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.     

低秩特征选择多输出回归算法

针对现有回归算法没有考虑利用特征与输出的关系,各输出之间的关系,以及样本之间的关系来处理高维数据的多输出回归问题易输出不稳定的模型,提出一种新的低秩特征选择多输出回归方法。该方法采用低秩约束去构建低秩回归模型来获取多输出变量之间的关联结构;同时创新地在该低秩回归模型上使用[L2,p]-范数来进行样本选择,合理地去除噪音和离群点的干扰;并且使用[L2,p]-范数正则化项惩罚回归系数矩阵进行特征选择,有效地处理特征与输出的关系和避免“维灾难”的影响。通过实际数据集的实验结果表明,提出的方法在处理高维数据的多输出回归分析中能获得非常好的效果。     

Hammerstein system identification by non-parametric instrumental variables

A mixed, parametric–non-parametric routine for Hammerstein system identification is presented. Parameters of a non-linear characteristic and of ARMA linear dynamical part of Hammerstein system are estimated by least squares and instrumental variables assuming poor a priori knowledge about the random input and random noise. Both subsystems are identified separately, thanks to the fact that the unmeasurable interaction inputs and suitable instrumental variables are estimated in a preliminary step by the use of a non-parametric regression function estimation method. A wide class of non-linear characteristics including functions which are not linear in the parameters is admitted. It is shown that the resulting estimates of system parameters are consistent for both white and coloured noise. The problem of generating optimal instruments is discussed and proper non-parametric method of computing the best instrumental variables is proposed. The analytical findings are validated using numerical simulation results.     

一类参数线性系统辨识的最优输入设计

对未知参数进行估计时,得到的结果与激励系统所选用的输入信号有较大的关系.针对一类参数可线性化系统,本文提出了一种利用多维同步正交信号和直接配点法设计最优输入信号的方法.首先根据最小二乘原理,利用法矩阵构造Mayer型性能指标函数.然后利用不同频率的正弦基函数构造相互正交的多维输入,通过添加幅值与相位的等式约束,使得输入信号在初/末时刻取值均为零.之后采用直接配点法离散状态变量,将动态的最优输入问题转化为静态的非线性规划问题.最后采用从可行解到优化解的串行优化策略进行求解,不仅提高了寻优效率,还确保了优化结果为原问题的可行解.仿真结果表明,与工程上常用的输入信号相比,本文方法获取的最优输入信号可以提高参数估计精度并加快收敛速率.     

Design of sampled-data critical control systems based on the fast-discretization technique

The fast-discretization is known as an approximate but efficient technique for design and analysis of sampled-data systems. In this paper, we propose a fast-discretization-based design for sampled-data critical control systems. Supposing a tracking problem or a slow-changing disturbance rejection problem, we assume that an exogenous input is a persistent and/or transient input with bound on the rate of change. It is shown that the critical constraint for such exogenous inputs can be given in the form of the inequality constraint on the unit step response. The design parameters are determined by a numerical search method subject to this constraint. However, instead of evaluating it strictly, we check the corresponding constraint which is obtained from the fast-discretized system. Although this approach is approximate, it provides an efficient numerical procedure for a computer-aided design. To show the validity of the proposed method, an example of a multi-objective critical control system design is presented.     

具有安全性保证的基于增强主动学习的模型预测控制

本文提出了一种基于主动学习的增强模型预测控制方法. 该方案克服了大多数基于学习的方法的缺点, 即只能 被动地利用可获得的系统数据并导致学习缓慢. 首先应用高斯过程来评估残差模型的不确定性并构建多步预测模型. 然 后提出了一个两阶段主动学习策略, 通过在优化问题中引入信息增益作为对偶目标来激励系统探测. 最后, 基于鲁棒不 变集定义了安全控制输入集保证了状态约束满足与系统安全性. 本文提出的方法在保证系统安全的情况下提高了学习 能力和闭环控制性能, 实验说明了本文方案的优越性.     

Modeling hysteresis in piezoelectric actuators using NARMAX models

This paper presents a non-linear moving average model with exogenous inputs (NMAX) and a non-linear auto-regressive moving average model with exogenous inputs (NARMAX) respectively to model static and dynamic hysteresis inherent in piezoelectric actuators. The modeling approach is based on the expanded input space that transforms the multi-valued mapping of hysteresis into a one-to-one mapping. In the expanded input space, a simple hysteretic operator is proposed to be used as one of the coordinates to specify the moving feature of hysteresis. Both the modified Akaike's information criterion (MAIC) and the recursive least squares (RLS) algorithm are employed to estimate the appropriate orders and coefficients of the models. The advantage of the proposed approach is in the systematic design procedure which can on-line update the model parameters so as to accommodate to the change of operation environment compared with the classical Preisach model. Moreover, the obtained model is non-linear in variables but linear in parameters so that it can avoid the problem of sticking in local minima which the neural network based models usually have. The results of the experiments have shown that the proposed models can accurately describe static and dynamic behavior of hysteresis in piezoelectric actuators.     

Asymptotic stabilization with group-wise sparse input based on control Lyapunov function approach

This study proposes a novel stabilizing controller for nonlinear systems using group-wise sparse inputs. The input variables are divided into several groups. In the situations when the input constraints can be ignored, one input becomes active for each group at each moment. Our method improves energy efficiency, as sparse input vectors often reduce the standby power of inactive actuators. Large-scale systems, such as those consisting of multiple subsystems, often require the manipulation of multiple inputs simultaneously to be controlled. Our method can be applied to such systems due to the group-wise sparsity of the inputs. The proposed controller is based on the control Lyapunov function approach and includes Sontag's universal formula as a special case. The controllers designed in our method have best-effort property, which means even when a restriction for the decreasing rate of the Lyapunov function cannot be fulfilled, the controller minimizes the time derivative of the Lyapunov function within the input constraint. The effectiveness of the proposed method can be confirmed through simulations.     

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.     

考虑事件触发输入的船舶自适应动力定位控制

为解决实际海况下全驱动船舶的动力定位控制任务存在参数不确定、模型结构不确定和通信资源限制等问题,本文提出一种具有事件触发输入的鲁棒自适应动力定位控制算法.该算法采用径向基函数神经网络对系统模型不确定进行逼近,同时针对通信带宽受限问题,设计了一种具有事件触发机制的执行器输入,降低了控制器和执行器之间的信道占用.此外,该算法还解决了状态变量与执行器增益不确定性之间的强耦合问题,并且设计了在线更新的自适应参数去补偿执行器增益不确定,以确保船舶能够稳定执行动力定位任务.利用Lyapunov稳定性理论证明了闭环控制系统中所有误差变量都满足半全局一致最终有界收敛.通过对比仿真实验验证了所提出算法的有效性.     

A hybrid stock selection model using genetic algorithms and support vector regression

In the areas of investment research and applications, feasible quantitative models include methodologies stemming from soft computing for prediction of financial time series, multi-objective optimization of investment return and risk reduction, as well as selection of investment instruments for portfolio management based on asset ranking using a variety of input variables and historical data, etc. Among all these, stock selection has long been identified as a challenging and important task. This line of research is highly contingent upon reliable stock ranking for successful portfolio construction. Recent advances in machine learning and data mining are leading to significant opportunities to solve these problems more effectively. In this study, we aim at developing a methodology for effective stock selection using support vector regression (SVR) as well as genetic algorithms (GAs). We first employ the SVR method to generate surrogates for actual stock returns that in turn serve to provide reliable rankings of stocks. Top-ranked stocks can thus be selected to form a portfolio. On top of this model, the GA is employed for the optimization of model parameters, and feature selection to acquire optimal subsets of input variables to the SVR model. We will show that the investment returns provided by our proposed methodology significantly outperform the benchmark. Based upon these promising results, we expect this hybrid GA-SVR methodology to advance the research in soft computing for finance and provide an effective solution to stock selection in practice.     

A new Chance-Variance optimization criterion for portfolio selection in uncertain decision systems

The Markowitz’s mean-variance (M-V) model has received widespread acceptance as a practical tool for portfolio optimization, and his seminal work has been widely extended in the literature. The aim of this article is to extend the M-V method in hybrid decision systems. We suggest a new Chance-Variance (C-V) criterion to model the returns characterized by fuzzy random variables. For this purpose, we develop two types of C-V models for portfolio selection problems in hybrid uncertain decision systems. Type I C-V model is to minimize the variance of total expected return rate subject to chance constraint; while type II C-V model is to maximize the chance of achieving a prescribed return level subject to variance constraint. Hence the two types of C-V models reflect investors’ different attitudes toward risk. The issues about the computation of variance and chance distribution are considered. For general fuzzy random returns, we suggest an approximation method of computing variance and chance distribution so that C-V models can be turned into their approximating models. When the returns are characterized by trapezoidal fuzzy random variables, we employ the variance and chance distribution formulas to turn C-V models into their equivalent stochastic programming problems. Since the equivalent stochastic programming problems include a number of probability distribution functions in their objective and constraint functions, conventional solution methods cannot be used to solve them directly. In this paper, we design a heuristic algorithm to solve them. The developed algorithm combines Monte Carlo (MC) method and particle swarm optimization (PSO) algorithm, in which MC method is used to compute probability distribution functions, and PSO algorithm is used to solve stochastic programming problems. Finally, we present one portfolio selection problem to demonstrate the developed modeling ideas and the effectiveness of the designed algorithm. We also compare the proposed C-V method with M-V one for our portfolio selection problem via numerical experiments.     

基于多变量广义预测控制的不稳定系统控制结构选择方法

对于多输入多输出系统, 在控制系统设计时首先要对被控变量和操纵变量进行控制结构选择. Bristol提出的相关增益矩阵(Relative gain array, RGA)法, 以及学者们后来提出的各种改进方法, 都只适用于稳定系统. 本文针对不稳定系统, 基于多变量广义预测控制(Generalized predictive control, GPC)的闭环控制律提出了一种控制结构的变量匹配准则. 通过对预测时域、控制时域等各个参数的优化选择, 使系统闭环稳定; 由闭环控制律得到被控变量期望值与操纵变量的相关性矩阵, 以此得出控制结构的变量配对方案. 通过实例研究表明, 对于开环不稳定系统, 该方法可以得出正确的变量配对结果.     

A Directional Modifier-Adaptation Algorithm for Real-Time Optimization

The steady advances of computational methods make model-based optimization an increasingly attractive method for process improvement. Unfortunately, the available models are often inaccurate. The traditional remedy is to update the model parameters, but this generally leads to a difficult parameter estimation problem that must be solved on-line. In addition, the resulting model may not represent the plant well when there is structural mismatch between the two. The iterative optimization method called Modifier Adaptation overcomes these obstacles by directly incorporating plant measurements into the optimization framework, principally in the form of constraint values and cost and constraint gradients. However, the number of experiments required to estimate these gradients increases linearly with the number of process inputs, which tends to make the method intractable for processes with many inputs. This paper presents a new algorithm, called Directional Modifier Adaptation, that overcomes this limitation by only estimating the plant gradients in certain privileged input directions. It is proven that plant optimality with respect to these privileged directions can be guaranteed upon convergence. A novel, statistically optimal, gradient estimation technique is developed. The algorithm is illustrated through the simulation of a realistic airborne wind-energy system, a promising renewable energy technology that harnesses wind energy using large kites. It is shown that Directional Modifier Adaptation can optimize in real time the path followed by the kite.     

一类MIMO系统连续状态空间模型的参数辨识频域方法

在连续时间状态空间模型的参数辨识中,针对系统状态微分项获取困难这一问题,对输入、状态及输出序列应用离散傅里叶变换,得到复数域线性回归方程,并给出了不同形式的最小二乘解估计式.以飞行器多输入多输出(Multiple-input multiple-output, MIMO)状态空间模型为例,设计正交多正弦信号对系统进行多通道同时激励,在一次激励的情况下就可以辨识出所有模型参数,从而提高辨识实验效率.仿真实验证明了方法的有效性和结果的准确性.     

Neural network-based identification of SMB chromatographic processes

In this contribution, the identification problem for the control of nonlinear simulated moving bed (SMB) chromatographic processes is addressed. For process control the flow rates of extract, desorbent, and recycle of the SMB process, and the switching time are the manipulated variables. But these variables influence the process in a strongly coupled manner. Therefore, a new set of input variables is introduced by a nonlinear transformation of the physical inputs, such that the couplings are reduced considerably. The front positions of the axial concentration profile are taken as model outputs. Multilayer feedforward neural networks (NN) are utilized as approximating models of the nonlinear input–output behavior. The gradient distribution of the model outputs with respect to the inputs is used to determine their structural parameters and the network size is chosen by the SVD method. To illustrate the effectiveness of the identification method, a laboratory scale SMB process is used as an example. The simulation results of the identified model confirm a very good approximation of the first principles models and exhibit a satisfactory long-range prediction performance.     

On the persistency of excitation in radial basis function networkidentification of nonlinear systems

Considers radial basis function (RBF) network approximation of a multivariate nonlinear mapping as a linear parametric regression problem. Linear recursive identification algorithms applied to this problem are known to converge, provided the regressor vector sequence has the persistency of excitation (PE) property. The main contribution of this paper is formulation and proof of PE conditions on the input variables. In the RBF network identification, the regressor vector is a nonlinear function of these input variables. According to the formulated condition, the inputs provide PE, if they belong to domains around the network node centers. For a two-input network with Gaussian RBF that have typical width and are centered on a regular mesh, these domains cover about 25% of the input domain volume. The authors further generalize the proposed solution of the standard RBF network identification problem and study affine RBF network identification that is important for affine nonlinear system control. For the affine RBF network, the author formulates and proves a PE condition on both the system state parameters and control inputs.     

Mining the customer credit using hybrid support vector machine technique

Credit scoring has become a critical and challenging management science issue, as the credit industry has been facing fiercer competition in recent years. Many methods have been suggested to tackle this problem in the literature. In this paper, we proposed hybrid support vector machine technique based on three strategies: (1) using CART to select input features, (2) using MARS to select input features, (3) using grid search to optimize model parameters. In order to verify the feasibility and effectiveness of the proposed hybrid SVM model, one credit card dataset provided by a local bank in China is used in this study. Analytic results demonstrate that the hybrid SVM technique not only has the best classification rate, but also has the lowest Type II error in comparison with CART, MARS and SVM and justify the presumptions that SVM having better capability of capturing nonlinear relationship among variables.     

Robust H∞ dynamic output feedback control for spacecraft rendezvous with poles and input constraint

This paper is concerned with the output feedback control problem for spacecraft rendezvous subject to target angular velocity uncertainty and controller uncertainty, external disturbance and input constraint. A general full-order dynamic output feedback (DOF) controller is proposed. As a stepping-stone, the H_∞ performance requirement, poles and input constraint are analysed separately via linear matrix inequalities (LMIs). Then, with the obtained results, the controller design problem is cast into a convex problem subject to a set of LMI constraints through a critical change of controller variables. Furthermore, when the system states are all available, a reduced sufficient condition of the non-fragile state feedback controller is given. Compared with existing results, the designed controller has overcome the disadvantage of strictly proper DOF controller, where the initial value of the control input is zero. Besides, the constraint on poles placement is relaxed. A numerical simulation is performed to verify the effectiveness of the proposed method.     

一种分布式智能推荐系统的设计

为提高支持向量回归算法的学习能力和泛化性能,提出了一种优化支持向量回归参数的混合选择算法.根据训练样本的规模和噪声水平等信息,确定支持向量回归参数的取值范围,用实数编码的免疫遗传算法搜索最佳参数值.混合选择算法具有较高的精度和效率,在选择支持向量回归参数时,不必考虑模型的复杂度和变量维数.仿真实验结果表明,该算法是选择支持向量回归参数的有效方法,应用到函数逼近问题时具有优良的性能.