Identification Of Dynamic Systems Research Articles

Nonlinear system identification via data augmentation

This paper presents a novel nonparametric approach to the identification of nonlinear dynamical systems. The proposed methodology exploits the potential of manifold learning on an artificially augmented dataset, obtained without running new experiments on the plant. The additional data are employed for approximating the manifold where input regressors lie. The knowledge of the manifold acts as a prior information on the system, that induces a proper regularization term on the identification cost. The new regularization term, as opposite to the standard Tikhonov one, enforces local smoothness of the function along the manifold. A graph-based algorithm tailored to dynamical systems is proposed to generate the augmented dataset. The hyperparameters of the method, along with the order of the system, are estimated from the available data. Numerical results on a benchmark Nonlinear Finite Impulse Response (NFIR) system show that the proposed approach may outperform the state of the art nonparametric methods.

Neural activity inspired asymmetric basis function TV-NARX model for the identification of time-varying dynamic systems

Inspired by the unique neuronal activities, a new time-varying nonlinear autoregressive with exogenous input (TV-NARX) model is proposed for modelling nonstationary processes. The NARX nonlinear process mimics the action potential initiation and the time-varying parameters are approximated with a series of postsynaptic current like asymmetric basis functions to mimic the ion channels of the inter-neuron propagation. In the model, the time-varying parameters of the process terms are sparsely represented as the superposition of a series of asymmetric alpha basis functions in an over-complete frame. Combining the alpha basis functions with the model process terms, the system identification of the TV-NARX model from observed input and output can equivalently be treated as the system identification of a corresponding time-invariant system. The locally regularised orthogonal forward regression (LROFR) algorithm is then employed to detect the sparse model structure and estimate the associated coefficients. The excellent performance in both numerical studies and modelling of real physiological signals showed that the TV-NARX model with asymmetric basis function is more powerful and efficient in tracking both smooth trends and capturing the abrupt changes in the time-varying parameters than its symmetric counterparts.

Adaptive switching control based on limited multiple models

SummaryIn this paper, the limited multiple models system identification scheme with third‐level adaptation is proposed to build the virtual identification model for the control of the closed‐loop system. First, the dynamical switching identification models subbank is constructed based on the performance index. Next, the virtual identification model is build through the combination of the identification models in the dynamical switching subbank. Then, the combination proportion of the models is adaptively tuning with the third‐level adaptation. The main contribution of this paper is that the proposed dynamical system identification method can overcome system resources waste of the multiple models switching with second‐level adaptation, and it does not require that all of the identification models combine directly. Finally, the simulation is provided to illustrate its effectiveness.

Semicool Temperature Compensation Algorithm Based on the Double Exponential Model in the Ultrasonic Positioning System

This paper proposes a semicool temperature compensation algorithm based on the double exponential model of the transient temperature rise curve to improve the performance of the 3-D ultrasonic positioning system. The error model of the 3-D ultrasonic positioning system is derived and the importance of temperature to the positioning accuracy is demonstrated. Then, the double exponential model of the transient temperature rise curve derived by the difference principle is established through a dynamic system identification method. On this basis, the semicool temperature compensation algorithm is proposed, which includes the estimation of the initial time $t_{0}$ , the principle of the choice of parameter $k$ . The effectiveness of the algorithm is verified by temperature measurement experiments. The impact of the ambient temperature on the algorithm is also analyzed qualitatively. In the end, the semicool temperature compensation algorithm is proved to be able to improve the performance of the 3-D ultrasonic positioning system by the comparison experiments respectively under static measurement of a fixed point and dynamic measurement of a fixed line.

Detection of reaching intention using EEG signals and nonlinear dynamic system identification

Background and objectivesLow frequency electroencephalography (EEG) signals are associated with preparation of movement and thus provide valuable information for brain-machine interface applications. The purpose of this study was to detect movement intention from EEG signals before execution of self-paced arm reaching movements. MethodsTen healthy individuals were recruited. Movement onset was determined from surface electromyography recordings time-locked with EEG signals. Unlike previous studies, which employed feature extraction and classification for decoding, a nonlinear dynamic multiple-input/single output (MISO) model was developed. The MISO model consisted of a cascade of Volterra structures and a threshold block, generating the binary output corresponding to intention/no-intention. The modeling process included input selection from a pool of different EEG channels. The predictive performance of the model was evaluated using the receiver operating characteristics curve, from which the optimum threshold was also selected. The Mann–Whitney statistics was employed to select the significant EEG channels for the output by examining the statistical significance of improvement in the predictive capability of the model when the respective channels were included. ResultsWith the proposed approach, movement intention was detected approximately 500 ms before the movement onset and on average, with an accuracy of 96.37 ± 0.94%, a sensitivity of 77.93 ± 4.40% and a specificity of 98.52 ± 1.19%. ConclusionsThe model output can be converted to motion commands for neuroprosthetic devices and exoskeletons in future applications.

Identification of piecewise linear dynamical systems using physically-interpretable neural-fuzzy networks: Methods and applications to origami structures

Self-locking origami structures are characterized by their piecewise linear constitutive relations between force and deformation, which, in practice, are always completely opaque and unmeasurable: the number of piecewise segments, the positions of non-smooth points, and the linear parameters of each segment are unknown a priori. However, acquiring this information is of fundamental importance for understanding the origami structure’s dynamic folding process and predicting its dynamic behaviors. This, therefore, arouses our interest in adopting a dynamical identification process to determine the model and to estimate the parameters. In this research, based on the piecewise linear assumption, a physically-interpretable neural-fuzzy network is built to correlate the measured input and output data. Unlike the conventional approaches, the constructed neural network possesses specific physical meaning of its components: the number of neurons relates to the number of piecewise segments, the coefficients of the local linear models relate to the parameters of the constitutive relations, and the validity functions relate to the positions of non-smooth points. By addressing several examples with different backgrounds, the network’s underlying data training methods are illustrated, including the local linear optimization for linear parameters, nested optimization for nonlinear partitions, and Local Linear Model Tree optimization for model selection. Noting that the tackled origami problem holds strong universality in terms of the unknown piecewise characteristics, the proposed approach would thus provide an effective, generic, and physically significant means for handling piecewise linear dynamical systems and meanwhile bring fresh vitality to the artificial neural network research.

Identification of nonlinear block-oriented systems with backlash and saturation

Abstract A new approach to modeling and identification of discrete-time nonlinear dynamic systems with input backlash and output saturation nonlinearities is presented. The proposed three-block cascade mathematical model results from successive applications of the key-term separation principle. This provides special nonlinear model description that is linear in parameters. An iterative technique with internal variable estimation is proposed for estimation of all the model parameters based on measured input/output data and minimizing the least-squares criterion. Illustrative example of cascade system identification with backlash and saturation is included.

Online Identification of Aircraft Dynamics in the Presence of Actuator Faults

In this paper, a multiple model-based nonlinear identification approach is introduced for a conventional aircraft in the presence of different types of actuator faults. Occurrence of actuator faults can obviously reduce the validity of a predetermined dynamic model of nonlinear systems. In such cases, use of multi-model structures can be an effective choice. However, determining the optimal validity functions of the local models in a multi-model structure is still a challenging problem. This problem becomes even more challenging in case of unpredictable faults, which are not considered in training the local models. In this paper, two effective techniques are proposed for online determination of the validity functions of local models called the Error-based Gaussian validity functions (E-GVF) and the Online Sequential Extreme Learning Machine (OSELM)-based approach. Accordingly, there is no need to employ a separate Fault Detection and Isolation (FDI) block in the proposed identification approach. Also, due to great capabilities of neural networks for modeling complex nonlinear systems, recurrent neural networks are used as the local models of the proposed multi-model structure. The obtained simulation results indicate the capability of the proposed OSELM-based multi-model structure for nonlinear identification of complex dynamic systems in the presence of both predictable and unpredictable actuator faults.

Prediction and identification of discrete-time dynamic nonlinear systems based on adaptive echo state network

In this paper, a new prediction and identification method based on adaptive echo state network (AESN) is proposed to identify a class of discrete-time dynamic nonlinear systems (DDNS). Firstly, according to the characteristics of input signals, the reservoir state update equation of AESN can be adaptively adjusted. In order to guarantee the echo state property of AESN, a sufficient condition for echo state property is given. Secondly, the reservoir parameters of AESN are optimized to improve the identification and prediction performance of AESN. Thirdly, an improved online output weights learning method based on historical reservoir state and output error is given. Finally, the effectiveness of the proposed method is verified by simulation examples.

Recovery of the Input Signals of Eddy-Current Displacement Transducers Under Thermal-Shock Actions

We propose a method for the recovery of input signals of eddy-current displacement transducers under thermal-shock action. The recovery of the input signals was performed with correction of the output data of a primary measuring transducer. The procedure of correction is based on the methods of identification of nonlinear dynamic systems described by the discrete Volterra series.

A stochastic variational framework for Recurrent Gaussian Processes models

Gaussian Processes (GPs) models have been successfully applied to the problem of learning from sequential observations. In such context, the family of Recurrent Gaussian Processes (RGPs) have been recently introduced with a specifically designed structure to handle dynamical data. However, RGPs present a limitation shared by most GP approaches: they become computationally infeasible when facing very large datasets. In the present work, with the aim of improving scalability, we modify the original variational approach used with RGPs in order to enable inference via stochastic mini-batch optimization, giving rise to the Stochastic Recurrent Variational Bayes (S-REVARB) framework. We review recent related literature and comprehensively contextualize it with our approach. Moreover, we propose two learning procedures, the Local and Global S-REVARB algorithms, which prevent computational costs from scaling with the number of training samples. The global variant permits even greater scalability by also preventing the number of variational parameters from increasing with the training set, through the use of neural networks as sequential recognition models. The proposed framework is evaluated in the task of dynamical system identification for large scale datasets, a scenario not readily supported by the standard batch inference for RGPs. The promising results indicate that the S-REVARB framework opens up the possibility of applying powerful hierarchical recurrent GP-based models to massive sequential data.

Parametric Identification Using Weighted Null-Space Fitting

In identification of dynamical systems, the prediction error method with a quadratic cost function provides asymptotically efficient estimates under Gaussian noise, but in general it requires solving a nonconvex optimization problem, which may imply convergence to nonglobal minima. An alternative class of methods uses a nonparametric model as intermediate step to obtain the model of interest. Weighted null-space fitting (WNSF) belongs to this class, starting with the estimate of a nonparametric ARX model with least squares. Then, the reduction to a parametric model is a multistep procedure where each step consists of the solution of a quadratic optimization problem, which can be obtained with weighted least squares. The method is suitable for both open- and closed-loop data, and can be applied to many common parametric model structures, including output-error, ARMAX, and Box–Jenkins. The price to pay is the increase of dimensionality in the nonparametric model, which needs to tend to infinity as function of the sample size for certain asymptotic statistical properties to hold. In this paper, we conduct a rigorous analysis of these properties: namely, consistency, and asymptotic efficiency. Also, we perform a simulation study illustrating the performance of WNSF and identify scenarios where it can be particularly advantageous compared with state-of-the-art methods.

Convex Bounds for Equation Error in Stable Nonlinear Identification

Equation error, also known as one-step-ahead prediction error, is a common quality-of-fit metric in dynamical system identification and learning. In this letter, we use Lagrangian relaxation to construct a convex upper bound on equation error that can be optimized over a convex set of nonlinear models that are guaranteed to be contracting, a strong form of nonlinear stability. We provide theoretical results on the tightness of the relaxation, and show that the method compares favorably to established methods on a variety of case studies.

Using self-constructing recurrent fuzzy neural networks for identification of nonlinear dynamic systems

In this paper, the self-constructing recurrent fuzzy neural network (SCRFNN) is applied for nonlinear dynamical system identification (NDSI). The SCRFNN is a novel fuzzy neural network (FNN) by adding a recurrent path in each node of the hidden layer of self-constructing FNN, which contains two learning phases. Specifically, the structure learning is based on partition of the input space and the parameter learning is based on the supervised gradient descent method using a delta adaptation law. The SCRFNN can decrease the minimum firing strength in each learning cycle and the number of hidden neurons which is an FNN with high accuracy and compact structure compared with several other neural networks. The performance of SCRFNN in NDSI is further verified in simulation.

Structure Identification of Continuous-Time Block-Oriented Nonlinear Systems in the Frequency Domain

Abstract A problem of structure identification of nonlinear dynamic systems on the set of continuous block-oriented models with nonlinear elements in the form of polynomial functions of finite degree and stable linear elements in the frequency domain is considered. Method of structure identification in steady state based on the observation of the system’s input and output variables at the input sinusoidal influences is proposed. The problem of the structure identification is considered according to the classical definition of identification of Zadeh. The structure definition criterion of the model is developed. The identification method is investigated by theoretical analysis and computer modelling.

Using self-constructing recurrent fuzzy neural networks for identification of nonlinear dynamic systems

Using self-constructing recurrent fuzzy neural networks for identification of nonlinear dynamic systems

Discovery of Nonlinear Multiscale Systems: Sampling Strategies and Embeddings

A major challenge in the study of dynamical systems is that of model discovery: turning data into models that are not just predictive, but provide insight into the nature of the underlying dynamical system that generated the data. This problem is made more difficult by the fact that many systems of interest exhibit diverse behaviors across multiple time scales. We introduce a number of data-driven strategies for discovering nonlinear multiscale dynamical systems and their embeddings from data. We consider two canonical cases: (i) systems for which we have full measurements of the governing variables, and (ii) systems for which we have incomplete measurements. For systems with full state measurements, we show that the recent sparse identification of nonlinear dynamical systems (SINDy) method can discover governing equations with relatively little data and introduce a sampling method that allows SINDy to scale efficiently to problems with multiple time scales. Specifically, we can discover distinct governing equations at slow and fast scales. For systems with incomplete observations, we show that the Hankel alternative view of Koopman (HAVOK) method, based on time-delay embedding coordinates, can be used to obtain a linear model and Koopman invariant measurement system that nearly perfectly captures the dynamics of nonlinear quasiperiodic systems. We introduce two strategies for using HAVOK on systems with multiple time scales. Together, our approaches provide a suite of mathematical strategies for reducing the data required to discover and model nonlinear multiscale systems.

Relay Feedback Identification with Additional Integrator

Abstract This paper presents a relay feedback technique for identification of dynamical systems for control purposes. The proposed technique uses a biased relay test with an added integration to determine three frequency response points for a phase lag in the range from 0 to 180° from a single experiment. This approach is based on a recently published method called “shifting method”. The additional integrator helps to improve the position of the frequency points obtained by the shifting method. The three frequency response points can be used for fitting up to five parameters of a process transfer function with various structures. The paper provides explicit formulas for determining the parameters of the second order model with a time delay from the obtained frequency response points. This approach can be used for the purpose of the controller design. The method is demonstrated on lag dominated, balanced and delay dominated processes. Matlab/Simulink programming environment was used for all experiments.

Dynamic methods of identification of electromagnetic parameters of power transformers in non-stationary mode

The report reflects the promising solutions for the creation of adaptive protection means and emergency automatics in the implementation of methods of identification of dynamic systems. Presented original research assigned at directly addressing the causes of the sensitivity lack of the transformer equipment protection - compensation for the magnetizing current of the power transformers by linearizing their transfer characteristics.

Vibro-Acoustic Methods in the Condition Assessment of Power Transformers: A Survey

It has been over two decades since the publication of pioneer works about the power transformer diagnostics based on monitoring of their acoustic fingerprints. Since then, there has been great progress in this field and the methods used are as complex as ever. Any unnecessary intervention on a power transformer implies its temporary disconnection from the power grid. The inability to supply electricity to the customer means not only financial loss for the utility but also generates a non-material loss, e.g., the loss of reputation to the customer. Faster, more accurate, more reliable, and less invasive diagnosis is the main reason behind development and improvement in this field. The main goal of this paper is to categorize and review state-of-the art of vibro-acoustic diagnostic methods for power transformers. This paper opens with a brief note about continuous condition monitoring, after which we overview the causes of transformer vibrations as well as the collection and preprocessing of diagnostic data. Then, we review and categorize works related to the acoustic condition assessment of power transformers considering both: feature extraction in the time, frequency, time-frequency domain, and mathematical modeling and system identification of dynamic systems.