Identification Of Nonlinear Dynamic Models Research Articles

Polynomial NARX-based nonlinear model predictive control of modular chemical systems

The design of control systems for modular chemical systems typically requires the identification of nonlinear dynamic models. Mechanistic models for modular chemical systems are typically of high order, which results in high online computational cost when the models are incorporated into the nonlinear model predictive control (NMPC) formulations developed for explicitly taking constraints into account. This article proposes the use of a particular class of nonlinear input–output models, polynomial nonlinear-autoregressive-with-exogenous-inputs (NARX) models, in the NMPC formulations. A machine learning algorithm, elastic net, is used to select which terms to include within the NARX polynomial series representation. The approach for constructing sparse predictive models and their use in real-time implementable NMPC are demonstrated in a two-input two-output chemical reactor case study. The Julia programming language is used to solve the NMPC optimization problem, resulting in low online computational cost.

THE PROBLEM OF MINIMIZING DISPERSION

The work is related to the problem of finding the probability density of a continuous random variable in such a way that the variance or initial moments of this variable would be the smallest. The problem of minimizing the variance is solved under the condition that the probability density u x of a continuous random variable does not exceed a given function q x . The result of the work is obtaining such a density: it should be equal to the given function q x in some interval , , outside this interval the density should be zero. The numbers α and β are find from the system of nonlinear equations and are included in these equations as limits of definite integrals. By substituting the found function in the extreme condition, the smallest variance value for any continuous random variable is obtained. The problem of finding the probability density of a random variable is also considered under the conditions x u x dx u x dx u x q k              min, 1, 0 , where q and k are given positive numbers. The described problems belong to the class of Lyapunov extremal problems containing integrals. When solving them, the minimum principle and the method of Lagrange multipliers were applied. As a consequence of the Weierstrass theorem, it follows that the found stationary points are the points of the smallest values of the considered functionals. Substituting the solution of the problem into an extreme condition, an inequality for the initial moments of any continuous random variable, which is bounded from above by a positive constant q is obtained. It is emphasized that the determination of parameters as a result of minimization will allow to determine more accurate estimates in other values and to achieve an effective level of parameter optimization. The results of solving mathematical problems are given. An exemplary application of the given problem is the implementation of adaptive forecasting and statistical identification of nonlinear dynamic models of physical and economic processes. The scientific novelty of the obtained solution lies in the fact that, for the first time, a system was obtained in which the mathematical expectation of an extreme random variable is located in the middle of the segment , , due to which, by substituting the found function in an extreme condition, the smallest variance value for any continuous random variable is obtained.

Nonlinear dynamic model identification methodology for real robotic surface vessels

This paper presents a methodology for identifying the nonlinear dynamic model of underactuated surface vessels for the purpose of model-based controller design. The methodology outlines the required tests that need to be performed and the formulations that need to be used for sequentially identifying the model parameters one by one. The identification methodology is performed on a robotic vessel by testing in outdoor environments and the accuracy of the dynamic model is verified. The physical control inputs to the vessel are a propeller rotational speed and a rudder angle. 3 degrees of freedom are assumed for the nonlinear dynamic model of the surface vessel. Finally, an approach is proposed that discusses how the identified full nonlinear dynamic model can be used for control design. Results of typical closed-loop control tests are presented.

Nonlinear Model Identification From Multiple Data Sets Using an Orthogonal Forward Search Algorithm

A basic assumption on the data used for nonlinear dynamic model identification is that the data points are continuously collected in chronological order. However, there are situations in practice where this assumption does not hold and we end up with an identification problem from multiple data sets. The problem is addressed in this paper and a new cross-validation-based orthogonal search algorithm for NARMAX model identification from multiple data sets is proposed. The algorithm aims at identifying a single model from multiple data sets so as to extend the applicability of the standard method in the cases, such as the data sets for identification are obtained from multiple tests or a series of experiments, or the data set is discontinuous because of missing data points. The proposed method can also be viewed as a way to improve the performance of the standard orthogonal search method for model identification by making full use of all the available data segments in hand. Simulated and real data are used in this paper to illustrate the operation and to demonstrate the effectiveness of the proposed method.

Identification and estimation of nonlinear dynamic panel data models with unobserved covariates

This paper considers nonparametric identification of nonlinear dynamic models for panel data with unobserved covariates. Including such unobserved covariates may control for both the individual-specific unobserved heterogeneity and the endogeneity of the explanatory variables. Without specifying the distribution of the initial condition with the unobserved variables, we show that the models are nonparametrically identified from two periods of the dependent variable Yit and three periods of the covariate Xit. The main identifying assumptions include high-level injectivity restrictions and require that the evolution of the observed covariates depends on the unobserved covariates but not on the lagged dependent variable. We also propose a sieve maximum likelihood estimator (MLE) and focus on two classes of nonlinear dynamic panel data models, i.e., dynamic discrete choice models and dynamic censored models. We present the asymptotic properties of the sieve MLE and investigate the finite sample properties of these sieve-based estimators through a Monte Carlo study. An intertemporal female labor force participation model is estimated as an empirical illustration using a sample from the Panel Study of Income Dynamics (PSID).

Diagnostic Inferring on the Bases of Nonlinear Models

Physical phenomena accompanying destruction processes of technical systems are nonlinear and “low-energetic” by nature, while during wearing out mainly a nonlinear disturbance changes. Out of many inference techniques — on the observation basis of the state of the system — the best one is undoubtedly the well-defined mathematical model, allowing inferring ‘backwards’ and ‘forward’, which means finding the genesis and prognosis of the phenomenon. However, such model should be nonlinear. Problems related to the identification of nonlinear dynamic models in a frequency domain and a proposition of solving this problem for the needs of technical diagnostics, i.e. in situations when the observed wear out effects are significantly smaller than the dynamic effects — are discussed in the hereby paper. The bases of the proposed method constitute the discussion of possible solutions of a certain class of nonlinear differential equations and resulting from that statements on the possibility of nonlinear disturbance approximations by a series of the selected harmonic frequencies.

Identification of nonlinear dynamic models of electrostatically actuated MEMS

This paper focuses on the identification of nonlinear dynamic models for physical systems such as electrostatically actuated micro-electro-mechanical systems (MEMS). The proposed approach consists in transforming, by means of suitable global operations, the input–output differential model in such a way that the new equivalent formulation is well adapted to the identification problem, thanks to the following properties: first, the linearity with respect to the parameters to be identified is preserved, second, the continuous dependence on noise measurements is restored. Consequently, a simple least-square resolution can be used, in such a way that some of the difficulties classically encountered with identification methods are by-passed. The method is implemented on real measurement data from a physical system.

Generalized solutions to integral equations in the problem of identification of nonlinear dynamic models

Classes of nonlinear integral Volterra equations occurring in identifying dynamic systems are studied. A solution to a nonlinear system of integral Volterra equations of the first kind is constructed in the class of generalized functions with a point support in the form of a sum of singular and regular parts. In obtaining a singular part of the solution, a determined system of linear algebraic equations is used. The method of sequential approximations together with the method of undetermined coefficients allow constructing a regular part. Theorems of existence and uniqueness of generalized solutions are proved.

Identification of Electrostatically Actuated MEMS Models from Real Measurement Data

This paper focuses on the identification of nonlinear dynamic models for physical systems such as Micro-Electro-Mechanical Systems (MEMS) from measurement data. The proposed approach consists in transforming, by means of suitable global operations, the specific input-output differential physical model of the system elaborated from physical analysis, in such a way that we get a new equivalent model formulation specifically adapted to the identification problem. Thanks to the equivalence of the dynamic model and the derived identification problem, the so-identified model remains of continuous-time type, with a clear physical meaning of any of its components, which is not the case when using, for example, black-boxes approaches. The method is implemented on real measurement data from a physical system.

Engine load prediction in off-road vehicles using multi-objective nonlinear identification

The multi-objective identification of nonlinear dynamic models consisting of local linear models is considered. The tradeoff between global model accuracy and local model interpretability is explicitly considered by introducing weights on the criteria for local model accuracy. A strategy is proposed to tune the local weights in order to achieve similar tradeoff for each local model. In this way, better generalization is achieved. The multi-objective identification algorithm has been applied to predict the engine load of an off-road vehicle operating under varying working load conditions. The analysis tools have proven useful for the construction of an accurate and robust engine load prediction model. The resulting model can directly be used in model-based control algorithms in automatic tuning systems that explicitly deal with constraints on the working region.

Identification of Nonlinear Dynamic Models with Partially Connected Neural Networks Trained Using Orthogonal Least Square Estimation

Identification of Nonlinear Dynamic Models with Partially Connected Neural Networks Trained Using Orthogonal Least Square Estimation

Identification of structurally constrained second-order Volterra models

Continuing advances in industrial control hardware and software have increased interest in the identification of nonlinear dynamic models from chemical process data. Two practically important issues are those of nonlinear model structure selection and input sequence design for adequate model identification. While the "general nonlinear model identification problem" is intractably complex, we may obtain useful insights into both of these issues by restricting our attention to special cases, building incrementally on our "linear intuition". We consider the special case of second-order Volterra models, focusing on the effects of structural restrictions and non-Gaussian input sequences on the model identification problem. The results presented build on the work of Powers and his co-workers, who considered the unconstrained Gaussian problem, certain constrained special cases (e.g., the Hammerstein model), and identification using non-i.i.d. input sequences. Besides extending these results to a wider class of model structure constraints and input sequences, the results presented yield some useful insights into the issue of input sequence design.

Structural system identification using genetic programming and a block diagram oriented simulation tool

Genetic programming can be used for structural optimisation. Combined with a hybrid simplex/simulated annealing algorithm, it is applied to the identification of nonlinear dynamic models from simulated experimental data. Nonlinear models similar to the original test model of the system are identified, yielding both correct structures and accurate parameters.

A non-linear dynamic model identification challenge problem

A non-linear dynamic model identification challenge problem is proposed. The problem is to identify a dynamic model from single input single output data from a laboratory surge tank system that was built expressly for generating non-linear input output data. The problem is divided into six separate tests that challenge the ability of the modeling method to produce a model that interpolates well, degrades gracefully when extrapolating and is robust to noise in the identification data. Instructions are given for the development and testing of the models and for reporting the results. It is hoped that this problem will lead to a more constructive comparison of non-linear modeling methods than has been seen to date.