Identification Of Nonlinear Processes Research Articles

Two-dimensional identification of time-varying batch nonlinear processes with input dead-zone nonlinearity

ABSTRACT In the time dimension, the batch process with input dead-zone nonlinearity often has the characteristics of short operation time and time-varying process parameters. A two-dimensional recursive least squares (2D-RLS) identification method for time-varying nonlinear systems with input dead zone is proposed. By mining system dynamic information from the time direction of the same batch and different batch directions, the identification parameters are updated. The proposed two-dimensional identification strategy converts the time-varying parameter estimation problem of time dimension into the equivalent time-invariant parameter estimation problem of batch dimension. Sufficient production data in batch dimension ensure that the proposed identification algorithm can eliminate the influence of random measurement noise. The identification strategy with unequal length of batch data is also given. The convergence of the proposed algorithm is analysed. Finally, numerical simulation and experimental tests are used to verify the effectiveness and superiority of the proposed algorithm.

Identification of nonlinear process described by neural fuzzy Hammerstein-Wiener model using multi-signal processing

Identification of nonlinear process described by neural fuzzy Hammerstein-Wiener model using multi-signal processing

Pulse response method for the Wiener-type nonlinear process identification

The Wiener-type nonlinear process where a nonlinear static block follows a linear dynamic subsystem is widely used to describe the dynamics of chemical processes. The present study proposes a new Wiener-type process identification method based on a narrow pulse response to cope with the relatively long process excitation requirement in the previous methods. The proposed identification method is developed based on the property of the Wiener-type nonlinear process that outputs of a linear dynamic subsystem is the same at two points when process outputs are equivalent at those points. The proposed method requires a relatively short process excitation (a single pulse response) but almost exactly estimates the Wiener-type nonlinear process. The simulation and experimental studies show the outstanding performance of the proposed method.

Fixed-budget approximation of the inverse kernel matrix for identification of nonlinear dynamic processes

The paper considers the identification of nonlinear dynamic processes using kernel algorithms. Kernel algorithms rely on a nonlinear transformation of the input data points into a high-dimensional space that allows solving nonlinear problems through the construction of kernelized counterparts of linear methods by replacing the inner products with kernels. A key feature of the kernel algorithms is high complexity of the inverse kernel matrix calculation. Nowadays, there are two approaches to this problem. The first one is based on using a reduced training data sample instead of a full one. In case of kernel methods, this approach could cause model misspecification, since kernel methods are directly based on training data. The second one is based on the reduced-rank approximations of the kernel matrix. A major limitation of this approach is that the rank of the approximation is either unknown until approximation is done or it is predefined by the user, both of which are not efficient enough. In this paper, we propose a new regularized kernel least squares algorithm based on the fixed-budget approximation of the kernel matrix. The proposed algorithm allows regulating the computational burden of the identification algorithm and obtaining the least approximation error. We have shown some simulations results illustrating the efficiency of the proposed algorithm compared to other algorithms. The application of the proposed algorithm is considered on the identification problem of the input and output pressure of the pump station.

The impact of the nonlinear effects on thermally stimulated depolarization currents in ion dielectrics

In this paper, the methods described the calculation of thermally stimulated depolarization currents in materials of the HBC class. In the identification of nonlinear processes of thermally stimulated depolarization, at this stage of the research, as defining criteria the authors consider the calculation of the dielectric initial polarization in the infinite approximation of perturbation theory (at the fundamental frequency fields) and calculation of kinetic coefficients in functions of the polarizing field intensity. Generalized nonlinear expressions for the complex dielectric constant and polarization are formulated, which are performed at the fundamental frequency of the alternating polarizing field. The generalized equations that are nonlinear by the field for kinetic coefficients of the kinetic equation are formulated. The obtained theoretical results are of current interest from the perspective of further development of analytical and computer methods of research and prediction of HBC properties as perspective nonlinear materials for a number of branches of modern industry.

The impact of the nonlinear effects on thermally stimulated depolarization currents in ion dielectrics

In this paper, the methods described the calculation of thermally stimulated depolarization currents in materials of the HBC class. In the identification of nonlinear processes of thermally stimulated depolarization, at this stage of the research, as defining criteria the authors consider the calculation of the dielectric initial polarization in the infinite approximation of perturbation theory (at the fundamental frequency fields) and calculation of kinetic coefficients in functions of the polarizing field intensity. Generalized nonlinear expressions for the complex dielectric constant and polarization are formulated, which are performed at the fundamental frequency of the alternating polarizing field. The generalized equations that are nonlinear by the field for kinetic coefficients of the kinetic equation are formulated. The obtained theoretical results are of current interest from the perspective of further development of analytical and computer methods of research and prediction of HBC properties as perspective nonlinear materials for a number of branches of modern industry.

Multi-Output Selective Ensemble Identification of Nonlinear and Nonstationary Industrial Processes.

A key characteristic of biological systems is the ability to update the memory by learning new knowledge and removing out-of-date knowledge so that intelligent decision can be made based on the relevant knowledge acquired in the memory. Inspired by this fundamental biological principle, this article proposes a multi-output selective ensemble regression (SER) for online identification of multi-output nonlinear time-varying industrial processes. Specifically, an adaptive local learning approach is developed to automatically identify and encode a newly emerging process state by fitting a local multi-output linear model based on the multi-output hypothesis testing. This growth strategy ensures a highly diverse and independent local model set. The online modeling is constructed as a multi-output SER predictor by optimizing the combining weights of the selected local multi-output models based on a probability metric. An effective pruning strategy is also developed to remove the unwanted out-of-date local multi-output linear models in order to achieve low online computational complexity without scarifying the prediction accuracy. A simulated two-output process and two real-world identification problems are used to demonstrate the effectiveness of the proposed multi-output SER over a range of benchmark schemes for real-time identification of multi-output nonlinear and nonstationary processes, in terms of both online identification accuracy and computational complexity.

Dynamic nonlinear batch process fault detection and identification based on two‐directional dynamic kernel slow feature analysis

AbstractThe batch process generally covers high nonlinearity and two‐directional dynamics: time‐wise dynamics, which correspond to inherently time‐varying dynamics resulting from the slowly varying underlying driving forces within each batch duration; and batch‐wise dynamics, which are associated with different operating modes among different batches. However, most existing dynamic nonlinear monitoring methods cannot extract the slowly varying underlying driving forces of the nonlinear batch process and rarely tackle the batch‐wise dynamic characteristics among batch runs. In order to address these issues, a new monitoring scheme based on two‐directional dynamic kernel slow feature analysis (TDKSFA) is developed by combining kernel SFA with a global modelling strategy. In the TDKSFA method, kernel SFA is integrated with the ARMAX time series model to mine the nonlinear and time‐wise dynamic properties within a batch run due to its capability of extracting the slowly varying underlying driving forces. Furthermore, the global modelling strategy is presented to handle the batch‐wise dynamics among batches by calculating the total average kernel matrix of all training batches. After the slow features are extracted, Hotelling's T2 and SPE statistics are built to detect faults. To solve the issue of fault variable nonlinear identification, a novel nonlinear contribution plot inspired by the pseudo‐sample variable projection trajectories in the TDKSFA model is further proposed to identify fault variables. Finally, the feasibility and effectiveness of the TDKSFA‐based fault diagnosis strategy is demonstrated through a numerical system and the penicillin fermentation process.

Research on TE process fault diagnosis method based on DBN and dropout

AbstractIn recent years, deep learning has shown outstanding performance and potential in pattern recognition and feature extraction, which has attracted an increasing amount of attention from engineering researchers and academics. Fault diagnosis methods based on deep learning have also become the focus of a significant amount of research. In this paper, a nonlinear process fault diagnosis and identification method based on DBN‐dropout is proposed. The deep belief network (DBN) has significant advantages in dealing with nonlinear processes, and it can extract the abstract representation of nonlinear process data to build a deep network to achieve the real‐time monitoring of process operations. Dropout technology can reduce overfitting and improve the generalization ability of the model. Afterwards, the Tennessee Eastman (TE) process is employed to analyze the performance of the proposed approach.

WH-MOEA: A Multi-Objective Evolutionary Algorithm for Wiener-Hammerstein System Identification. A Novel Approach for Trade-Off Analysis Between Complexity and Accuracy

Several approaches have been presented to identify Wiener-Hammerstein models, most of them starting from a linear dynamic model whose poles and zeros are distributed around the static non-linearity. To achieve good precision in the estimation, the Best Linear Approximation (BLA) has usually been used to represent the linear dynamics, while static non-linearity has been arbitrarily parameterised without considering model complexity. In this paper, identification of Wiener, Hammerstein or Wiener-Hammerstein models is stated as a multiobjective optimisation problem (MOP), with a trade-off between accuracy and model complexity. Precision is quantified with the Mean-Absolute-Error (MAE) between the real and estimated output, while complexity is based on the number of poles, zeros and points of the static non-linearity. To solve the MOP, WH-MOEA, a new multiobjective evolutionary algorithm (MOEA) is proposed. From a linear structure, WH-MOEA will generate a set of optimal models considering a static non-linearity with a variable number of points. Using WH-MOEA, a procedure is also proposed to analyse various linear structures with different numbers of poles and zeros (known as design concepts). A comparison of the Pareto fronts of each design concept allows a more in-depth analysis to select the most appropriate model according to the user’s needs. Finally, a complex numerical example and a real thermal process based on a Peltier cell are identified, showing the procedure’s goodness. The results show that it can be useful to consider the simultaneously precision and complexity of a block-oriented model (Wiener, Hammerstein or Wiener-Hammerstein) in a non-linear process identification.

Recursive NARX model identification of nonlinear chemical processes with matrix invertibility analysis

In the learning techniques based on kernel or orthogonal basis functions, the nonlinearity in the underlying complex dynamic process is modelled by a linear combination of a set of kernel or orthogonal basis functions. Once these functional parameters are selected, the learning task boils down to solving linear least squares (LS). This has motivated the development of various recursive learning algorithms, where matrix inversion is intrinsic in solving LS problems. However, what has not attracted much attention along this track is the analysis of the matrix invertibility conditions in the recursive algorithms. This analysis is especially important when a model is sequentially downdated from the data, which may lead to rank deficiency. The main contribution of this work is the analysis of these conditions, in the formulation of a recursive NARX algorithm based on radial basis functions (RBF-NARX). Aiming at identifying nonlinear and nonstationary time series, RBF-NARX also features a fast algorithm with combined downdating and updating in a single learning step. Both the necessary conditions for checking the singularity of the regressor matrices and the sufficient conditions for ensuring their invertibility are proved. The performance of RBF-NARX and the invertibility conditions are tested and verified by the data from chemical processes.

Model reduction and identification of nonlinear reactive sputter processes

A model for nonlinear reactive sputter processes is developed based on a system theoretic analysis. Hence, a physical model from the fields of thin film science and vacuum science is analysed and reduced in order to describe the input/output behavior of the process by a nonlinear Abel differential equation. Hereby the input/output behavior is related to a supercritical Pitchfork-bifurcation. The parameter identification of the reduced model is discussed and an experiment for model validation is presented. The experiment shows high conformity between the reduced model and the measured input/output behavior of the process. The reduced model can be used as basis for control design for process stabilization.

Iterative Excitation Signal Design for Nonlinear Dynamic Black-Box Models

A new method to generate excitation signals for the identification of nonlinear dynamic processes is introduced. The objective of the optimization is a uniform data point distribution in the input space of the nonlinear approximator. This optimization of the excitation signal is passive, thus the whole signal is optimized prior to the measurement of the process and no online adaptation is performed. The possibility to reuse already existing data sets is one of the key features of the proposed excitation signal optimization. The existing data sets are considered during the optimization, thus operating points with a high data point density are omitted and unexplored areas are filled with new data points. The advantages of the continued optimization are highlighted on artificial processes.

Nonlinear Process Fault Diagnosis Based on Serial Principal Component Analysis.

Many industrial processes contain both linear and nonlinear parts, and kernel principal component analysis (KPCA), widely used in nonlinear process monitoring, may not offer the most effective means for dealing with these nonlinear processes. This paper proposes a new hybrid linear-nonlinear statistical modeling approach for nonlinear process monitoring by closely integrating linear principal component analysis (PCA) and nonlinear KPCA using a serial model structure, which we refer to as serial PCA (SPCA). Specifically, PCA is first applied to extract PCs as linear features, and to decompose the data into the PC subspace and residual subspace (RS). Then, KPCA is performed in the RS to extract the nonlinear PCs as nonlinear features. Two monitoring statistics are constructed for fault detection, based on both the linear and nonlinear features extracted by the proposed SPCA. To effectively perform fault identification after a fault is detected, an SPCA similarity factor method is built for fault recognition, which fuses both the linear and nonlinear features. Unlike PCA and KPCA, the proposed method takes into account both linear and nonlinear PCs simultaneously, and therefore, it can better exploit the underlying process's structure to enhance fault diagnosis performance. Two case studies involving a simulated nonlinear process and the benchmark Tennessee Eastman process demonstrate that the proposed SPCA approach is more effective than the existing state-of-the-art approach based on KPCA alone, in terms of nonlinear process fault detection and identification.

A Developed Local Polynomial Neuro-Fuzzy Model for Nonlinear System Identification

This paper proposes a local polynomial model tree (LPMT) learning technique for prediction and identification of nonlinear systems and processes. The proposed LPMT learning algorithm is applied to a local polynomial neuro fuzzy (LPNF) model, which includes local polynomial models (LPMs), as Taylor series expansion of any unknown function. . The LPMT algorithm is established based on the concept of hierarchical binary tree and heuristically partitions the input space into smaller subdomains through axis-orthogonal splits. The proposed learning algorithm starts from a single local polynomial model and then refines the LPNF model by increasing the degree of the worstperforming LPM or by further partitioning of the input space. During the learning procedure, the validity functions automatically form a partition of unity and therefore normalization side effects, e.g. reactivation and poor extrapolation performance, are prevented. The LPNF model, trained by the proposed LPMT algorithm, is used for prediction and identification of the nonlinear processes and systems in three case studies. The obtained results and comparisons to other methods revealed the promising performance of the proposed model.

Nonlinear process identification in the presence of multiple correlated hidden scheduling variables with missing data

Identification of nonlinear processes in the presence of noise corrupted and correlated multiple scheduling variables with missing data is concerned. The dynamics of the hidden scheduling variables are represented by a state‐space model with unknown parameters. To assure generality, it is assumed that the multiple correlated scheduling variables are corrupted with unknown disturbances and the identification dataset is incomplete with missing data. A multiple model approach is proposed to formulate the identification problem of nonlinear systems under the framework of the expectation‐maximization algorithm. The parameters of the local process models and scheduling variable models as well as the hyperparameters of the weighting function are simultaneously estimated. The particle smoothing technique is adopted to handle the computation of expectation functions. The efficiency of the proposed method is demonstrated through several simulated examples. Through an experimental study on a pilot‐scale multitank system, the practical advantages are further illustrated. © 2015 American Institute of Chemical Engineers AIChE J, 61: 3270–3287, 2015

Численно-аналитическое моделирование и идентификация нестационарного теплового процесса с учетом радиационного теплообмена

Численно-аналитическое моделирование и идентификация нестационарного теплового процесса с учетом радиационного теплообмена

Neural Network Predictive Controller Based Nonlinearity Identification Case Study: Nonlinear Process Reactor - CSTR

In the last decades, a substantial amount of research has been carried out on identification of nonlinear processes. Dynamical systems can be better represented by nonlinear models, which illustrate the global behavior of the nonlinear process reactor over the entire range. CSTR is highly nonlinear chemical reactor. A compact and resourceful model which approximates both linear and nonlinear component of the process is of highly demand. Process modeling is an essential constituent in the growth of sophisticated model-based process control systems. Driven by the contemporary economical needs, developments in process design point out that deliberate operation requires better models. The neural network predictive controller is very efficient to identify complex nonlinear systems with no complete model information. Closed loop method is preferred because it is sensitive to disturbances, no need identify the transfer function model of an unstable system. In this paper identification nonlinearities for a nonlinear process reactor CSTR is approached using neural network predictive controller. KEYWORDS Continuous Stirred Tank Reactor, Multi Input Multi Output, Neural Networks, Chebyshev Neural Networks, Predictive Controller.

Online Identification of Multivariable Nonlinear Processes with Iterative Structure Learning and Application to a Diesel Engine

This contribution presents a new methodology for the online identification, which allows the modeling of the stationary and dynamic behavior of nonlinear combustion engines with many input and output variables in short time with an appropriate model structure. The used models are local polynomial model trees. The necessary enhancements and adaptations of the identification algorithm for local polynomial model trees for the online methodology are presented. To enable an online identification, not only the parameters but also the structure of the models has to be adapted to the ongoing measuring procedure at a test bench. This structure adaptation methods use iteratively recorded measured data for the determination of an optimized model partition and regressor selection regarding the quality and complexity of the model. This maximizes the iterative improvement of the mathematical model, leading to a reduced test bench time. The applicability of the developed methodology is shown for the identification of a model from both, an artificial test function as well as a real diesel engine.

Vehicle dynamic analysis using neuronal network algorithms

AbstractTheoretical developments of certain engineering areas, the emergence of new investigation tools, which are better and more precise and their implementation on-board the everyday vehicles, all these represent main influence factors that impact the theoretical and experimental study of vehicle’s dynamic behavior. Once the implementation of these new technologies onto the vehicle’s construction had been achieved, it had led to more and more complex systems. Some of the most important, such as the electronic control of engine, transmission, suspension, steering, braking and traction had a positive impact onto the vehicle’s dynamic behavior. The existence of CPU on-board vehicles allows data acquisition and storage and it leads to a more accurate and better experimental and theoretical study of vehicle dynamics. It uses the information offered directly by the already on-board built-in elements of electronic control systems. The technical literature that studies vehicle dynamics is entirely focused onto parametric analysis. This kind of approach adopts two simplifying assumptions. Functional parameters obey certain distribution laws, which are known in classical statistics theory. The second assumption states that the mathematical models are previously known and have coefficients that are not time-dependent. Both the mentioned assumptions are not confirmed in real situations: the functional parameters do not follow any known statistical repartition laws and the mathematical laws aren’t previously known and contain families of parameters and are mostly time-dependent. The purpose of the paper is to present a more accurate analysis methodology that can be applied when studying vehicle’s dynamic behavior.A method that provides the setting of non-parametrical mathematical models for vehicle’s dynamic behavior is relying on neuronal networks. This method contains coefficients that are time-dependent. Neuronal networks are mostly used in various types’ system controls, thus being a non-linear process identification algorithm. The common use of neuronal networks for non-linear processes is justified by the fact that both have the ability to organize by themselves. That is why the neuronal networks best define intelligent systems, thus the word ‘neuronal’ is sending one’s mind to the biological neuron cell. The paper presents how to better interpret data fed from the on-board computer and a new way of processing that data to better model the real life dynamic behavior of the vehicle.