Auxiliary error and probability density function based neuro-fuzzy model and its application in batch processes

This paper focuses on resolving the identification problemof a neuro-fuzzymodel (NFM) applied in batch processes. A hybrid learning algorithm is introduced to identify the proposed NFM with the idea of auxiliary error model and the identification principle based on the probability density function (PDF). The main contribution is that the NFM parameter updating approach is transformed into the shape control for the PDF ofmodeling error.More specifically, a virtual adaptive control systemis constructed with the aid of the auxiliary errormodel and then the PDF shape control idea is used to tune NFM parameters so that the PDF of modeling error is controlled to follow a targeted PDF, which is in Gaussian or uniform distribution. Examples are used to validate the applicability of the proposed method and comparisons are made with the minimum mean square error based approaches.     

与机理杂交的支持向量机为发酵过程建模

针对生物发酵过程机理复杂、高度非线性的特点,采用基于结构风险最小的支持向量机为发酵过程建模,其算法规范,建模复杂度低于神经网络方法,所建模型的预测效果更好.还将生化过程的动力学机理与支持向量机相结合,采用串联和串并联结构,提出与机理杂交的支持向量机建模方法,并为间歇式酒精发酵过程中酵母菌体浓度变化建立了预测模型.原理分析与试验结果表明与机理杂交的支持向量机建模方法,相比于单一近似的动力学模型、单一的支持向量机模型,以及机理杂交的神经网络模型,它的预测精度高,泛化能力强,性能更为优越.     

一种基于增量式SVR学习的在线自适应建模方法

训练样本的数量与质量对于过程建模至关重要,在很大程度上影响所建模型的质量。基于增量式支持向量回归(SVR)学习算法,提出一种在线自适应建模方法以实现有选择地添加和删除训练样本。该方法利用SVR模型的KKT条件选择出那些包含足够多新信息的样本进行增量学习,能够在保证模型泛化能力的同时降低模型更新频率。另外,为快速准确地跟踪过程特性的变化,将通过评价当前模型对新增训练样本的学习能力来决定是否需要删除旧样本。当需要删除样本时,基于样本间的相似度,选择淘汰与当前过程特性差别最大的旧样本。将该方法用于建立工业聚丙烯熔融指数预报模型,结果表明,与其他方法相比,获得的预测模型具有更好的泛化性能,且模型更新频率明显降低,能有效地适应工况的变化。     

Hybrid modeling of penicillin fermentation process based on least square support vector machine

According to the problem of the pre-estimation with least square support vector machine (LSSVM) modeling is not ideal in the initial stages of penicillin fermentation process, two hybrid models are designed by utilizing the advantage of LSSVM and kinetics model. Through selecting the appropriate state variables and adopting these methods for penicillin fermentation, the mycelial concentration can be pre-estimated. Experiment results show that these hybrid modeling methods not only improve the above problem, but also have higher predicting accuracy and more powerful generalization ability than the single LSSVM method.     

基于FCMISVM的自适应软测量建模算法及其在PX吸附分离过程中的应用

To overcome the problem that soft sensor models cannot be updated with the process changes, a soft sensor modeling algorithm based on hybrid fuzzy c-means (FCM) algorithm and incremental support vector machines (ISVM) is proposed. This hybrid algorithm FCMISVM includes three parts: samples clustering based on FCM algorithm, learning algorithm based on ISVM, and heuristic sample displacement method. In the training process, the training samples are first clustered by the FCM algorithm, and then by training each clustering with the SVM algorithm, a sub-model is built to each clustering. In the predicting process, when an incremental sample that represents new operation information is introduced in the model, the fuzzy membership function of the sample to each clustering is first computed by the FCM algorithm. Then, a corresponding SVM sub-model of the clustering with the largest fuzzy membership function is used to predict and perform incremental learning so the model can be updated on-line. An old sample chosen by heuristic sample displacement method is then discarded from the sub-model to control the size of the working set. The proposed method is applied to predict the p-xylene (PX) purity in the adsorption separation process. Simulation results indicate that the proposed method actually increases the model’s adaptive abilities to various operation conditions and improves its generalization capability.     

Subspace based model identification for missing data

This article addresses the problem of missing process data in data-driven dynamic modeling approaches. The key motivation is to avoid using imputation methods or deletion of key process information when identifying the model, and utilizing the rest of the information appropriately at the model building stage. To this end, a novel approach is developed that adapts nonlinear iterative partial least squares (NIPALS) algorithms from both partial least squares (PLS) and principle component analysis (PCA) for use in subspace identification. Note that the existing subspace identification approaches often utilize singular value decomposition (SVD) as part of the identification algorithm which is generally not robust to missing data. In contrast, the NIPALS algorithms used in this work leverage the inherent correlation structure of the identification matrices to minimize the impact of missing data values while generating an accurate system model. Furthermore, in computing the system matrices, the calculated scores from the latent variable methods are utilized as the states of the system. The efficacy of the proposed approach is shown via simulation of a nonlinear batch process example.     

Hybrid semi-parametric modeling in process systems engineering: Past,present and future

Hybrid semi-parametric models consist of model structures that combine parametric and nonparametric submodels based on different knowledge sources. The development of a hybrid semi-parametric model can offer several advantages over traditional mechanistic or data-driven modeling, as reviewed in this paper. These advantages, such as broader knowledge base, transparency of the modeling approach and cost-effective model development, have been widely recognized, not only in academia but also in the industry.In this paper, the most common hybrid semi-parametric modeling and parameter identification techniques are revisited. Applications in the areas of (bio)chemical engineering for process monitoring, control, optimization, scale-up and model-reduction are reviewed. It is outlined that the application of hybrid semi-parametric techniques does not automatically lead into better results but that rational knowledge integration has potential to significantly improve model-based process operation and design.     

混杂模型模拟甘油发酵过程

以1,3-丙二醇为研究对象,首先建立了甘油发酵的混合半参数模型。混杂半参数模型就是机理与经验模型之间的平衡,特别适用于复杂系统,当然也包括非常复杂的生物系统,可以不通过机理阐明而得到大量数据,近来受到人们的重视。根据建立好的混杂模型,我们利用提前终止法提高了BP神经网络的泛化能力,最终确定了隐含层神经元个数为8,训练函数为traingdx。根据已经建立好了的人工神经网络结构,利用ODE45函数对间歇和批示流加过程混杂模型的微分方程组进行积分求解,最后得到了较好的模拟结果。     

一种新的选择性神经网络集成方法及其在PTA中的应用

神经网络集成可以显著提高神经网络的泛化性能。传统的集成方法中大都采用将训练的所有网络直接进行组合的方式形成集成网络,而实际上这些网络可能具有一定的相关性。为此,选择性神经网络集成成为目前研究的热点,它能够进一步提高集成网络的泛化性能。本文提出了一种利用网络权值计算网络模型之间差异度的新的选择性神经网络集成方法DWSEN。UCI数据测试表明,与流行的集成方法Bagging和Boosting比较,本方法有着更好的泛化能力和稳定性。将DWSEN应用于精对苯二甲酸（PTA）溶剂系统脱水塔装置的建模过程,结果显示,利用该方法训练得到的集成模型具有更好的泛化性能,能够较好地模拟生产运行过程。     

RBF-CSR-EHCGA模型及其在脉冲萃取中的应用

径向基函数-循环子空间回归（RBF-CSR）是一种有效的非线性网络模型,以高斯条为基函数,性能更优,但其参数多,且难以选定,将显著影响模型性能.为此,本文提出基于优进策略的混合编码遗传算法（EHCGA）,以不同的方式为各类参数编码,并引入确定性的Powell算子,提高全局搜优效率.EHCGA算法以模型预报性能为目标,优选参数,以此建立RBF-CSR-EHCGA模型,它的预报精度高、稳定性良好.已成功应用于回收己内酰胺的脉冲萃取过程建模,效果良好,明显优于其他网络模型,也优于近似机理模型.     

Nonlinear dimension reduction based neural modeling for distributed parameter processes

Many chemical processes are nonlinear distributed parameter systems with unknown uncertainties. For this class of infinite-dimensional systems, the low-order model identification from process data is very important in practice. The dimension reduction with a principal component analysis (PCA) is only a linear approximation for nonlinear problem. In this study, a nonlinear dimension reduction based low-order neural model identification approach is proposed for nonlinear distributed parameter processes. First, a nonlinear principal component analysis (NL-PCA) network is designed for the nonlinear dimension reduction, which can transform the high-dimensional spatio-temporal data into a low-dimensional time domain. Then, a neural system can be easily identified to model this low-dimensional temporal data. Finally, the spatio-temporal dynamics can be reproduced using the nonlinear time/space reconstruction. The simulations on a typical nonlinear transport-reaction process show that the proposed approach can achieve a better performance than the linear PCA based modeling approach.     

基于仿射传播聚类的发酵过程建模

针对花生四烯酸(ARA)发酵过程复杂,机理模型表达不够准确以及单模型泛化能力弱的问题,提出采用基于仿射传播聚类的支持向量机(SVM)多模型建模算法进行该过程建模。该算法首先用仿射传播聚类(AP)算法对ARA样本数据进行聚类,再用SVM算法对各子类样本分别建立子模型。测试样本根据相似性的测度进行归类,并用所属子类的模型进行预测输出。ARA发酵过程的建模实验表明,与其他建模算法相比,基于仿射传播聚类的SVM多模型建模算法所建立的模型具有更高的回归精度和良好的泛化能力。     

Nonlinear empirical modeling techniques

One of the key enabling technologies for computer-based process control is dynamic model development. This problem can be approached from several different perspectives and this survey focuses on one of them: the empirical development of nonlinear, discrete-time dynamic models. Critical issues considered here include the formulation of multivariable problems, the range of popular model representations available and their practical implications for model development, the selection of useful identification inputs, the utility of constraints and regularization in parameter estimation, the treatment of data anomalies and the comparative assessment of modeling results.     

基于改进WOA-LSTM的焦炭质量预测

“双碳”背景下，提升焦炭质量是保证钢铁行业高质量发展的研究重点之一，而炼焦行业存在着在线实时监测难、焦炭质量预测模型泛化能力差等问题。为此，提出一种通过自适应全局搜索算法，即改进鲸鱼优化算法（WOA）与长短期记忆（LSTM）循环神经网络综合建模的方法来解决这一问题。首先选取出配合煤中可反映焦炭质量的可测参数，再运用主成分分析（PCA）去除变异性小的冗余因子后，得到预测因子，将其作为LSTM网络的外部输入；通过加入自适应惯性权重以及最佳扰动更新改进WOA，从而训练LSTM网络的超参数，采用均方根误差（RMSE）和R-squared 进行算法检验；最后将改进后的AGWOA-LSTM模型与典型的LSTM、WOA-LSTM模型进行对比，以验证本方法的优越性。结果表明AGWOA-LSTM模型预测焦炭质量具有精度高、运行速度快等特点。研究对焦炭生产具有一定的理论指导意义。     

基于谱峰分解的拉曼光谱定量分析方法

目前用于拉曼光谱定量分析的方法,如PCA、PLS及SVM等算法需要较多的训练样本,且所建回归模型的外推性较差。间接硬建模（indirect hard modeling,IHM）是一种新型的光谱定量分析技术,适用于光谱的叠加及非线性变化情况,只需少量训练样本即可得到外推性较高的回归模型。但IHM方法需要已知混合物中所有常成分的光谱,这一条件在实际应用中较难达到。为此,提出了一种新的定量分析方法--直接硬建模算法（direct hard modeling,DHM）。新算法不需已知待测成分光谱,而是直接在混合物光谱中确定待测成分所对应的特征峰,然后利用特征峰面积与待测成分浓度之间建立线性模型。通过对PX装置中二甲苯成分的定量分析实验证明DHM具有训练样本数量少、回归模型稳健性强等优点。     

Unification of neural and statistical modeling methods that combine inputs by linear projection

Empirical modeling methods that combine inputs by linear projection include linear methods such as, ordinary least-squares regression, partial least-squares regression, principal components regression, and nonlinear methods such as, backpropagation networks with a single hidden layer, projection pursuit regression, nonlinear partial least-squares regression, and nonlinear principal components regression. In this paper, these popular modeling techniques are unified to yield a single method called nonlinear continuum regression (NLCR). This unification is based on the insight provided by a common framework for empirical modeling methods, and is achieved by using activation functions that adapt to the measured data, a common optimization criterion for finding the projection directions, and a hierarchical training methodology that allows efficient modeling. The adaptive-shape activation functions are determined by univariate smoothing in the space of the projected input versus output. The NLCR optimization criterion contains an adjustable parameter that controls the degree of overfitting or bias of the model, and spans the continuum of methods from projection pursuit regression or backpropagation networks to nonlinear principal components regression. Consequently, NLCR results in models that are usually more general and compact than those obtained by existing methods based on linear projection, while eliminating the need for arbitrary selection of an empirical modeling method based on linear projection for a given task. The improved modeling ability of NLCR and its performance on different types of training data are illustrated by examples based on simulated and industrial data.     

Identification of semi-parametric hybrid process models

Hybrid models are mathematical models that comprise both mechanistic and black-box or data-driven components. Typically, the parameters in the mechanistic part of a hybrid model (if any) are assumed to be known. However in this research, a two-level approach is proposed for the identification of hybrid models where some parameters in the mechanistic part of the model are unknown. At the first level, the black-box component is identified using a regularization method with given values for the regularization and mechanistic parameters. At the second level, the regularization and mechanistic parameters are determined simultaneously and optimized according to a specific criterion placed on the predictive performance of the hybrid model. This approach is tested through the modelling of a toluene nitration process, where a support vector machine (SVM) model is used to represent the chemical kinetics, with the mass transfer-related mechanistic parameters being estimated simultaneously. The case study shows that good results can be obtained in terms of both the prediction of the process variables of interest and the estimates of the mechanistic parameters, when the measurement error in the training data is small whilst when the magnitude of the measurement error increases, the accuracy of the estimates of the mechanistic parameters decreases. However, the predictive performance of the resulting hybrid model in the latter case is still acceptable, and can be much better than that attained from the application of a pure black-box model under certain extrapolation conditions.     

Hybrid modelling and self-learning system for dextrose crystallization process

This paper deals with the modelling of a continuous cooling column crystallizer. An accurate model of this system is needed for complex process control. The investigated system consists on dextrose monohydrate in aqueous solution. An adaptive hybrid model is presented. The model consists of two parts: the phenomenological model, expressed by a set of differential algebraic equations, and a neural network, based on historical data, developed by the fuzzy ARMAP technique. The empirical part of the hybrid model is aimed at eliminating the deviations of the prediction of the phenomenological model caused mainly by incrustations over the surface of the cooling coils located along the column crystallizer. The model is adaptive since neural network parameters are updated by a self-learning system (SLS) based on the acquired process data storage of the DCS of an industrial plant. Firstly, the hybrid model was implemented by using the data of a three-month campaign of the crystallizer, then the self-learning technique was checked on site in a subsequent campaign.     

基于小波网络的非线性动态过程建模和在环氧氯丙烷生产过程中的应用

A type of wavelet neural network, in which the scale function is adopted only,is proposed in this paper for non-linear dynamic process modelling.Its network size is decreased significantly and the weight coefficients can be estimated by a linear algorithm.The wavelet neural network holds some advantages supeiior to other types of neural networks.First, its network structure is easy to specify based on its theoretical analysis and intuition.Secondly, network training does not rely on stochastic gradient type techniques and avoidd the problem of poor convergence or undesirable local minima.The excellent statistic properties of the weight parameter estimations can be proven here.Both theoretical analysis and simulation study show that the identification method is robust and reliable. Furthermore,a hybrid network structure incorporating first-principle knowledge and wavelet network is developed to solve a commonly existing problem in chemical production processes.Applications of the hybrid network to a practical production process demonstrates that model generalisation capability is significantly improved.