Introduction to the Special Issue

In the model, each person in a large population chooses between two options, such as adhering to or not adhering to a social norm. People observe each others’ choices at random and adjust their adherence probabilities in imitative directions. It is known from earlier work that, under strong restrictions on the imitation, the distribution of adherence probabilities will either evolve upward toward a high adherence equilibrium or downward toward a low adherence equilibrium, depending on initial conditions. The intuition is that imitation leads to uniformity. Here we show that more general forms of imitation allow a much wider variety of outcomes. There can be a sizable number of equilibria and a variety of stability patterns. In mathematical form, the model is an interactive Markov chain.     

On the Generation of Timed Discrete Approximations for Continuous Systems

In this contribution we present two procedures to systematically derive timed discrete approximations from continuous models. Both methods are based on a rectangular state space partition and aim at mapping continuous dynamic behaviours described by ODE-systems with switched inputs onto timed state transition systems: In the first approach the transitions between the discrete states are determined by analysing the flow between rectangular cells of the state space. The second one uses numerical integration of the ODE-system between partitions of the boundaries of the cells. The application of both approaches is illustrated by a chemical process example. The paper discusses completeness and consistency properties of the approximation mappings as well as issues of accuracy and computational effort.     

图论在离散事件动态系统中的应用

运用图论方法和极大代数方法,研究了非强连通图中的强连通分支的最大圈长平均值与该图的赋权邻接矩阵的特征值之间的关系,并进一步证明了其等价性.     

Case studies in dynamic modelling of large-scale wastewater treatment plants

Several large-scale wastewater treatment plants have been modelled successfully using an extensive modelling library in the General Purpose Simulator, GPS-X. The mathematical models included all important processes on the selected wastewater treatment plants, i.e. primary sedimentation, activated sludge biokinetics and final clarification.The models have been used in different areas, such as: a)analysis of operational scenarios; b) determenation of sustained and peak capacity of plants(rated plant capacity) and c) investigation of plant expansion scenarios. Out of more than twenty documented cases four, involving simulation studies on large-scale wastewater plants are discussed.     

Performance Optimization of a Class of Discrete Event Dynamic Systems Using Calculus of Variations Techniques

We explore an approach involving the use of calculus of variations techniques for discrete event dynamic system (DEDS) performance optimization problems. The approach is motivated by the observation that such problems can be described by separable cost functions and recursive dynamics of the same form as that used to describe conventional discrete-time continuous-variable optimal control problems. Three important difficulties are that DEDS are generally stochastic, their dynamics typically involve max and min operations, which are not everywhere differentiable, and the state variables are often discrete. We demonstrate how to overcome these difficulties by applying the approach to a transportation problem, modeled as a polling system, where we are able to derive an explicit and intuitive analytic expression for an optimal control policy.     

Dynamics of Continuous,Discrete and Impulsive Systems Series B (Algorithm and Applications) A Special Issue on Financial Optimization Call For Papers

We invite quality papers that are solicited on issues of financial optimization with applications, i     

A Learning Algorithm for the Control of Continuous Action Set-Point Regulator Systems

The convergence properties for reinforcement learning approaches, such as temporal differences and Q-learning, have been established under moderate assumptions for discrete state and action spaces. In practice, however, many systems have either continuous action spaces or a large number of discrete elements. This paper presents an approximate dynamic programming approach to reinforcement learning for continuous action set-point regulator problems, which learns near-optimal control policies based on scalar performance measures. The continuous-action space (CAS) algorithm uses derivative-free line search methods to obtain the optimal action in the continuous space. The theoretical convergence properties of the algorithm are presented. Several heuristic stopping criteria are investigated and practical application is illustrated by two example problems—the inverted pendulum balancing problem and the power system stabilization problem.     

Strong Consistency of Bayes Estimates in Stochastic Regression Models

Under minimum assumptions on the stochastic regressors, strong consistency of Bayes estimates is established in stochastic regression models in two cases: (1) When the prior distribution is discrete, the p.d.f.fof i.i.d. random errors is assumed to have finite Fisher informationI=∫^∞_−∞(f′)²/f dx<∞; (2) for general priors, we assumefis strongly unimodal. The result can be considered as an application of a theorem of Doob to stochastic regression models.     

图书编校质量控制模型

建立了图书编校质量控制的统计模型,可用其讨论达到某种质量标准所需校对次数和对校对人员的素质要求,有助于制订量化的质量管理方案.     

Reduced order dynamic model of the flat-plate solar collector

Padé approximation techniques are applied to obtain a reduced order dynamic model for the partial differential system representing the dynamic behaviour of the flat-plate solar collector. According to a prespecified accuracy, the collector is divided into n sections. At any position along each section the reduced order dynamic model is decoupled second order state equation, the input of which is the output of the preceding section. Numerical solutions obtained from the reduced order dynamic model are in very close agreement with the exact solution. Moreover, the computational efforts as well as the computer storage requirements are considerably reduced in comparison with other methods.The results obtained from the dynamic model are compared with those based on a simple steady-state model. The comparison reveals that the steady-state expression may only be used for collectors having a low thermal inertia and a high fluid-stream heat capacity.     

大数据背景下水厂自动投矾模型研究

根据某市自来水有限责任公司第二水厂的历史矾耗数据，建立矾耗流量关于原水浊度、温度等的动态矾耗模型. 通过对数据进行处理得到10900个合格且净水效果高效的数据，将筛选出的数据分为训练样本集和测试样本集. 在回归拟合中，通过拟合R2的大小将原水浊度划分为“低浊”“中浊”“高浊”3个区间，利用泰勒展开公式的非线性变量代换分别对3个区间建立不同的多项式回归模型，得到预测正确率约为72%，总的矾耗流量值约减少了9.6%的结果；在随机森林模型中，使用10900个合格数据，利用训练样本集，以“原水浊度”“pH值”“原水流量”和“水温”为输入变量，建立包含2000棵决策树的随机森林模型，得到预测正确率约为44. 21%，总的矾耗流量值增加了0.04%的结果. 从模型对合格数据的拟合优度看，随机森林模型比非线性回归模型效果更好；在平均绝对误差、平均绝对偏差百分比等评价指标上，前者均优于后者；但从历史数据检验的结果，模型的可解读性，模型的操作难度和推广角度看，分段二元非线性回归模型的优势更为突出.     

Gearbox failure diagnosis based on vector autoregressive modelling of vibration data and dynamic principal component analysis

Email: mgt.liu{at}utoronto.ca Email: makis{at}mie.utoronto.ca Received on 4 August 2006. Accepted on 14 December 2006. An effective gearbox failure diagnosis helps prevent catastrophicgearbox failure and can contribute to significant economic benefits.This paper proposes a gear failure diagnosis method based onvector autoregressive modelling of high-frequency vibrationdata, dimensionality reduction applying dynamic principal componentanalysis (PCA) and condition monitoring using a multivariatecontrol chart. After extracting useful information from thevibration data obtained from distinct directions via dynamicPCA, a failure diagnosis scheme is implemented and tested usingreal gearbox vibration data. It is shown that the failure diagnosisscheme can indicate the gear teeth failure pattern when thegear is damaged, which has not been demonstrated in the previousstudies. For a comparison, PCA is applied to the same data set.The results show that the advantages of dynamic PCA over PCAfor failure diagnosis using vibration data consist not onlyin indicating more accurately the occurrence of incipient faultand the actual gear condition, but also in a much lower falsealarm rate.     

基于产业结构优化的节能减排离散动态演化模型

从中国能源环境现状出发,基于产业结构发展趋势及其演变规律,运用动态投入产出分析法,对现有数据进行分析,结合演化理论,提出能源消耗演化目标和污染排放演化目标,建立节能减排下的离散动态演化模型,深入探讨节能减排策略和优化产业结构方法.模型对中国2000-2008年的数据进行拟合检验,得出中国三次产业经济产值、中国能源消耗量及污染排放量,并将其与实际情况进行比较,从节能减排和产业结构优化两个方面给予实证分析.基于建立的模型,结合情景分析法对中国2015年的经济产值、能源消耗及污染排放进行预测并对预测结果进行演化情景分析为中国制定相应的节能减排策略、实现产业结构优化提供了理论依据,为中国实现能源环境可持续发展提供了一个全新的视角和路线.     

直接配置法求解连续铸钢过程中的最优控制问题

利用描述连续铸钢过程二冷区喷水控制下钢的热传导的半离散化模型 ,我们构造一包含温度梯度约束的最优控制问题 .针对此最优控制问题 ,采用直接配置法进行数值求解 ,得出相应的近似最优控制 .     

Regularized Adaptation of Fuzzy Inference Systems. Modelling the Opinion of a Medical Expert about Physical Fitness: An Application

This study presents a new approach to adaptation of Sugeno type fuzzy inference systems using regularization, since regularization improves the robustness of standard parameter estimation algorithms leading to stable fuzzy approximation. The proposed method can be used for modelling, identification and control of physical processes. A recursive method for on-line identification of fuzzy parameters employing Tikhonov regularization is suggested. The power of approach was shown by applying it to the modelling, identification, and adaptive control problems of dynamic processes. The proposed approach was used for modelling of human-decisions (experience) with a fuzzy inference system and for the fuzzy approximation of physical fitness with real world medical data.     

Improved Self-Feedback Gain in the Context Layer of a Modified Elman Neural Network

The use of a range of values for the self-feedback gains in the context layer of a modified Elman neural network is shown to reduce RMS error when modelling a non-linear dynamic system.     

基于FUDAN-CCDC模型对新冠肺炎的建模和确诊人数的预测

科学地预测疫情发展趋势对疫情防控至关重要.在新时滞动力学模型(TDD-NCP)的基础上,提出基于随机动力学的时滞卷积模型和离散卷积模型,并基于中国疾病预防控制中心的相关研究结果及公开数据以及Wallinga和Lipsitch的工作,反演出COVID-19的重要参数,拟合了武汉及上海市疫情发展趋势.     

Switching Control of Nonlinear Systems Based on the Quasi-ARX Model and the SVR Algorithm北大核心CSCD

该文基于改进的含有外部输入项的准线性自回归(准ARX)径向基函数(RBF)网络模型和支持向量回归(SVR)算法,提出了一种非线性切换控制方法.改进的准ARX模型非线性部分采用RBF网络.控制系统设计过程分为三个部分:首先,利用聚类方法确定模型的非线性参数;然后,采用线性SVR算法来解决控制系统的鲁棒性问题;接下来,基于控制误差给出切换判定函数,确定切换律给出控制序列.最后通过数值仿真验证了该方法的有效性.