System Identification Algorithm Research Articles

Convex Combination of Nonlinear Filters using Improved Proportionate Least Mean Square/Fourth Algorithm for Sparse System Identification

Convex Combination of Nonlinear Filters using Improved Proportionate Least Mean Square/Fourth Algorithm for Sparse System Identification

High Precision Sinusoidal Position Tracking of a Voice-Coil Linear Servomotor Using Resonant Control

This paper presents a new sinusoidal position-tracking control scheme with a resonant controller for linear motor drive systems. The sinusoidal tracking controller is designed without any added algorithm for system identification and requires only approximate values of the mechanical parameters. Therefore, the controller is simple and robust to parameter variations. The proposed sinusoidal tracking resonant-based controller (STRC) is designed to track reference positions using a cascade control structure with an inner current/force control with hysteresis current control followed by a speed control loop with a resonant controller, and an outer position loop with a proportional and velocity-feedforward controller. The stability of the cascade feedback scheme and its parameter tuning are analyzed using the Routh–Hurwitz criterion. The performance of the proposed control scheme is validated using simulations and experiments on a voice-coil linear stage. The proposed STRC strategy is characterized by ease of implementation and shows excellent performance with fast response and high accuracy at different frequencies with a maximum error of 0.58% at 0.25 Hz.

A new approach of ensemble learning in fully automated identification of structural modal parameters of concrete gravity dams: A case study of the Koyna dam

This study proposes a new automatic modal identification algorithm that identifies the system's modal parameters based on output-only data. The identification process is based on a stochastic subspace algorithm. Stochastic subspace algorithms only need the model degree to identify the modal parameters of the system. A model degree is an appropriate degree of the state-space model and it is estimated by using the Singular Value Criterion. Several clustering algorithms with different approaches have been used. The most powerful data fusion algorithm, which is called Dempster-Schaffer Theory is applied for integrating the results of the algorithms and preventing divergence of results. Furthermore, it focused on measuring the uncertainty of the identified modal parameters. In the proposed modal identification algorithm, only one data set is used for identification. In this situation, the variety of data is small and limited, and statistical resampling methods seem to be a good option. Establishing the above cycle enables the identification algorithm to identify modal parameters and quantify their uncertainty based only on a data set. This algorithm uses many fields, such as data collection, signal processing techniques, model reduction, feature extraction, clustering and data fusion. The Koyna gravity dam is selected as a case study to evaluate the performance of the developed algorithm. In the first step, a comparative study is carried out to verify the developed finite element model of the Koyna dam. Afterwards, the dam is excited by the Koyna earthquake, and dynamic responses of the dam are collected from the minimum number of points required for system identification. It is noteworthy the number of modes that are identified in this work is equal to 4 vibration modes. The maximum difference between the natural frequencies identified by the present algorithm and the finite element model does not exceed 4.33%. Also, the average difference is less than two percent, which indicates the high accuracy of the system identification algorithm. Also, all the vibration modes in the desired frequency range have been correctly identified. The results indicate that modal parameters with remarkable precision have been extracted by the modified algorithm.

Interval type-2 fuzzy neural networks with asymmetric MFs based on the twice optimization algorithm for nonlinear system identification

This paper proposes a novel algorithm twice optimization for interval type-2 fuzzy neural networks with asymmetric membership functions (TOIT2FNN-AMF), for nonlinear system identification problems. The proposed TOIT2FNN-AMF uses an asymmetric Gaussian interval type-2 membership function to enhance the network’s ability to describe and solve nonlinear and uncertain problems. The twice optimization algorithm consists of structure learning and parameter learning. Firstly, this paper proposes a multi-strategy adaptive differential evolution (MSADE) algorithm as the first optimization algorithm, which is used to determine the structure and the initial values of the parameters of the TOIT2FNN-AMF. It applies the root mean square error (RMSE) of the TOIT2FNN-AMF as the fitness function to determine the structure (number of rules) and initial parameters of the IT2FNN by searching for the RMSE values under different structures. When the fitness value reaches the minimum, that is, the RMSE value of the TOIT2FNN-AMF, the corresponding number will become the optimal one of fuzzy rules of the TOIT2FNN-AMF. Then, the second optimization algorithm of the TOIT2FNN-AMF turns into a hybrid optimization algorithm composed of an adaptive moment estimation (Adam) algorithm and recursive least squares (RLS) algorithm. Adam is used to optimize the antecedent parameters of TOIT2FNN-AMF rules, so as to maintain rapid convergence without generating oscillation during the training process; RLS is used to optimize the consequent parameters of TOIT2FNN-AMF rules, so that the network parameters can be optimized rapidly. In this way, the problems of excessive parameters to be adjusted and excessive slow convergence of the network can be solved. Finally, this paper evaluates the proposed TOIT2FNN-AMF by testing on problems of nonlinear system identification and chaotic time-series prediction. The simulation results are compared with those of similar methods in the existing literatures, which demonstrates that the proposed TOIT2FNN-AMF model yields a lower RMSE value and a simpler network structure than the other type-2 fuzzy neural networks (T2FNNs).

Comparison of the characteristics of the control strategies based on artificial neural network and genetic algorithm for air conditioning systems

Air conditioning systems are playing an increasingly important role in our daily life, and the control of air conditioning systems is related to the intelligence of the system, indoor thermal comfort and energy consumption. Therefore, the control of air conditioning systems has always been an important research topic. Artificial neural network (ANN) and genetic algorithm (GA) are two commonly used intelligent control methods. However, there is no guidance until now on the applicability of these two control methods and how to make a choice between them in the control of air conditioning systems. In this study, an ANN control strategy and a GA control strategy were developed and experimentally verified. The experimental results indicated that both the ANN control strategy and the GA control strategy could control the air conditioning system properly under different control commands. To compare the control performances, the convergence speed, discrete characteristic, energy consumption and interference resistance ability were calculated or experimentally validated. The ANN control strategy showed better performances in the convergence speed and energy consumption. While the GA control strategy performed better in maintaining the stable state of the air conditioning system.The innovation of this study lies in two points. First, when designing the ANN control strategy and the GA control strategy, ANN and GA were applied as the central control algorithm, rather than only as auxiliary algorithms for system identification, prediction or optimization. This methodology is relatively novel in the design of ANN and GA control strategies for the air conditioning system, and could further expand the application of ANN and GA. Second, this study employed 4 evaluating indicators including convergence speed, discrete characteristic, energy consumption and interference resistance ability, to comprehensively evaluated the control performance of ANN control strategy and GA control strategy.

Fractional derivative truncation approximation for real-time applications

Fractional derivatives are non local operators as they are well-suited for modeling long-memory phenomena such as heat transfers or fluid dynamics. However, such non-locality implies a constant knowledge of the full past of the functions to differentiate. In the context of real-time (online) system identification, such a global property may limit the implementation as calculations can become slower as time grows. Also, instead of using the full data length to compute fractional order derivatives, truncated fractional derivatives are used. However, such a truncation windowing will bring inaccuracy on the computation of fractional derivatives. This study deals with the relationship between the signal frequency content, the fractional derivative truncated approximation as well as the fractional system relaxation in order to get a good approximation of the truncated fractional derivative and consequently, to help providing real-time exploitable system identification algorithms that uses such truncated fractional derivatives.

Modeling and Identification of Li-ion Cells

To develop a full battery model in view to accurate battery management, Li-ion cell dynamics is modelled by a capacitor in series with a simplified Randles circuit. The open circuit voltage is the voltage at the capacitor terminals, allowing, in this way, for the dependence of the open circuit voltage on the state-of-charge to be embedded in its capacitance. The Randles circuit is recognised as a trusty description of a cell dynamics. It contains a semi-integrator of the current, known as the Warburg impedance, that is a special case of a fractional integrator. To enable the formulation of a time-domain system identification algorithm, the Warburg impedance impulse response was calculated and normalised, in order to derive a finite order state-space approximation, using the Ho-Kalman algorithm. Thus, this Warburg impedance LTI model, with known parameters (normalised impedance) in series with a gain block, is suitable for system identification, since it has only one unknown parameter. A LTI System identification Algorithm was formulated to estimate the model parameters and the initial values of both the open circuit voltage and the states of the normalised Warburg impedance. The performance of the algorithm was very satisfactory on the whole state-of-charge region and when compared with low order Thévenin models. Once it is understood the parameters variability on the state-of-charge, temperature and ageing, we envisage to continue the work using parameter-varying algorithms.

An Adaptive Predictive Control Algorithm for Comprehensive Dendritic Canal Systems

Automatic canal control is essential to improve water utilization efficiency in irrigation districts. Water level error in the model used by the control algorithm significantly impacts performance. The integrator delay model, which has a linear structure, is widely used in multi-input/multioutput control algorithms, including linear-quadratic control and model predictive control. However, the integrator delay model is suboptimal for large irrigation districts; the canals are long, the flows are large, there are many scattered offtakes, and the operating conditions vary. We developed an adaptive predictive control mode for the Qinhan Canal in Ningxia Province, China. We used a segment integrator delay model for this large irrigation district and employed a differential evolution algorithm for online system identification; this minimizes error. We analyzed and controlled for various uncertainties (i.e., flow observation noise, geometric and hydraulic parameter errors, and accidental interference with the automatic control system). Simulations indicated that the water level fitting errors were significantly reduced compared with the original model, and water level regulation was significantly improved, especially in terms of the maximum absolute error. Adaptive predictive control was better than linear-quadratic control and model predictive control approach for water level. Adaptive predictive control coped well with several uncertainties. The main factors affecting water level control were the flow observation and gate opening control accuracy, and the extent of real-time data coverage. These features require careful attention when automating and modernizing irrigation districts.

An EM Algorithm for Lebesgue-sampled State-space Continuous-time System Identification*

This paper concerns the identification of continuous-time systems in state-space form that are subject to Lebesgue sampling. Contrary to equidistant (Riemann) sampling, Lebesgue sampling consists of taking measurements of a continuous-time signal whenever it crosses fixed and regularly partitioned thresholds. The knowledge of the intersample behavior of the output data is exploited in this work to derive an expectation-maximization (EM) algorithm for parameter estimation of the state-space and noise covariance matrices. For this purpose, we use the incremental discrete-time equivalent of the system, which leads to EM iterations of the continuous-time state-space matrices that can be computed by standard filtering and smoothing procedures. The effectiveness of the identification method is tested via Monte Carlo simulations.

An Efficient q-Markov Covariance Equivalent Realization Approach to System Identification

An efficient q-Markov covariance equivalent realization (QMC) formulation is presented in this paper. This efficient solution matches all Markov and Covariance parameters of a finite-dimensional system using a finite amount of data. The frequency responses of that system is also matched by the efficient QMC solution. The existence condition of this efficient QMC solution and its parametrization is given in this paper. Then, a generalized algorithm for system identification using the efficient QMC is given. The example is set up by a cantilever beam. Results show that the efficient QMC fully captures Markov and covariance parameters and frequency responses of the cantilever beam.

Sample Complexity of the Sign-Perturbed Sums Identification Method: Scalar Case*

Sign-Perturbed Sum (SPS) is a powerful finite-sample system identification algorithm which can construct confidence regions for the true data generating system with exact coverage probabilities, for any finite sample size. SPS was developed in a series of papers and it has a wide range of applications, from general linear systems, even in a closed-loop setup, to nonlinear and nonparametric approaches. Although several theoretical properties of SPS were proven in the literature, the sample complexity of the method was not analysed so far. This paper aims to fill this gap and provides the first results on the sample complexity of SPS. Here, we focus on scalar linear regression problems, that is we study the behaviour of SPS confidence intervals. We provide high probability upper bounds, under three different sets of assumptions, showing that the sizes of SPS confidence intervals shrink at a geometric rate around the true parameter, if the observation noises are subgaussian. We also show that similar bounds hold for the previously proposed outer approximation of the confidence region. Finally, we present simulation experiments comparing the theoretical and the empirical convergence rates.

System Identification and Mathematical Modeling of A Piezoelectric Actuator through A Practical Three-Stage Mechanism.

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.

Parallel Algorithm for Parametric Identification of Dynamical Systems with Interval Parameters

The paper presents a parallel algorithm for the parametric identification of dynamical systems with interval parameters. The algorithm is based on the previously developed, substantiated and tested adaptive interpolation algorithm, which makes it possible to explicitly obtain the dependence of the states of a dynamic system on interval parameters. The solution of the problem of parametric identification is reduced to the problem of minimizing a certain objective function in the space of boundaries of interval parameter estimates. Due to the use of the adaptive interpolation algorithm when calculating the gradient of the objective function, there is no need for additional analysis and modeling of the original dynamic system, so it is convenient to use first-order methods for optimization. However, the task of calculating the objective function and the gradient includes a set of conditional minimization problems for explicit functions that can be solved independently of each other. The article discusses the main aspects and features of parallelization and implementation of the parametric identification algorithm and tests it on several representative examples. The acceleration and efficiency of parallelization are analyzed.

TUNNEL REACTION TO GROUND MOVEMENT USING A SIMPLIFIED MODEL

Purpose: the analysis is performed by modal superposition of the response of a simplified model containing connected bending and shear beams supported by Winkler-type springs.
 Objective: to present a simplified model using coupled Bernoulli and shear beams supported by Winkler-type springs for the systematic identification of tunnels subject to earthquake-induced ground motions. A model formulation is introduced and closed-form solutions for the modal characteristic equation and mode shape are derived.
 Research methods: the formulation of the model is introduced and closed-form solutions are derived for the equation of modal characteristic and mode shape. The latter are checked by the results of numerical models. A system identification algorithm is then presented, demonstrating its ability to recover the model parameters when the recorded acceleration time intervals along the tunnel are perturbed by noise and sensor locations change. The presented framework can be used for initial and simple recovery of tunnel response in the presence of monitoring data or for planning monitoring campaigns in newly constructed or existing tunnels.
 Main results: using a simple genetic algorithm and the proposed simplified model, it was shown that system identification can be performed for variable conditions. The model was tested for two different earthquakes of different frequencies, and the influence of the distribution of sensors along the length of the tunnel was also parametrically investigated. The test results were intentionally compromised by adding white Gaussian noise with a variance equal to that observed during ground motion. It was observed that for values ​​of α >3.0 (ie, when the effect of the shear beam is significant), the model parameters can be successfully recovered. Therefore, for such conditions, the proposed approach can be used to recover important tunnel dynamic properties (e.g., T1 or α) as well as soil-structure interaction by tracking kb changes after earthquakes. For values ​​< 3, a Bernoulli beam with a Winkler basis is a valid representation, while observing differences with a model involving a Pasternak basis are marginal.
 Scientific novelty: another approach to parametric system identification using simplified models. For tunnels, such models usually consist of beams on independent Winkler-type springs, including both numerical and analytical schemes. However, the seismic response of the continuum (i.e., soil) can be better modeled by including a transverse beam above the Winkler foundation, which allows interaction between individual springs, rather than using a single layer of independent springs. In geotechnical seismic resistance, a similar approach was used to assess the seismic response of pile foundations and retaining walls.
 Conclusions and practical challenge: different sensor distributions and reduced number of sensors did not lead to significant differences in the final results. This first shows that sensor position is not the dominant parameter for the case of five sensors along the length of the tunnel, fixed at both ends, and uniform soil conditions and other assumptions made in the paper. Further tests should be performed on real data and sensors to examine the impact of other aspects such as sensor noise.
 Key words: winkler springs, soil; soil; model; system identification algorithm is presented.

Design of a supervisory control system for autonomous operation of advanced reactors

Advanced reactors to be deployed in the coming decades will face deregulated energy markets, and may adopt flexible operation to boost profitability. To aid in the transition from baseload to flexible operation paradigm, autonomous operation is sought. This work focuses on the control aspect of autonomous operation. Specifically, a hierarchical control system is designed to support constraint enforcement during routine operational transients. Within the system, data-driven modeling, physics-based state observation, and classical control algorithms are integrated to provide an adaptable and robust solution. A 320MW Fluoride-cooled High-temperature Pebble-bed Reactor is the design basis for demonstrating the proposed control system.The hierarchical control system consists of a supervisory layer and low-level layer. The supervisory layer receives requests to change the system’s operating conditions (e.g., the current reactor power to meet a load-follow), and accepts or rejects them based on constraints that have been assigned. Constraints are issued to keep the plant within an optimal operating region. The low-level layer interfaces with the actuators of the system to fulfill requested changes, while maintaining tracking and regulation duties. To accept requests at the supervisory layer, the Reference Governor algorithm was adopted. To model the dynamics of the reactor, a system identification algorithm, Dynamic Mode Decomposition, was utilized. To estimate the evolution of process variables that cannot be directly measured (e.g., the propagation of delayed neutron precursors), the Unscented Kalman Filter, incorporating a nonlinear model of nuclear dynamics, was adopted. The composition of these algorithms led to a numerical demonstration of constraint enforcement during a 40% power drop transient (at a rate of 5%/min). Uncontrolled secondary-side temperatures were successfully constrained. Adaptability of the proposed system was demonstrated by modifying the constraint values, and enforcing them during the transient. Robustness was also demonstrated by enforcing constraints under noisy environments.

Finite-Memory-Structured Online Training Algorithm for System Identification of Unmanned Aerial Vehicles With Neural Networks

In this article, we propose a novel finite-memory-structured online training algorithm (FiMos-TA) for neural networks to identify and predict the unknown functions and states of an unmanned aerial vehicle (UAV). The proposed FiMos-TA is designed based on a system reconstructed by accumulating the states from the UAV dynamics. The system is redefined by replacing the unknown nonlinear functions of the UAV with neural networks, and a random walk modeling is adopted to design a training algorithm. The proposed FiMos-TA with a finite memory structure updates the weights of the neural network by accumulating the refined measurements of a UAV on the receding horizon. The training law of the proposed FiMos-TA is obtained by introducing the Frobenius norm and confirms a robust performance against modeling uncertainties and identification errors. The robustness and accuracy of the proposed FiMos-TA are verified through experiments.

Modelling of an interacting series process for rector cooling system using system identification method

This research presents the modelling of cooling system plant in the TRIGA PUSPATI reactor (RTP). The RTP cooling system involves the interacting series process which are reactor model and heat exchanger model. The behaviour process is complex due to the nonlinearity, uncertainty, and time variation of the system. Due to the nonlinearity and interacting series process of system, the numerical algorithm for subspace state space system identification (N4SID) was proposed in the modelling of RTP cooling system. However, the model was converted to the transfer function form. The output response from the simulation model of RTP cooling subsystems were analysed by comparing the model with the real operational data. The responses of the model were within the respective range of a good model data. The residual analysis for each output was also calculated. The comparison and residual analysis were done to validate the model accuracy to determine the behaviour of the model. Overall, the model accuracy assessment shows that all models are still fit in the good model region (<10%) and has a good representation of a real plant.

A novel system identification algorithm for nonlinear Markov jump system

System identification of nonlinear Markov jump systems (NMJSs) is crucial in modeling complex systems that contain unknown continuous and discrete states. In this system, the dynamics of continuous states is governed by the discrete states, which means the system can operate among different modes. The existing studies primarily identify the mode transition probability and noise model, whereas the parameters concerning the nonlinear continuous state transition function and observation function are commonly not considered. To identify all the parameters, a novel NMJSs identification algorithm based on a new particle system is proposed. The hidden state inference is implemented via an extended smoother that embodies the new particle system and Rao-Blackwellized particle Gibbs ancestor sampling kernel. The smoother not only estimates hidden state but also enables parameter update of the nonlinear functions. After inferencing the hidden states’ posterior density, a log-likelihood-based loss function is utilized to reduce the uncertainty of identifying the parameters related to the continuous state transition function. Then expectation–maximization and gradient descent are adopted to update the parameters. Finally, different experiments are conducted to verify the proposed algorithm. The results show that the proposed algorithm can approximate the parameter that well describes the data, and outperform other related approaches.

Problem of Modeling and Control of Multi-Dimensional Timeless Processes with Dependent Output Variables

In this paper, we consider the problems of modeling and controlling multidimensional inertialess systems with delay under nonparametric uncertainty. We are talking about the multidimensional processes which are in conditions where the form of parametric equations for various channels of the object is absent due to lack of a priori information. The main emphasis is placed on the case when the components of the vector of output variables are randomly connected in an unforeseen way. In the case of a stochastic dependence of the output variables, the mathematical description of the object is reduced to a system of implicit equations, the form of which is unknown. Therefore, the main task of modeling is to find the predicted values of output variables from known input variables. When managing a multidimensional object, an important feature is the definition of setting actions. The main thing here is that the setting influences of the control system should not be chosen arbitrarily from the corresponding areas, but depending on the definition of the previous ones. Nonparametric identification and control algorithms for multidimensional systems are proposed. Computational experiments that show the efficiency of using the proposed nonparametric identification and control algorithms are presented.

Ekblom promoting adaptive algorithm for system identification

We propose an Ekblom promoting adaptive algorithm (EPAA) which uses Ekblom norm to construct a data reusing scheme to achieve better performance under impulsive noise (IN) environments. By exerting Ekblom-norm constraint on the posterior error vector, a sliding window cost function is created to realize the EPAA that is derived to reduce IN effects. The derivation and theoretical convergence analysis of the EPAA are presented in detail. The simulation examples are setup to illustrate the superior performance of the EPAA compared to popular data reusing algorithms for system identification and echo cancellation under IN environments.