Nonlinear Identification Algorithm Research Articles

CFD based heat transfer parameter identification of greenhouse and greenhouse climate prediction method

Predicting the greenhouse environment is important for crop yield and energy consumption projections. This study proposes a dynamic greenhouse temperature and humidity modeling method based on integrating CFD simulation and measured data. This method utilizes computational fluid dynamics to analyze the greenhouse's two key heat transfer characteristics. The effect of wind speed and temperature differences on the heat transfer coefficient of the cover is first analyzed under the condition that the inner thermal screen is folded. Secondly, the effect of temperature differences inside and outside the greenhouse, outdoor wind speed, sky temperature, and the internal thermal screen on the heat transfer coefficient between the greenhouse's indoor and outdoor environments is investigated. Based on the thermodynamic parameters of the greenhouse microclimate obtained through CFD simulation, a regression model of the greenhouse climate model parameters with respect to the influencing variables is built using a nonlinear identification algorithm. By analyzing the mechanism of greenhouse environmental changes, this work proposes a universal structure for the agricultural greenhouse climate model and uses identified heat transfer parameters to correct the universal mechanism model of the greenhouse climate. Considering complex environmental dynamics and unmodeled factors, this study proposes a weighted parameter correction method based on adaptive particle swarm optimization (APSO). Finally, the model was validated using climate data from Venlo-type greenhouses in Shanghai. The validation results indicate that the greenhouse climate model can accurately approximate the real greenhouse climate.

Regression-based identification and order reduction method for nonlinear dynamic structural models

In this paper, we propose a regression-based nonlinear reduced-order model for nonlinear structural dynamics problems, called the Nonlinear Identification and Dimension-Order Reduction (NLIDOR) algorithm. We evaluate the algorithm using a simple toy model, a chain of coupled oscillators and an actual three-dimensional flat plate. The results show that NLIDOR can accurately identify the natural frequencies and modes of the system and capture the nonlinear dynamical features, while the linear Dynamic Mode Decomposition (DMD) method can only capture linear features and is influenced by nonlinear terms. Compared with the full-order model (FOM), NLIDOR can effectively reduce computational cost, while compared with DMD, NLIDOR significantly improves computational accuracy. The results demonstrate the effectiveness and potential of NLIDOR for solving nonlinear dynamic problems in various applications.

Neural network and Sparse identification of Nonlinear Dynamics Integrated Algorithm for Digital Twin identification

Digital twins play a critical role in simulating industrial manufacturing systems to increase productivity and reduce time spent on troubleshooting. Owing to the complexity of real-world industrial systems, automatic sparse identification has emerged as an attractive approach to perform digital twin modelling. The sparse identification of nonlinear dynamics (SINDy) is a machine learning algorithm that performs feature engineering by generating a model term library and then solves a sparse regression problem between the objective outputs and the generated features. By solving a linear-in-parameter sparse regression problem, SINDy provides automatic discovery of system governing equations. However, the performance of SINDy-based algorithms may decline dramatically when applied to identify complex nonlinear relationships, such as implicit relationships. The substantial number of input variables for a real industrial process may further complicate the modelling procedure. We therefore propose the neural network and SINDy integrated algorithm to automatically select the critical features from a model term library and utilize the neural network to capture the process nonlinearity that cannot be captured by a linear-in-parameter model. SINDy performs feature generation considering both numerical methods and first-principles knowledge, making the proposed algorithm a hybrid system identification approach. A diesel hydrotreating unit case study with 37 input variables is analyzed in this paper to demonstrate the advantages of the proposed algorithm for nonlinear digital twin identification. By combining the advantages from both SINDy and neural networks, the proposed algorithm is able to improve the output prediction accuracy for all the three objectives.

A High-Order Sliding-Mode Adaptive Observer for Uncertain Nonlinear Systems

A high-order sliding-mode adaptive observer is proposed to solve the problem of an adaptive estimation, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i.e.,</i> the simultaneous estimation of the state and parameters, for a class of uncertain nonlinear systems in the presence of external disturbances, which do not need to satisfy a relative degree condition equal to one. This approach is based on a high-order sliding-mode observer and a nonlinear parameter identification algorithm. The practical, global, and uniform asymptotic stability of the adaptive estimation error, despite the external disturbances, is guaranteed through the small-gain theorem. The convergence proofs are developed based on the Lyapunov and input-to-state stability theories. Some simulation results illustrate the performance of the proposed high-order sliding-mode adaptive observer.

Mixed third- and fourth-order cumulants-based algorithm for nonlinear kernels identification in cubic systems

Mixed third- and fourth-order cumulants-based algorithm for nonlinear kernels identification in cubic systems

A novel strategy for force identification of nonlinear structures

Dynamic force is the key indicator for monitoring the condition of a mechanical product. These mechanical structures always encompass some nonlinear factors. Most previous studies focused on obtaining the dynamic force of linear structures. Consequently, this study focuses on the nonlinear mechanical structure, and a novel identification strategy is proposed to indirectly identify the excitation force. For the identification strategy, based on a nonlinear state-space model, a force identification equation for the nonlinear structure is built, wherein the transfer matrix consists of coefficient matrices of the nonlinear state-space model, and these coefficient matrices are calculated by a nonlinear subspace identification algorithm. Then, under the generalized cross-validation criterion, the truncated total least squares method is introduced to solve the ill-posed equation to eventually obtain the excitation force of the nonlinear structure. The identification results from two numerical simulation cases and one experimental case illustrate that the proposed identification strategy can stably and accurately identify the excitation force of nonlinear structures.

Improved parameter identification algorithm for ship model based on nonlinear innovation decorated by sigmoid function

Abstract This paper investigates the problem of parameter identification for ship nonlinear Nomoto model with small test data, a nonlinear innovation-based identification algorithm is presented by embedding sigmoid function in the stochastic gradient algorithm. To demonstrate the validity of the algorithm, an identification test is carried out on the ship ‘SWAN’ with only 26 sets of test data. Furthermore, the identification effects of the least squares algorithm, original stochastic gradient algorithm and the improved stochastic gradient algorithm based on nonlinear innovation are compared. Generally, the stochastic gradient algorithm is not suitable for the condition of small test data. The simulation results indicate that the improved stochastic gradient algorithm with sigmoid function greatly increases its accuracy of parameter identification and has 14.2% up compared with the least squares algorithm. Then the effectiveness of the algorithm is verified by another identification test on the ship ‘Galaxy’, the accuracy of parameter identification can reach more than 95% which can be used in ship motion simulation and controller design. The proposed algorithm has advantages of the small test data, fast speed and high accuracy of identification, which can be extended to other parameter identification systems with less sample data.

Research and dynamic analysis based on nonlinear identification of sports goods Econometrics

On the basis of literature research, this paper analyses the sports econometric analysis method, discusses the contribution of sports goods sales and economic growth in China, and analyses the dynamic relationship between them. In this paper, a nonlinear identification algorithm based on the econometric economics of sporting goods is proposed, and a nonlinear identification model based on the econometrics of sporting goods is established. Finally, through the MATLAB simulation analysis, the results show that: sports goods econometric nonlinear identification method is suitable for the coordinated development of regional economy, social environment and sports industry. The simulation results verify the feasibility and effectiveness of the nonlinear identification method of sports econometrics, and provide reference for the stable development of sports economy.

The impact of static output nonlinearities on the control strategies that humans use in command-following tasks

The results of a human-in-the-loop experiment are used to investigate the control strategies that humans use to interact with nonlinear dynamic systems. Two groups of human subjects interact with a dynamic system and perform a command-following task. The first group interacts with a linear time-invariant (LTI) dynamic system. The second group interacts with a Wiener system, which consists of the same LTI dynamics cascaded with a static output nonlinearity. Both groups exhibit improved performance over the trials, but the average of the linear group’s performance is better on more than three-fourths of the trials. A new nonlinear subsystem identification algorithm is presented and used to identify the feedback and feedforward control strategies used by the subjects in both groups. The identification results for the linear group agree with prior studies suggesting that adaptive feedforward inversion is a primary control strategy used by humans for command-following tasks. The main results of this paper address an open question of whether a similar control strategy is used for nonlinear systems. The identification results for the nonlinear group suggest that those subjects also use adaptive feedforward inversion. However, the static output nonlinearity inhibits the human’s ability to approximate the inverse.

ALVEN: Algebraic learning via elastic net for static and dynamic nonlinear model identification

An algorithm is proposed that combines nonlinear feature generation and sparse regression to learn interpretable nonlinear models from noisy and limited data. This Algebraic Learning Via Elastic Net for Static and Dynamic Nonlinear Model Identification algorithm employs automated feature generation including families of ubiquitous chemical and biological nonlinear transformations. ALVEN balances model complexity and prediction accuracy through a two-step feature selection procedure, to produce an interpretable model useful for process applications while avoiding overfitting. The generalization to nonlinear dynamical systems, Dynamic ALVEN, is then described. The model accuracy of the algorithms is compared to well-established machine learning methods for a 3D printer and a chemical reactor.

Parameter Identification and Control Algorithm of Electrohydraulic Servo System for Robotic Excavator Based on Improved Hammerstein Model

In view of the nonlinearity and time-varying characteristics of the electrohydraulic servo system of the robotic excavator, a nonlinear adaptive identification and control algorithm based on improved Hammerstein model is proposed. The Hammerstein algorithm model can approximate the nonlinear system with enough precision, but for the time-varying systems is not satisfactory. In order to compensate for the influence of time-varying factors, the fuzzy control module is designed to adaptively update the forgetting factor. The experimental results show that the improved Hammerstein model error is about 40.11% less than the classical Hammerstein model error. This proves that the improved Hammerstein model is feasible and effective to describe the electrohydraulic servo system of the robotic excavator.

Experimental identification of distributed nonlinearities in the modal domain

This paper deals with the nonlinear system identification of structures exhibiting distributed nonlinearities, which has become of great interest recently, due to the continuous interest to improve the performance of structures. This brings the need for designing lighter and more flexible structural elements, which are usually characterized by moderate and large deformation, resulting in a distributed nonlinear behavior. In this framework, system identification remains a particularly challenging problem, especially when experimental measurements are considered. This work proposes a method to perform such a task, based on a convenient model order reduction of the considered structure, followed by a nonlinear system identification algorithm. The methodology is validated on a very thin beam undergoing large-amplitude oscillations, firstly using numerical data and then considering an experimental test bench. On the experimental side, the nonlinearity is first characterized using just the measured data, in order to acquire information that would help the identification process. Eventually, nonlinear system identification is performed in the reduced-order domain. An ad-hoc version of the nonlinear subspace identification (NSI) algorithm is used, but the presented methodology can also be applied with other nonlinear identification tools. Results confirm the goodness of the identification strategy in obtaining a reliable model which takes into account the distributed nonlinear behavior.

Neuro-Fuzzy Modeling of Data Singular Spectrum Decomposition and Traffic Flow Prediction

Dynamic traffic flow prediction is one of the important topics in traffic engineering and intelligent transportation systems. The traffic flow has stochastic nature and nonlinear dynamics which make accurate prediction of traffic flow a challenging process. In most existing methods, the nonlinear and stochastic qualities of traffic flow have not been taken into consideration simultaneously and these methods do not possess satisfactory accuracy either. In this paper, in order to reduce the prediction error based on traffic flow characteristics, we applied two different methods. At first, we applied a locally linear neuro-fuzzy method using local linear model tree learning algorithm for nonlinear identification of traffic flow. Then, to eliminate the noisy components and also to increase the prediction accuracy, we proposed a method, which is the combination of singular spectrum analysis (SSA) and locally linear neuro-fuzzy model (LLNF). In this method, firstly, the principal components of the traffic flow time series were extracted, several noisy and unimportant components were thrown out and then every remained important component was modeled by using a LLNF network, the trained networks were utilized for one-step-ahead prediction, and finally the predicted patterns were combined to construct the general prediction. Moreover, we compared the results of these two methods with each other and also with those of several other intelligent methods such as multi-layer perceptron, radial-basis function, network and adaptive network fuzzy inference system. The simulation results revealed that the proposed SSA + LLNF approach for traffic flow prediction had promising and superior performance.

Improved differential evolutionary algorithm for nonlinear identification of a novel vibration‐assisted swing cutting system

SummaryVibration‐assisted swing cutting (VASC) is a new precision machining technology. VASC not only inherits the characteristics of EVC intermittent cutting but also alleviates the problem of EVC residual height. However, system identification is key if you want to achieve precise control. In order to solve this problem, a new improved differential evolutionary (IDE) algorithm is proposed to identify and optimize the Hammerstein‐Wiener model parameter in VASC system. IDE algorithm is applied to transform the identification problem of the model into the optimization problem in the parameter space, and the optimal solution of the parameter of the model in the parameter space is obtained. Meanwhile, the IDE algorithm and the conventional five differential evolutionary algorithms perform performance comparison tests on six different test functions. The test results show that the IDE algorithm is strengthening the global search capability, accelerate the convergence rate to the global optimal solution, and indicate that the IDE algorithm can be effectively applied to the parameter optimization of Hammerstein‐winner model. Based on the input and output data collected from the experiment, the accuracy of the identification model can be up to 98%, which prove the superiority of the proposed IDE algorithm for system identification.

Force Reconstruction for Nonlinear Structures in Time Domain

With growing complexity of mechanical structure, nonlinear factors existing in the structure have drawn much attention in recent years. Meanwhile, accurate information of dynamic force is an important index for analyzing nonlinear mechanical structure. However, these data are always difficult and even impossible to be measured directly. Therefore, in this paper, a novel reconstruction strategy is proposed to calculate the external force of the nonlinear structure on the basis of measured response at the reference position. For the reconstruction strategy, the force reconstruction equation of nonlinear structure is established by the nonlinear state-space model, and nonlinear subspace identification (NSI) algorithm is utilized to estimate coefficient matrices of the nonlinear state-space model to form the transfer matrix. And then, considering the illcondition of the transfer matrix, the regularization method combined with the generalized cross-validation criterion is utilized to solve the ill-posed reconstruction equation to obtain the unknown external force. Numerical study is conducted to illustrate the feasibility of the reconstruction strategy. The results demonstrate that the proposed reconstruction strategy can be utilized to accurately obtain the external force of the nonlinear structure.

A modified time domain subspace method for nonlinear identification based on nonlinear separation strategy

Nonlinear factors existing in engineering structures have drawn considerable attention, and nonlinear identification is a competent technique to understand the dynamic characteristics of nonlinear structures. Therefore, in this paper, a novel nonlinear separation subspace identification (NSSI) algorithm based on subspace algorithm and nonlinear separation strategy is proposed to conduct nonlinear parameter identification of nonlinear structures. For the proposed NSSI algorithm, the low-level excitation test is firstly conducted to obtain the transfer matrix in the linear response formula. Then, the obtained transfer matrix is used in the high-level excitation test to calculate the nonlinear response part by the proposed nonlinear separation strategy, and the subspace algorithm is utilized to identify the nonlinear parameter on the modified state-space model including only the nonlinear part. The proposed NSSI algorithm can reduce the coupling error caused by simultaneously processing both the large number part (corresponding to the linear part) and small number part (corresponding to the nonlinear part) in the traditional nonlinear subspace identification (NSI) algorithm. At last, two numerical experiments are given to validate the effectiveness of the developed novel nonlinear identification method. Furthermore, some influence factors are discussed to show the stability of the identification algorithm, and some comparisons between the proposed NSSI method and traditional NSI method are also conducted to demonstrate the advantages of the novel method.

Improved memetic algorithm for nonlinear identification of a three-dimensional elliptical vibration cutting system

This article focuses on the nonlinear Wiener system identification of three-dimensional elliptical vibration cutting. The developed three-dimensional elliptical vibration cutting device is actuated by four piezoelectric stacks, which have hysteresis nonlinear characteristics. Our research proposes an improved memetic algorithm in order to identify the nonlinear elliptical vibration cutting model. The improved memetic algorithm displays the advantages of both particle swarm optimization and genetic algorithm, while simultaneously overcoming these programs’ shortcomings. Moreover, it can quickly and efficiently search for the global optimization. The improved memetic algorithm’s identification performance may be compared with the conventional memetic algorithm, particle swarm optimization, and genetic algorithm using two well-known test functions. Test results demonstrate that the improved memetic algorithm can search the global optimal solution more efficiently than available state-of-the-art algorithms. Based on the input–output data collected from experiments, the accuracy of the identification model can potentially reach 97.55%. This relatively small margin of error verifies the efficiency of the proposed improved memetic algorithm for system identification.

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.

Population balance model: Breakage kernel parameter estimation to emulsification data

AbstractMany processes used across, for example the cosmetics, pharmaceutical, food and chemical industries involve two‐phase liquid–liquid interactions. The quality of liquid–liquid emulsification systems may be related to the droplet size distribution. The population balance equation (PBE) can be used as a modelling tool when accurate description of the dispersed phase is required. Still, the key challenge with the formulation of predictive population balance (PB) models is experimental determination of unknown breakage and coalescence functions. The complexity in the processes and phenomena governing the changes of dispersed systems makes the derivation of the corresponding models a significant challenge.The present study considers a PBE optimisation problem to allow parameter identification to experimental data. The experimental data are measured for a breakage dominated liquid–liquid emulsification system in a stirred tank. Parameter identifications to the breakage frequency models proposed by Coulaloglou and Tavlarides,[26] Alopaeus et al.[28] and Baldyga and Podgorska[27] are performed. The PBE is numerically solved using the high‐order least‐squares method. Moreover, the nonlinear parameter identification algorithm is based on the minimisation of the residual between the experimental data and the numerical solution in a least‐squares sense. The problem has been implemented in the programming language MATLAB where the fmincon function has been used.Parameter estimation can sometimes be straight forward, for instance when the process and formulated model are relatively simple and sufficient data are available. These conditions are not always met, which may result in difficulties in determining accurate parameter values. A thorough statistical analysis is required in order to explore the actual accuracy of the estimated parameter values. The present study presents a relative comprehensive statistical study of the fit compared to what has been provided in previous PBE parameter estimation studies. Moreover, the optimisation algorithm and challenges associated with parameter estimation are discussed. The present study revealed, by systematically assessing the problem formulation and the fit, that a better understanding of the model and more successful parameter estimation can be achieved, or a limitation of the model is unveiled.

Comparison of Four Neural Network Learning Methods Based on Genetic Algorithm for Non-linear Dynamic Systems Identification

Non-linear dynamical systems are difficult to control due to the model uncertainties and external disturbances that may occur in these systems. This paper addresses the problem of identification using dynamic neural networks (DNNs) based on genetic algorithm (GA) for nonlinear dynamic systems. Four different dynamic neural networks are used for identification of the same nonlinear dynamic system, using the genetic algorithm (GA) to train the LayerRecurrent Network (LRN), Focused Time-Delay Neural Network (FTDNN), the Elman Network, and Nonlinear Autoregressive Network with Exogenous inputs (NARX). The simulation results show the generalization ability of the four dynamic neural networks which provide the high precision of model of the nonlinear dynamic system. Also this paper illustrates the advantages and disadvantages of the different dynamic neural networks trained by GA.