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On-line principal component analysis with application to process modeling

NEUROCOMPUTING 2012年 82卷 167-178页

作者： Tang, Jian Yu, Wen Chai, Tianyou Zhao, Lijie Northeastern Univ State Key Lab Synthet Automat Proc Ind Shenyang 110004 Peoples R China IPN CINVESTAV Dept Automat Control Mexico City 07360 DF Mexico Northeastern Univ Ctr Automat Res Shenyang 110004 Peoples R China Shenyang Inst Chem Technol Coll Informat Engn Shenyang 110142 Peoples R China

Principal component analysis (PCA) has been widely applied in process monitoring and modeling. The time-varying property of industrial processes requires the adaptive ability of the PCA. This paper introduces a novel PCA algorithm, named on-line PCA (OLPCA). It updates the PCA model according to the process status. The approximate linear dependence (ALD) condition is used to check each new sample. A recursive algorithm is proposed to reconstruct the PCA model with selected samples. Three types of experiments, a synthetic data, a benchmark problem, and a ball mill load experimental data, are used to illustrate our modeling method. The results show that the proposed OLPCA is computationally faster, and the modeling accuracy is higher than conventional moving window PCA (MWPCA) and recursive PCA (RPCA) for time-varying process modeling. (c) 2011 Elsevier By. All rights reserved.

关键词： Principal component analysis recursive algorithm On-line modeling Process modeling

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Modeling of a new telerobot

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MULTIBODY SYSTEM DYNAMICS 2001年第4期6卷 343-353页

作者： Schlotter, A Pfeiffer, F Tech Univ Munich Lehrstuhl Mech B D-85747 Garching Germany

This paper deals with the modeling of a robot with a new kinematic design. All joint movements in this robot are transmitted via concentric tubes and bevel gears. D'Alembert's principle is used to derive the equations of motion for rigid and elastic models, considering the elastic deflections of the arms and inner tubes. Implementing the recursive algorithm, both symbolical and numerical methods were tested. The advantages and problems are discussed. In order to verify the model, simulation results are compared with measurements.

关键词： robotics modeling elastic multibody systems recursive algorithm symbolic programming numerical programming

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Scattered data interpolation based upon bivariate recursive polynomials

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2018年 329卷 223-243页

作者： Qian, Jiang Wang, Fan Zhu, Chungang Hohai Univ Coll Sci Nanjing 211100 Jiangsu Peoples R China Nanjing Agr Univ Coll Engn Nanjing 210031 Jiangsu Peoples R China Dalian Univ Technol Sch Math Sci Dalian 116024 Peoples R China

In this paper, firstly, based on new recursive algorithms of non-tensor-product-typed bivariate divided differences, scattered data interpolation schemes are constructed in the cases of odd and even interpolating nodes, respectively. Moreover, the corresponding error estimation is worked out, and equivalent formulae are obtained between bivariate high order non-tensor-product-typed divided differences and high-order partial derivatives. Furthermore, the operation count for the addition/subtractions, multiplication, and divisions approximates O(n(2)) in the computation of the interpolating polynomials presented, while the operation count approximates O(n(3)) in the case of radial basis functions for sufficiently large n. Finally, several numerical examples show that it is valid for the recursive interpolating polynomial schemes, and these interpolating polynomials change as the order of the interpolating nodes, although the node collection is the same. (C) 2017 Elsevier B.V. All rights reserved.

关键词： Scattered data interpolation recursive algorithm Bivariate divided difference Non tensor product type Radial basis function

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CONTACT DYNAMICS OF A SPHERICAL JOINT AND A JOINTED TRUSS-CELL SYSTEM

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AIAA JOURNAL 1991年第1期29卷 81-88页

作者： TZOU, HS RONG, Y University of Kentucky Lexington Kentucky 40506

This paper presents a mathematical modeling and stochastic simulation study of a three-dimensional spherical joint, a design feature of importance to a class of deployable space structures. An analytical model of the joint including friction and clearance effects is studied, and a system equation with time-variant coefficient matrices is then derived. A parametric study, including joint clearance size, joint rigidity/damping, and link elasticity/damping, of a jointed truss-cell model is investigated. The friction is assumed to be a normally distributed random variable and the external excitation is also treated random in a stochastic simulation study using an auto-regressive moving average (ARMA) model. This study shows that the joint dynamic contacts are affected by joint surface condition (stiffness/damping), joint clearance, link stiffness/damping, excitation, etc. Friction contacts dominate the system dynamics when the clearance is small and normal contacts dominate when the clearance is large.

关键词： Trusses Contact Dynamics Space Structures Mathematical Models Elasticity Damping Coefficient Coefficient of Friction Stiffness Matrices recursive algorithm Flexible Structures

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Searching for d-MPs for All Level d in Multistate Two-Terminal Networks Without Duplicates

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IEEE TRANSACTIONS ON RELIABILITY 2021年第1期70卷 319-330页

作者： Bai, Guanghan Xu, Bei Chen, Xiaoguang Zhang, Yun-An Tao, Junyong Natl Univ Def Technol Lab Sci & Technol Integrated Logist Support Coll Intelligent Sci & Technol Changsha 410073 Peoples R China Nanchang HangKong Univ Sch Gen Aviat Nanchang 330063 Jiangxi Peoples R China China Aerodynam Res & Dev Ctr High Speed Aerodynam Inst Mianyang 621000 Sichuan Peoples R China

The reliability evaluation of multistate networks is primarily using minimal path (cut) vectors, namely d-MPs (d-MCs), which are the lower (upper) boundary vectors that satisfy the system demand d. The generation of all d-MPs (d-MCs) is an NP-hard problem. Thus, it is important to develop an efficient algorithm to search for d-MPs (d-MCs). Existing algorithms searching for d-MPs based on MPs all generate duplicate d-MP candidates, and extra steps are required to detect and remove those duplicates. In this article, we propose an improved algorithm to search for d-MPs for all d levels without generating duplicate d-MP candidates for two-terminal multistate networks. First, we discover and prove the mechanism of generating duplicate d-MP candidates based on MPs. Second, a novel method is proposed to prevent generating duplicate d-MP candidates. Third, an improved algorithm is developed by combining the proposed method to search for d-MPs without generating duplicate d-MP candidates for all d levels. Through computational experiments, it is found that the proposed algorithm is more efficient than existing algorithms for finding all d-MPs for all possible d values.

关键词： Duplicate d-minimal path (d-MP) candidates multistate networks MP vectors network reliability recursive algorithm

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EXPECTED TIME ANALYSIS OF A SIMPLE recursive POISSON RANDOM VARIATE GENERATOR

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COMPUTING 1991年第2期46卷 165-173页

作者： DEVROYE, L 1. School of Computer Science McGill University 805 Sherbrooke Street West H3A 2K6 Montreal Canada

We consider a well-known recursive method for generating Poisson random variables with parameter lambda, and show how it can be manipulated to produce random variates at an expected time cost of O(log log lambda). Despite the fact that the expected time is not uniformly bounded in lambda, the algorithm should prove useful for extremely large values of lambda because virtually all numerical problems associated with the evaluation of the factorial function are eliminated. The probabilistic analysis presented here is applicable in other situations as well, in which there are a random number of levels of recursion.

关键词： RANDOM VARIATE GENERATION POISSON DISTRIBUTION recursive algorithm EXPECTED TIME ANALYSIS PROBABILISTIC METHODS

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A sequential learning algorithm for online constructing belief-rule-based systems

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EXPERT SYSTEMS WITH APPLICATIONS 2010年第2期37卷 1790-1799页

作者： Zhou, Zhi-Jie Hu, Chang-Hua Yang, Jian-Bo Xu, Dong-Ling Chen, Mao-Yin Zhou, Dong-Hua Tsinghua Univ Dept Automat TNList Beijing 100084 Peoples R China High Tech Inst Xian Xian 710025 Shaanxi Peoples R China Univ Manchester Manchester Business Sch Manchester M15 6PB Lancs England

A belief rule base inference methodology using the evidential reasoning (RIMER) approach has been developed recently. A belief rule base (BRB). which can be treated as a more generalized expert system, extends traditional IF-THEN rules, but requires the assignment of some system parameters including rule weights, attribute weights, and belief degrees. These parameters need to be determined with care for reliable system simulation and prediction. Some off-line optimization models have been proposed, but it is expensive to train and re-train these models in particular for large-scale systems. Moreover, the recursive algorithms are also proposed to fine tune a BRB online. which require less calculation time and satisfy the real-time requirement. However, the earlier mentioned learning algorithms are all based on a predetermined structure of the BRB. For a complex system, prior knowledge may not be perfect, which leads to the construction of an incomplete or even inappropriate initial BRB structure. Also, too many rules in an initial BRB may lead to over fitting, whilst too few rules may result in under fitting. Consequently, such a BRB system may not be capable of achieving overall optimal performance. In this paper, we consider one realistic and important case where both a preliminary BRB structure and system parameters assigned to given rules can be adjusted online. Based on the definition of a new statistical utility for a belief rule as investigated in this paper, a sequential learning algorithm for online constructing more compact BRB systems is proposed. Compared with the other learning algorithms, a belief rule can be automatically added into the BRB or pruned from the BRB, and our algorithm can also satisfy the real-time requirement. In addition, our algorithm inherits the feature of RIMER, i.e., only partial input and output information is required, which could be either incomplete or vague, either numerical or judgmental, or mixed. In order to verify the effe

关键词： Belief rule base Expert system Evidential reasoning recursive algorithm Utility

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Modelling, performance evaluation and optimisation of (s, Q) retrial inventory system with partial backlogging demands: a GSPN approach

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EUROPEAN JOURNAL OF INDUSTRIAL ENGINEERING 2023年第4期17卷 529-569页

作者： Bazizi, Lydia Rahmoune, Fazia Lekadir, Ouiza Labadi, Karim Univ Bejaia Fac Exact Sci Res Unit LaMOS Modeling & Optimizat Syst Bejaia 06000 Algeria ECAM EPMI Quartz Lab Cergy Pontoise France

In this article, we model and analyse by using generalised stochastic Petri nets (GSPNs), an inventory system according to the (s, Q) replenishment policy, Poissonian batch arrivals in deterministic size n, immediate batch service and retrials. In out-of-stock situation, the arriving demands at the system join a limited orbit, if it is not full, and retry again after a random time exponentially distributed, following the classic retrial policy. However, in the case of a full orbit, these demands are definitively rejected from the system. We describe the dynamic of this inventory system using a two-dimensional continuous time Markov chain (CTMC), which expresses the inventory level and the number of demands in the orbit. Then, we recover the stationary distribution, using a recursive algorithm, from which we derive various performance measures. Finally, we investigate some numerical analysis of the reward-cost function induced by this model.

关键词： inventory control system (s, Q) policy generalised stochastic Petri nets GSPNs continuous time Markov chain CTMC recursive algorithm reward-cost function

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Cluster computing of mechanisms dynamics using recursive formulation

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MULTIBODY SYSTEM DYNAMICS 2008年第2期20卷 177-196页

作者： Malczyk, Pawel Fraczek, Janusz Warsaw Univ Technol Inst Aeronaut & Appl Mech PL-00665 Warsaw Poland

This paper presents the O(n) recursive algorithm for forward dynamics of closed loop kinematic chains adapted to parallel computations on a cluster of workstations. The Newton-Euler equations of motion are formulated in terms of relative coordinates. Closed loop kinematic chains are transformed into open loop chains by cut joint technique. Cut joint constraint and Lagrange multipliers are introduced to complete the equations of motion. Constraint stabilization is performed using the Baumgarte stabilization technique with application to multibody systems with large number of degrees of freedom. Numerical simulations are carried out to study the influence of the degrees of freedom of the multibody system on computational efficiency of the algorithm using the Message Passing Interface (MPI). We also consider the ways of minimization of communication overhead which has significant impact on efficiency in case of cluster computing.

关键词： recursive algorithm distributed computing closed loop constraint stabilization

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On the Distributions of Two Classes of Multiple Dependent Aggregate Claims

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Acta Mathematicae Applicatae Sinica 2008年第4期24卷 655-668页

作者： Rong-ming Wang Kam C. Yuen Li-xing Zhu School of Finance and Statistics East China Normal University Shanghai 200241 China Department of Statistics and Actuarial Science The University of Hong Kong Department of Mathematics Hongkong Baptist University Kowloon Tong Hong Kong

In this paper we examine two classes of correlated aggregate claims distributions, with univariate claim counts and multivariate claim sizes. Firstly, we extend the results of Hesselager [ASTIN Bulletin, 24： 19-32（1994）] and Wang ＆ Sobrero＇s [ASTIN Bulletin, 24：161-166 （1994）] concerning recursions for compound distributions to a multivariate situation where each claim event generates a random vector. Then we give a multivariate continuous version of recursive algorithm for calculating a family of compound distribution. Especially, to some extent, we obtain a continuous version of the corresponding results in Sundt [ASTIN Bulletin, 29：29-45 （1999）] and Ambagaspitiya [Insurance： Mathematics and Economics, 24：301-308 （1999）]. Finally, we give an example and show how to use the algorithm for aggregate claim distribution of first class to compute recursively the compound distribution.

关键词： Compound distribution recursive algorithm collective risk model aggregate claim distribution,absolutely continuous

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