Optimal determination of rate coefficients in multiple-reaction systems

An efficient methodology is developed for parameter estimation and is applied by fitting 6 unknown rate coefficients. The estimation procedure is generally applicable to any system, although development has currently been limited to first-order systems of ordinary differential equations (ODE), such as those describing multiple chemical reactions. The objective is to find parameter values so as to minimize the sum of squared error (SSE), where each error term is the difference between the calculated system solution at a point and a selected data value. Since the calculated solution is generally quite nonlinear, an iterative solution is required. At each iteration, parameter values are supplied, the system is solved, and the SSE is determined. In addition, efficient algorithms require the SSE gradient (with respect to the vector of unknown parameters) in order to provide updated parameter estimates. Using conventional techniques, determination of this gradient involves solution of an ODE system for each parameter to be estimated. ff more than a few parameters are involved, the cost could be prohibitive. However, a procedure using adjoint operators is developed in which the SSE gradient can be calculated by solving only one additional ODE system, regardless of the number of parameters being optimized. Combined with a quasi-Newton updating system, an efficient methodology results. This methodology has been applied to a set of six chemical reactions describing the aqueous speciation (hydrolysis) of iodine.     

Flank wear detection of cutting tool inserts in turning operation: application of nonlinear time series analysis

It has been established that turning process on a lathe exhibits low dimensional chaos. This study reports the results of nonlinear time series analysis applied to sensor signals captured real time. The purpose of this chaos analysis is to differentiate three levels of flank wears on cutting tool inserts—fresh, partially worn and fully worn—utilizing the single value index extracted from the reconstructed chaotic attractor; the correlation dimension. The analysis reveals distinguishable dynamics of cutting characterized by different values for the dimension of the attractor when different quality tool inserts are used. This dependence can be effectively utilized as one of the indicators in tool condition monitoring in a lathe. This paper presents the experimental results and shows that tool vibration signals can transmit tool wear conditions reliably.     

Transition Dynamics in Endogenous Recombinant Growth Models by Means of Projection Methods

This study provides a step further in the computation of the transition path of a continuous time endogenous growth model discussed by Privileggi (Nonlinear dynamics in economics, finance and social sciences: essays in honour of John Barkley Rosser Jr., Springer, Berlin, Heidelberg, pp. 251–278, 2010)—based on the setting first introduced by Tsur and Zemel (J Econ Dyn Control 31:3459–3477, 2007)—in which knowledge evolves according to the Weitzman (Q J Econ 113:331–360, 1998) recombinant process. A projection method, based on the least squares of the residual function corresponding to the ODE defining the optimal policy of the ‘detrended’ model, allows for the numeric approximation of such policy for a positive Lebesgue measure range of values of the efficiency parameter characterizing the probability function of the recombinant process. Although the projection method’s performance rapidly degenerates as one departs from a benchmark value for the efficiency parameter, we are able to numerically compute time-path trajectories which are sufficiently regular to allow for sensitivity analysis under changes in parameters’ values.     

基于自适应同步的混沌调制保密通信

针对基于参数调制的自适应混沌保密通信问题,设计一种自适应混沌响应系统,将信息信号调制到混沌系统的某个参数中,通过构造自适应参数辨识与单个自适应控制器,实现混沌系统的同步与参数估计。在接收端,通过构造非线性滤波器,使信息信号有效恢复,实现保密通信。仿真结果表明,该系统同步性较好,解调信号逼近于信息信号,具有较强的保密性。     

Global optimization of an optical chaotic system by Chaotic Multi Swarm Particle Swarm Optimization

The control and estimation of unknown parameters of chaotic systems are a daunting task till date from the perspective of nonlinear science. Inspired from ecological co-habitation, we propose a variant of Particle Swarm Optimization (PSO), known as Chaotic Multi Swarm Particle Swarm Optimization (CMS-PSO), by modifying the generic PSO with the help of the chaotic sequence for multi-dimension unknown parameter estimation and optimization by forming multiple cooperating swarms. This achieves load balancing by delegating the global optimizing task to concurrently operating swarms. We apply it successfully in estimating the unknown parameters of an autonomous chaotic laser system derived from Maxwell-Bloch equations. Numerical results and comparison demonstrate that for the given system parameters, CMS-PSO can identify the optimized parameters effectively evolving at each iteration to attain the pareto optimal solution with small population size and enhanced convergence speedup.     

Joint state and parameter robust estimation of stochastic nonlinear systems

Successful implementation of many control strategies is mainly based on accurate knowledge of the system and its parameters. Besides the stochastic nature of the systems, nonlinearity is one more feature that may be found in almost all physical systems. The application of extended Kalman filter for the joint state and parameter estimation of stochastic nonlinear systems is well known and widely spread. It is a known fact that in measurements, there are inconsistent observations with the largest part of population of observations (outliers). The presence of outliers can significantly reduce the efficiency of linear estimation algorithms derived on the assumptions that observations have Gaussian distributions. Hence, synthesis of robust algorithms is very important. Because of increased practical value in robust filtering as well as the rate of convergence, the modified extended Masreliez–Martin filter presents the natural frame for realization of the joint state and parameter estimator of nonlinear stochastic systems. The strong consistency is proved using the methodology of an associated ODE system. The behaviour of the new approach to joint estimation of states and unknown parameters of nonlinear systems in the case when measurements have non‐Gaussian distributions is illustrated by intensive simulations. Copyright © 2015 John Wiley & Sons, Ltd.     

基于改进的布谷鸟搜索算法对分数阶生物系统的参数估计

近年来,非线性分数阶系统的参数估计问题已经在许多科学和工程领域特别是计算生物学中,引起了广泛的兴趣.本文针对分数阶生物系统的参数估计问题,将系统参数和分数阶导数同时作为独立的未知参数来进行估计,并提出了一种改进的布谷鸟搜索(improved cuckoo search, ICS)算法来求解该问题.在ICS算法中,通过引入一个自适应参数控制机制,同时结合反向学习方法,从而达到提高算法收敛速度和估计值精度的目的.最后,以三种经典的分数阶生物动力系统模型为例进行了数值仿真,其中还考虑了有测量误差和噪声数据的情形.仿真结果表明ICS算法具有良好的适应性、较高的收敛可靠性及精度,为求解非线性分数阶系统参数估计问题提供了一种有效工具.     

基于模糊自适应免疫算法的非线性系统模型参数估计

复杂生产工艺中非线性系统的模型参数估计是系统建模优化问题中的难点, 为避免优化算法过早收敛于错误的参数估计值, 根据生物免疫机理和模糊逻辑原理提出了一种新颖的模糊自适应免疫算法, 该算法采用混沌超变异操作增强算法搜索能力, 并用免疫网络调节策略保持抗体群的多样性, 同时采用模糊逻辑调节算法参数以提高算法的自适应能力. 函数优化仿真结果表明其具有较好的收敛性能, 并能够克服早收敛问题. 最后将其成功应用于重油热解非线性模型参数估计中, 验证了该算法解决实际建模问题的可行性和有效性.     

Near-optimal state estimation for interconnected systems

A new algorithm is proposed for estimating the state of a nonlinear stochastic system when only noisy observations of the state are available. The state estimation problem is formulated as a modal-trajectory, maximum likelihood estimation problem. The resulting minimization problem is analogous to the nonlinear tracking problem in optimal control theory. By viewing the system as an interconnection of lower-dimension subsystems and applying the so-called ε-coupling technqiue, which originated in the study of sensitivity of control systems to parameter variations, a near-optimal state estimation algorithm is derived which has the properties that all computations can be performed in parallel at the subsystem level and only linear equations need be solved. The principal attraction of the method is that significant reductions in the computational requirements relative to other approximate algorithms can be achieved when the system is large-dimensional.     

Set membership state and parameter estimation for systems described by nonlinear differential equations

This paper investigates the use of guaranteed methods to perform state and parameter estimation for nonlinear continuous-time systems, in a bounded-error context. A state estimator based on a prediction-correction approach is given, where the prediction step consists in a validated integration of an initial value problem for an ordinary differential equation (IVP for ODE) using interval analysis and high-order Taylor models, while the correction step uses a set inversion technique. The state estimator is extended to solve the parameter estimation problem. An illustrative example is presented for each part.     

L1 adaptive control for general partial differential equation (PDE) systems

This paper addresses the L₁ adaptive control problem for general Partial Differential Equation (PDE) systems. Since direct computation and analysis on PDE systems are difficult and time-consuming, it is preferred to transform the PDE systems into Ordinary Differential Equation (ODE) systems. In this paper, a polynomial interpolation approximation method is utilized to formulate the infinite dimensional PDE as a high-order ODE first. To further reduce its dimension, an eigenvalue-based technique is employed to derive a system of low-order ODEs, which is incorporated with unmodeled dynamics described as bounded-input, bounded-output (BIBO) stable. To establish the equivalence with original PDE, the reduced-order ODE system is augmented with nonlinear time-varying uncertainties. On the basis of the reduced-order ODE system, a dynamic state predictor consisting of a linear system plus adaptive estimated parameters is developed. An adaptive law will update uncertainty estimates such that the estimation error between predicted state and real state is driven to zero at each time-step. And a control law is designed for uncertainty handling and good tracking delivery. Simulation results demonstrate the effectiveness of the proposed modeling and control framework.     

Stabilization of a class of nonlinear uncertain ordinary differential equation by parabolic partial differential equation controller

This article is concerned with stabilization for a class of uncertain nonlinear ordinary differential equation (ODE) with dynamic controller governed by linear 1?d heat partial differential equation (PDE). The control input acts at the one boundary of the heat's controller domain and the second boundary injects a Dirichlet term in ODE plant. The main contribution of this article is the use of the recent infinite‐dimensional backstepping design for state feedback stabilization design of coupled PDE‐ODE systems, to stabilize exponentially the nonlinear uncertain systems, under the restrictions that (a) the right‐hand side of the ODE equation has the classical particular form: linear controllable part with an additive nonlinear uncertain function satisfying lower triangular linear growth condition, and (b) the length of the PDE domain has to be restricted. We solve the stabilization problem despite the fact that all known backstepping transformation in the literature cannot decouple the PDE and the ODE subsystems. Such difficulty is due to the presence of a nonlinear uncertain term in the ODE system. This is done by introducing a new globally exponentially stable target system for which the PDE and ODE subsystems are strongly coupled. Finally, an example is given to illustrate the design procedure of the proposed method.     

Parameter estimation of chaotic systems by a nonlinear time-varying evolution PSO method

An important issue in nonlinear science is parameter estimation for Lorenz chaotic systems. There has been increasing interest in this issue in various research fields, and it could essentially be formulated as a multidimensional optimization problem. A novel evolutionary computation algorithm, nonlinear time-varying evolution particle swarm optimization (NTVEPSO), is employed to estimate these parameters. In the NTVEPSO method, the nonlinear time-varying evolution functions are determined by using matrix experiments with an orthogonal array, in which a minimal number of experiments would have an effect that approximates tothe full factorial experiments. The NTVEPSO method and other PSO methods are then applied to identify the Lorenz chaotic system. Simulation results demonstrate the feasibility and superiority of the proposed NTVEPSO method.     

Inverse modeling technology for parameter estimation

Computational simulation models are extensively used in the development, design, and analysis of an aircraft engine and its components to represent the physics of an underlying phenomenon. The use of such a model-based simulation in engineering often necessitates the need to estimate model parameters based on physical experiments or field data. This class of problems, referred to as inverse problems (Woodbury KA 2003 Inverse engineering handbook. CRC, Boca Raton) in the literature, can be classified as well-posed or ill-posed depending on the quality (uncertainty) and quantity (amount) of data that are available to the engineer. The development of a generic inverse modeling solver in a probabilistic design system (PEZ version 2.6 user-manual. Probabilistic design system at General Electric Aviation, Cincinnati) requires the ability to handle diverse characteristics in various models. These characteristics include (a) varying fidelity in model accuracy with simulation times from a couple of seconds to many hours; (b) models being black-box, with the engineer having access to only the input and output; (c) nonlinearity in the model; and (d) time-dependent model input and output. This paper demonstrates methods that have been implemented to handle these features, with emphasis on applications in heat transfer and applied mechanics. A practical issue faced in the application of inverse modeling for parameter estimation is ill-posedness, which is characterized by instability and nonuniqueness in the solution. Generic methods to deal with ill-posedness include (a) model development, (b) optimal experimental design, and (c) regularization methods. The purpose of this paper is to communicate the development and implementation of an inverse method that provides a solution for both well-posed and ill-posed problems using regularization based on the prior values of the parameters. In the case of an ill-posed problem, the method provides two solution schemes—a most probable solution closest to the prior, based on the singular value decomposition (SVD), and a maximum a posteriori probability (MAP) solution. The inverse problem is solved as a finite dimensional nonlinear optimization problem using the SVD and/or MAP techniques tailored to the specifics of the application. The objective of the paper is to demonstrate the development and validation of these inverse modeling techniques in several industrial applications, e.g., heat transfer coefficient estimation for disk quenching in process modeling, material model parameter estimation, sparse clearance data modeling, and steady state and transient engine high-pressure compressor heat transfer estimation.     

POP: Patchwork of Parts Models for Object Recognition

We formulate a deformable template model for objects with an efficient mechanism for computation and parameter estimation. The data consists of binary oriented edge features, robust to photometric variation and small local deformations. The template is defined in terms of probability arrays for each edge type. A primary contribution of this paper is the definition of the instantiation of an object in terms of shifts of a moderate number local submodels—parts—which are subsequently recombined using a patchwork operation, to define a coherent statistical model of the data. Object classes are modeled as mixtures of patchwork of parts POP models that are discovered sequentially as more class data is observed. We define the notion of the support associated to an instantiation, and use this to formulate statistical models for multi-object configurations including possible occlusions. All decisions on the labeling of the objects in the image are based on comparing likelihoods. The combination of a deformable model with an efficient estimation procedure yields competitive results in a variety of applications with very small training sets, without need to train decision boundaries—only data from the class being trained is used. Experiments are presented on the MNIST database, reading zipcodes, and face detection.     

船舶动力定位非线性自适应反步控制器设计

针对扰动不确定非线性船舶动力定位问题,提出了一种带观测器的不确定扰动非线性船舶动力定位自适应输出反馈控制.设计了一个非线性观测器,从附有噪声的输出中估计出船舶位置以及运动速度.用滤波后的位置信号,针对扰动不确定非线性船舶设计带观测器的自适应反步控制器,该控制在Backstepping设计方法的基础上引入积分环节,对存在未知参数和动态不确定扰动的船舶能有效的改善系统性能.根据Lyapunov稳定性理论证明所设计的控制器是全局渐近稳定的,仿真结果验证了该方法的有效性.     

混沌噪声的神经网络建模应用于参数估计问题中

提出了基于神经网络预测器的参数估计算法，该算法将神经网络拟合非线性函数的能力和功率谱分析技术相结合．文中介绍了相空间重建技术和神经网络的原理，对于神经网络预测模型，给出了所提算法的原理和步骤，针对具体应用问题，用计算机仿真实验验证了该算法提取混沌噪声中信号参数的有效性,给出了实验结果和必要的分析．     

基于人工蜂群算法的混沌系统参数估计

为了更准确的估计混沌系统的未知参数,提出了一种基于人工蜂群算法的混沌系统参数辨识方法,该方法将混沌系统中参数估计转化为多维变量的函数优化问题,利用搜索方程对多维空间变量进行充分搜索,通过优化人工蜂群算法计算估计值与真值之间的均方差,从而估计出混沌系统的参数. Lorenz混沌系统的参数辨识仿真实验结果表明了该方法的可行性,并且算法收敛速度快,估计精度高.     

Effect of noise on chaotic behavior in Roessler-type nonlinear system

The effects of noise on chaotic behaviors of a nonlinear dynamic model were described from a point of view of the system analysis and the previous studies associated with chaos and noise were reviewed as well. The quasi-white noise was used as the observation noise as well as the system noise to clarify the deterioration of the chaotic patterns of the Roessler model. The effects of the noise intensity on the chaotic signal were observed through the deformation of the attractors, increase of the correlation dimension, and change of the maximum Lyapunov exponent. It has been found that the deterioration of the chaotic patterns is more pronounced in the case of the observation noise than the system noise for the Roessler model. As an example of noisy time series data, the laser speckles time series data was employed and discussed from the point of view of the necessity of noise reduction and possible chaos extraction. © 1997 John Wiley & Sons, Inc.     

Periodic signal analysis by maximum likelihood modeling of orbits of nonlinear ODEs

This paper treats a new approach to the problem of periodic signal estimation. The idea is to model the periodic signal as a function of the state of a second-order nonlinear ordinary differential equation (ODE). This is motivated by Poincare theory, which is useful for proving the existence of periodic orbits for second-order ODEs. The functions of the right-hand side of the nonlinear ODE are then parameterized by a multivariate polynomial in the states, where each term is multiplied by an unknown parameter. A maximum likelihood algorithm is developed for estimation of the unknown parameters, from the measured periodic signal. The approach is analyzed by derivation and solution of a system of ODEs that describes the evolution of the Cramer-Rao bound over time. This allows the theoretically achievable accuracy of the proposed method to be assessed in the ideal case where the signals can be exactly described by the imposed model. The proposed methodology reduces the number of estimated unknowns, at least in cases where the actual signal generation resembles that of the imposed model. This in turn is expected to result in an improved accuracy of the estimated parameters.