Identification of the Tennessee Eastman challenge process with subspace methods

The Tennessee Eastman challenge process is a realistic simulation of a chemical process that has been widely used in process control studies. In this case study, several identification methods are examined and used to develop MIMO models that contain seven inputs and ten outputs. ARX and finite impulse response models are identified using reduced-rank regression techniques (PLS and CCR) and state-space models identified with prediction error methods and subspace algorithms. For a variety of reasons, the only successful models are the state-space models produced by two popular subspace algorithms, N4SID and canonical variate analysis (CVA). The CVA model is the most accurate. Important issues for identifying the Tennessee Eastman challenge process and comparisons between the subspace algorithms are also discussed.     

Change point determination for a multivariate process using a two-stage hybrid scheme

Effective identification of the change point of a multivariate process is an important research issue since it is associated with the determination of assignable causes which may seriously affect the underlying process. Most existing studies either use the maximum likelihood estimator (MLE) method or the machine learning (ML) method to estimate or identify the change point of a process. Typically, the MLE method may be criticized for its assumption that the process distribution is known, and the ML method may have the deficiency of using a large number of input variables in the modeling procedure. Diverging from existing approaches, this study proposes an integrated hybrid scheme to mitigate the difficulties of the MLE and ML methods. The proposed scheme includes four components: the logistic regression (LR) model, the multivariate adaptive regression splines (MARS) model, the support vector machine (SVM) classifier and the change point identification strategy. It performs three tasks in order to effectively identify the change point in a multivariate process. The initial task is to use the LR and MARS models to reduce and refine the whole set of input or explanatory variables. The remaining variables are then served as input variables to the SVM in the second task. The last task is to integrate use of the SVM outputs with our proposed identification strategy to determine the change point in a multivariate process. Experimental simulation results reveal that the proposed hybrid scheme is able to effectively identify the change point and outperform the typical statistical process control (SPC) chart alone and the single stage SVM methods.     

On-line model identification for the machining process based on multirate process data

Accurate identification of the model parameters of the machining process based on on-line process data is a crucial prerequisite for its model-based control and diagnostics. A typical machining process generates multi-output and multirate data streams. Whereas various sensors provide in-process information about the process, many important process outcomes including product qualities can be only measured in postprocess manner. This paper proposes to improve the identification by using both in-process and postprocess data and by analyzing the identifiability of model parameters. The identification of the model parameters based on multirate output is formulated using the maximum-likelihood estimation and the Fisher information matrix for a multirate-sampled system is derived to study the identifiability of model parameters. A strategy is developed to improve accuracy and robustness of the model identification considering the identifiability. The proposed method is tested on two batches of multirate process data from the cylindrical grinding process. The test results demonstrate using both in-process and postprocess data improves the identifiability and the proposed identification strategy results in improved prediction performance.     

Mimo and siso self-tuning hybrid position/force control of robotic manipulators

This article presents a new approach for the hybrid position/force control of a manipulator by using self-tuning regulators (STR). For this purpose, the discrete-time stochastic multi-input multi-output (MIMO) and single-input single-output (SISO) models are introduced. The MIMO model's output vector has the positions and velocities of the gripper expressed in the world (xyz) coordinate system as the components. The SISO model outputs are the hybrid errors consisting of the derivatives of the position and force errors at the joints. The inputs of both models are the joint torques. The unknown parameters of those models can be calculated recursively on-line by the square-root estimation algorithm (SQR). An adaptive MIMO and SISO self-tuning type controllers are then designed by minimizing the expected value of a quadratic criterion. This performance index penalizes the deviations of the actual position and force path of the gripper from the desired values expressed in the Cartesian coordinate system. An integrating effect is also included in the performance index to remove the steady-state errors. Digital simulation results using the parameter estimation and the control algorithms are presented and the performances of those two controllers are discussed. © 1996 John Wiley & Sons, Inc.     

基于Frobenius和$L_{2,1}$范数的多输出宽度学习系统

宽度学习系统(broad learning system,BLS)因其特征提取能力强、计算效率高而被广泛应用于众多领域.然而,目前BLS主要用于单输出回归,当BLS存在多个输出时,BLS无法有效发掘多个输出权重之间的相关性,会导致模型预测性能的下降.鉴于此,通过Frobenius和$L_{2,1     

具有多分段损失函数的多输出支持向量机回归

对多维输入、多维输出数据的回归,可以采用多输出支持向量机回归算法.本文介绍具有多分段损失函数的多输出支持向量机回归,其损失函数对落在不同区间的误差值采用不同的惩罚函数形式,并利用变权迭代算法,给出回归函数权系数和偏置的迭代公式.仿真实验表明,该算法的精确性和计算工作量都优于使用多个单输出的支持向量机回归算法.     

genEnsemble: A new model for the combination of classifiers and integration of biological knowledge applied to genomic data

In the last years, microarray technology has become widely used in relevant biomedical areas such as drug target identification, pharmacogenomics or clinical research. However, the necessary prerequisites for the development of valuable translational microarray-based diagnostic tools are (i) a solid understanding of the relative strengths and weaknesses of underlying classification methods and (ii) a biologically plausible and understandable behaviour of such models from a biological point of view. In this paper we propose a novel classifier able to combine the advantages of ensemble approaches with the benefits obtained from the true integration of biological knowledge in the classification process of different microarray samples. The aim of the current work is to guarantee the robustness of the proposed classification model when applied to several microarray data in an inter-dataset scenario. The comparative experimental results demonstrated that our proposal working with biological knowledge outperforms other well-known simple classifiers and ensemble alternatives in binary and multiclass cancer prediction problems using publicly available data.     

Multiple-step-ahead prediction in control systems with Gaussian process models and TS-fuzzy models

In this paper one-step-ahead and multiple-step-ahead predictions of time series in disturbed open loop and closed loop systems using Gaussian process models and TS-fuzzy models are described. Gaussian process models are based on the Bayesian framework where the conditional distribution of output measurements is used for the prediction of the system outputs. For one-step-ahead prediction a local process model with a small past horizon is built online with the help of Gaussian processes. Multiple-step-ahead prediction requires the knowledge of previous outputs and control values as well as the future control values. A “naive” multiple-step-ahead prediction is a successive one-step-ahead prediction where the outputs in each consecutive step are used as inputs for the next step of prediction. A global TS-fuzzy model is built to generate the nominal future control trajectory for multiple-step-ahead prediction. In the presence of model uncertainties a correction of the so computed control trajectory is needed. This is done by an internal feedback between the two process models. The method is tested on disturbed time invariant and time variant systems for different past horizons. The combination of the TS-fuzzy model and the Gaussian process model together with a correction of the control trajectory shows a good performance of the multiple-step-ahead prediction for systems with uncertainties.     

Multi-Output Regularized Feature Projection

Dimensionality reduction by feature projection is widely used in pattern recognition, information retrieval, and statistics. When there are some outputs available (e.g., regression values or classification results), it is often beneficial to consider supervised projection, which is based not only on the inputs, but also on the target values. While this applies to a single-output setting, we are more interested in applications with multiple outputs, where several tasks need to be learned simultaneously. In this paper, we introduce a novel projection approach called multi-output regularized feature projection (MORP), which preserves the information of input features and, meanwhile, captures the correlations between inputs/outputs and (if applicable) between multiple outputs. This is done by introducing a latent variable model on the joint input-output space and minimizing the reconstruction errors for both inputs and outputs. It turns out that the mappings can be found by solving a generalized eigenvalue problem and are ready to extend to nonlinear mappings. Prediction accuracy can be greatly improved by using the new features since the structure of outputs is explored. We validate our approach in two applications. In the first setting, we predict users' preferences for a set of paintings. The second is concerned with image and text categorization where each image (or document) may belong to multiple categories. The proposed algorithm produces very encouraging results in both settings     

Identification of Kalman-Bucy filters from noisy measurement arrays

The paper presents a method for jointly identifying all the parameters of the transition, input-covariance and measurement-noise eovarianee matrices from noisy measurements if no a priori parameter knowledge is available. The method is first derived for single-input—single-output processes and is further extended to single-input-multi-output processes and finally to multi-input-multi-output processes. The convergence of the resulting parameter estimates is discussed and computation results are given for the singlo-input—single-output ease, for the single-input-multi-output case (two outputs) ami for the multi-input—multi-output ease (two inputs and two outputs) to demonstrate the readability of the method.     

Multi-block synchronous prediction of concrete dam displacements using MIMO machine learning paradigm

The integration of numerous monitoring points poses a significant challenge to the efficient modeling of dam displacement behavior, and multi-point synchronous prediction is an effective solution. However, traditional approaches usually construct site-specific data-driven models for each monitoring point individually, which focus on single-target regression and discard the underlying spatial correlation among different displacement monitoring points. This study therefore proposes a multi-input multi-output (MIMO) machine learning (ML) paradigm based on support vector machine (SVM) for synchronous modeling and prediction of multi-point displacements from various dam blocks. In this method, a novel multi-output data-driven model, termed as multi-target SVM (MSVM), is formulated through a deep hybridization of classical SVM architecture and multi-target regression. During the initialization of MSVM, the intercorrelation of multiple target variables is fully exploited by decomposing and regulating the weight vectors. The proposed MSVM is designed to capture the complex MIMO mapping from influential factors to multi-block displacements, while taking into account the correlation between multi-block displacement outputs. Additionally, in order to avoid obtaining the unreliable prediction results due to the empirical selection of parameters, an efficient optimization strategy based on the parallel multi-population Jaya (PMP-Jaya) algorithm is used to adaptively tune the hyperparameters involved in MSVM, which contains no algorithm-specific parameters and is easy to implement. The effectiveness of the proposed model is verified using monitoring data collected from a real concrete gravity dam, where its performance is compared with conventional single-target SVM (SSVM)-based models and state-of-the-art ML-based models. The results indicate that our proposed MSVM is much more promising than the SSVM-based models because only one prediction model is required, rather than constructing multiple site-specific SSVM-based models for different dam blocks. Moreover, MSVM can achieve better performance than other ML-based models in most cases, which provides an innovative modeling tool for dam multi-block behavior monitoring.     

Closed-loop identification of unstable systems using noncausal FIR models

Noncausal finite impulse response (FIR) models are used for closed-loop identification of unstable multi-input, multi-output plants. These models are shown to approximate the Laurent series inside the annulus between the asymptotically stable pole of the largest modulus and the unstable pole of the smallest modulus. By delaying the measured output relative to the measured input, the identified FIR model is a noncausal approximation of the unstable plant. We present examples to compare the accuracy of the identified model obtained using least squares, instrumental variables methods, and prediction error methods for both infinite impulse response (IIR) and noncausal FIR models under arbitrary noise that is fed back into the loop. Finally, we reconstruct an IIR model of the system from its stable and unstable parts using the eigensystem realisation algorithm.     

Persistence of excitation in linear systems

This paper develops output reachability characterizations of linear finite dimensional multivariate systems, so as to translate excitation properties of system inputs to excitation properties of system outputs, states, or associated regression vectors. Such properties are of fundamental concern for convergence of algorithms involving on-line identification, adaptive state estimation, prediction and control. Persistence of excitation guarantees convergence without a priori stability assumptions and ensures robustness properties.     

Model predictive control monitoring using multivariate statistics

Control loop monitoring has become an important research field over the past decade. Research has primarily targeted single-input single-output (SISO) feedback control systems with limited progress being made on the monitoring of multi-input multi-output (MIMO) control systems and large scale model predictive control (MPC) systems in particular. The size and complexity of MPC systems means that identifying and diagnosing problems with their operation can be challenging. This paper presents an MPC condition monitoring tool based on multivariate statistical process control (MSPC) techniques. The proposed tool uses intuitive charts to enable casual users of MPC technology to detect abnormal controller operation and to identify possible causes for this behaviour. Through its application to data collected from a large scale MPC system, the proposed technique is shown to be able to identify and diagnose poor control performance resulting from various issues including inappropriate interaction by process operators.     

Identification of multi-input systems based on correlation techniques

This article proposes a correlation analysis-based identification method for multi-input single-output systems. The basic idea is to estimate the equivalent FIR model parameters with the orders increasing, and to compute the parameter estimates of the original systems (i.e. each fictitious subsystem) using the system inputs and the outputs of the estimated FIR models and using the least squares optimisation. Simulation results indicate that the proposed algorithm can work well.     

Global linearizing control of MIMO microwave-assisted thawing

The application of a global linearizing control algorithm to a multi-input–multi-output (MIMO) microwave thawing process is addressed in this paper. The objective is to control the defrosting time while preventing thermal runaway. A model of the heat transfer with a source term is proposed and is reduced to a system of nonlinear ordinary differential equations using a finite volumes scheme. The control consists of multivariable trajectory tracking, while acting on the microwave power and on the air velocity of a tangential cooling air blast. Experimental and simulation results are discussed in MIMO and single-input–single-output (SISO) configurations.     

Identification of Hammerstein models for control using ASYM

Identification of single-input single-output Hammerstein models is studied in this work. The basic idea here is to extend the recently developed asymptotic method (ASYM) of linear model identification to include input non-linearity in the model set. First identification test design will be discussed. In parameter estimation, prediction error criterion is used in order to maintain consistence when the process is operating in closed-loop. A relaxation iteration scheme is proposed by making use of a model structure in which the error is bilinear in the parameters. The order of the linear part and nonlinear part are determined by looking at an output error related criterion which is control-relevant. The frequency domain upper error bound of the linear part will be derived and used for model validation. Simulation study will be used to illustrate the method and comparisons with other methods are also given.     

Improvement of identification of blast furnace ironmaking process by outlier detection and missing value imputation

The control of blast furnace ironmaking process requires model of process dynamics accurate enough to facilitate the control strategies. However, data sets collected from blast furnace contain considerable number of missing values and outliers. These values can significantly affect subsequent statistical analysis and thus the identification of the whole process, so it becomes much important to deal with these values. This paper considers a data processing procedure including missing value imputation and outlier detection, and examines the impact of processing to the identification of blast furnace ironmaking process. Missing values are imputed based on the decision tree algorithm and outliers are identified and discarded through a set of multivariate outlier detection methods. The data sets before and after processing are then used for identification. Two classic identification methods, N4SID (numerical algorithms for state space subspace system identification) and PEM (prediction error method) are considered and a comparative study is presented.     

多输入多输出单边逻辑函数补集算法的研究

介绍一种多输入多输出单边逻辑函数补集算法,该算法通过对多输入多输出逻辑函数的分离,形成多输入单输出的分支逻辑函数,对多输入单输出分支逻辑函数求出其特征矩阵和状态矢量,根据特征矩阵的特性进行最小列覆盖的选取形成多输入单输出分支逻辑函数补集覆盖的特征矩阵、状态矢量和补集矩阵,最后对多输入单输出分支逻辑函数的补集矩阵进行合并形成多输入多输出逻辑函数的补集,通过测试结果表明性能良好.     

Modelling and control of chaotic processes through their bifurcation diagrams generated with the help of recurrent neural network models. Part 2: An industrial study

Many real-world processes tend to be chaotic and are not amenable to satisfactory analytical models. It has been shown here that for such chaotic processes represented through short chaotic noisy observed data, a multi-input and multi-output recurrent neural network can be built which is capable of capturing the process trends and predicting the behaviour for any given starting condition. It is further shown that this capability can be achieved by the recurrent neural network model when it is trained to very low value of mean squared error. Such a model can then be used for constructing the bifurcation diagram of the process leading to determination of desirable operating conditions. Further, this multi-input and multi-output model makes the process accessible for control using open-loop/closed-loop approaches or bifurcation control, etc.