CA based parallel computational models for nonlinear parabolic systems

This paper presents the results of the nonlinear system modelling approach based on the use of fuzzy rules optimized by different population based optimization algorithms. Fuzzy rule based models with different number of the rules are used to describe the some nonlinear systems in the literature. Firstly, parameters of the fuzzy models are determined by the artificial bee colony (ABC) algorithm. To demonstrate the efficiency of the ABC algorithm, its modelling ability is compared with the other two powerful population based algorithms, particle swarm optimization (PSO) and differential evolution algorithm (DEA). Simulation results show that a successful model performance with good description ability in the modelling of nonlinear or complex systems can be obtained by using one of the population based algorithms in design of the fuzzy rule based models. DOI: http://dx.doi.org/10.5755/j01.eie.22.5.16336

This introductory paper gives a short survey of cellular automata (CAs), from different points of view. It starts with the main definitions and theoretical results about CAs as an abstract model of computation or as discrete dynamical systems. Then, the main applications of CAs in different fields (biology, physics, etc.) as a model of complex systems are illustrated. Finally, implementations of the CA model on parallel computing platforms are surveyed.

This article introduces a novel modular approach to the modelling of nonlinear interconnected complex systems. In the approach, a complex system is decomposed into self-contained easily identified modules to achieve easy linking of individual models. Our proposed approach to modelling differs from the traditional approaches in the following important aspects: (1) it is nonlinear, modular based, systematic, and graphical; (2) it is suitable for fault diagnosis; (3) depending on the level of complexity required, each module may be changed separately quite easily without having to change the other modules; and (4) it draws from the powerful capabilities of the widely used packages of Simulinkand Matlab. These features provide for a generic package that can simulate a complex interconnected system of any description and configuration, as well as simulating any kind of fault anywhere in the system by merely changing the input vector. Examples of two power systems are used as case studies, where it is shown that complex systems can be constructed and simulated easily by appropriately combining components together. The simulation studies show the dynamical behaviour of the two systems with and without faults being applied to them.

This article introduces a novel modular approach to the modelling of nonlinear interconnected complex systems. In the approach, a complex system is decomposed into self-contained easily identified modules to achieve easy linking of individual models. Our proposed approach to modelling differs from the traditional approaches in the following important aspects: (1) it is nonlinear, modular based, systematic, and graphical; (2) it is suitable for fault diagnosis; (3) depending on the level of complexity required, each module may be changed separately quite easily without having to change the other modules; and (4) it draws from the powerful capabilities of the widely used packages of SimulinkTM and MatlabTM . These features provide for a generic package that can simulate a complex interconnected system of any description and configuration, as well as simulating any kind of fault anywhere in the system by merely changing the input vector. Examples of two power systems are used as case studies, where it is shown that complex systems can be constructed and simulated easily by appropriately combining components together. The simulation studies show the dynamical behaviour of the two systems with and without faults being applied to them.

The efficacy of the multimodel framework (MMF) in modeling and identification of complex, nonlinear, and uncertain systems has been widely recognized in the literature owing to its simplicity, transparency, and mathematical tractability, allowing the use of well-known modeling analysis and control design techniques. The approach proved to be effective in addressing some of the shortcomings of other modeling techniques such as those based on a single nonlinear autoregressive network with exogenous inputs model or neural networks. A great number of researchers have contributed to this active field. Due to the significant amount of contributions and the lack of a recent survey, the review of recent developments in this field is vital. In this two-part paper, we attempt to provide a comprehensive coverage of the multimodel approach for modeling and identification of complex systems. The study contains a classification of different methods, the challenges encountered, as well as recent applications of MMF in various fields. Part 1 of this paper presents an overview of MMF for modeling and identification of nonlinear systems as well as the review of recent developments in the partitioning strategies employed.

Theoretical models of computation (automata, Turing machines, random access machines, etc.) define not only what is computable but determine how much time and/or space is required for a computation. The parallel extensions of the sequential models usually offer significant speedup in algorithm execution (not all algorithms can be parallelized, however). Real parallel computer architectures based on these parallel computation models should exhibit the same algorithmic speedup. A complexity hierarchy can be defined for parallel computation models based on the space and/or time speedup of certain classes of algorithms. In particular the parallel shared memory models1 are some of the more powerful of the parallel computation models. Their close resemblance to actual computer architectures provide guidance for real architectural design and their massive interconnection requirements are well suited for implementation in optical computing architectures. In addition, the shared memory models have recently been shown to simulate deterministic Boltzmann machines and threshold-logic Turing machines. Thus optical machines based on these parallel models can potentially exhibit the computational power of the shared memory models. These parallel computation models and their implications for optical computing are discussed.

Unconventional modelling of complex system via cellular automata and differential evolution

PurposeThe purpose of this paper is to propose a new method for computing validities in the multimodel approach.Design/methodology/approachThe multimodel approach offers an interesting alternative and a powerful tool to bypass the difficulties to model, control and diagnose a nonlinear and complex system. Its idea is defined as the apprehension of a nonlinear behaviour of a system by a set of local models characterizing the system operation in different operating zones. In spite of the success of its application in different fields, many problems related to the synthesis of multimodel approach remain open. These include, in particular, the method of obtaining the contribution degrees, also called validities, of the base-models for the deduction of the multimodel output.FindingsThe presented method may lead to superior results in comparison with the residue approach commonly used in the calculation of validities. Numerical simulation results and an experimental validation on a semi-batch reactor clearly illustrated the effectiveness of the proposed method and proved its impact on the improvement of the performances of the multimodel approach. Moreover, the multimodel approach using the new validities’ computation method can lead to perfect modelling of the process.Practical implicationsThe proposed method discussed in the paper has the potential to make the multimodel approach more efficient in the modelling of complex real systems.Originality/valueA significant contribution of the paper is the formulation of a new constrained optimization problem that can be solved by using a powerful mathematical tool such as the active set method, allowing to estimate the validity indexes in the multimodel approach. The obtained optimal solution can lead to perfect modelling of nonlinear and complex real systems.

A method for identifying nonlinear dynamic systems with noise is proposed by using probabilistic universal learning networks (PrULNs). PrULNs are extensions of universal learning networks (ULNs). ULNs form a superset of neural networks and were proposed to provide a universal framework for modeling and control of nonlinear large-scale complex systems. But the ULN does not provide any stochastic characteristics of the signals propagating through it. The PrULNs are equipped with machinery to calculate stochastic properties of signals and to train network parameters so that the signals behave with the pre-specified stochastic properties. On the other hand it is generally recognized that there exists an overfitting problem when identification of nonlinear dynamic systems with noise is done by neural networks. In this paper, it is shown from simulation results of identification of a nonlinear robot dynamics that PrULNs are useful for avoiding the overfitting.

Designing minimum variance controllers (MVC) for nonlinear systems is confronted with many difficulties. The methods which are able to identify MIMO nonlinear systems are scarce, and linear models are not accurate in modeling nonlinear systems. In this paper, Vector ARX (VARX) models are proposed for designing MVC and generalized minimum variance controller (GMVC) for linear and nonlinear systems, and the accuracy of these models in approximating the nonlinear MIMO system is studied. However, the VARX is a linear model. It is shown that this model can identify some kinds of nonlinear systems with any desired accuracy. Therefore, the controller designed by the VARX is accurate, even for these nonlinear systems. The proposed controller is tested on a both linear system and a nonlinear four-tank benchmark process. In spite of the simplicity of designing GMVCs for the VARX models, the results show that the proposed method is accurate and implementable.

Image scrambling is the process of converting an image to an unintelligible format, mainly for security reasons. The scrambling is considered as a pre-process or a post-process of security related applications such as watermarking, information hiding, fingerprinting, and encryption. Cellular automata are parallel models of computation that prove an interesting concept where a simple configuration can lead to a complex behavior. Since there are a lot of parameters to configure, cellular automata have many types and these types differ in terms of complexity and behavior. Cellular automata were previously used in scrambling different types of multimedia, but only complex two-dimensional automata were explored. We propose a scheme where the simplest type of cellular automata is used that is the elementary type. We test the scrambling degree for different cellular automata rules that belong to classes three and four of Wolfram's classification which correspond to complex and chaotic behavior; we also check the effect of other parameters such as the number of generations and the boundary condition. Experimental results show that our proposed scheme outperforms other schemes based on cellular automata in terms of scrambling degree.

The service life and efficiency of proton exchange membrane fuel cells (PEMFCs) are significantly related to the control performance of the air supply system. Therefore, this research develops a novel robust observer-based- [Formula: see text]-variable model-free supertwisting fractional-order sliding mode control ([Formula: see text]-MF-STFOSMC) for complex nonlinear PEMFC air supply system with unmeasurable state variables, model uncertainties, and external disturbance. First, the fifth-order nonlinear PEMFC air supply system model is presented, and the unmeasured state variables are estimated using a nonlinear disturbance observer (NDOB1). Second, the ultra-local model (ULM) algorithm is employed to reconstruct the complex nonlinear PEMFC air supply system, avoiding the need for precise modeling and reducing the controller design difficulty. To estimate and compensate for the uncertain dynamics in the ULM algorithm, another NDOB2 is proposed to realize zero estimation error and finite-time observation. Besides, to achieve optimal control performance with less input chattering, finite-time convergence, and fast response speed, the [Formula: see text]-MF-STFOSMC is designed using super-twisting fractional-order sliding mode control (STFOSMC) algorithm. Furthermore, the stability of [Formula: see text]-MF-STFOSMC via a closed-loop system is verified using the Lyapunov theorem. Finally, the nonlinear PEMFC air supply system model with the proposed controller is realized in MATLAB/Simulink environment, and the simulation results are given to show the superiority and effectiveness of the proposed technique.

Fuzzy recurrent stochastic configuration networks (FRSCNs) are a class of randomized neurofuzzy models that have shown success in modeling nonlinear dynamic systems. However, the data generated from the real-world industry process often exhibits nonstationary characteristics, which could lead to the resulting model with poor generalization performance. This article presents an online self-learning FRSCN (OSL-FRSCN) for problem-resolving. OSL-FRSCNs integrate the self-organizing learning strategies into FRSCNs, maintaining the model's strong fuzzy inference capabilities while enhancing their continuous learning abilities for nonstationary data streams. The network parameters are updated online using the projection algorithm based on the newly arriving data streams. Moreover, the network structure can be dynamically adjusted in the light of the fuzzy recurrent stochastic configuration (FRSC) algorithm and an improved sensitivity analysis. Comprehensive comparisons over two nonlinear system identification tasks and two industrial applications are carried out. Numerical results clearly demonstrate that the proposed OSL-FRSCNs outperform other neurofuzzy and nonfuzzy models with sound generalization, verifying their effectiveness in modeling nonlinear systems with nonstationary dynamics.

The objective of this study is to enhance the responsiveness and precision of control systems through the acceleration of evolutionary programming in the optimization of nonlinear fuzzy control systems. Nonlinear systems are ubiquitous in engineering practice, presenting significant challenges due to their complexity and uncertainty for traditional control methodologies. Fuzzy control, an intelligent control approach rooted in empirical rules, possesses the capability to navigate uncertain and nonlinear issues. However, conventional fuzzy controllers struggle to achieve optimal control performance when confronted with highly complex nonlinear systems. Consequently, this paper introduces the application of accelerated evolutionary programming (RGA) for the optimization of fuzzy controllers, aiming to augment their performance in nonlinear systems. By merging genetic algorithms with a fuzzy adaptive PID controller, the optimized fuzzy controller is better equipped to adapt to the dynamic changes of nonlinear systems, offering robust and efficient control strategies. The results of simulation experiments demonstrate a marked improvement in response time, stability, and error reduction with the fuzzy control system based on RGA optimization. This study offers novel insights and methodologies for the further optimization of control within nonlinear systems, while providing theoretical support for the practical applications of complex systems.

摘要: 确定学习运用自适应控制和动力学系统的概念与方法, 研究未知动态环境下的知识获取、表达、存储和利用等问题. 针对产生周期或回归轨迹的连续 非线性动态系统, 确定学习可以对其未知系统动态进行局部准确建模, 其基本要 素包括: 1)使用径向基函数(Radial basis function, RBF)神经网络; 2)对于周期(或回归)状态轨迹 满足部分持续激励条件; 3)在周期(或回归)轨迹的邻域内实现对非线性系统动态的局部准确神经网络逼近(局部准确建模); 4)所学的知识以时不变且空间分布的方式表达、以常值神经网络权值的方式存储, 并可在动态环境下用于动态模式的快速识别或者闭环神经网络控制. 本文针对离散动态系统, 扩展了确定学习理论, 提出一个根据时态数据序列对离散动态系统进行建模与控制的框架. 首先, 运用确定学习原理和离散系统的自适应辨识方法, 实现对产生时态数据的离散非线性系统的未知动态进行局部准确的神经网络建模, 并利用此建模结果对时态数据序列进行时不变表达. 其次, 提出时态数据序列的基于动力学的相似性定义, 以及对离散动态系统产生的时态数据序列(亦可称为动态模式)进行快速识别方法. 最后, 针对离散非线性控制系统, 实现了基于时态数据序列对控制系统动态的闭环辨识(局部准确建模). 所学关于闭环动态的知识可用于基于模式的智能控制. 本文表明确定学习可以为时态数据挖掘的研究提供新的途径, 并为基于数据的建模与控制等问题提供新的研究思路. 关键词: 确定学习 / 时态数据序列 / 离散动态系统 / 基于数据的建模 / 部分持续激励条件 / 时态数据挖掘 / 动态模式识别 / 基于模式的控制