuromuscular blockade to a desired reference, tracking a constant or varying profile. It is also able to deal with parameter-varying systems and works well in noisy scenarios. These capabilities are crucial when testing this structure in a real clinical environment.

Keywords: Identification for Control, Multivariable System Identification, Biological Systems
Abstract: General anaesthesia is characterized by unconsciousness through the action of hypnotics, and by loss of the ability to perceive pain through the action of analgesics. Because most hypnotic drugs (i.e. Propofol) have no pain relieving properties, they are used together with analgesic drugs (i.e. Remifentanil). In this paper, we perform a robustness analysis against interval uncertainty in the model parameters for closed-loop anesthesia control. These uncertainties are taken from the model parameters of 9 patients in response to Propofol and Remifentanil drug infusions. Based on this data, we develop a method to determine the effect of the additive uncertainties on the stability and robustness of the closed-loop. The response of the Bispectral index has been then tested in simulation on 24 mimicked patient models, showing good performance.

Keywords: Identification for Control, Frequency Domain Identification, Multivariable System Identification
Abstract: This paper proposes a control-oriented modeling and identification framework for flexible-joint robot arms using motor-side measurements only. From the perspective of model-based control strategies including an inner feedback linearization loop, the proposed method allows an explicit treatment of the vibrational behavior induced by the flexibilities. A theoretical model of the partially decoupled system is derived and a frequency-domain identification procedure allowing an estimation of the flexible parameters is detailed. The obtained description of the system is experimentally validated on the CEA lightweight robot arm ASSIST.

Keywords: Identification for Control, Frequency Domain Identification, Nonparametric Methods
Abstract: With knowledge of the internal stability of a closed-loop system with an unknown plant P and a known controller C1, we search for a controller better than the currently stabilizing controller in the sense of a certain performance measure. This searching procedure is formulated in the form of an optimization problem. Nonparametric identification of P or other transfer functions is performed with known error bounds from a limited amount of signal data collected from experiments on the closed-loop system with the currently stabilizing controller excited by designed reference signals and corrupted by disturbances and, then, the optimization problem is built in terms of these estimates. In order to reduce the numerical difficulty of the optimization problem, we employ a controller parameterization and propose an algorithm that may not produce the optimal controller but has fast computation ability. A focus of the study is to understand what can be achieved and under what assumptions for controller redesign using such limited identified system data.

Keywords: Frequency Domain Identification, Basis Functions, Identification for Control
Abstract: Parametric identification of lightweight motion systems requires solving large weighted least-squares problems. The numerical conditioning of such problems, which determines the solution accuracy, crucially depends on the polynomial basis that is used to formulate the problem. The aim of this paper is to optimize numerical conditioning by constructing a polynomial basis that is orthonormal with respect to a data-dependent inner product. This basis is constructed in a computationally efficient way by exploiting underlying structure of the problem, related to polynomial recurrence relations. Through a confrontation with an industrial system with large dynamical complexity, numerical accuracy and efficiency of the method are confirmed.

Keywords: Identification for Control, Mechanical and Aerospace, Multivariable System Identification
Abstract: The selection of uncertainty structures is an important aspect in system identification for robust control. The aim of this paper is to investigate the consequences for multivariable systems. Hereto, first a theoretical analysis is performed that establishes the connection between the associated model set and the robust control criterion. Second, an experimental case study for an automotive application confirms these connections. In addition, the experimental results provide new insights in the shape of associated model sets by using a novel validation procedure. Finally, the improved connections are confirmed through a robust controller synthesis. Both the theoretical and experimental results confirm that a recently developed robust-control-relevant uncertainty structure outperforms general dual-Youla-Kucera uncertainty, which in turn outperforms traditional uncertainty structures, including additive uncertainty.

Keywords: Fault Detection and Diagnosis, Other
Abstract: For the diagnosis of inhomogeneous insulation degradation in electrical cables, the estimation of the distributed shunt conductance is studied in this paper. Gradual growth of the shunt conductance is a consequence of degradation of the dielectric properties of the insulator. The proposed estimation method is based on voltage and current measurements at a single end of the cable. After the linearization of the bilinear term of the telegrapher's equations through a perturbation approach, the Kalman filter is applied to transform the problem of dynamic system parameter estimation to a simple linear regression problem. Results of numerical simulations are presented to demonstrate the feasibility of the proposed method. In particular, it is shown that the weak sensitivity of the available measurements to the shunt conductance can be compensated by long time data samples.

Keywords: Fault Detection and Diagnosis, Identification for Control, Mechanical and Aerospace
Abstract: This paper proposes a scheme of self-recovery for spaceborne digital circuits using a control theoretic approach. The considered circuit, modelled as an asynchronous sequential machine, suffers from the state transition fault caused by the radiation effect. Using corrective control for asynchronous sequential machines, we present the existence condition for an output feedback controller that automatically counteracts the effects of disturbance inputs and restores a desirable behavior to the controlled machine. As a case study, the architecture of an asynchronous clock divider working in space environment is presented and the procedure of controller synthesis is verified.

Keywords: Fault Detection and Diagnosis, Process Control, Biological Systems
Abstract: This paper presents a new monitoring technique to improve performance of plant operation based on multivariate statistical process control (MSPC). The proposed method combines with MSPC by principal component analysis (PCA-MSPC) and monitoring of a pre-defined performance index for efficient and stable plant operation. Fault detection and isolation (FDI) related to the performance index is selectively performed by monitoring the time series data of the performance index wherein the sample points violating the control limit of Q statistic or that of T² statistic in PCA-MSPC are indicated.Hidden patterns of likely cause to deteriorate the performance index are discovered from the FDI by observing the time series data of the isolated variables. Applications of the proposed method to real wastewater treatment plants illustrate the effectiveness of the proposed method by showing possible improvement for energy-saving operation and stable plant operation.

Keywords: Fault Detection and Diagnosis
Abstract: This paper describes a statistical approach to fault detection and isolation for linear time-varying (LTV) systems subject to parametric additive faults. The proposed approach combines a GLR test with a recursive filter that cancels out the dynamics of the monitored faults effects. To our knowledge, the proposed recursive filter is new for the considered faults with time-varying profiles. The resulting algorithm handles fault diagnosis with weaker assumptions than usual, in particular on the number of sensors and on the stability of the monitored system.