Error-In-Variables Methods for Efficient System Identification with Finite-Sample Guarantees

Piezoelectric elements (PEMs) are used in a variety of applications. In this paper, we developed a full analytical model and a simple system identification (SI) method of a piezoelectric actuator, which includes piezostack elements and a three-stage amplification mechanism. The model was derived separately for each unit of the system. Next, the units were combined, while taking into account their coupling. The hysteresis phenomenon, which is significant in piezoelectric materials, is described extensively. The theoretical model was verified in a laboratory setup. This setup includes a piezoelectric actuator, measuring devices and an acquisition system. The measured results were compared to the theoretical results. Some of the most well-known forms of system identification are shown briefly, while a new and simple algorithm is described systematically and verified by the model. The main advantage of this work is to provide a solid background and domain knowledge of modelling and system identification methods for further investigations in the field of piezoelectric actuators. Due to their simplicity, both the model and the system identification method can be easily modified in order to be applied to other PEMs or other amplification mechanism methods. The main novelty of this work lies in applying a simple system identification algorithm while using the system-level approach for piezoelectric actuators. Lastly, this review work is concluded and some recommendations for researchers working in this area are presented.

Measurement and identification of the nonlinear dynamics of a jointed structure using full-field data, Part I: Measurement of nonlinear dynamics

Click to increase image sizeClick to decrease image size Abstract A simple method for system identification is presented. A deterministic aperiodical signal, such as a step, ramp, or acceleration signal, is used as the input signal for the system. According to Green's function in transient state, the parameters of the ARMA model of the system can be estimated by means of the linear least squares method. Then the dominant dynamic characteristics of the system can be determined. Nonminimum phase systems and systems with transportation lag may also be identified if the stable conditions are satisfied. In addition, a satisfactory result is obtained when the method is applied to a system with noise. A set of experimental data from an electro‐hydraulic servo system is used to demonstrate the application of the method for system identification.

In this paper we formulate and solve a control-oriented system identification problem for single-input, single-output, linear, shift-invariant, distributed parameter plants. In this problem the available a priori information is minimal, consisting only of worst-case/deterministic, time dependent, upper and lower bounds on the plant impulse response and the additive output noise. The available a posteriori information consists of a corrupt finite output time series obtained in response to a known, non-zero but otherwise arbitrary, applied input. A novel system identification method is presented for this problem. This method yields an “uncertain model” of the plant, which is comprised of a nominal plant model, a bounded additive output noise, and a bounded additive model uncertainty measured in both the l1 and H∞ system norms. Both the identification method and the resulting uncertain model are computationally simple and possess certain desirable properties.

In this paper the advance in the study of system identification is summarized. Some traditional system identification methods are introduced, Least Squares Method, Recursive Gradient Correction and Recursive Maximum Likelihood. Some disadvantages are introduced too so that some new identification methods based on neural network, genetic algorithms, fuzzy logic and wavelet network are presented. After all, one system identification method based on adaptive filter ,the method has been usually used in active vibration control.

Flight test activities that expand the flight envelope are inherently expensive and at times dangerous, particularly when approaching stability and/or flutter boundaries. With the computational power now available, on-line software applications have emerged that can clear test points while a flight is in progress. For flying qualities evaluations, it is important to identify accurate frequency responses from which the parameters associated with commonly used criteria are obtained. Typically, these frequency responses are generated from long duration test inputs such as frequency sweeps that may be minutes long depending on the frequency range of interest. To meet goals set by the Air Force Flight Test Center, a new system identification method – the Narrowband Signature (NBS) – has been developed to obtain accurate frequency responses from short duration (five seconds or less) test inputs. A flying qualities flight test database was created using the Calspan Corporation Learjet In-Flight Simulator to exercise the new identification method. Comparisons were made against industry standard fast Fourier transform (FFT)-based identification techniques for both long and short duration inputs with a longitudinal axis cruise configuration that featured well-damped short period dynamics as well as a lateraldirectional approach configuration that featured a lightly damped Dutch roll mode. The identification results for the cruise configuration found that all methods identified the system accurately with minimal adjustment of the default identification parameters for the long duration input. For those configurations with lightly damped modes, even with the long duration inputs, adjustment of the recommended window sizes was necessary for proper identification of the lightly damped mode. For the short duration input cases, NBS showed a clear advantage over the FFT-based techniques for both configurations. To demonstrate accuracy of the methods, the results are compared against transfer function models of the selected configurations.

Neural networks are popular data-driven modeling tools that come with high data collection costs. This paper proposes a residual-based multipeaks adaptive sampling (RMAS) algorithm, which can reduce the demand for a large number of samples in the identification of stochastic dynamical systems. Compared to classical residual-based sampling algorithms, the RMAS algorithm achieves higher system identification accuracy without relying on any hyperparameters. Subsequently, combining the RMAS algorithm and neural network, a few-shot identification (FSI) method for stochastic dynamical systems is proposed, which is applied to the identification of a vegetation biomass change model and the Rayleigh-Van der Pol impact vibration model. We show that the RMAS algorithm modifies residual-based sampling algorithms and, in particular, reduces the system identification error by 76% with the same sample sizes. Moreover, the surrogate model accurately predicts the first escape probability density function and the P bifurcation behavior in the systems, with the error of less than 1.59×10-2. Finally, the robustness of the FSI method is validated.

Experimental modal analysis of a single-link flexible robotic manipulator with curved geometry using applied system identification methods

The Alfred Zampa Memorial Bridge (AZMB), a newly built long-span suspension bridge, is located 32km northeast of San Francisco on interstate Highway I-80. A set of dynamic field tests were conducted on the AZMB in November 2003, just before the bridge opening to traffic. These tests provided a unique opportunity to identify the modal properties of the bridge in its as-built condition with no previous traffic loads or seismic excitation. A benchmark study on modal identification of the AZMB is performed using three different state-of-the-art system identification algorithms based on ambient, as well as forced vibration measurements. These system identification methods consist of: (1) the multiple-reference natural excitation technique combined with the eigensystem realization algorithm; (2) the data-driven stochastic subspace identification method; and (3) the enhanced frequency domain decomposition method. Overall, the modal parameters identified using these system identification methods are found to be in very good agreement for each type of tests (ambient and forced vibration tests). For most vibration modes, the natural frequencies and mode shapes identified using the two different types of test data also match very well. However, the modal damping ratios identified from forced vibration test data are, in general, higher than those estimated from ambient vibration data. The identified natural frequencies and mode shapes are finally compared with their analytical counterparts from a three-dimensional finite-element model of the AZMB. The modal properties of the AZMB presented in this paper can be used as baseline in future health monitoring studies of this bridge.

Data based modelling is an important tool for the efficient planning and management of river systems. In this paper models of the water level in the upper part of Murray River in Australia are derived from observed operational river data by system identification methods. We consider Prediction Error Method (PEM) and Subspace Identification Method (SIM) and present the system identification procedure from collecting prior physical knowledge to model validation. It is shown that first order models capture the main trends in the data and perform well on validation datasets from different years.

This paper proposes a modified linear prediction method for speech analysis, using two system identification methods—the least‐square method and the instrument variable method—for the estimation of the coefficients of an all‐pole filter. Whereas the linear prediction method estimates the coefficients of all‐pole filters from speech signals, which are observed output signals, the system identification method estimates coefficients of all‐pole filters from observed output signals and the input signals. This paper derives a novel technique that estimates input signals from speech signals that are observed output signals with a high degree of accuracy and robustness with respect to added noise, by generating improved prediction error signals. The paper also shows that when voiced speech is to be analyzed, if input signals, which are an impulse chain, can be accurately estimated, the estimation of filter coefficients can yield a high degree of accuracy provided that the least‐square method is used, and that in this manner, the pitch period dependency can be removed. We also show that by applying the instrument variable method using an auxiliary model, the accuracy of estimation of filter coefficients in a noisy environment can be substantially improved while maintaining the properties of the least‐square method. The effectiveness of these system identification methods for speech analysis is demonstrated through computer simulations. © 2002 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 86(3): 20–32, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.1137

A novel nonlinear modelling approach has been developed and implemented on Alstom gasifier using Wiener model. The linear element of the Wiener model was identified by a combined subspace state space method, which integrated MOESP (Multivariable Output-Error State Space) and N4SID (Numerical algorithms for subspace state space system identification) method in the estimation of system matrices. Then a single layer neural network was chosen as the nonlinearity of the model. The proposed model identification method was used to model Alstom gasifier with strong nonlinearity and multivariable couples. The results compared to a combined linear subspace identification method demonstrate that the nonlinear method proposed in this paper behave better approximation.

A system identification method is proposed which can be used to characterize the distribution system load as a function of the substation voltage. The primary objective of this technique is to capture the dynamic variation of the composite system load on distribution feeders so that the most effective substation voltage level can be obtained and applied to conserve energy over specified control periods. The proposed system identification method is implementable on actual distribution systems by utilizing existing capabilities of the distribution automation hardware. Also, the impulse response of a space heating load is identified using the proposed technique to demonstrate the applicability of the identification method.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Many practical situations involve synthesizing controllers for systems where a priori models are not available and thus must be identified from experimental data. In most cases, it is possible to find multiple models that are consistent with the data. It is of interest to identify a simpler model compatible with the available information whenever possible than a more complex one. One of the motivations is the fact that the order of the plant model is reflected in the order of the resulting controllers. Another reason is the simplicity of analysis with low order models.

In this paper we give an overview of errors-in-variables methods in system identification. Background and motivation are given. Simple examples illustrate why the identification problem can be difficult. Under general weak assumptions, the systems are not uniquely identifiable, but can be parameterized using one degree of freedom. Examples where identifiability is achieved under additional assumptions are also provided. A number of approaches for parameter estimation of errors-in-variables models are presented. The underlying assumptions and principles for each approach are highlighted.