System Identification Framework Research Articles

Revealing Time-Varying Joint Impedance With Kernel-Based Regression and Nonparametric Decomposition

During movements, humans continuously regulate their joint impedance to minimize control effort and optimize performance. Joint impedance describes the relationship between a joint's position and torque acting around the joint. Joint impedance varies with joint angle and muscle activation and differs from trial-to-trial due to inherent variability in the human control system. In this paper, a dedicated time-varying system identification (SI) framework is developed involving a parametric, kernel-based regression, and nonparametric, “skirt decomposition,” SI method to monitor the time-varying joint impedance during a force task. Identification was performed on single trials and the estimators included little a priori assumptions regarding the underlying time-varying joint mechanics. During the experiments, six (human) participants used flexion of the wrist to apply a slow sinusoidal torque to the handle of a robotic manipulator, while receiving small position perturbations. Both methods revealed that the sinusoidal change in joint torque by activation of the wrist flexor muscles resulted in a sinusoidal time-varying joint stiffness and resonance frequency. A third-order differential equation allowed the parametric kernel-based estimator to explain on average 76% of the variance (range 52%-90%). The nonparametric skirt decomposition method could explain on average 84% of the variance (range 66%-91%). This paper presents a novel framework for identification of time-varying joint impedance by making use of linear time-varying models based on a single trial of data.

Stochastic Analysis of the Recursive Least Squares Algorithm for Cyclostationary Colored Inputs

This paper studies the stochastic behavior of the recursive least squares (RLS) algorithm in a system identification framework for a cyclostationary colored input. The input cyclostationary signal is modeled by a colored random process with periodically time-varying power. The system parameters vary according to a random-walk. Mathematical models are derived for the mean and mean-square-deviation (MSD) behavior of the adaptive weights as a function of the input cyclostationarity. The MSD behaviors of the RLS and LMS algorithms are compared for cyclostationary colored input. Monte Carlo simulations provide strong support for the theory. A separate analysis for white Gaussian and non-Gaussian inputs is presented in support of the assumptions made for the mathematical model above.

Multi-objective evolutionary framework for non-linear system identification: A comprehensive investigation

The present study proposes a multi-objective framework for structure selection of nonlinear systems which are represented by polynomial NARX models. This framework integrates the key components of Multi-Criteria Decision Making (MCDM) which include preference handling, Multi-Objective Evolutionary Algorithms (MOEAs) and a posteriori selection. To this end, three well-known MOEAs such as NSGA-II, SPEA-II and MOEA/D are thoroughly investigated to determine if there exists any significant difference in their search performance. The sensitivity of all these MOEAs to various qualitative and quantitative parameters, such as the choice of recombination mechanism, crossover and mutation probabilities, is also studied. These issues are critically analyzed considering seven discrete-time and a continuous-time benchmark nonlinear system as well as a practical case study of non-linear wave-force modeling. The results of this investigation demonstrate that MOEAs can be tailored to determine the correct structure of nonlinear systems. Further, it has been established through frequency domain analysis that it is possible to identify multiple valid discrete-time models for continuous-time systems. A rigorous statistical analysis of MOEAs via performance sweet spots in the parameter space convincingly demonstrates that these algorithms are robust over a wide range of control parameters.

Köprü Yapılarının Eş Zamanlı Sistem ve Girdi Tanılaması

Bu makale, deprem kayıtlarını kullanarak köprü yapılarının sistem tanılaması için yeni bir yöntem sunmaktadır. Köprüler, genellikle yapısal elemanlarının geniş mesafelere yayılmasından ötürü, diğer yapılara nispeten yer hareketlerinin uzamsal değişkenliğine daha hassastırlar. Bu nedenle, özellikle temelleri değişik zemin türlerine oturan uzun ve çok kolonlu köprülerin simülasyonlarında kullanılacak nitelikte yer hareketi kayıtlarının ölçümü karmaşık bir süreçtir. Bilhassa hem eylemsizlik hem de kinematik Zemin-Yapı Etkileşimi etkilerinin yaygın olduğu durumlarda, köprü Temel Girdi Hareketlerinin doğrudan ölçümü mümkün olmayabilir. Bu çalışmada, uzamsal olarak seyrek bir şekilde ölçülmüş sismik yapı davranış kayıtlarını kullanarak eş zamanlı sistem ve girdi tanılaması sağlayan yeni bir yöntem önerilmektedir. Önerilen metodun teyidi ve gerçek ölçekte problemlere uygulanabilirliğini doğrulamak adına, yöntem Golden Gate Köprüsü'ne uygulanmış ve elde edilen sonuçlar mevcut veriler ile karşılaştırılmıştır.

Bayesian inference for damage identification based on analytical probabilistic model of scattering coefficient estimators and ultrafast wave scattering simulation scheme

Ultrasonic Guided Waves (GW) actuated by piezoelectric transducers installed on structures have proven to be sensitive to small structural defects, with acquired scattering signatures being dependent on the damage type. This study presents a generic framework for probabilistic damage characterization within complex structures, based on physics-rich information on ultrasound wave interaction with existent damage. To this end, the probabilistic model of wave scattering properties estimated from measured GWs is inferred based on absolute complex-valued ratio statistics. Based on the probabilistic model, the likelihood function connecting the scattering properties predicted by a computational model containing the damage parametric description and the scattering estimates is formulated within a Bayesian system identification framework to account for measurement noise and modelling errors. The Transitional Monte Carlo Markov Chain (TMCMC) is finally employed to sample the posterior probability density function of the updated parameters. However, the solution of a Bayesian inference problem often requires repeated runs of “expensive-to-evaluate” Finite Element (FE) simulations, making the inversion procedure firmly demanding in terms of runtime and computational resources. To overcome the computational challenges of repeated likelihood evaluations, a cheap and fast Kriging surrogate model built and based on a set of training points generated with an experiment design strategy in tandem with a hybrid Wave and Finite Element (WFE) computational scheme is proposed in this study. In each “numerical experiment”, the training outputs (i.e. ultrasound scattering properties) are efficiently computed using the hybrid WFE scheme which combines conventional FE analysis with periodic structure theory. By establishing the relationship between the training outputs and damage characterization parameters statistically, the surrogate model further enhances the computational efficiency of the exhibited scheme. Two case studies including one numerical example and an experimental one are presented to verify the accuracy and efficiency of the proposed algorithm.

Measurement of train-induced vibration for track parameter identification: Bayesian probabilistic approach

The train-induced vibration response is used to develop a comprehensive finite element model for the railway track, which considered rail-sleeper-ballast interaction. This model can be further use in the development of an operational monitoring system for railway track by following the Bayesian statistical system identification framework. However, it is believed that the uncertainties associated with the measured train-induced test data and model parameters are relatively high, therefore, the corresponding model updating problem will very likely to be in the category of unidentifiable case. Therefore, Markov chain Monte Carlo (MCMC) simulation was used in generating the samples for the approximation of the posterior uncertainties. The measurements also provide not only reference values suitable for model fitting, but also a good insight into the main features of the dynamic behaviour of the railway track system. Finally, the reliability and accuracy of the proposed method are demonstrated by numerically reproducing the system responses. Modelling assumptions are discussed, together with their implications on numerical results of the time-domain analysis, which were found to be in good agreement with experimental results.

Enhancing MPC formulations by identification and estimation of valve stiction

A common source of poor control performance in industrial processes is represented by stiction in control valves, which often induces offset, oscillating behavior, and even loss of stability. Recent studies have investigated the effectiveness of embedding stiction models into model predictive controller (MPC) schemes, moving from stiction unaware to different stiction aware formulations, which help to remove fluctuations and may guarantee higher set-point tracking ability. To this aim, along with the process model the controller needs to use a dynamic model of sticky valves. This paper proposes an efficient, computational approach to obtain both valve and process dynamics, under the framework of Hammerstein system identification, which is based on nonlinear, gradient-based, numerical optimization. In order to improve the computational behavior and effectiveness of the methodology, a recently proposed smoothed model of stiction is deployed. The proposed methodology is validated in several (single-input single-output, and multivariable) examples, where the effectiveness of the obtained stiction aware MPC regulator is also evaluated against a stiction unaware counterpart.

A Loewner Interpolation Method for Power System Identification and Order Reduction

An accurate framework for power system identification and model order reduction based on the Loewner matrix method is proposed. In this approach, frequency responses corresponding to non-symmetrical non-square MIMO transfer functions are introduced as tangential data in the Loewner interpolation process. Such responses can be either computed efficiently when explicit large sparse models are available or measured when only black-box models are at disposal. Numerical results are discussed for a couple of well-reported multi-machine test systems. The accuracy of the produced models and comparison against other state-of-the-art techniques are then discussed.

Dynamic Mode Decomposition for Compressive System Identification

Dynamic mode decomposition has emerged as a leading technique to identify spatiotemporal coherent structures from high-dimensional data, benefiting from a strong connection to nonlinear dynamical systems via the Koopman operator. In this work, two recent innovations that extend dynamic mode decomposition to systems with actuation and systems with heavily subsampled measurements are integrated and unified. When combined, these methods yield a novel framework for compressive system identification. It is possible to identify a low-order model from limited input–output data and reconstruct the associated full-state dynamic modes with compressed sensing, adding interpretability to the state of the reduced-order model. Moreover, when full-state data are available, it is possible to dramatically accelerate downstream computations by first compressing the data. This unified framework is demonstrated on two model systems, investigating the effects of sensor noise, different types of measurements (e.g., point sensors, Gaussian random projections, etc.), compression ratios, and different choices of actuation (e.g., localized, broadband, etc.). In the first example, this architecture is explored on a test system with known low-rank dynamics and an artificially inflated state dimension. The second example consists of a real-world engineering application given by the fluid flow past a pitching airfoil at low Reynolds number. This example provides a challenging and realistic test case for the proposed method, and results demonstrate that the dominant coherent structures are well characterized despite actuation and heavily subsampled data.

Analysing the impact of system dimension on the performance of a variable-tap-length adaptive algorithm

The variable-tap-length algorithms try to find out the optimum number of adaptive filter coefficients that are necessary to model an unknown plant. The most recent variable-tap-length algorithms claim themselves to be independent of the order of the unknown channel, even though the convergence rate of an adaptive finite impulse response filter that is used for identifying an unknown plant in a system identification framework may be affected by the characteristics of the input signal and time-varying filter parameters. The system dimension may vary notably from one application to others, such as acoustic echo cancellation in a big conference hall needs thousands of filter weights, whereas feedback cancellation in hearing-aids requires less than a hundred coefficients. Hence, there is a need to analyze the convergence of the variable-tap-length algorithm for these time-varying applications of adaptive filters of different dimensions. In this paper, we develop and propose a novel technique to measure the convergence and transient behavior of the variable-tap-length adaptive algorithm. Using this analysis, we also arrive at conclusion that the median rate of convergence declines with the rise in system dimension to a limit determined by the reference input. It is proved that the limiting point can be obtained by the level of the autocorrelation of the input signal.

Stochastic analysis of the LMS algorithm for cyclostationary colored Gaussian and non-Gaussian inputs

This paper studies the stochastic behavior of the LMS algorithm in a system identification framework for a cyclostationary colored input without assuming a Gaussian distribution for the input. The input cyclostationary signal is modeled by a colored random process with periodically time-varying power. The generation of the colored non-Gaussian random process is parametrized in novel manner by passing a Gaussian random process through a coloring filter followed by a zero memory nonlinearity. The unknown system parameters are fixed in most of the cases studied here. Mathematical models are derived for the behavior of the mean and mean-square-deviation (MSD) and the excess mean-square error (EMSE) of the adaptive weights as a function of the input cyclostationarity. The models display the dependence of the algorithm upon the input nonlinearity and coloration. Three nonlinearities that are studied in detail with Monte Carlo simulations provide strong support for the theory.

Stochastic analysis of the LMS algorithm for cyclostationary colored Gaussian inputs

Abstract This paper studies the stochastic behavior of the LMS algorithm for a system identification framework when the input signal is a cyclostationary colored Gaussian process. The unknown system is modeled by the standard random walk model. Well-known results for the LMS algorithm are extended to the cyclostationary case and used for predicting the mean-square weight deviation (MSD) and excess mean-square error (EMSE) behavior of the algorithm. Monte Carlo simulations provide strong support for the theory.

Sparse Deconvolution of Electrodermal Activity via Continuous-Time System Identification.

Electrodermal activity (EDA) indicates different eccrine sweat gland activity caused by the stimulation of the autonomic nervous system. Recovering the number, timings, and amplitudes of underlying neural stimuli and physiological system parameters from the EDA is a challenging problem. One of the challenges with the existing methods is the non-convexity of the optimization formulations for estimating the parameters given the stimuli. We solve this parameter estimation problem using the following continuous-time system identification framework: 1) we specifically use the Hartley modulating function (HMF) for parameter estimation so that the optimization formulation for estimating the parameters given the stimuli is convex; and 2) we use Kaiser windows with different shape parameters to put more emphasis on the significant spectral components so that there is a balance between filtering out the noise and capturing the data. We apply this algorithm to skin conductance (SC) data, a measure of EDA, collected during cognitive stress experiments. Under a sparsity constraint, in the HMF domain, we successfully deconvolve the SC signal. We obtain number, timings, and amplitudes of the underlying neural stimuli along with the system parameters with R2 above 0.915. Moreover, using simulated data, we illustrate that our approach outperforms the existing EDA data analysis methods, in recovering underlying stimuli. We develop a novel approach for deconvolution of SC by employing the HMF method and capturing the significant spectral components of SC data. Recovering the underlying neural stimuli more accurately using this approach will potentially improve tracking emotional states in affective computing.

Robust Identification Method for LPV ARX Systems and its Application to a Mechanical Unit

This paper introduces a robust identification solution for the linear parameter varying Autoregressive Exogenous systems with outlier-contaminated outputs. The Laplace distribution with heavy tails and the expectation maximization algorithm are combined to build the robust system identification framework. To overcome the obstacles brought by the outliers, the Laplace distribution which can be decomposed into infinite Gaussian components, is applied to mathematically model the system noise. The problem of parameter estimation is solved using the expectation maximization algorithm, and the equations to infer the system model and noise parameters are simultaneously provided in the developed identification method. Finally, the verification tests performed on a numerical example and a mechanical unit are used to prove the validity of the developed identification method.

Modeling of multiple-input, time-varying systems with recursively estimated basis expansions

Abstract We present novel computational schemes for estimating single- (SI) and multiple-input (MI) time-varying (TV) systems, combining a Laguerre–Volterra model formulation with improved recursive schemes based on conventional Recursive Least Squares (RLS) and Kalman Filtering (KF). The proposed recursive estimators achieve superior performance, particularly in the case of TV systems with multiple-inputs or systems that exhibit mixed-mode variations. RLS-based schemes were found to perform better in the case of TV linear systems, while the KF-based schemes were found to perform considerably better in the case of TV nonlinear systems. Model order selection and tuning of the estimator hyperparameters were implemented using Genetic Algorithms (GA), significantly improving performance and reducing computation time. Furthermore, exploiting the search efficiency in hyperparameter space yielded by the proposed GA, we rigorously examined the correlations between the hyperparameter values, the model complexity and the TV characteristics of the true underlying system. The performance of the proposed TV system identification framework was assessed using simulations and experimental data from patients undergoing head-up tilt testing for the diagnosis of vasovagal syncope.

A control-theoretic system identification framework and a real-time closed-loop clinical simulation testbed for electrical brain stimulation

Objective. Closed-loop electrical brain stimulation systems may enable a precisely-tailored treatment for neurological and neuropsychiatric disorders by controlling the stimulation based on neural activity feedback in real time. Developing model-based closed-loop systems requires a principled system identification framework to quantify the effect of input stimulation on output neural activity by learning an input-output (IO) dynamic model from data. Further, developing these systems needs a realistic clinical simulation testbed to design and validate the closed-loop controllers derived from the IO models before testing in human patients. Approach. First, we design a control-theoretic system identification framework to build dynamic IO models for neural activity that are amenable to closed-loop control design. To enable tractable model-based control, we use a data-driven linear state-space IO model that characterizes the effect of input on neural activity in terms of a low-dimensional hidden neural state. To learn the model parameters, we design a novel input waveform—a pulse train modulated by stochastic binary noise (BN) parameters—that we show is optimal for collecting informative IO datasets in system identification and conforms to clinical safety requirements. Second, we further extend this waveform to a generalized BN (GBN)-modulated waveform to reduce the required system identification time. Third, to enable extensive testing of system identification and closed-loop control, we develop a real-time closed-loop clinical hardware-in-the-loop (HIL) simulation testbed using the microelectrode recording and stimulation device, which incorporates stochastic noises, unknown disturbances and stimulation artifacts. Using this testbed, we implement both the system identification and the closed-loop controller by taking control of mood in depression as an example. Results. Testbed simulation results show that the closed-loop controller designed from IO models identified with the BN-modulated waveform achieves tight control, and performs similar to a controller that knows the true IO model of neural activity. When system identification time is limited, performance is further improved using the GBN-modulated waveform. Significance. The system identification framework with the new BN-modulated waveform and the clinical HIL simulation testbed can help develop future model-based closed-loop electrical brain stimulation systems for treatment of neurological and neuropsychiatric disorders.

Stochastic Analysis of the LMS and NLMS Algorithms for Cyclostationary White Gaussian and Non-Gaussian Inputs

This paper studies the stochastic behavior of the LMS and NLMS algorithms in a system identification framework for a cyclostationary white input without assuming a Gaussian distribution for the input. The input cyclostationary signal is modeled by a white random process with periodically time-varying power. The system parameters vary according to a random-walk. Mathematical models are derived for the mean and mean-square-deviation behavior of the adaptive weights as a function of the input cyclostationarity. Analytical models are first derived for the LMS and NLMS algorithms for cyclostationary white inputs. These models show the dependence of the two algorithms upon the kurtosis of the input. Significant differences are found between the behaviors of the two algorithms when the analysis is applied to non-Gaussian cases. Monte Carlo simulations provide strong support for the theory.

A Unified Framework for Wavelet-Packet Identification of Dynamic Systems

This work proposes a unified framework for linear system identification in frequency subbands using wavelet packets. To that end, a previous wavelet-packet technique is extended to allow for the use of general model structures and standard identification procedures. The technique can be straightforwardly applied to the identification of models with different structures, such as subspace models, provided that their parameters can be identified using a least-squares approach. Models with autoregressive structures are used here for means of illustration. The proposed technique is illustrated with the examples of the longitudinal dynamics of a flexible aircraft and with the model of a cantilever beam. The proposed wavelet-packet approach is favorably compared with the technique on which it was based and with a recently proposed wavelet-based subspace identification technique.

Proportionate adaptive filtering algorithms based on mixed square/fourth error criterion with unbiasedness criterion for sparse system identification

SummaryTwo novel adaptive filtering algorithms based on the mixed square/fourth error criterion are proposed for solving sparse system identification problems. Motivated by the fact that the proportionate update scheme can enhance the tracking ability of the system, we develop a proportionate least mean square/fourth (PLMS/F) algorithm in this paper. Combining the proportionate update scheme and the LMS/F algorithm, the proposed PLMS/F algorithm shows superiority for non‐Gaussian noise environments. Moreover, to further improve the performance of the PLMS/F algorithm in the noisy input cases, a bias‐compensated PLMS/F algorithm is developed by incorporating an unbiased criterion to compensate the bias caused by input noises. Simulation results in the context of the sparse system identification framework demonstrate that the proposed PLMS/F and bias‐compensated PLMS/F algorithms can achieve excellent identification performance in terms of steady‐state misalignment and convergence speed under noisy input and non‐Gaussian output noise environments.

An Improved D-S Evidence Theory in Tire Pressure Monitoring System

D-S evidence theory can bring incorrect results when there is inconsistent and conflicting among the evidences, in order to solve this problem, a method based on reliability and falsity is proposed in the paper. Firstly, the reliability of each evidence in the system identification framework is calculated according to the Lance distance, then, falsity of evidence is adopted to measure the degree of conflict between different evidences, combining reliability and falsity determines corrected coefficient of evidences, and basic probability assignment is reconfigured, finally, modified basic probability assignment are fused by D-S combination rule. The experimental results show that the proposed method can effectively handle the problem of conflict evidence, meanwhile the method is applied to the tire pressure monitoring system, which can identify the target well and has high reliability.