基于高阶偏最小二乘的间歇过程建模

间歇过程的产品与现代人的生活息息相关,而建立可靠的模型是保障间歇过程安全运行的基础。针对间歇过程的数据特点,引入一种新的广义线性回归模型——高阶偏最小二乘(higher order partial least squares,HOPLS)。它与传统的间歇过程建模方法具有本质的不同,三维数据(批次×变量×时间)不需要展开成二维矩阵,而是直接被分解成一组正交的Tucker矩阵之和。通过高阶奇异值分解(high order singular value decomposition,HOSVD),张量变换和高阶正交迭代(higher order orthogonal iteration,HOOI)找到能同时包含自变量和因变量最大信息的潜向量,与此同时得到对应的负载向量。对于新观测值,通过模型就可以实现对因变量的预测。最后利用PenSim2.0,对青霉素发酵过程进行仿真研究,验证了该间歇过程建模方法的有效性。     

基于LWPT-DTW的间歇过程不等长时段数据同步化

间歇过程不等长时段数据直接影响数据驱动的多元统计分析时段建模精度,导致间歇过程的监控性能降低。针对间歇过程不等长时段数据问题,提出一种基于提升小波包变换（LWPT）和动态时间规整（DTW）算法的间歇过程不等长时段数据同步化方法。该方法引入LWPT对间歇过程不等长时段数据轨迹进行高低频的多级分解,充分提取数据轨迹的所有时频域信息;采用DTW算法对不同频段的系数矩阵进行同步化,并利用提升小波包逆变换对同步化后的系数矩阵进行合成,降低吉布斯现象对数据轨迹合成的影响,获得等长的时段轨迹,实现了间歇过程不等长时段数据同步化。青霉素发酵过程仿真实验表明,所提出的方法运算速度快、稳定,不等长时段数据的同步化结果具有较高的准确性,为间歇过程时段建模提供了可靠的过程数据。     

基于多尺度核JYMKPLS迁移模型的间歇过程产品质量的在线预测方法

针对过程数据不足,且具有强非线性和多尺度特性的新间歇过程,结合迁移学习方法与多尺度核学习方法的优势,提出了一种基于多尺度核JYMKPLS（Joint-Y multi-scale kernel partial least squares）迁移模型的间歇过程产品质量在线预测方法。该方法首先通过迁移学习利用相似源域的旧过程数据提高新间歇过程建模效率和质量预测的精度。然后,针对间歇过程数据的非线性和多尺度特性问题,引入了多尺度核函数以更好地拟合数据变化的趋势,从而提高模型的预测精度。此外,提出模型在线更新和数据剔除,通过在线持续改善迁移模型对新间歇过程的匹配程度,以消除相似过程间的差异性给迁移学习带来的不利影响,从而不断地提升预测精度。最后,通过仿真验证了所提方法的有效性,结果表明,与传统的数据驱动建模方法相比,本文所提方法能够有效提高建模效率和预测精度。     

基于过程迁移的间歇过程终点质量预报方法

提出了一种基于过程迁移的间歇过程质量预报方法,旨在解决新间歇过程数据不足难以建立准确预报模型的问题。该方法基于多元统计回归分析模型,通过构建相似间歇过程间的共同潜变量空间,将已有相似间歇过程的数据信息迁移应用到未建模的新间歇过程中,实现新间歇过程的快速建模和质量预报。在线应用时,利用在线数据不断更新过程迁移模型;同时,实时估计模型预测误差的置信区间,判断预报模型预测误差的稳定性;为克服相似过程间可能存在的差异给迁移模型带来的不利影响,根据数据相似度逐步剔除相似间歇过程数据。最后,通过仿真实验验证了所提方法的有效性。     

基于过程迁移的间歇过程终点质量预报方法

提出了一种基于过程迁移的间歇过程质量预报方法,旨在解决新间歇过程数据不足难以建立准确预报模型的问题。该方法基于多元统计回归分析模型,通过构建相似间歇过程间的共同潜变量空间,将已有相似间歇过程的数据信息迁移应用到未建模的新间歇过程中,实现新间歇过程的快速建模和质量预报。在线应用时,利用在线数据不断更新过程迁移模型;同时,实时估计模型预测误差的置信区间,判断预报模型预测误差的稳定性;为克服相似过程间可能存在的差异给迁移模型带来的不利影响,根据数据相似度逐步剔除相似间歇过程数据。最后,通过仿真实验验证了所提方法的有效性。     

基于多阶段多向核熵成分分析的间歇过程故障检测方法

针对间歇过程的非线性、多阶段特性,提出一种基于多阶段多向核熵成分分析（multistage-MKECA,MsMKECA）的故障检测方法。针对间歇过程的多阶段特性,建立一种时序核熵主元关联度的矩阵相似性阶段划分方法,实现对间歇生产过程的多阶段划分;针对传统批次展开方式在线监控需要预估批次未来值的缺陷,进一步引入一种批次-变量三维数据展开方式建立每个阶段的MKECA非线性统计模型,实现对间歇过程的分阶段监控。最后对盘尼西林发酵过程开展仿真研究,结果表明所提方法能够比传统MKECA方法更为快速地进行故障检测。     

基于LWPT-DTW的间歇过程不等长时段数据同步化

间歇过程不等长时段数据直接影响数据驱动的多元统计分析时段建模精度,导致间歇过程的监控性能降低。针对间歇过程不等长时段数据问题,提出一种基于提升小波包变换(LWPT)和动态时间规整(DTW)算法的间歇过程不等长时段数据同步化方法。该方法引入LWPT对间歇过程不等长时段数据轨迹进行高低频的多级分解,充分提取数据轨迹的所有时频域信息;采用DTW算法对不同频段的系数矩阵进行同步化,并利用提升小波包逆变换对同步化后的系数矩阵进行合成,降低吉布斯现象对数据轨迹合成的影响,获得等长的时段轨迹,实现了间歇过程不等长时段数据同步化。青霉素发酵过程仿真实验表明,所提出的方法运算速度快、稳定,不等长时段数据的同步化结果具有较高的准确性,为间歇过程时段建模提供了可靠的过程数据。     

基于变量分组DTW-MCVA的不等长间歇过程故障检测方法

针对不等长间歇过程监控中批次数据同步化未能充分挖掘局部信息的问题,提出一种基于变量分组DTW-MCVA（VGDTW-CVA）的不等长间歇过程故障检测方法。首先,利用互信息矩阵描述不等长间歇过程测量变量之间的相关性,并基于互信息矩阵进行变量分组。然后利用DTW算法对各个变量组分别进行同步化,并将同步化后的变量组整合为完整的三维数据集。最后,利用MCVA方法建立动态监控模型实现对间歇生产过程的在线监控。盘尼西林发酵过程的仿真结果表明,VGDTW-MCVA能够比基本的DTW-MCVA方法更好地监控间歇过程故障。     

PDPSO优化多阶段AR-PCA间歇过程监测方法

针对间歇过程固有的多阶段特性和动态性,提出基于种群多样性的自适应惯性权重粒子群算法（PDPSO）优化的多阶段自回归主元分析（AR-PCA）间歇过程监测方法。该方法引入了PDPSO算法指导AP聚类偏向参数的选取,避免了传统方法依据聚类评价指标选取参考度时的盲目性。对PDPSO优化AP聚类的多阶段发酵过程的数据样本建立AR-PCA模型能够消除各阶段的动态性及变量之间的自相关和互相关影响。最后,对自回归（AR）模型的残差矩阵建立主成分分析（PCA）模型用于发酵过程监测。将该方法应用到青霉素发酵过程,并与传统方法进行对比,结果表明,该方法能够有效进行间歇过程阶段划分并降低故障的漏报和误报。     

一种基于聚类方法的多阶段间歇过程监控方法

针对阶段不等长的多阶段间歇过程,提出了一种基于k-均值聚类方法的阶段分段策略,可以将不等长的阶段准确分类。首先,将间歇过程的三维训练数据按变量方向展开成二维矩阵,再通过k-均值聚类的方法按照相关性将数据聚成多类并运用主元分析（PCA）方法分别对每一类建立模型。在线监控时,通过计算样本与模型之间的相似系数以选择最合适的模型进行在线监控。此方法可以将不同批次在同一采样时刻的过程数据按照相关性分到多个阶段,更符合生产过程中常见的过程数据阶段不等长的情况。最后利用青霉素仿真验证了该方法的有效性。     

Three-way data analysis with time lagged window for on-line batch process monitoring

In this paper, on-line batch process monitoring is developed on the basis of the three-way data structure and the time-lagged window of process dynamic behavior. Two methods, DPARAFAC (dynamic parallel factor analysis) and DTri-PLS (dynamic trilinear partial least squares), are used here depending on the process variables only or on the process variables and quality indices, respectively. Although multivariate analysis using such PARAFAC (parallel factor analysis) and Tri-PLS (trilinear partial least squares) models has been reported elsewhere, they are not suited for practicing on-line batch monitoring owing to the constraints of their data structures. A simple modification of the data structure provides a framework wherein the moving window based model can be incorporated in the existing three-way data structure to enhance the detectability of the on-line batch monitoring. By a sequence of time window of each batch, the proposed methodology is geared toward giving meaningful results that can be easily connected to the current measurements without the extra computation for the estimation of unmeasured process variables. The proposed method is supported by using two sets of benchmark fault detection problems. Comparisons with the existing two-way and three-way multiway statistical process control methods are also included.     

A novel adaptive surrogate modeling‐based algorithm for simultaneous optimization of sequential batch process scheduling and dynamic operations

A novel adaptive surrogate modeling‐based algorithm is proposed to solve the integrated scheduling and dynamic optimization problem for sequential batch processes. The integrated optimization problem is formulated as a large scale mixed‐integer nonlinear programming (MINLP) problem. To overcome the computational challenge of solving the integrated MINLP problem, an efficient solution algorithm based on the bilevel structure of the integrated problem is proposed. Because processing times and costs of each batch are the only linking variables between the scheduling and dynamic optimization problems, surrogate models based on piece‐wise linear functions are built for the dynamic optimization problems of each batch. These surrogate models are then updated adaptively, either by adding a new sampling point based on the solution of the previous iteration, or by doubling the upper bound of total processing time for the current surrogate model. The performance of the proposed method is demonstrated through the optimization of a multiproduct sequential batch process with seven units and up to five tasks. The results show that the proposed algorithm leads to a 31% higher profit than the sequential method. The proposed method also outperforms the full space simultaneous method by reducing the computational time by more than four orders of magnitude and returning a 9.59% higher profit. © 2015 American Institute of Chemical Engineers AIChE J, 61: 4191–4209, 2015     

A geometric time series model with dependent Bernoulli counting series

A new stationary first‐order integer‐valued autoregressive process with geometric marginal distribution based on the generalized binomial thinning is introduced. The model involves dependent count variables. Some properties of the process are determined. A set of estimators are obtained, and their asymptotic distributions are considered. Some numerical results of the estimates are presented. Possible application of the process is discussed through the real data example.     

Dynamic model-based batch process monitoring

An integrated framework consisting of a multivariate autoregressive (AR) model and multi-way principal component analysis (MPCA) is described for the monitoring of the performance of a batch process. After pre-processing the data, i.e., batch data unfolding, mean-centring and scaling, the data are then filtered using an AR model to remove the auto- and cross-correlation inherent within the pre-processed batch data. Model order is determined using Akaike information criterion and the model parameters are estimated through the application of partial least squares to attain a stable solution. MPCA is then applied to the residuals from the AR model. Three monitoring statistics are considered for the detection of the onset of process abnormalities in the batch process. The main advantage of the proposed approach is that it can monitor batch dynamics along the mean trajectory without the requirement to estimate future observed values. The proposed AR model-based approach is illustrated through its application to two polymerization processes. The case studies indicate that it gives better monitoring results in terms of sensitivity and time to fault detection than the approaches proposed by Nomikos and MacGregor [1994. Monitoring batch processes using multi-way principal components. A.I.Ch.E. Journal 40(8), 1361-1375] and Wold et al. [1998. Modelling and diagnostics of batch processes and analogous kinetic experiments. Chemometrics and Intelligent Laboratory Systems 44, 331-340].     

A new model of batch biodrying of sewage sludge,Part 2: Model calibration and validation

The calibration and validation of a new model of batch biodrying of sewage sludge are presented. The calibration was performed with experimental data from the literature, while the validation was performed with new experimental data. The model was successfully calibrated with experimental data, with the values of parameters falling in the range of values reported. The new model also represented the behavior of the experimental data for all the variables measured, showing that it is robust and valid for the simulated conditions. Simulations showed that continuous high aeration increased the efficiency of the process.     

KINETIC CHARACTERISTICS OF A BATCH ADSORBER OR AN ION EXCHANGE DEVICE OPERATED UNDER NONISOTHERMAL CONDITIONS

A model was formulated for a batch adsorber or ion exchange device with heat generation inside the bulk liquid due to mixing or electrical heating and due to heat of adsorption. Internal and external particle mass and heat transfer gradients and heat transfer through the vessel wall were included. The effective diffusion coefficient was taken to be temperature dependent. Numerical calculations (by orthogonal collocation) give conditions for the existence of intra particle nonisothermity and show the effect of mixing and process temperature on adsorption kinetics.     

基于半监督正交因子分析的过程质量监控方法

实际工业过程中的观测样本大多会受到随机噪声的污染,因此带有噪声假设的概率模型得到广泛应用。传统方法直接对模型的因子进行监控,但由于建模所得因子中可能包含质量无关的信息,因此会增加质量相关故障的误报率,这对主要关心产品质量的生产过程是无益的。同时,针对实际过程与质量样本采样率不同导致的难以精确建模的问题,提出一种半监督正交因子分析（semi-supervised orthogonal factor analysis,Semi-SOFA）方法,建立概率模型,并对因子进行质量相关的正交分解,分别构造T²统计量;根据新样本是否含质量标签的数据性质计算相应的SPE统计量。提出的Semi-SOFA可有效检测出发生的故障是否影响质量,最后通过数值例子和Tennessee Eastman（TE）过程仿真验证了所提方法的有效性。