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A common process control application is the cascaded two-tank system, where the level is controlled in the second tank. A nonlinear system identification approach is presented in this work to predict the model structure parameters that minimize the difference between the estimated and measured data, using benchmark datasets. The general suggested structure consists of a static nonlinearity in cascade with a linear dynamic filter in addition to colored noise element. A one-step ahead prediction error-based technique is proposed to estimate the model. The model is identified using a separable least squares optimization, where only the parameters that appear nonlinearly in the output of the predictor are solved using a modified Levenberg–Marquardt iterative optimization approach, while the rest are fitted using simple least squares after each iteration. Finally, MATLAB simulation examples using benchmark data are included. [ABSTRACT FROM AUTHOR]

This paper extends the algorithms used to fit standard support vector machines (SVMs) to the identification of auto-regressive exogenous (ARX) input Hammerstein models consisting of a SVM, which models the static nonlinearity, followed by an ARX representation of the linear element. The model parameters can be estimated by minimizing an \varepsilon-insensitive loss function, which can be either linear or quadratic. In addition, the value of the uncertainty level, \varepsilon, can be specified by the user, which gives control over the sparseness of the solution. The effects of these choices are demonstrated using both simulated and experimental data. [ABSTRACT FROM AUTHOR]

Abstract: The iterative optimizations often used to identify Wiener–Hammerstein models, pairs of linear filters separated by memoryless nonlinearities, require good initial estimates of the linear elements in order to avoid them getting caught in local minima. Previous work has shown that initial estimates of the two linear elements can be formed by splitting the poles and zeros of the best linear approximation of the Wiener–Hammerstein system between the two linear elements, an approach which can generate a large number of initializations. This paper develops a scanning technique that can efficiently evaluate each of the proposed initializations using estimates of some carefully constructed nonlinear characteristics of the system, estimates which can be formed using linear system identification techniques after some data pre-processing. This approach results in a much smaller number, often only one, of potential starting points for the optimization. The proposed algorithm is demonstrated using a Monte Carlo simulation using data from the SYSID 2009 Wiener–Hammerstein Benchmark system. [Copyright &y& Elsevier]

Estimates of joint or limb impedance are commonly used in the study of how the nervous system controls posture and movement, and how that control is altered by injury to the neural or musculoskeletal systems. Impedance characterizes the dynamic relationship between an imposed perturbation of joint position and the torques generated in response. While there are many practical reasons for estimating impedance rather than its inverse, admittance, it is an acausal representation of the limb mechanics that can lead to difficulties in interpretation or use. The purpose of this study was to explore the acausal nature of nonparametric estimates of joint impedance representations to determine how they are influenced by common experimental and computational choices. This was accomplished by deriving discrete-time realizations of first- and second-order derivatives to illustrate two key difficulties in the physical interpretation of impedance impulse response functions. These illustrations were provided using both simulated and experimental data. It was found that the shape of the impedance impulse response depends critically on the selected sampling rate, and on the bandwidth and noise characteristics of the position perturbation used during the estimation process. These results provide important guidelines for designing experiments in which nonparametric estimates of impedance will be obtained, especially when those estimates are to be used in a multistep identification process. [ABSTRACT FROM PUBLISHER]

The force and position data used to construct models of limb impedance are often obtained from closed-loop experiments. If the system is tested in a stiff environment, it is possible to treat the data as if they were obtained in open loop. However, when limb impedance is studied in a compliant environment, the presence of feedback cannot be ignored. While unbiased estimates of a system can be obtained directly using the prediction error method, the same cannot be said when linear regression or correlation analysis is used to fit nonparametric time- or frequency-domain models. We develop a prediction error minimization-based identification method for a nonparametric time-domain model augmented with a parametric noise model. The identification algorithm is tested on a dynamic mass–spring–damper system and returns consistent estimates of the system's properties under both stiff and compliant feedback control. The algorithm is then used to estimate the impedance of a human elbow joint in both stiff and compliant environments. [ABSTRACT FROM PUBLISHER]

Abstract: An identification algorithm for a power system load model is proposed in this paper. The overall non-convex identification problem is separated into convex and non-convex subproblems, allowing for a global optimum to be found. Numerical experiments using data from both simulated and physical systems illustrate the accuracy of the proposed algorithm. Experiments are performed to investigate the robustness of the algorithm. [Copyright &y& Elsevier]

• Decoupling technique proposed for polynomial NARX model. • Proposed decoupling technique reduces parameter count but not accuracy. • Tensor factorization based initializations for non-convex optimization based solution. • Algorithms validated in both prediction and simulation using 2 benchmark datasets. System identification uses measurements of a dynamic system's input and output to reconstruct a mathematical model for that system. These can be mechanical, electrical, physiological, among others. Since most of the systems around us exhibit some form of nonlinear behavior, nonlinear system identification techniques are the tools that will help us gain a better understanding of our surroundings and potentially let us improve their performance. One model that is often used to represent nonlinear systems is the polynomial NARX model, an equation error model where the output is a polynomial function of the past inputs and outputs. That said, a major disadvantage with the polynomial NARX model is that the number of parameters increases rapidly with increasing polynomial order. Furthermore, the polynomial NARX model is a black-box model, and is therefore difficult to interpret. This paper discusses a decoupling algorithm for the polynomial NARX model that substitutes the multivariate polynomial with a transformation matrix followed by a bank of univariate polynomials. This decreases the number of model parameters significantly and also imposes structure on the black-box NARX model. Since a non-convex optimization is required for this identification technique, initialization is an important factor to consider. In this paper the decoupling algorithm is developed in conjunction with several different initialization techniques. The resulting algorithms are applied to two nonlinear benchmark problems: measurement data from the Silver-Box and simulation data from the Bouc-Wen friction model, and the performance is evaluated for different validation signals in both simulation and prediction. [ABSTRACT FROM AUTHOR]