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Optimizing multivariate alarm systems: A study on joint false alarm rate, and joint missed alarm rate using linear programming technique

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PROCESS SAFETY AND ENVIRONMENTAL PROTECTION 2024年 191卷 1775-1783页

作者： Taheri-Kalani, J. Latif-Shabgahi, Gh. Shoorehdeli, M. Aliyari Lorestan Univ Dept Elect Elect Engn Khorramabad Iran Shahid Beheshti Univ Dept Elect Engn Tehran Iran KN Toosi Univ Dept Elect Engn Tehran Iran

In modern complex industrial systems, multiple process variables interact with one another. The role of alarm systems in ensuring the safety of these systems is of utmost importance. Consequently, there is an increasing value placed on the assessment of the performance of multivariate alarm systems. As the dimensions of the system and the number of variables grow, designing optimal parameters for the multivariate alarm system using traditional approaches such as probability density function estimation becomes increasingly convoluted. In this paper, an approximate method is proposed for calculating two indices known as the Joint False Alarm Rate (JFAR) and Joint Missed Alarm Rate (JMAR), which are used to evaluate the performance of multivariate alarm systems. These indices are computed using the multivariate Markov chain method. The Markov chain is constructed by solving an optimal linear programming (LP) problem. Subsequently, joint indices are defined based on steady state estimations of a multivariate Markov chain. To validate the theoretical results obtained on the JFAR and JMAR and to demonstrate the proposed performance assessment and alarm system design procedures, numerical example and an industrial case study are provided.

关键词： Multivariate alarm systems Joint false alarm rate Joint missed alarm rate Multivariate Markov chain linear programming problem

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A Novel Neurodynamic Model for Data Envelopment Analysis: A Case Study on Iran's Olympic Sports Caravan

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NEURAL PROCESSING LETTERS 2023年第9期55卷 12079-12092页

作者： Hassan, Javad Bani Mirzazadeh, Zahra Sadat Abdi, Shahram Eshaghnezhad, Mohammad Mansoori, Amin Ferdowsi Univ Mashhad Fac Sport Sci Mashhad Iran Shahid Sattari Univ Aeronaut Sci & Technol Fac Basic Sci Dept Appl Math Tehran Iran Ferdowsi Univ Mashhad Dept Appl Math Mashhad Iran Mashhad Univ Med Sci Int UNESCO Ctr Hlth Related Basic Sci & Human Nutr Mashhad Iran

Data envelopment analysis (DEA) is one of the non-parametric approaches for evaluating efficiency. The present paper investigates a novel recurrent neural network (RNN) model for solving DEA problems. To the best of our knowledge, there is no attempt for this kind of problem using RNN. Thus, this paper is going to show the effectiveness of RNN models for solving DEA problems. As a matter of fact, we give a novel RNN model to solve a general linear programming problem. Moreover, the stability in the sense of Lyapunov for the developed RNN model is proved. Finally, to show the performance of the method we consider a general case model and a case study on Iran's Olympic Sports Caravan and solve with the novel proposed RNN model.

关键词： linear programming problem Data envelopment analysis Recurrent neural networks Lyapunov stability

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Polynomial time decision algorithms for probabilistic automata

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INFORMATION AND COMPUTATION 2015年 244卷 134-171页

作者： Turrini, Andrea Hermanns, Holger Chinese Acad Sci Inst Software State Key Lab Comp Sci Beijing Peoples R China Univ Saarland Comp Sci D-66123 Saarbrucken Germany

Deciding in an efficient way weak probabilistic bisimulation in the context of probabilistic automata is an open problem for about a decade. In this work we close this problem by proposing a procedure that checks in polynomial time the existence of a weak combined transition satisfying the step condition of the bisimulation. This enables us to arrive at a polynomial time algorithm for deciding weak probabilistic bisimulation, and also branching probabilistic bisimulation. We furthermore present several extensions to interesting related problems, in particular weak and branching probabilistic simulation, setting the ground for the development of more effective and compositional analysis algorithms for probabilistic systems. (C) 2015 Elsevier Inc. All rights reserved.

关键词： Probabilistic automata Weak probabilistic bisimulation Branching probabilistic bisimulation Weak probabilistic simulation Branching probabilistic simulation linear programming problem Polynomial decision algorithm

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Delay-dependent stability and stabilisation of two-dimensional positive Markov jump systems with delays

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IET CONTROL THEORY AND APPLICATIONS 2017年第10期11卷 1603-1610页

作者： Le Van Hien Hieu Trinh Deakin Univ Sch Engn Geelong Vic 3217 Australia Hanoi Natl Univ Educ Dept Math Hanoi Vietnam

This study considers the problem of exponential mean stability and stabilisation of two-dimensional positive Markov jump systems with delays. Necessary and sufficient delay-dependent conditions for exponential mean stability of the closed-loop system are first derived. Then, a design scheme based on a linear programming problem is proposed for obtaining parameters of a mode-dependent controller that makes the closed-loop system positive and exponentially mean stable. Finally, two numerical examples are presented to illustrate the effectiveness of the obtained results.

关键词： delays stochastic systems closed loop systems linear programming asymptotic stability Markov processes mode-dependent controller linear programming problem closed-loop system exponential mean stability Markov jump systems delay-dependent stability

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Eliciting dual interval probabilities from interval comparison matrices

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INFORMATION SCIENCES 2012年 190卷 17-26页

作者： Guo, Peijun Wang, Yuanbin Yokohama Natl Univ Fac Business Adm Hodogaya Ku Yokohama Kanagawa 2408501 Japan

In recent years, dealing with uncertainty using interval probabilities, such as combination, marginalization, condition, Bayesian inferences, has received considerable attention. However, how to elicit interval probabilities from subjective judgment is still a fundamental problem in applications of interval probabilities. In this paper, interval-valued pairwise comparisons of events are used to characterize the judgment of a person about which one is more likely to occur between each pair of events. From the interval comparison matrix, we elicit the dual interval probabilities by linear programming problems. The ratios of the estimated interval probabilities are used to approximate the interval comparison values from the outside and the inside of them. In other words, the inclusion relations between the interval comparison values and the ratios of the obtained interval probabilities hold. A numerical example concerning a new product development is presented to illustrate how to estimate dual interval probabilities and use interval probabilities to make a decision. (C) 2011 Elsevier Inc. All rights reserved.

关键词： Interval probabilities Uncertainty modeling linear programming problem

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Optimisation-based deployment of beacons for indoor positioning using wireless communications and signal power ranking

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IET COMMUNICATIONS 2020年第17期14卷 2915-2923页

作者： Chang, Ching-Lung Chang, Chuan-Yu Chen, Shuo-Tsung Syu, Jhe-Ming Natl Yunlin Univ Sci & Technol Dept Comp Sci & Informat Engn Touliu 64002 Yunlin Taiwan Natl Yunlin Univ Sci & Technol Intelligence Recognit Ind Serv Res Ctr Touliu 64002 Yunlin Taiwan

Beacon-based indoor positioning is popular in recent years. In this work, the authors aim to enhance the positioning accuracy by proposing signal power ranking (SPR) and solving related optimisation-based deployment problem of beacons using wireless communication and Bluetooth 4.0 Bluetooth low-energy network technologies. The authors first adopt grid-based field to be the proposed deployment field. Second, they convert the received signal strength indicator (RSSI) to several levels called SPR. Third, an optimisation-based model for deployment problem of beacons in indoor positioning is proposed on the basis of the above two considerations. The proposed model is to minimise the number of beacons required under some fundamental conditions including full coverage and full discrimination, respectively. Finally, the algorithm of simulated annealing is applied to solve the linear programming problem in this model. By the optimal results, the user can obtain a vector table of RSSI for each location efficiently in the test field. On the other hand, the user in the test field can receive the beacon RSSI value at the same time. In order to determine the user's location, the received beacon RSSI value is compared with the values in the vector table.

关键词： linear programming Bluetooth Global Positioning System simulated annealing vectors wireless communication signal power ranking beacon-based indoor positioning positioning accuracy SPR grid-based field deployment field received signal strength indicator optimisation-based model linear programming problem test field received beacon RSSI value Bluetooth 4 0 low-energy network technologies simulated annealing vector table

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A SIMPLE VARIANT OF THE MIZUNO-TODD-YE PREDICTOR-CORRECTOR ALGORITHM AND ITS OBJECTIVE-FUNCTION-FREE COMPLEXITY

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SIAM JOURNAL ON OPTIMIZATION 2013年第3期23卷 1890-1903页

作者： Kitahara, Tomonari Tsuchiya, Takashi Tokyo Inst Technol Grad Sch Decis Sci & Technol Meguro Ku Tokyo 1528552 Japan Natl Grad Inst Policy Studies Minato Ku Tokyo 1068677 Japan

In this paper, we propose a simple variant of the Mizuno-Todd-Ye predictor-corrector algorithm for linear programming. Our variant employs a simple and a natural scaling-invariant search direction aiming at finite-termination, and, even if finite-termination fails, the same direction is occasionally used instead of the ordinary predictor step. Our algorithm is scaling-invariant, is easy to implement, and enjoys an objective-function-free polynomial-time complexity for a linear program with bounded feasible region.

关键词： linear programming problem interior point method layered least squares interior point method iteration complexity strong polynomiality

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APPLICATION OF SPHERE PACKING THEORY IN FINANCIAL MANAGEMENT

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JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION 2023年第5期19卷 3436-3443页

作者： Chuluunbaatar, Ankhbayar Galaa, Burmaa Rentsen, Enkhbat Natl Univ Mongolia Sch Business Ulaanbaatar 14192 Mongolia Mongolian Acad Sci Inst Math & Digital Technol Ulaanbaatar 13330 Mongolia

The paper illustrates an application of sphere packing theory based on the capital structure of financial management. The entire process is mod-elled as a new optimization problem formulated as the sphere packing prob... 详细信息

关键词： Financial ratios capital structure linear programming problem

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Shape Optimization of a Nozzle with Specified Flow Field Including Viscosity Effect

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ACTA APPLICANDAE MATHEMATICAE 2008年第3期104卷 243-256页

作者： Farhadinia, B. Farahi, M. H. Esfahani, J. A. Univ Mohaghegh Ardabili Dept Math Ardebil Iran Ferdowsi Univ Mashhad Mashhad Iran

In this article we intend to find the optimal shape of a nozzle respecting to some given target flow fields including viscosity effect. Via an approach based on measure theory which is not an iterative method and need not to any initial guess, each shape optimization problems are solved and consequently each geometry of the nozzle corresponding to prescribed flow fields is determined. Analyzing several case studies make us to confident on the use of the presented approach, because the obtained results give entirely the same as what we expect physically.

关键词： Navier-Stokes equations Optimal shape design (OSD) Optimal control Measure theory linear programming problem

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Solution of matrix games with rough interval pay-offs and its application in the telecom market share problem

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INTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS 2021年第10期36卷 6066-6100页

作者： Seikh, Mijanur R. Dutta, Shibaji Li, Deng-Feng Kazi Nazrul Univ Dept Math Asansol 713340 W Bengal India Univ Elect Sci & Technol China Sch Management & Econ Chengdu Peoples R China

Rough interval (RI) is an appropriate generalization of the crisp interval and is very much useful to express uncertain parameters or partially unknown variables when they contain dual-layer information. In real-life problems, there are many situations where players of a matrix game cannot assess their pay-offs by using fuzzy sets/intuitionistic fuzzy sets or ordinary intervals. RIs are used as an excellent tool to handle such situations. This paper explores matrix games with RI pay-offs and investigates two different solution methodologies to solve such a game. In the first approach, a pair of auxiliary linear programming problems with RI coefficients for the players has been constructed. Then each of the two auxiliary programming problems is converted into two linear programming problems with interval coefficients (LPPICs) using lower and upper approximation intervals of the RI. Finally from each LPPIC, two classical linear programming problems (LPPs) are constructed. In the second approach, the expected value technique for RI is used for transforming auxiliary mathematical programming models under the RI environment to crisp LPP. A case study on the telecom market share problem is considered to show the applicability of the proposed approaches and results are compared and analyzed with an existing method.

关键词： expected value linear programming problem matrix game rough interval

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