Developing a soft sensor based on sparse partial least squares with variable selection

Soft sensors are used to predict response variables, which are difficult to measure, using the data of predictors that can be obtained relatively easier. Arranging time-lagged data of predictors and applying partial least squares (PLS) to the dataset is a popular approach for extracting the correlation between data of the responses and predictors of the process dynamic. However, the model input dimension dramatically soars once multiple time delays are incorporated. In addition, the selection of variables in the dynamic PLS (DPLS) model is a critical step for the robustness and the accuracy of the inferential model, since irrelevant inputs deteriorate the prediction performance of the soft sensor. The sparse PLS (SPLS) is a variable selection method that simultaneously selects the important predictors and finds the correlation between the predictors and responses. The sparsity of the model is dependent on a cut-off value in the SPLS algorithm that is determined using a cross-validation procedure. Therefore, the threshold is a compromise for all latent variable directions. It is necessary to further shrink the inputs from the result of SPLS to obtain a more compact model. In the presented work, named SPLS-VIP, the variable importance in projection (VIP) method was used to filter out the insignificant inputs from the SPLS result. An industrial soft sensor for predicting oxygen concentrations in the air separation process was developed based on the proposed approach. The prediction performance and the model interpretability could be further improved from the SPLS method using the proposed approach.     

Developing a soft sensor with online variable reselection for unobserved multi-mode operations

Soft sensors are used to predict response variables, as these variables are difficult to measure, the prediction models use data of predictors that are relatively easier to obtain. Arranging time-lagged data of predictors and applying the partial least squares (PLS) method to the dataset is a popular approach for extracting the correlation between data of the responses and predictors of the process dynamic. Because irrelevant inputs deteriorate the prediction performance of the soft sensor, the selection of variables in the PLS-based model is a critical step for developing a robust and accurate model. Furthermore, it is necessary to reselect the important predictors of a soft sensor when the operating mode is changed. However, a switch in the operating mode may not be measured, directly. In this study, two statistics are proposed to detect a change of operating mode to enable the reselection of the predictors of the soft sensor. This work involved the development of a soft sensor based on operating data from the industrial ethane removal (de-ethane) process. The changeover of crude oil types cannot be observed from the data of process variables; however, the correlation between input and output variables is significantly affected by the different types of crude oil. The result shows that the use of a soft sensor with online variable reselection is capable of maintaining the accuracy and robustness of the inferential model, effectively.     

Comparison of variable selection methods for PLS-based soft sensor modeling

Data-driven soft sensors have been widely used in both academic research and industrial applications for predicting hard-to-measure variables or replacing physical sensors to reduce cost. It has been shown that the performance of these data-driven soft sensors could be greatly improved by selecting only the vital variables that strongly affect the primary variables, rather than using all the available process variables. In this work, a comprehensive evaluation of different variable selection methods for PLS-based soft sensor development is presented, and a new metric is proposed to assess the performance of different variable selection methods. The following seven variable selection methods are compared: stepwise regression (SR), partial least squares with regression coefficients (PLS-BETA), PLS with variable importance in projection (PLS-VIP), uninformative variable elimination with PLS (UVE-PLS), genetic algorithm with PLS (GA-PLS), least absolute shrinkage and selection operator (Lasso), and competitive adaptive reweighted sampling with PLS (CARS-PLS). Their strengths and limitations for soft sensor development are demonstrated by a simulated case study and an industrial case study.     

Optimal selection of soft sensor inputs for batch distillation columns using principal component analysis

In this paper, a novel methodology based on principal component analysis (PCA) is proposed to select the most suitable secondary process variables to be used as soft sensor inputs. In the proposed approach, a matrix is defined that measures the instantaneous sensitivity of each secondary variable to the primary variables to be estimated. The most sensitive secondary variables are then extracted from this matrix by exploiting the properties of PCA, and they are used as input variables for the development of a regression model suitable for on-line implementation.This method has been evaluated by developing a soft sensor that uses temperature measurements and a process regression model to estimate on-line the product compositions for a simulated batch distillation process. The identification of the optimal soft sensor inputs for this case study has been discussed with respect to the definition of the sensitivity matrix, the data sampling interval, the presence of measurement noise, and the size of the input set. The simulation results demonstrate that the proposed approach can effectively identify the size and configuration of the input set that leads to the optimal estimation performance of the soft sensor.     

A unified approach to LMI-based reduced order self-scheduling control synthesis

We consider a reduced order controller synthesis for a general class of control specifications for linear parameter-varying (LPV) systems, when some of state variables are exactly available. The class is defined in an abstract manner so that it uniformly deals with many significant specifications. A necessary and sufficient condition for the existence of a reduced order controller is given in terms of linear matrix inequalities (LMIs). We also show that the order of the controller can be reduced by the number of the state variables exactly available in the measurements. Moreover, in the case of linear time invariant (LTI) systems, a parameterization of all desirable reduced order LTI controllers is given by means of solutions of LMIs. The results in this paper generalize the class of control specifications in which a reduced order controller exists, making it possible to synthesize a reduced order controller based on LMIs for multi-objective control specifications. Furthermore, these results uniformly describe and generalize the existing results on synthesis of a constant state and a full order output feedback controller for LTI and LPV systems such that the specification is given by the existence of a constant positive definite matrix.     

混合核函数PLS建模方法及在软测量中的应用

针对核函数方法中单个核函数的局限性,以及PLS非线性处理能力差的特点,提出混合核函数PLS建模方法,以提高模型的推广能力和非线性处理能力。混合核函数集中了多个局部和全局核函数,兼具局部和全局特性,并可以通过参数调节局部和全局核函数对混合核函数的作用,将过程的先验知识融入到核函数的确定,进而适合具有不同数据特征的工业过程。工业丙烯腈收率软测量建模的应用表明,混合核函数PLS软测量模型具有较好的数据适应性和非线性特性,满足了工业应用要求。     

Ensemble deep learning based semi-supervised soft sensor modeling method and its application on quality prediction for coal preparation process

Coal preparation is the most effective and economical technique to reduce impurities and improve the product quality for run-of-mine coal. The timely and accurate prediction for key quality characteristics of separated coal plays a significant role in condition monitoring and production control. However, these quality characteristics are usually difficult to directly measure online in industrial practices Although some computation intelligence based soft sensor modeling methods have been developed and reported in existing research for these quality variables estimation, some problems still exist, i.e., manual feature extraction, considerable unlabeled data, temporal dynamic behavior in data, which will influence the accuracy and efficiency for established soft sensor model. To address above-mentioned problem and develop an more excellent quality prediction model for coal preparation process, a novel deep learning based semi-supervised soft sensor modeling approach is proposed which combining the advantage of unsupervised deep learning technique (i.e., Stacked Auto-Encoder (SAE)) with the advantage of supervised deep bidirectional recurrent learner (i.e., Bidirectional Long Short-Term Memory (BLSTM)). More specifically, the unsupervised SAE networks are implemented to learn the representative features hidden in all available input data (labeled and unlabeled samples) and store them as context vector. Then, partial context vector with corresponding labels and the quality variable measure value at previous time are concatenated to form a new merged input feature vector. After that, the temporal and dynamic features are further extracted from the new merged input feature vector via BLSTM networks. Subsequently, the fully connected layers (FCs) are exploited to learn the higher-level features from the last hidden layer of the BLSTM. Lastly, the learned output features by FCs are fed into a supervised liner regression layer to predict the coal quality metrics. Meanwhile, to avoid over-fitting, some regularization techniques are utilized and discussed in proposed network. The application in ash content estimation for a real dense medium coal preparation process and some comparison experiment result demonstrate that the effectiveness and priority of proposed soft sensor modeling approach.     

KLE-(V)AR: A new identification technique for reduced order disturbance models with application to sheet forming processes

A new identification technique that combines the Karhunen–Loève expansion (KLE) with the use of Vector AutoRegressive processes (VAR) is presented in this paper. Given measurements, collected over a period of time, of a set of correlated random variables the method generates a reduced order state-space dynamic model describing the spatial and temporal relationship among the variables. Some of the advantages of the new method are the fewer number of parameters needed to be estimated compared with traditional subspace methods, and its ability to efficiently track nonstationary random processes. Simulation examples from high dimensional sheet forming processes are included for illustration.     

优化岭参数的非线性岭回归及4-CBA含量软测量

针对二甲苯氧化反应过程中影响主要副产物对羧基苯甲醛含量的因素众多且呈高度非线性的问题,提出基于优化岭参数的非线性岭回归MNRR算法,并应用于建立4 CBA含量软测量模型,获得满意的结果.MNRR采用非线性变换对原始模式特征空间进行扩张,以预测性能为指标,采用进化算法确定最佳岭参数,最终建立具有强非线性表达能力以及预测性能良好的模型.与非线性最小二乘回归和基于广义交叉有效性逐步估计岭参数的非线性岭回归相比,MNRR模型具有更高的预测精度且克服了传统岭回归算法最佳岭参数难以确定的缺点.     

变尺度粒子群算法及其在工业软测量中的应用

粒子群优化算法是一种基于群体智能的随机优化算法,具有收敛速度快、设置参数少、算法简单、容易实现等优点,其缺点是容易陷入局部最优解。变尺度法是一种可靠的局部快速寻优方法。为了解决了基本粒子群优化算法易陷入局部最优的问题,本文提出了一种基于变尺度方法的自适应变异粒子群优化算法。在本文算法中,粒子群每进化一代后,对所有粒子执行变尺度搜索,寻找更优个体,从而使算法具有动态自适应性,能够较容易地跳出局部最优。在延迟焦化生产过程中,汽油干点是衡量汽油的一个关键指标,建立汽油干点的软测量对延迟焦化生产实现卡边控制和提高装置的经济效益是有必要的。在实际生产过程中,无法在线测量延迟焦化汽油干点,只能采用离线实验室分析的方法获得,但离线分析不能满足控制的要求。基于软测量技术而开发的延迟焦化汽油干点软测量模型,使汽油干点的在线测量成为可能。目前,工程上一般采用BP神经网络来训练软测量模型。BP神经网络的学习算法是决定BP神经网络预测质量的关键。鉴于此,本文将所提出的变尺度粒子群优化算法用于BP神经网络学习过程中,并将本文方案的预测结果与文献方案进行了对比实验。实验结果表明,与文献方案相比,本文方案具有较好预测精度和良好的泛化能力,具有较好的应用价值。