基于变分贝叶斯算法的线性变参数系统辨识

线性变参数系统(LPV)将多阶段、非线性的过程建模转化为线性多模型的辨识问题,是解决非线性过程建模的一个有效手段。由于实际工业过程存在各种干扰因素,导致被建模系统呈现随机性及模型参数的不确定性。针对这一问题,考虑采用变分贝叶斯(VB)算法对LPV模型进行辨识。该算法首先给定参数相应的先验分布,通过最大化目标函数的下界,从而估计得到参数的后验分布。不仅可实现对参数的点估计,同时量化了估计值的不确定性。针对典型二阶过程和连续搅拌反应釜(CSTR),运用提出的算法进行仿真实验,表明了该贝叶斯估计方法的优越性。     

缺失数据下基于EM算法的非线性过程建模

线性时变参数系统(LPV)将多阶段、非线性的过程建模转化为线性多模型的辨识问题,近年来得到了极大关注。考虑缺失数据下LPV系统的离线建模问题,首先引入一个二进制变量表征输出样本缺失状态,选取过程关键变量作为调度变量,确定主要工况点;然后围绕不同工况点建立局部子模型,将输出缺失部分和采样数据的模型归属当作隐藏变量,利用EM算法进行参数估计,再采用高斯权重函数融合各子模型。最后分别针对典型二阶过程和连续搅拌反应釜(CSTR),运用提出的多模型和算法进行仿真实验,表明有效性。     

基于LPV模型的燃料电池空气进气系统控制

质子交换膜燃料电池是一种通过氢气和氧气的电化学反应将化学能直接转化为电能的装置。提出一种改进的四阶燃料电池进气系统模型,分析了系统的约束性。针对系统模型所具有的非线性特性,提出建立线性变参数（LPV）模型用于对系统的控制。针对状态变量不可测的问题引入卡尔曼滤波器,同时通过可观性分析得出系统所需测量的最佳变量。在符合约束条件下设计基于线性变参数模型的状态空间模型预测控制器,控制空压机的工作电压保证氢气燃料的充分反应。仿真结果表明,基于LPV模型的模型预测控制器能够对空气进气系统进行有效的控制,且满足空压机喘振和阻塞边界等约束条件,与单模型预测控制相比具有更好的控制效果。     

一种基于速率线性化的非线性预测控制算法

提出了一种基于速率线性化方法的非线性预测控制算法。该算法采用速率线性化方法得到与原系统非线性模型相对应的线性变参数模型,这类变参数模型在结构上是线性的,而模型参数将随工作条件的变化而变化,在系统的整个工作区间内都能很好地逼近原非线性模型。在此模型的基础上设计了预测控制器,并利用基于置信域的Levenberg-Marquardt算法在线求得预测控制率。最后对连续搅拌反应釜进行了仿真研究,仿真结果表明了该算法的可行性和有效性。     

一种基于数据驱动的模糊系统建模方法

针对工业生产中的一些复杂、非线性模糊系统,传统的建模方法很难描述其特性,而在实际生产中存在大量输入输出数据,提出了一种通用的基于数据驱动的模糊系统建模方法.采用减法聚类和模糊C-均值相结合的模糊聚类算法对输入空间进行划分,进而从输入输出采样数据中提取系统模糊规则,这样使得被辨识模型可用若干局部线性模型表示,然后利用递推最小二乘法对后件参数进行辨识,从而建立了非线性系统的T-S模糊模型.最后,应用该方法对一个非线性系统进行辨识,仿真结果验证了所提方法的有效性.     

基于最小二乘支持向量机的MIMO线性参数变化模型辨识及预测控制

将现有的面向单输入单输出系统的基于最小二乘支持向量机的参数变化模型辨识算法(SISO-LSSVM-LPV), 推广到多输入多输出系统, 实现了面向多输入多输出系统的基于最小二乘支持向量机的参数变化模型辨识算法(MIMO-LSSVM-LPV), 进一步结合基于遗传算法的预测控制算法(GA-MPC), 提出并实现了MIMO-LSSVM-LPV+ GA-MPC的建模控制一体化新架构。仿真结果表明, 该辨识算法可逼近复杂非线性MIMO系统, 辨识精度高, 并且保留了线性回归低计算量的优点, 结合了GA的MPC可实现最优控制量的在线实时寻优, 并取得了良好控制效果。     

基于自适应模糊推理的非线性系统辨识器设计

针对传统模糊建模方法中模型参数都是根据经验选取的局限性,提出一种类高斯隶属函数,推导了基于类高斯隶属函数的自适应模糊推理模型,利用Stone-Weierstrass定理证明了该模型能以任意精度逼近非线性系统.将自适应模糊推理模型应用于非线性动态系统辨识中,设计了非线性系统辨识器,采用梯度下降算法学习模型中参数,通过仿真得到了较好的辨识效果.     

基于径向基函数的非线性系统近似偏最小一乘准则辨识算法

针对输入信号非线性相关的非线性系统,提出了基于径向基函数的近似偏最小一乘准则辨识算法。首先对观测数据矩阵进行列扩展,以径向基函数（radial basis function,RBF）网络的输出作为观测数据矩阵的扩展项,然后利用近似偏最小一乘算法对扩展的观测矩阵和输出矩阵进行线性回归。近似偏最小一乘算法用确定性可导函数近似代替残差绝对值,可以抑制对称α稳定（symmetrical alpha stable,SαS）分布的尖峰噪声。同时,通过主成分分析去除非线性系统数据向量矩阵之间的非线性相关,得出模型参数的唯一解。仿真实验表明,本文算法可以对输入信号存在非线性相关的非线性系统进行直接辨识,抑制了尖峰噪声对辨识结果的影响,具有优良的稳健性。     

一种扰动自适应的鲁棒预测控制算法

针对实际生产中扰动的时变性,提出了一种扰动自适应的鲁棒预测控制（RAMPC）算法以提高扰动抑制性能。采用时间序列（ARMA）模型在线辨识系统的不可测扰动,通过基于多次迭代思想的递推辨识算法（multi-iteration pseudo-linear regression,MIPLR）来保证在线辨识的质量和收敛速度。考虑到数据与辨识模型的不确定性,改用min-max形式描述MPC算法的控制作用优化命题,并将在线辨识过程中的误差数据引入min-max命题,使在线辨识与控制作用鲁棒优化求解紧密结合起来,提高算法鲁棒性。进一步将此min-max问题转换为一个等效的非线性min问题,并采用多步线性化方法实现快速求解,解决了传统min-max方法在线计算负荷高的问题。仿真结果表明了该算法的有效性。     

一类非线性系统的变负荷预测控制

生产过程的变负荷运行使得其非线性动态特性的影响凸显。针对变负荷生产过程中机理模型为常微分方程或半显式Heisenberg微分-代数方程的一类非线性动态系统,采用非线性预测控制算法,构造出稳态优化与动态优化的两层控制结构,并采用联立法进行优化数值求解。最后对化工过程的夹套CSTR进行仿真验证,表明该算法的有效性。     

Bayesian Models for Non-linear Autoregressions

We discuss classes of Bayesian mixture models for nonlinear autoregressive times series, based on developments in semiparametric Bayesian density estimation in recent years. The development involves formal classes of multivariate discrete mixture distributions, providing flexibility in modeling arbitrary nonlinearities in time series structure and a formal inferential framework within which to address the problems of inference and prediction. The models relate naturally to existing kernel and related methods, threshold models and others, although they offer major advances in terms of parameter estimation and predictive calculations. Theoretic al and computational aspects are developed here, the latter involving efficient simulation of posterior and predictive distributions. Various examples illustrate our perspectives on identification and inference using this mixture approach     

Dynamic optimization of bioreactors using probabilistic tendency models and Bayesian active learning

Due to the complexity of metabolic regulation, first-principles models of bioreactor dynamics typically have built-in errors (structural and parametric uncertainty) which give rise to the need for obtaining relevant data through experimental design in modeling for optimization. A run-to-run optimization strategy which integrates imperfect models with Bayesian active learning is proposed. Parameter distributions in a probabilistic model of bioreactor performance are re-estimated using data from experiments designed for maximizing information and performance. The proposed Bayesian decision-theoretic approach resorts to probabilistic tendency models that explicitly characterize their levels of confidence. Bootstrapping of parameter distributions is used to represent parametric uncertainty as histograms. The Bajpai & Reuss bioreactor model for penicillin production validated with industrial data is used as a representative case study. Run-to-run convergence to an improved policy is fast despite significant modeling errors as long as data are used to revise iteratively posterior distributions of the most influencing model parameters.     

Estimating reaction model parameter uncertainty with Markov Chain Monte Carlo

Predicting the performance of chemical reactions with a mechanistic model is desired during the development of pharmaceutical and other high value chemical syntheses. Model parameters usually must be regressed to experimental observations. However, experimental error may not follow conventional distributions and the validity of common statistical assumptions used for regression should be examined when fitting mechanistic models.This paper compares different techniques to estimate parameter confidence for reaction models encountered in pharmaceutical manufacturing, simulated with either normally distributed or experimentally measured noise. Confidence intervals were calculated following standard linear approaches and two Markov Chain Monte Carlo algorithms utilizing a Bayesian approach to parameter estimation: one assuming a normal error distribution, and a new non-parametric likelihood function. While standard frequentist approaches work well for simpler nonlinear models and normal distributions, only MCMC accurately estimates uncertainty when the system is highly nonlinear, and can account for any measurement bias via customized likelihood functions.     

An approach to multicriteria optimization under uncertainty

Inherent in chemical process models are parameters that have uncertainty associated with them. This paper addresses multicriteria optimization that accounts for model and process uncertainty at the design stage. Specifically the authors have developed extensions of the average criterion method, the worst-case strategy and the ε-constraint method under the following conditions: (a) at the design stage the only information available about the uncertain parameters is that they are bounded by a known uncertainty region T, and (b) at the operation stage, process data is rich enough to allow the determination of exact values of all the uncertain parameters. The suggested formulation assumes that at the operation stage, certain process variables (called control variables) can be tuned or manipulated in order to offset the effects of uncertainty. Three illustrative examples (two benchmark and one direct methanol fuel cell) have been employed.     

Parameter estimation in models with hidden variables : An application to a biotech process

Biological processes are often characterised by significant nonlinearities, noisy measurements and hidden process variables. The dynamic behaviour of such processes can be represented by stochastic differential equations obtained from physical laws. We propose a Bayesian algorithm for parameter estimation in stochastic nonlinear biological processes with unmeasured (or hidden) variables. The proposed algorithm, involves drawing random samples iteratively from a posterior density functions of the parameters and the hidden variables. A Bayesian sampling techniques is used to approximate these posterior density functions. Both Metropolis–Hastings algorithm and Gibbs sampling are used for sample generation. The algorithm is extended to handle multiple data sets and missing observations. The algorithm is applied to an experimental data set collected from an algal bioreactor system. © 2011 Canadian Society for Chemical Engineering     

Fault detection and identification using a Kullback-Leibler divergence based multi-block principal component analysis and bayesian inference

Considering the huge number of variables in plant-wide process monitoring and complex relationships (linear, nonlinear, partial correlation, or independence) among these variables, multivariate statistical process monitoring (MSPM) performance may be deteriorated especially by the independent variables. Meanwhile, whether related variables keep high concordance during the variation process is still a question. Under this circumstance, a multi-block technology based on mathematical statistics method, Kullback-Leibler Divergence, is proposed to put the variables having similar statistical characteristics into the same block, and then build principal component analysis (PCA) models in each low-dimensional subspace. Bayesian inference is also employed to combine the monitoring results from each sub-block into the final monitoring statistics. Additionally, a novel fault diagnosis approach is developed for fault identification. The superiority of the proposed method is demonstrated by applications on a simple simulated multivariate process and the Tennessee Eastman benchmark process.     

Bayesian calibration of thermodynamic parameters for geochemical speciation modeling of cementitious materials

Chemical equilibrium modeling of cementitious materials requires aqueous–solid equilibrium constants of the controlling mineral phases (K_sp) and the available concentrations of primary components. Inherent randomness of the input and model parameters, experimental measurement error, the assumptions and approximations required for numerical simulation, and inadequate knowledge of the chemical process contribute to uncertainty in model prediction. A numerical simulation framework is developed in this paper to assess uncertainty in K_sp values used in geochemical speciation models. A Bayesian statistical method is used in combination with an efficient, adaptive Metropolis sampling technique to develop probability density functions for K_sp values. One set of leaching experimental observations is used for calibration and another set is used for comparison to evaluate the applicability of the approach. The estimated probability distributions of K_sp values can be used in Monte Carlo simulation to assess uncertainty in the behavior of aqueous–solid partitioning of constituents in cement-based materials.     

Estimation of parameters in monte carlo modelling

This paper presents a general method for estimating model parameters from experimental data when the model relating the parameters and input variables to the output responses is a Monte Carlo simulation. From a statistical point of view a Bayesian approach is used in which the distribution of the parameters is handled in discretized form as elements of an array in computer storage. The stochastic nature of the Monte Carlo model allows only an estimate of the distribution to be calculated from which the true distribution must then be estimated. For this purpose an exponentiated polynomial function has been found to be useful. The method provides point estimates as well as joint probability regions. Marginal distributions and distributions of functions of the parameters can also be handled. The motivation for exploring this alternative parameter estimation technique comes from the recognition that for some systems, particularly when the underlying process is stochastic in nature, Monte Carlo simulation often is the most suitable way of modelling. As such, the Monte Carlo approach increases the range of problems which can be handled by mathematical modelling. The technique is applied to the modelling of binary copolymerization. Two models, the Mayo-Lewis and the Penultimate Group Effects models, are considered and a method for discriminating between these models in the light of sequence distribution data is proposed.     

Acoustic emission analysis using Bayesian model selection for damage characterization in ceramic matrix composites

Acoustic emission (AE) during tensile testing of three-dimensional woven SiC/SiC composites was analyzed by a statistical modeling method based on a Bayesian approach to quantitatively evaluate the fracture process. Gaussian mixture models and Weibull mixture models were utilized as candidate models describing the AE time-series data. After fitting AE time-series data to these models with Markov Chain Monte Carlo (MCMC) methods, the model selection was conducted by stochastic complexity. Among the candidate models, the two-component Weibull mixture model was automatically selected. It was confirmed that the component distributions in the two-component Weibull mixture model were corresponding to the evolution of matrix cracking and fiber breakage, respectively. Since the proposed AE analysis method can determine the number of component distributions without the decision of researchers and inspectors, it is expected to be useful for an understanding of the fracture process in newly developed materials and the reliability assessment in service.