基于泡沫尺寸随机分布的铜粗选药剂量控制

为了稳定铜粗选选矿指标,提高矿产资源的利用水平, 根据铜粗选过程中泡沫尺寸分布随药剂量改变而动态变化的特点, 提出一种基于泡沫尺寸随机分布的铜粗选过程药剂量控制方法.首先, 针对泡沫尺寸分布具有非高斯统计特性, 基于方差和均值的统计参量难以表征该分布形态变化的问题, 提出了B样条估计方法以描述泡沫尺寸的概率密度函数(Probability density function, PDF); 然后, 针对B 样条权值相互关联的特点, 建立多输出最小二乘支持向量机模型(Multi-output least square support vector machine, MLS-SVM)以表征权值和药剂量的动态关系; 最后, 为减少系统的随机性, 采用基于熵的优化算法以确定药剂量, 实现对给定泡沫尺寸分布的跟踪控制.工业数据仿真验证了所提方法的有效性, 能有效稳定铜粗浮选的生产指标.     

Combined fuzzy based feedforward and bubble size distribution based feedback control for reagent dosage in copper roughing process

A combined fuzzy based feedforward (FBF) and bubble size distribution (BSD) based feedback reagent dosage control strategy is proposed to implement the product indices in copper roughing process. A fuzzy theory based feedforward compensator will be used to calculated the reagent dosage in advance to eliminate the influence of large disturbances according to ore grade and handling capacity. Since the bubble size is believed to be closely related to flotation performance and responds to changes in the reagent dosage, using BSD based feedback predictive control calculates the reagent dosage to stabilize the flotation running. Instead of simple statistic feature, the bubble size with non-Gaussian feature is characterized to be probability density function (PDF) by using B-spline. A multi-output least square support vector machine (MLS-SVM) based is then applied to establish a dynamical relationship between the weights of B-spline and the reagent dosage since the weights are interrelated and related to the reagent dosage. A multiple step based optimization algorithm is finally proposed to determine the reagent dosage. Experimental results can show the effectiveness of the proposed method.     

基于输出PDF的浮选故障检测和诊断方法

针对浮选中泡沫尺寸分布的特殊性,如非高斯分布,左偏斜,高峰值等,常规分析方法无法准确描述尺寸分布的特点,因此无法准确检测和诊断浮选过程中出现的故障。提出对泡沫尺寸分布的输出概率密度函数(PDF)的统计分析,形成了一种新的浮选过程故障检测和诊断方法。通过采用自设计的核方法逼近将输出PDF转化为动态权系数,建立带有时滞的非线性不确定性权动态模型,基于线性矩阵不等式设计得到可行的故障检测和诊断算法。通过仿真验证分析,证明此算法的有效性。结合现场浮选过程,讨论了此方法的应用前景和优势。     

Multi-step Predictive Control of a PDF-shaping Problem

A predictive control strategy is proposed for the shaping of the output probability density function (PDF) of linear stochastic systems. The B-spline neural network is used to set up the output PDF model and therefore converts the PDF-shaping into the control of B-spline weights vector. The Diophantine equation is then introduced to formulate the predictive PDF model, based on which a moving-horizon control algorithm is developed so as to realize the predictive PDF tracking performance.     

输出概率密度函数形状的多步预测控制

A predictive control strategy is proposed for the shaping of the output probability density function (PDF) of linear stochastic systems. The B-spline neural network is used to set up the output PDF model and therefore converts the PDF-shaping into the control of B-spline weights vector. The Diophantine equation is then introduced to formulate the predictive PDF model, based on which a moving-horizon control algorithm is developed so as to realize the predictive PDF tracking performance.     

Shaping of Output PDF Based on the Rational Square-root B-spline Model

This paper presents a new method for the modeling and control of the output probability density functions (PDFs) of linear stochastic systems.At first,a new PDF approximation method, namely the rational square-root B-spline model is proposed and the innovative concept of pseudo- weights is introduced.The new model is then compared with the existing B-spline models in terms of feasible domains.Next,a controller is developed to realize the output PDF tracking performance. An alternative minimal entropy control strategy is also provided for the case that no target PDF is available.Finally,illustrative examples indicate the effectiveness of the proposed algorithms.     

Minimum entropy of B-spline PDF systems with mean constraint

For the B-spline approximation of the continuous probability density function (PDF), the relationships between the B-spline weights and entropy both in general and under the mean constraint have been analyzed. It provides the conditions under which the minimum entropy can be achieved subject to the mean constraint. The difference between the entropy of continuous and discrete distributions has also been clarified. A minimum entropy controller with the mean constraint is then developed and several simulations are performed to verify the main results.     

基于LMI的参数随机变化系统的概率密度函数控制

针对模型参数在有界区域内随机变化的系统, 基于平方根 B 样条模型, 提出了输出概率密度函数 (Probability density function, PDF) 跟踪控制策略. 目标是控制系统输出的概率密度函数跟踪给定的概率密度函数. 通过 B 样条逼近建立了输出 PDF 和权值之间的对应关系, 把 PDF 的跟踪转化为权值的跟踪, 同时系统转化为 MIMO 系统,从而权值向量的跟踪就转化为 MIMO 系统的跟踪问题, 接着给出了系统输出概率密度函数跟踪给定概率密度函数的控制器存在的充分条件, 通过求解线性矩阵不等式完成状态反馈和输出反馈跟踪控制器的设计, 得到了系统具有 Hinfinity 范数界 Gamma 鲁棒镇定的结果. 仿真结果表明本文提出的控制算法是有效的.     

Statistic PID tracking control for non-Gaussian stochastic systems based on T-S fuzzy model

A new robust proportional-integral-derivative （PID） tracking control framework is considered for stochastic systems with non-Gaussian variable based on B-spline neural network approximation and T-S fuzzy model identification. The tracked object is the statistical information of a given target probability density function （PDF）, rather than a deterministic signal. Following B-spline approximation to the integrated performance function, the concerned problem is transferred into the tracking of given weights. Different from the previous related works, the time delay T-S fuzzy models with the exogenous disturbances are applied to identify the nonlinear weighting dynamics. Meanwhile, the generalized PID controller structure and the improved convex linear matrix inequalities （LMI） algorithms are proposed to fulfil the tracking problem. Furthermore, in order to enhance the robust performance, the peak-to-peak measure index is applied to optimize the tracking performance. Simulations are given to demonstrate the efficiency of the proposed approach.     

PID controller design for output PDFs of stochastic systems using linear matrix inequalities

This paper presents a pseudo proportional-integral-derivative (PID) tracking control strategy for general non-Gaussian stochastic systems based on a linear B-spline model for the output probability density functions (PDFs). The objective is to control the conditional PDFs of the system output to follow a given target function. Different from existing methods, the control structure (i.e., the PID) is imposed before the output PDF controller design. Following the linear B-spline approximation on the measured output PDFs, the concerned problem is transferred into the tracking of given weights which correspond to the desired PDF. For systems with or without model uncertainties, it is shown that the solvability can be casted into a group of matrix inequalities. Furthermore, an improved controller design procedure based on the convex optimization is proposed which can guarantee the required tracking convergence with an enhanced robustness. Simulations are given to demonstrate the efficiency of the proposed approach and encouraging results have been obtained.     

基于泡沫大小动态分布的浮选生产过程加药量健康状态分析

针对矿物浮选过程泡沫大小分布随着药剂量的改变而动态变化的特点,提出一种基于泡沫大小动态分布特征的具有自学习功能的浮选生产过程加药量健康状态统计模式识别方法.首先,通过泡沫图像分割、气泡尺寸分布核密度估计获得浮选气泡大小的概率密度分布函数,采用无监督的最远邻聚类方法获得典型药剂量添加状态下的气泡尺寸统计分布特征集;然后,采用简单的贝叶斯推理方法获得测试时间段对应的药剂添加健康状态分析识别结果,并根据浮选生产工况状态的动态变化对各典型药剂状态下的气泡大小统计分布特征集进行在线学习修正.实验结果表明,所提出方法能实时获取泡沫尺寸分布的动态变化,实现浮选药剂操作健康状态的自动识别与评价,为进一步实现浮选生产过程的加药量优化控制奠定了基础.     

Constrained discrete-time PI controller design for output PDFs of stochastic systems with time delays

This article presents a new proportional-integral (PI) tracking control strategy for non-Gaussian stochastic systems based on a square root B-spline model for the output probability density functions (PDFs). Following the square root B-spline approximation to the measured output PDF, a non-linear discrete-time dynamical model can be established between the control input and the weights related to the PDFs. It is noted that the PDF tracking is transformed to a constrained dynamical tracking control problem for weight dynamics. For the non-linear discrete-time weight model including time-delay terms and exogenous disturbances, convex linear matrix inequality optimisation algorithms are used to design a generalised PI controller such that stabilisation, state constraint and tracking performance can be guaranteed simultaneously. Furthermore, in order to enhance the robustness, the peak-to-peak measure index is applied to optimise the tracking performance. Simulations are given to demonstrate the efficiency of the proposed approach.     

基于有理平方根B样条模型的概率密度函数形状控制

This paper presents a new method for the modeling and control of the output probability density functions (PDFs) of linear stochastic systems. At first, a new PDF approximation method, namely the rational square-root B-spline model is proposed and the innovative concept of pseudoweights is introduced. The new model is then compared with the existing B-spline models in terms of feasible domains. Next, a controller is developed to realize the output PDF tracking performance. An alternative minimal entropy control strategy is also provided for the case that no target PDF is available. Finally, illustrative examples indicate the effectiveness of the proposed algorithms.     

Fault diagnosis and fault tolerant control for non-Gaussian time-delayed singular stochastic distribution systems

Stochastic distribution control (SDC) is a new branch of stochastic system control that the system output is the probability density function (PDF) of the output. In practice, some algebraic relations exist between the input and the weights of SDC systems, leading to a singular state space model between the weights and the control input which increases the complexity of the system. The ignorance of time delay in practical systems will make the effectiveness of the fault diagnosis (FD) and fault tolerant control (FTC) be reduced. In this paper, the linear B-spline basis functions are used to approximate the output PDF. A FD approach based on the adaptive observer is established to diagnose the size of fault in the singular time-delayed SDC system. With the fault diagnosis information, a fault tolerant controller based on PI tracking control scheme is constructed to make the post-fault PDF still track the given distribution. The post-fault closed-loop stability analysis with the practical fault tolerant controller is carried out based on the Lyapunov stability theorem. Finally, a numerical simulation is provided to demonstrate the effectiveness of the proposed approach.     

Stochastic controller as an active queue management based on B-spline kernel observer via particle swarm optimization

Given the fact that the current Internet is getting more difficult in handling the traffic congestion control, the proposed method is compatible with the stochastic nature of network dynamics. Most conventional active queue management is based on the first stochastic moment. In stochastic theory, the first moment is not efficient for non-Gaussian systems that are the same as the network queue size. We propose a new stochastic active queue management technique, based on stochastic control and B-spline window observer, called intelligent probability density function AQM (IPDF-AQM). The IPDF-AQM is based on a PDF control and particle swarm optimization, which not only considers the average queue length at the current time slot, but also takes into consideration the PDF of queue lengths within a round-trip time. We provide a guideline for the selection of the probability of dropping as control input for TCP/AQM system to make the PDF of queue length converge at a certain PDF target based on B-spline approximation and improve the network performance. Simulation results show that the proposed stochastic AQM scheme does improve the end-to-end performance.     

Stochastic Distribution Control of Singular Systems: Output PDF Shaping

This paper presents a new algorithm designed to control the shape of the output probability density function (PDF) of singular systems subjected to non-Gaussian input. The aim is to select a control input uk such that the output PDF is made as close as possible to a given PDF. Based on the B-spline neural network approximation of the output PDF, the control algorithm is formulated by extending the developed PDF control strategies of non-singular systems to singular systems. It has been shown that under certain conditions the stability of the closed-loop system can be guaranteed. Simulation examples are given to show the effectiveness of the proposed control algorithm.     

基于有理平方根逼近的非高斯随机分布系统的故障诊断和容错控制

随机分布系统指的是输入为常规向量而输出为系统输出的概率密度函数所描述的一类随机系统．该类系统控制算法的目标是选择一个控制输入使得系统的实际输出概率密度函数尽可能跟踪一个事先给定的概率密度函数．本文对采用有理平方根B样条逼近其输出概率密度函数的非高斯动态随机分布系统,提出了一种基于非线性自适应观测器的故障诊断方法．该方法可快速有效地诊断出非高斯随机分布系统故障．通过对故障系统的重组,使故障后系统的输出概率密度函数仍能跟踪给定的分布,实现了该随机系统的容错控制,提高了随机系统的可靠性．     

Multi-objective PID control for non-Gaussian stochastic distribution system based on two-step intelligent models

A new method for controlling the shape of the conditional output probability density function (PDF) for general nonlinear dynamic stochastic systems is proposed based on B-spline neural network (NN) model and T-S fuzzy model. Applying NN approximation to the measured PDFs, we transform the concerned problem into the tracking of given weights. Meanwhile, the complex multi-delay T-S fuzzy model with exogenous disturbances, parametric uncertainties and state constraints is used to represent the nonlinear weigh...     

Fault diagnosis and fault-tolerant control for non-Gaussian nonlinear stochastic systems via entropy optimisation

ABSTRACT

In this paper, the fault diagnosis (FD) and fault tolerant control (FTC) problems are studied for non-linear stochastic systems with non-Gaussian disturbance and fault. Unlike classical FD algorithms, the minimum entropy FD is adopted to minimise the residual entropy and control the shape of the probability density function (PDF) of the residual signal. The observation error system can be proved to be locally and ultimately bounded in the mean square sense. Since entropy can be used to characteriSe the uncertainty of the tracking error for non-Gaussian stochastic systems, the FTC controller is obtained by minimising the performance function with regard to the entropy of the tracking error in this paper. The PDF of the output tracking error is approximated by the B-spline model. An illustrative example is utilised to demonstrate the effectiveness of the FD and FTC algorithm, and satisfactory results have been obtained.     

A new froth image classification method based on the MRMR-SSGMM hybrid model for recognition of reagent dosage condition in the coal flotation process

Intelligent separation is a core technology in the transformation, upgradation, and high-quality development of coal. Realising the intelligent recognition and accurate classification of coal flotation froth is a key technology of intelligent separation. At present, the coal flotation process relies on artificial recognition of froth features for adjusting the reagent dosage. However, owing to the low accuracy and subjectivity of artificial recognition, some problems arise, such as reagent wastage and unqualified product quality. Thus, this paper proposes a new froth image classification method based on the maximal-relevance-minimal-redundancy (MR MR)-semi-supervised Gaussian mixture model (SSGMM) hybrid model for recognition of reagent dosage condition in the coal flotation process. First, the features of morphology, colour, and texture are extracted, and the optimal froth image features are screened out using the maximal-relevance-minimal-redundancy (MRMR) feature selection algorithm based on class information. Second, the traditional GMM clusterer is improved, called SSGMM, by introducing a small number of marked samples, the traditional GMM’ problems of unclear training goals, invisible clustering results, and artificially judged clustering results are solved. Then a new hybrid classification model is proposed by combining the MRMR with the modified GMM (SSGMM) which can be named as (MRMR - SSGMM). The optimal froth image features are screened by MRMR to provide the SSGMM classifier. In the process of training and learning the feature samples, using the marked feature samples of froth images to guide the unmarked feature samples. The information of marked feature samples of froth images is mapped to the unmarked feature samples, the classification of the froth images were realised. Finally, the accuracy of the SSGMM classifier is used as the evaluation criterion for the screened features by MRMR. By automatically executing the entire learning process to find the best number of froth image features and the optimal image features, so that the classifier achieves the maximum classification accuracy. Experimental results show that the proposed classification method achieves the best results in accuracy and time, compared with other benchmark classification methods. Application results show that the method can provide reliable guidance for the adjustment of the reagent dosage, realize the accurate and timely control of the reagent dosage, reduce the consumption of the reagent and the incidence of production accidents, and stabilize the product quality in the coal flotation production process.