David T. Westwick

Identifying MIMO Hammerstein systems in the context of subspace model identification methods

In this paper, we outline the extension of the MOESP family of subspace model identification schemes to the Hammerstein-type of nonlinear system. Two types of identification problem are considered. The first type assumes the (polynomial) structure of the static nonlinearity to be given and the task is to identify both the linear system dynamics and the unknown proportional constants in the para-metrization of the static nonlinearity. The second type addresses the identification of both the linear dynamic part and the static nonlinearity, where only limited a priori information regarding the structure of the nonlinearity is available. The improved robustness properties of the algorithms developed for this second type of Hammerstein identification problem over existing correlation-based schemes is illustrated by a numerical example.

Multiple Model Predictive Control for Wind Turbines With Doubly Fed Induction Generators

A multivariable control strategy based on model predictive control techniques for the control of variable-speed variable-pitch wind turbines is proposed. The proposed control strategy is described for the whole operating region of the wind turbine, i.e., both partial and full load regimes. Pitch angle and generator torque are controlled simultaneously to maximize energy capture, mitigate drive train transient loads, and smooth the power generated while reducing the pitch actuator activity. This has the effect of improving the efficiency and the power quality of the electrical power generated, and increasing the life expectancy of the installation. Furthermore, safe and acceptable operation of the system is guaranteed by incorporating most of the constraints on the physical variables of the wind energy conversion system (WECS) in the controller design. In order to cope with nonlinearities in the WECS and continuous variations in the operating point, a multiple model predictive controller is suggested which provides acceptable performance throughout the whole operating region.

Separable least squares identification of nonlinear Hammerstein models: application to stretch reflex dynamics.

AbstractThe Hammerstein cascade, consisting of a zero-memory nonlinearity followed by a linear filter, is often used to model nonlinear biological systems. This structure can represent some high-order nonlinear systems accurately with relatively few parameters. However, it is not possible, in general, to estimate the parameters of a Hammerstein cascade in closed form. The most effective method available to date uses an iterative approach, which alternates between estimating the linear element from a crosscorrelation, and then fitting a polynomial to the nonlinearity via linear regression. This paper proposes the use of separable least squares optimization methods to estimate the linear and nonlinear elements simultaneously in a least squares framework. A separable least squares algorithm for the identification of Hammerstein cascades is developed and used to analyze stretch reflex electromyogram data from two experimental subjects. The results show that in each case the proposed algorithm produced a better model, in that it predicted the system’s response to novel inputs more accurately, than did models estimated using the traditional iterative algorithm. Monte-Carlo simulations demonstrated that when the input is a non-Gaussian, nonwhite signal, as is often the case experimentally, the traditional iterative identification approach produces biased models, whereas the separable least squares approach proposed in this paper does not.

Identification of Hammerstein models with cubic spline nonlinearities

This paper considers the use of cubic splines, instead of polynomials, to represent the static nonlinearities in block structured models. It introduces a system identification algorithm for the Hammerstein structure, a static nonlinearity followed by a linear filter, where cubic splines represent the static nonlinearity and the linear dynamics are modeled using a finite impulse response filter. The algorithm uses a separable least squares Levenberg-Marquardt optimization to identify Hammerstein cascades whose nonlinearities are modeled by either cubic splines or polynomials. These algorithms are compared in simulation, where the effects of variations in the input spectrum and distribution, and those of the measurement noise are examined. The two algorithms are used to fit Hammerstein models to stretch reflex electromyogram (EMG) data recorded from a spinal cord injured patient. The model with the cubic spline nonlinearity provides more accurate predictions of the reflex EMG than the polynomial based model, even in novel data.

Identification of Multiple-Input Systems with Highly Coupled Inputs: Application to EMG Prediction from Multiple Intracortical Electrodes

A robust identification algorithm has been developed for linear, time-invariant, multiple-input single-output systems, with an emphasis on how this algorithm can be used to estimate the dynamic relationship between a set of neural recordings and related physiological signals. The identification algorithm provides a decomposition of the system output such that each component is uniquely attributable to a specific input signal, and then reduces the complexity of the estimation problem by discarding those input signals that are deemed to be insignificant. Numerical difficulties due to limited input bandwidth and correlations among the inputs are addressed using a robust estimation technique based on singular value decomposition. The algorithm has been evaluated on both simulated and experimental data. The latter involved estimating the relationship between up to 40 simultaneously recorded motor cortical signals and peripheral electromyograms (EMGs) from four upper limb muscles in a freely moving primate.The algorithm performed well in both cases:it provided reliable estimates of the system output and significantly reduced the number of inputs needed for output prediction. For example, although physiological recordings from up to 40 different neuronal signals were available, the input selection algorithm reduced this to 10 neuronal signals that made signicant contributions to the recorded EMGs.

Tissue sensing adaptive Radar for breast cancer detection-investigations of an improved skin-sensing method

Active microwave breast imaging is being researched as a supplement to current breast imaging modalities. Ultra-wideband radar approaches involve analyzing reflections from the breast to identify the presence of tumors. Skin sensing, which involves estimating the location and thickness of the skin, is a key step in this process, as the reflections from the skin dominate the signal. Current methods employing a rudimentary peak detection process estimate the location of the breast with acceptable accuracy. However, estimates of skin thickness in the range of 1.0-2.0 mm have unacceptable error. A method using deconvolution to obtain the impulse response of a scattering object is investigated to improve the performance of the skin-sensing algorithm. The new method employs a calibration step using a perfect electric conductor. Application to simulated data shows success in reducing the error percentage in both breast skin location and thickness estimates by more than half.

Multiple model MIMO predictive control for variable speed variable pitch wind turbines

A multivariable control strategy based on model predictive control techniques for the control of variable speed variable pitch wind turbines is proposed. The proposed control strategy is described for the whole operating region of the wind turbine (both partial and full load regimes). Pitch angle and generator torque are controlled simultaneously to maximize energy capture, mitigate drive train transient loads and smooth the power generated while reducing the pitch actuator activity. This has the effect of improving the efficiency and the power quality of the electrical power generated, and of increasing the life time of the systems mechanical parts. Furthermore, safe and acceptable operation of the system is guaranteed by incorporating most of the constraints on the physical variables of the WECS in the controller design. In order to cope with nonlinearities in the WECS and continuous variations in the operating point, a multiple model predictive controller is suggested which provides near optimal performance throughout the whole operating region.

Initial estimates of the linear subsystems of Wiener-Hammerstein models

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.

Identification of a Hammerstein model of the stretch reflex EMG using separable least squares

The Hammerstein cascade, a zero-memory nonlinearity followed by a linear filter, is often used to model nonlinear biological systems. Using this structure, some high-order nonlinear systems can be represented accurately using relatively few parameters. However, because the model output is not a linear function of its parameters, in general they cannot be estimated in closed form. Currently, an iterative technique, which alternates between estimating the linear element from a cross-correlation, and then fitting a polynomial to the nonlinearity via linear regression, is used to identify these cascades. In this paper, separable least squares (SLS) optimization methods are proposed as a means of simultaneously estimating both the linear and nonlinear elements, in an exact least squares framework. A SLS algorithm for the identification of Hammerstein cascades is developed and used to analyze stretch reflex EMG data from a spinal cord injured patient. Results are compared to those obtained using the traditional, iterative, algorithm.

Tumor Response Estimation in Radar-Based Microwave Breast Cancer Detection

Radar-based microwave imaging techniques have been proposed for early stage breast cancer detection. A considerable challenge for the successful implementation of these techniques is the reduction of clutter, or components of the signal originating from objects other than the tumor. In particular, the reduction of clutter from the late-time scattered fields is required in order to detect small (subcentimeter diameter) tumors. In this paper, a method to estimate the tumor response contained in the late-time scattered fields is presented. The method uses a parametric function to model the tumor response. A maximum a posteriori estimation approach is used to evaluate the optimal values for the estimates of the parameters. A pattern classification technique is then used to validate the estimation. The ability of the algorithm to estimate a tumor response is demonstrated by using both experimental and simulated data obtained with a tissue sensing adaptive radar system.