Identification Of Dynamic Systems Research Articles

Mixed-effects modeling for concentration effect profiling in cardiomyocyte contractility assays

Background. With the advent of new realtime technologies such as impedance assays, extracellular field potential measurement and optical sensing for in vitro cardiac safety screening studies, researchers have now to frequently deal with analyzing voluminous amounts of complex time responses. In this context, main issues are to speed up the data analysis process and to extract accurate information for cardiotoxicity profiling. Objectives. A first objective is the development of an innovative computational method able to globally process a large set of in vitro cardiac signals (provided by 96, 384 and 1536-well microplates) instead of analyzing them once at a time. Such a statistical population approach has the advantage the account for the common characteristics between the individual responses. A second objective is to handle qualitative factors (type of cardiomyocytes, compounds and media, etc.) in the computational process. Methods. The proposed estimation method relies on the combination of a dynamic system identification method and a mixed-effect modeling technique. An output-error polynomial model structure is used for the system identification step and a stochastic approximation expectation maximization is implemented for the estimation of the hyperparameters. Input signals to be analyzed are the contractility amplitudes of cardiomyocytes submitted to compounds to be tested. Impedance signals and contractility amplitude were provided by a CardioExcyte96 system (Nanion Technologies). human iPSC-derived cardiomyocytes were provided by Cellartis Takara with 30,000 cells per well. Results. Our data-driven profiling method extracted four parameters that completely fit the contractility time variations and fully characterize the effect of compound concentration on the contractility amplitude. The proposed method not only estimates the values of the model parameters but also their uncertainty distribution. The latter allows to compute p-values associated with each effect. Conclusion. We show that the population-based estimation method developed in this study is suited to the fully characterize dynamic effects in cardiomyocyte contractility assays. Each parameter becomes a profiling characteristics of the concentration effect. It can be applied to estimate concentration and compounds effects with an optimal accuracy and could be extended directly to multielectrode array and optical sensing responses.

Externally Recurrent Neural Network based identification of dynamic systems using Lyapunov stability analysis

This paper proposes an Externally Recurrent Neural Network (ERNN) for approximating the unknown dynamics of complex nonlinear systems and time series prediction. The proposed model utilizes the present as well as delayed values of the system outputs as well as of the external input. The weight update equations are tested for their boundedness by applying the Lyapunov stability method. Further, the error convergence proof is also given. The proposed model is put to test by considering various nonlinear examples and its performance is also compared with other state of the art methods. The results obtained in the present study indicate that the method is efficient and has provided accurate results.

Discovering time-varying aerodynamics of a prototype bridge by sparse identification of nonlinear dynamical systems.

Vortex-induced vibrations (VIVs) have been observed on a long-span suspension bridge. The nonstationary wind in the field characterized by the time-varying mean wind speed is likely to lead to time-varying aerodynamics of the wind-bridge system during VIVs, which is different from VIVs induced by stationary or even steady wind in wind tunnels. In this paper, data-driven methods are proposed to reveal the time-varying aerodynamics of the wind-bridge system during VIV events based on field measurements on a long-span suspension bridge. First, a variant of the sparse identification of nonlinear dynamics algorithm is proposed to identify parsimonious, time-varying aerodynamical systems that capture VIV events of the bridge. Thus we are able to posit new, data-driven, and interpretable models highlighting the aeroelastic interactions between the wind and bridge. Second, a density-based clustering algorithm is applied to discovering the potential modes of dynamics during VIV events. As a result, the time-dependent model is obtained to reveal the evolution of the aerodynamics of the wind-bridge system over time during an entire VIV event. It is found that the level of self-excited effects of the wind-bridge system is significantly time varying with the real-time wind speed and bridge motion state. The simulations of VIVs by the obtained time-dependent models show high accuracies of the models with an averaged normalized mean-square error of 0.0023. The clustering of obtained models shows underlying distinct dynamical regimes of the wind-bridge system, which are distinguished by the level of self-excited effects.

Dynamic Response of Non-linear Beam Structures in Deterministic and Chaos Perspective

The behavior of large deformation beam structures can be modeled based on non-linear geometry due to geometricnonlinearity mid-plane stretching in the presence of axial forces, which is a form a nonlinear beam differential equationof Duffing equation type. Identification of dynamic systems from nonlinear beam differential equations fordeterministic and chaotic responses based on time history, phase plane and Poincare mapping. Chaotic response basedon time history is very sensitive to initial conditions, where small changes to initial terms leads to significant change inthe system, which in this case are displacement x (t) and velocity x’(t) as time increases (t). Based on the phase plane, itshows irregular and non-stationary trajectories, this can also be seen in Poincare mapping which shows strange attractorand produces a fractal pattern. The solution to this Duffing type equation uses the Runge-Kutta numerical method withMAPLE software application.

Nonlinear system identification model of the spread of TB disease using the genetic algorithm and multilayer perceptron

System identification is the process of building a mathematical model of a dynamic system based on the observed input-output data. Artificial neural networks have been shown to complete the identification of nonlinear systems with various learning algorithms. Identification of nonlinear dynamic systems in the model of TB disease spread is needed to predict the spread of TB disease. The model for the spread of TB disease has three compartments and six parameters. The process of identifying models for the spread of TB disease by estimating parameters using the genetic algorithm and validation of the model using multilayer perceptron. The choice of multilayer perceptron architecture determines the minimum error in the nonlinear system identification process for the model of TB disease spread. From the results of the trial, it was shown that the multilayer perceptron and genetic algorithm were able to identify the spread model of TB disease with MMRE of 0.00347

Data driven nonlinear dynamical systems identification using multi-step CLDNN

In many cases, the equations that dynamical systems are based on are unknown and hard to model and predict. On the other hand, machine learning algorithms are based on the data of a solution as it evolves and do not need equations. In the era of abundant data, using machine learning technology to discover accurate mathematical models of dynamical systems directly from time series data becomes increasingly important. Recently, a multi-step deep neural networks (multi-step DNN) model without need of direct access to temporal gradients is proposed, which can accurately learn the evolution from a given set of observed data, identify nonlinear dynamical systems, and forecast future states. However, the architecture lacks the capability to capture long term temporal dependencies from dynamical time-series data. In the paper, based on the multi-step time-stepping schemes, we proposed a new CLDNN model which combine convolutional layer, long short-term memory layer and fully connected layer, to address the aforementioned weakness. The effectiveness of our model is tested for several benchmark problems involving the identification and prediction of complex, nonlinear and chaotic dynamics. The experiment results show that the multi-step CLDNN has better identification and prediction performance than the multi-step DNN. The research provides possible corroboration for developing new deep learning based algorithms for nonlinear system identification.

Control and Identification Toolbox (CIT): An Android application for teaching automatic control and system identification

AbstractThis article presents a free Android application, named as Control and Identification Toolbox (CIT), for teaching and learning the system response, automatic control, and the parameter identification of dynamic systems. The CIT app performs real‐time experiments and permits tuning a traditional proportional‐integral‐derivative controller, whose performance under constant or noise disturbances, introduced by the app, can be analyzed. Moreover, this app allows estimating the parameters of first‐ and second‐order linear systems by means of the recursive least squares method. The parameter estimates as well as the control system signals produced under common test input signals are displayed by the app. It runs in any Android device supporting a universal serial bus, which is connected with Arduino Uno or Mega boards that carry out data acquisition. Experimental results obtained using first‐ and second‐order low‐pass filters confirm the effectiveness of the proposed application. Moreover, undergraduate students evaluated the CIT app, and their responses are also presented.

Identification in the delta domain: a unified approach via GWOCFA

The identification of linear dynamic systems in the delta domain has been proposed in this paper with the help of a hybrid metaheuristic algorithm combining chaotic firefly algorithm (CFA) and grey wolf optimiser (GWO). GWO performs the global search, while CFA fine-tunes the solutions through its local search abilities, thereby balancing exploration and exploitation features. Linear systems with static nonlinearities at the input are termed as the Hammerstein model, whereas linear systems with static nonlinearities at the output are known as the Wiener model. A test case with continuous polynomial nonlinearities has been taken up for Hammerstein and Wiener system identification in the delta domain. Delta operator parameterisation unifies identification of continuous-time systems with the discrete domain at a higher sampling rate. Pseudo-random binary sequence (PRBS), polluted with white Gaussian noise of fixed signal-to-noise ratio (SNR), has been considered as the input signal to estimate the unknown model parameters as well as static nonlinear coefficients. The hybrid algorithm not only supersedes the parent heuristics of which it is constituted but also proves better in comparison with some standard and latest heuristic approaches reported in the literature. Nonparametric statistical tests are performed to validate the results. The plots of fitness function (normalised value) against the number of iterations also support the convergence speed and accuracy of the results.

Frequency Domain Maximum Likelihood Identification With Gaussian Input–Output Uncertainty

This letter deals with the identification of dynamical systems corrupted by additive and independent identically distributed Gaussian noise sources when the noise-free-input is an arbitrary signal. We review two stochastic models: 1) the errors-in-variables (EIV) and 2) the random variable setting. We derive a maximum likelihood (ML) estimator for the latter and compare with a previously proposed EIV ML method. The problem is formulated in the frequency domain and it is assumed that the ratio of the noise variances is known. We discuss the similarity between the two approaches and prove that one can be seen as the regularized counterpart of the other, advocating the suggested estimator when only few data samples are available.

Efficient parameter identification and model selection in nonlinear dynamical systems via sparse Bayesian learning

Bayesian inference plays a central role in many of today’s system identification algorithms. However, one of its major drawbacks is that it often requires solutions to analytically intractable integrals, and this has led to solutions via Markov Chain Monte Carlo (MCMC). Today, few Bayesian system identification methods can compete with the robustness of the family of MCMC solutions. However, MCMC suffers severely from its computational cost.Partly fuelled by the field of Compressive Sensing (CS), an interest in the machine learning community has arisen in sparse linear regression. Its value in identification of dynamical systems has also recently started to receive some attention. The idea is to represent the range of possible candidate functional forms that have generated a specific data set using a dictionary, and to then apply standard Lasso regression to select the “best” basis, with sparsity constraints. A major problem in this approach is that Lasso regression (and its derivatives) requires tuning of the regularisation parameter. In this paper, a procedure for selecting the “best basis” (and thus performing both model selection and system identification) is presented through a sparse Bayesian learning approach. Sparsity is induced via a hierarchical Gaussian prior and an approximation to the posterior distribution is sought using an iterative optimisation scheme for finding the optimal hyper-priors that govern prior and hence, the level of sparsity in the solution. The method is applied to five systems of engineering interest, which include a baseline linear system, an additive quadratic damping term, cubic stiffness (Duffing oscillator), Coulomb damping and a Bouc-Wen hysteresis model. The results are shown using numerical simulations. It is shown that this approach can identify not only the correct model parameters, but whether a nonlinearity is present in the system as well its type. With the formulation being Bayesian, it also yields estimates of uncertainty over the selected basis functions and predicted responses.

Editorial: Introduction to the Special Section on Dynamic Modeling, System Identification, Analysis, and Control of Renewable Distributed Energy Resources for Grid Integration

Editorial: Introduction to the Special Section on Dynamic Modeling, System Identification, Analysis, and Control of Renewable Distributed Energy Resources for Grid Integration

Mechanical design and dynamics system identification of two-section Flapping Wing Aircraft

The mechanical design and system identification of the Flapping Wing Aircraft (FWA) has always been a problem. In this paper, we design a two-section FWA through the study of bird flight, where the wing structure is divided into the inner wing and outer wing, which can imitate the flight of birds. When flapping upward, the wings can be folded to reduce resistance, and when flapping downward, the wings can be expanded to increase lift. This flying method can improve the flight efficiency. The aircraft we designed has achieved flexible flight under human operation. Aiming at the complex problem of dynamic modeling of FWA, this paper proposes a linear system model by analyzing the force of the aircraft.We use the collected flight data to train the system model. The training of the model uses the gradient descent method to minimize the loss function, and the accuracy of the model is verified with the test data. The experimental results show that the system model can accurately calculate the acceleration, velocity, angle velocity and orientation of the aircraft based on the current control input.

Modeling, Identification, and Control of a Discrete Variable Stiffness Actuator (DVSA)

A branch of robotics, variable impedance actuation, along with one of its subfields variable stiffness actuation (VSA) targets the realization of complaint robotic manipulators. In this paper, we present the modeling, identification, and control of a discrete variable stiffness actuator (DVSA), which will be developed for complaint manipulators in the future. The working principle of the actuator depends on the involvement of series and parallel springs. We firstly report the conceptual design of a stiffness varying mechanism, and later the details of the dynamic model, system identification, and control techniques are presented. The dynamic parameters of the system are identified by using the logarithmic decrement algorithm, while the control schemes are based on linear quadratic control (LQR) and computed torque control (CTC), respectively. The numerical simulations are performed for the evaluation of each method, and results showed the good potentialities for the system. Future work includes the implementation of the presented approach on the hardware.

System Identification of Large-Scale Bridges Using Target-Tracking Digital Image Correlation

This paper characterizes the extensive research activities conducted in the Earthquake Engineering Laboratory of University of Nevada, Reno, in the field of dynamic monitoring and system identification of three 1/3-scale two-span bridges. The first part of the study briefly presents the verification of target-tracking Digital Image Correlation (DIC) results as compared to conventional sensors, e.g. string potentiometers and triaxial accelerometers from one of the three bridge tests. Structural system identification is presented in the second part for the other two bridges with focus on determining structural model parameters based on the DIC measured response data. All bridges were tested under bidirectional earthquake loading using the multiple shake table array. However, the system identification used data collected from the white noise runs before and after the seismic tests. A quasi-linear response of the system was assumed because of the low intensity white noise base excitation, and the modal parameters were estimated accordingly. Using the structural vibration data recorded by target-tracking DIC at various locations on the bridges, five system identification methods were applied to analyze the modal parameters of the tested bridges. The results were used to estimate the frequency, damping ratio, and mode shapes, of the bridges in two states. The initial state is before seismic testing and the end state is the damaged state after the completion of the seismic tests. The results show that the applied methods provide a reasonable estimate of the natural frequency and damping ratio of the bridge systems in the original and damaged states.

A Comparison of the Control Schemes of Human Response to a Dynamic Virtual 3D Face

This paper introduces the application of predictor-based control principles for the control of human response to a virtual 3D face. A dynamic woman 3D face is observed in virtual reality. We use changing distance-between-eyes in a 3D face as a stimulus – control signal. Human responses to the stimulus are observed using EEG-based excitement signals – output signal. The technique of dynamic systems identification which ensure stability and possible higher gain of the model for building a predictive input-output model of control plant is applied. Three predictor-based control schemes with a minimum variance or a generalized minimum variance control quality and constrained control signal magnitude and change rate are developed. High prediction accuracies and control quality are demonstrated by modelling results.

Evolving Neural Network CMAC and its Applications

The conventional CMAC (Cerebellar Model Articulation Controller) neural network (NN) can be applied in many real-world applications thanks to its high learning speed and good generalization capability. In this paper it is proposed to utilize a neuro-evolutional approach to adjust CMAC parameters and construct mathematical models of nonlinear objects in the presence of the gaussian noise. The general structure of the evolving CMAC NN is considered. The paper demonstrates that the evolving CMAC NN can be used effectively for the identification of nonlinear dynamical systems. The simulation of the proposed approach for various nonlinear objects is performed. The results proved the effectiveness of the developed methods.

A new Neuro-Fuzzy Inference System with Dynamic Neurons (NFIS-DN) for system identification and time series forecasting

A new Neuro-Fuzzy Inference System with Dynamic Neurons or NFIS-DN is presented here for discrete time dynamic system identification and time series forecasting problems. The proposed dynamic system based neuron, referred to as Dynamic Neuron (DN) is realized by a discrete-time nonlinear state-space model. The DN is designed such way, that the output considers only the effect of finite past instances, enabling the system with finite memory. The NFIS-DN model has five layers, and DNs are employed only in the layers handling crisp values. The antecedent and the consequent parameters of NFIS-DN are updated using a self-regulated backpropagation through time learning algorithm. The performance evaluation of NFIS-DN has been carried-out using benchmark problems in the areas of nonlinear system identification and time series forecasting. The results are compared with the state-of-the-art method on the neural fuzzy networks. The obtained results clearly suggest that the NFIS-DN performs significantly better while using a smaller or similar number of fuzzy rules. Finally the practical application of the NFIS-DN has been demonstrated using two real-world problems.

Max-plus linear inverse problems: 2-norm regression and system identification of max-plus linear dynamical systems with Gaussian noise

In this paper we present new theory and algorithms for 2-norm regression over the max-plus semiring. As an application we also show how max-plus 2-norm regression can be used in system identification of max-plus linear dynamical systems with Gaussian noise. We also introduce and provide methods for solving a max-plus linear inverse problem with regularization, which can be used when the original problem is not well posed.

Optimal Rule-Based Granular Systems From Data Streams

We introduce an incremental learning method for the optimal construction of rule-based granular systems from numerical data streams. The method is developed within a multiobjective optimization framework considering the specificity of information, model compactness, and variability and granular coverage of the data. We use $\alpha$ -level sets over Gaussian membership functions to set model granularity and operate with hyperrectangular forms of granules in nonstationary environments. The resulting rule-based systems are formed in a formal and systematic fashion. They can be useful in time series modeling, dynamic system identification, predictive analytics, and adaptive control. Precise estimates and enclosures are given by linear piecewise and inclusion functions related to optimal granular mappings.

NARX Model Identification Using Correntropy Criterion in the Presence of Non-Gaussian Noise

In past years, the system identification area has emphasized the identification of nonlinear dynamic systems. In this field, polynomial nonlinear autoregressive with exogenous (NARX) models are widely used due to flexibility and prominent representation capabilities. However, the traditional identification algorithms used for model selection and parameter estimation with NARX models have some limitation in the presence of non-Gaussian noise, since they are based on second-order statistics that tightly depend on the assumption of Gaussianity. In order to solve this dependence, a novel identification method called simulation correntropy maximization with pruning (SCMP) based on information theoretic learning is introduced by this paper. Results obtained in non-Gaussian noise environment in three experiments (numerical, benchmark data set and measured data from a real plant) are presented to validate the performance of the proposed approach when compared to other similar algorithms previously reported in the literature, e.g., forward regression with orthogonal least squares and simulation error minimization with pruning. The proposed SCMP method has shown increased accuracy and robustness for three different experiments.