Search results for: Markov Decision Process

Authors: Jong Woo Kim, Go Bong Choi, Sang Hwan Son, Dae Shik Kim, Jung Chul Suh, Jong Min Lee

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The Markov decision process (MDP) based methodology is implemented in order to establish the optimal schedule which minimizes the cost. Formulation of MDP problem is presented using the information about the current state of pipe, improvement cost, failure cost and pipe deterioration model. The objective function and detailed algorithm of dynamic programming (DP) are modified due to the difficulty of implementing the conventional DP approaches. The optimal schedule derived from suggested model is compared to several policies via Monte Carlo simulation. Validity of the solution and improvement in computational time are proved.

Keywords: Markov decision processes, Dynamic Programming, Monte Carlo simulation, Periodic replacement, Weibull distribution.

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Authors: Nam Lethanh, Bryan T. Adey

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In this paper, the potential use of an exponential hidden Markov model to model a hidden pavement deterioration process, i.e. one that is not directly measurable, is investigated. It is assumed that the evolution of the physical condition, which is the hidden process, and the evolution of the values of pavement distress indicators, can be adequately described using discrete condition states and modeled as a Markov processes. It is also assumed that condition data can be collected by visual inspections over time and represented continuously using an exponential distribution. The advantage of using such a model in decision making process is illustrated through an empirical study using real world data.

Keywords: Deterioration modeling, Exponential distribution, Hidden Markov model, Pavement management

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Authors: Ru-Shuo Sheu, Han-Hsin Chou, Te-Shyang Tan

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Considering a reservoir with periodic states and different cost functions with penalty, its release rules can be modeled as a periodic Markov decision process (PMDP). First, we prove that policy- iteration algorithm also works for the PMDP. Then, with policy- iteration algorithm, we obtain the optimal policies for a special aperiodic reservoir model with two cost functions under large penalty and give a discussion when the penalty is small.

Keywords: periodic Markov decision process, periodic state, policy-iteration algorithm.

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Authors: Rajneesh Sharma, M. Gopal

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Markov games are a generalization of Markov decision process to a multi-agent setting. Two-player zero-sum Markov game framework offers an effective platform for designing robust controllers. This paper presents two novel controller design algorithms that use ideas from game-theory literature to produce reliable controllers that are able to maintain performance in presence of noise and parameter variations. A more widely used approach for controller design is the H∞ optimal control, which suffers from high computational demand and at times, may be infeasible. Our approach generates an optimal control policy for the agent (controller) via a simple Linear Program enabling the controller to learn about the unknown environment. The controller is facing an unknown environment, and in our formulation this environment corresponds to the behavior rules of the noise modeled as the opponent. Proposed controller architectures attempt to improve controller reliability by a gradual mixing of algorithmic approaches drawn from the game theory literature and the Minimax-Q Markov game solution approach, in a reinforcement-learning framework. We test the proposed algorithms on a simulated Inverted Pendulum Swing-up task and compare its performance against standard Q learning.

Keywords: Reinforcement learning, Markov Decision Process, Matrix Games, Markov Games, Smooth Fictitious play, Controller, Inverted Pendulum.

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Authors: Viliam Makis, Farnoosh Naderkhani, Leila Jafari

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In this paper, we present a model and an algorithm for the calculation of the optimal control limit, average cost, sample size, and the sampling interval for an optimal Bayesian chart to control the proportion of defective items produced using a semi-Markov decision process approach. Traditional p-chart has been widely used for controlling the proportion of defectives in various kinds of production processes for many years. It is well known that traditional non-Bayesian charts are not optimal, but very few optimal Bayesian control charts have been developed in the literature, mostly considering finite horizon. The objective of this paper is to develop a fast computational algorithm to obtain the optimal parameters of a Bayesian p-chart. The decision problem is formulated in the partially observable framework and the developed algorithm is illustrated by a numerical example.

Keywords: Bayesian control chart, semi-Markov decision process, quality control, partially observable process.

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Authors: Boukelkoul Lahcen

Abstract:

The cumulative costs for O&M may represent as much as 65%-90% of the turbine's investment cost. Nowadays the cost effectiveness concept becomes a decision-making and technology evaluation metric. The cost of energy metric accounts for the effect replacement cost and unscheduled maintenance cost parameters. One key of the proposed approach is the idea of maintaining the WTs which can be captured via use of a finite state Markov chain. Such a model can be embedded within a probabilistic operation and maintenance simulation reflecting the action to be done. In this paper, an approach of estimating the cost of O&M is presented. The finite state Markov model is used for decision problems with number of determined periods (life cycle) to predict the cost according to various options of maintenance.

Keywords: Cost, finite state, Markov model, operation, maintenance.

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Authors: Oscar Vega Camacho, Andrea Vargas Guevara, Ellery Rowina Ariza

Abstract:

This paper presents the application of finite dynamic programming, specifically the "Markov Chain" model, as part of the decision making process of a company in the cosmetics sector located in the vicinity of Bogota DC. The objective of this process was to decide whether the company should completely reconstruct its wastewater treatment plant or instead optimize the plant through the addition of equipment. The goal of both of these options was to make the required improvements in order to comply with parameters established by national legislation regarding the treatment of waste before it is released into the environment. This technique will allow the company to select the best option and implement a solution for the processing of waste to minimize environmental damage and the acquisition and implementation costs.

Keywords: Decision making, Markov chain, optimization, wastewater.

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Authors: Nooshin Salari, Viliam Makis

Abstract:

In this paper, we propose a condition-based maintenance policy for multi-unit systems considering the existence of economic dependency among units. We consider a system composed of N identical units, where each unit deteriorates independently. Deterioration process of each unit is modeled as a three-state continuous time homogeneous Markov chain with two working states and a failure state. The average production rate of units varies in different working states and demand rate of the system is constant. Units are inspected at equidistant time epochs, and decision regarding performing maintenance is determined by the number of units in the failure state. If the total number of units in the failure state exceeds a critical level, maintenance is initiated, where units in failed state are replaced correctively and deteriorated state units are maintained preventively. Our objective is to determine the optimal number of failed units to initiate maintenance minimizing the long run expected average cost per unit time. The problem is formulated and solved in the semi-Markov decision process (SMDP) framework. A numerical example is developed to demonstrate the proposed policy and the comparison with the corrective maintenance policy is presented.

Keywords: Reliability, production, maintenance optimization, Semi-Markov Decision Process.

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Authors: Akram Khaleghei Ghosheh Balagh, Viliam Makis, Leila Jafari

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In this paper, we present a new maintenance model for a partially observable system subject to two failure modes, namely a catastrophic failure and a failure due to the system degradation. The system is subject to condition monitoring and the degradation process is described by a hidden Markov model. A cost-optimal Bayesian control policy is developed for maintaining the system. The control problem is formulated in the semi-Markov decision process framework. An effective computational algorithm is developed, illustrated by a numerical example.

Keywords: Partially observable system, hidden Markov model, competing risks, multivariate Bayesian control.

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Authors: R. Sharma, M. Gopal

Abstract:

This paper presents a new problem solving approach that is able to generate optimal policy solution for finite-state stochastic sequential decision-making problems with high data efficiency. The proposed algorithm iteratively builds and improves an approximate Markov Decision Process (MDP) model along with cost-to-go value approximates by generating finite length trajectories through the state-space. The approach creates a synergy between an approximate evolving model and approximate cost-to-go values to produce a sequence of improving policies finally converging to the optimal policy through an intelligent and structured search of the policy space. The approach modifies the policy update step of the policy iteration so as to result in a speedy and stable convergence to the optimal policy. We apply the algorithm to a non-holonomic mobile robot control problem and compare its performance with other Reinforcement Learning (RL) approaches, e.g., a) Q-learning, b) Watkins Q(λ), c) SARSA(λ).

Keywords: Markov Decision Process (MDP), Mobile robot, Policy iteration, Simulation.

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Authors: Leila Jafari, Viliam Makis, Akram Khaleghei G.B.

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In this paper, we present a maintenance model of a two-unit series system with economic dependence. Unit#1 which is considered to be more expensive and more important, is subject to condition monitoring (CM) at equidistant, discrete time epochs and unit#2, which is not subject to CM has a general lifetime distribution. The multivariate observation vectors obtained through condition monitoring carry partial information about the hidden state of unit#1, which can be in a healthy or a warning state while operating. Only the failure state is assumed to be observable for both units. The objective is to find an optimal opportunistic maintenance policy minimizing the long-run expected average cost per unit time. The problem is formulated and solved in the partially observable semi-Markov decision process framework. An effective computational algorithm for finding the optimal policy and the minimum average cost is developed, illustrated by a numerical example.

Keywords: Condition-Based Maintenance, Semi-Markov Decision Process, Multivariate Bayesian Control Chart, Partially Observable System, Two-unit System.

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Authors: Siliang Wang, Minghui Wang

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Many exist studies always use Markov decision processes (MDPs) in modeling optimal route choice in stochastic, time-varying networks. However, taking many variable traffic data and transforming them into optimal route decision is a computational challenge by employing MDPs in real transportation networks. In this paper we model finite horizon MDPs using directed hypergraphs. It is shown that the problem of route choice in stochastic, time-varying networks can be formulated as a minimum cost hyperpath problem, and it also can be solved in linear time. We finally demonstrate the significant computational advantages of the introduced methods.

Keywords: Markov decision processes (MDPs), stochastictime-varying networks, hypergraphs, route choice.

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Authors: Yi Yu, Lin Ma, Yong Sun, Yuantong Gu

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This paper presents a novel method for remaining useful life prediction using the Elliptical Basis Function (EBF) network and a Markov chain. The EBF structure is trained by a modified Expectation-Maximization (EM) algorithm in order to take into account the missing covariate set. No explicit extrapolation is needed for internal covariates while a Markov chain is constructed to represent the evolution of external covariates in the study. The estimated external and the unknown internal covariates constitute an incomplete covariate set which are then used and analyzed by the EBF network to provide survival information of the asset. It is shown in the case study that the method slightly underestimates the remaining useful life of an asset which is a desirable result for early maintenance decision and resource planning.

Keywords: Elliptical Basis Function Network, Markov Chain, Missing Covariates, Remaining Useful Life

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Authors: Jeng-Shin Sheu, Jenn-Kaie Lain, Tai-Kuo Woo, Jyh-Horng Wen

Abstract:

The least mean square (LMS) algorithmis one of the most well-known algorithms for mobile communication systems due to its implementation simplicity. However, the main limitation is its relatively slow convergence rate. In this paper, a booster using the concept of Markov chains is proposed to speed up the convergence rate of LMS algorithms. The nature of Markov chains makes it possible to exploit the past information in the updating process. Moreover, since the transition matrix has a smaller variance than that of the weight itself by the central limit theorem, the weight transition matrix converges faster than the weight itself. Accordingly, the proposed Markov-chain based booster thus has the ability to track variations in signal characteristics, and meanwhile, it can accelerate the rate of convergence for LMS algorithms. Simulation results show that the LMS algorithm can effectively increase the convergence rate and meantime further approach the Wiener solution, if the Markov-chain based booster is applied. The mean square error is also remarkably reduced, while the convergence rate is improved.

Keywords: LMS, Markov chain, convergence rate, accelerator.

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Authors: Chiung-Hui Chen

Abstract:

The Internet of Things (IoT) was designed for widespread convenience. With the smart tag and the sensing network, a large quantity of dynamic information is immediately presented in the IoT. Through the internal communication and interaction, meaningful objects provide real-time services for users. Therefore, the service with appropriate decision-making has become an essential issue. Based on the science of human behavior, this study employed the environment model to record the time sequences and locations of different behaviors and adopted the probability module of the hierarchical Hidden Markov Model for the inference. The statistical analysis was conducted to achieve the following objectives: First, define user behaviors and predict the user behavior routes with the environment model to analyze user purposes. Second, construct the hierarchical Hidden Markov Model according to the logic framework, and establish the sequential intensity among behaviors to get acquainted with the use and activity fabric of the intelligent environment. Third, establish the intensity of the relation between the probability of objects’ being used and the objects. The indicator can describe the possible limitations of the mechanism. As the process is recorded in the information of the system created in this study, these data can be reused to adjust the procedure of intelligent design services.

Keywords: Behavior, big data, hierarchical Hidden Markov Model, intelligent object.

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Authors: Chao Wang, Ting-Zhu Huang, Chen Jia

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In this paper, we present a simplified higher-order Markov chain model for multiple categorical data sequences also called as simplified higher-order multivariate Markov chain model.

Keywords: Higher-order multivariate Markov chain model, Categorical data sequences, Multivariate Markov chain.

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Authors: Miloš Šeda, Pavel Ošmera, Jindřich Petrucha

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In the queueing theory, it is assumed that customer arrivals correspond to a Poisson process and service time has the exponential distribution. Using these assumptions, the behaviour of the queueing system can be described by means of Markov chains and it is possible to derive the characteristics of the system. In the paper, these theoretical approaches are presented on several types of systems and it is also shown how to compute the characteristics in a situation when these assumptions are not satisfied

Keywords: Queueing theory, Poisson process, Markov chains.

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Authors: Abdelali Joumad, Abdelaziz Nasroallah

Abstract:

In unsupervised segmentation context, we propose a bi-dimensional hidden Markov chain model (X,Y) that we adapt to the image segmentation problem. The bi-dimensional observed process Y = (Y 1, Y 2) is such that Y 1 represents the noisy image and Y 2 represents a noisy supplementary information on the image, for example a noisy proportion of pixels of the same type in a neighborhood of the current pixel. The proposed model can be seen as a competitive alternative to the Hilbert-Peano scan. We propose a bayesian algorithm to estimate parameters of the considered model. The performance of this algorithm is globally favorable, compared to the bi-dimensional EM algorithm through numerical and visual data.

Keywords: Image segmentation, Hidden Markov chain with a bi-dimensional observed process, Peano-Hilbert scan, Bayesian approach, MCMC methods, Bi-dimensional EM algorithm.

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Authors: Eva Štěpánková

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The decision-making process is theoretically clearly defined. Generally, it includes the problem identification and analysis, data gathering, goals and criteria setting, alternatives development and optimal alternative choice and its implementation. In practice however, various modifications of the theoretical decision-making process can occur. The managers can consider some of the phases to be too complicated or unfeasible and thus they do not carry them out and conversely some of the steps can be overestimated. The aim of the paper is to reveal and characterize the perception of the individual phases of decision-making process by the managers. The research is concerned with managers in the military environment – commanders. Quantitative survey is focused cross-sectionally in the individual levels of management of the Ministry of Defence of the Czech Republic. On the total number of 135 respondents the analysis focuses on which of the decision-making process phases are problematic or not carried out in practice and which are again perceived to be the easiest. Then it is examined the reasons of the findings.

Keywords: Decision making, decision making process, decision problems.

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Authors: Seyedvahid Najafi, Viliam Makis

Abstract:

In recent years, maintenance optimization has attracted special attention due to the growth of industrial systems complexity. Maintenance costs are high for many systems, and preventive maintenance is effective when it increases operations' reliability and safety at a reduced cost. The novelty of this research is to consider general repair in the modeling of multi-unit series systems and solve the maintenance problem for such systems using the semi-Markov decision process (SMDP) framework. We propose an opportunistic maintenance policy for a series system composed of two main units. Unit 1, which is more expensive than unit 2, is subjected to condition monitoring, and its deterioration is modeled using a gamma process. Unit 1 hazard rate is estimated by the proportional hazards model (PHM), and two hazard rate control limits are considered as the thresholds of maintenance interventions for unit 1. Maintenance is performed on unit 2, considering an age control limit. The objective is to find the optimal control limits and minimize the long-run expected average cost per unit time. The proposed algorithm is applied to a numerical example to compare the effectiveness of the proposed policy (policy Ⅰ) with policy Ⅱ, which is similar to policy Ⅰ, but instead of general repair, replacement is performed. Results show that policy Ⅰ leads to lower average cost compared with policy Ⅱ. 

Keywords: Condition-based maintenance, proportional hazards model, semi-Markov decision process, two-unit series systems.

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Authors: Nasibeh Nasiri, Dawood Talebi Khanmiri

Abstract:

Performance of any continuous speech recognition system is highly dependent on performance of the acoustic models. Generally, development of the robust spoken language technology relies on the availability of large amounts of data. Common way to cope with little data for training each state of Markov models is treebased state tying. This tying method applies contextual questions to tie states. Manual procedure for question generation suffers from human errors and is time consuming. Various automatically generated questions are used to construct decision tree. There are three approaches to generate questions to construct HMMs based on decision tree. One approach is based on misrecognized phonemes, another approach basically uses feature table and the other is based on state distributions corresponding to context-independent subword units. In this paper, all these methods of automatic question generation are applied to the decision tree on FARSDAT corpus in Persian language and their results are compared with those of manually generated questions. The results show that automatically generated questions yield much better results and can replace manually generated questions in Persian language.

Keywords: Decision Tree, Markov Models, Speech Recognition, State Tying.

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Authors: P. C. Tewari, Rajiv Kumar, Dinesh Khanduja

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This paper discusses the performance modeling and availability analysis of Yarn Dyeing System of a Textile Industry. The Textile Industry is a complex and repairable engineering system. Yarn Dyeing System of Textile Industry consists of five subsystems arranged in series configuration. For performance modeling and analysis of availability, a performance evaluating model has been developed with the help of mathematical formulation based on Markov-Birth-Death Process. The differential equations have been developed on the basis of Probabilistic Approach using a Transition Diagram. These equations have further been solved using normalizing condition in order to develop the steady state availability, a performance measure of the system concerned. The system performance has been further analyzed with the help of decision matrices. These matrices provide various availability levels for different combinations of failure and repair rates for various subsystems. The findings of this paper are therefore, considered to be useful for the analysis of availability and determination of the best possible maintenance strategies which can be implemented in future to enhance the system performance.

Keywords: Availability Analysis, Markov Process, Performance Modeling, Steady State Availability.

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Authors: B. Mikulskienė

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Public administration institutions in cooperation with politicians are not the sole policy decision makers in full meaning any longer. Meanwhile, a special role, namely steering the decision making process, could be delegated to them. Despite the wide scientific discussion on different aspects what has direct impact on policy creation, there is a lack of holistic practical managerial advice, which could integrate infrastructure of policy decision making with intellectual capital and with interconnection of partnership. The proposed harmonized decision making model of process, people and partnership entitled by acronym HM-3P is analyzed as a framework for implementation of public administration steering role seeking the coherent social involvement in policy decision making.

Keywords: participatory decision making, partnership, stakeholders.

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Authors: Hong Son Hoang, Remy Baraille

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This paper addresses the problem of how one can improve the performance of a non-optimal filter. First the theoretical question on dynamical representation for a given time correlated random process is studied. It will be demonstrated that for a wide class of random processes, having a canonical form, there exists a dynamical system equivalent in the sense that its output has the same covariance function. It is shown that the dynamical approach is more effective for simulating and estimating a Markov and non- Markovian random processes, computationally is less demanding, especially with increasing of the dimension of simulated processes. Numerical examples and estimation problems in low dimensional systems are given to illustrate the advantages of the approach. A very useful application of the proposed approach is shown for the problem of state estimation in very high dimensional systems. Here a modified filter for data assimilation in an oceanic numerical model is presented which is proved to be very efficient due to introducing a simple Markovian structure for the output prediction error process and adaptive tuning some parameters of the Markov equation.

Keywords: Statistical simulation, canonical form, dynamical system, Markov and non-Markovian processes, data assimilation.

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Authors: Pathinathan Theresanathan, Ajay Minj

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Ignatian Discernment Process (IDP) is an intense decision-making tool to decide on life-issues. Decisions are influenced by various factors outside of the decision maker and inclination within. This paper develops IDP in the context of Fuzzy Multi-criteria Decision Making (FMCDM) process. Extended VIKOR method is a decision-making method which encompasses even conflict situations and accommodates weightage to various issues. Various aspects of IDP, namely three ways of decision making and tactics of inner desires, are observed, analyzed and articulated within the frame work of fuzzy rules. The decision-making situations are broadly categorized into two types. The issues outside of the decision maker influence the person. The inner feeling also plays vital role in coming to a conclusion. IDP integrates both the categories using Extended VIKOR method. Case studies are carried out and analyzed with FMCDM process. Finally, IDP is verified with an illustrative case study and results are interpreted. A confused person who could not come to a conclusion is able to take decision on a concrete way of life through IDP. The proposed IDP model recommends an integrated and committed approach to value-based decision making.

Keywords: Analytical hierarchy process, fuzzy multi-criteria decision making, Ignatian discernment process, Ignatian discernment, multi-criteria decision making, VIKOR.

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Authors: Anastasia Rita Widiarti, Phalita Nari Wastu

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Hidden Markov Model (HMM) is a stochastic method which has been used in various signal processing and character recognition. This study proposes to use HMM to recognize Javanese characters from a number of different handwritings, whereby HMM is used to optimize the number of state and feature extraction. An 85.7 % accuracy is obtained as the best result in 16-stated vertical model using pure HMM. This initial result is satisfactory for prompting further research.

Keywords: Character recognition, off-line handwritingrecognition, Hidden Markov Model.

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Authors: Y. K. Chen, K. C. Chiou, C. Y. Chen

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The cumulative conformance count (CCC) charts are widespread in process monitoring of high-yield manufacturing. Recently, it is found the use of variable sampling interval (VSI) scheme could further enhance the efficiency of the standard CCC charts. The average time to signal (ATS) a shift in defect rate has become traditional measure of efficiency of a chart with the VSI scheme. Determining the ATS is frequently a difficult and tedious task. A simple method based on a finite Markov Chain approach for modeling the ATS is developed. In addition, numerical results are given.

Keywords: Cumulative conformance count, variable sampling interval, Markov Chain, average time to signal, control chart.

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Authors: Ehsan Amid, Sina Rezaei Aghdam

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In this paper, a novel method for recognition of musical instruments in a polyphonic music is presented by using an embedded hidden Markov model (EHMM). EHMM is a doubly embedded HMM structure where each state of the external HMM is an independent HMM. The classification is accomplished for two different internal HMM structures where GMMs are used as likelihood estimators for the internal HMMs. The results are compared to those achieved by an artificial neural network with two hidden layers. Appropriate classification accuracies were achieved both for solo instrument performance and instrument combinations which demonstrates that the new approach outperforms the similar classification methods by means of the dynamic of the signal.

Keywords: hidden Markov model (HMM), embedded hidden Markov models (EHMM), MFCC, musical instrument.

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Authors: D. Pérez, M. M. E. Alemany

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In this work, a framework to model the Supply Chain (SC) Collaborative Planning (CP) process is proposed. The main contributions of this framework concern 1) the presentation of the decision view, the most important one due to the characteristics of the process, jointly within the physical, organisation and information views, and 2) the simultaneous consideration of the spatial and temporal integration among the different supply chain decision centres. This framework provides the basis for a realistic and integrated perspective of the supply chain collaborative planning process and also the analytical modeling of each of its decisional activities.

Keywords: Collaborative Planning, Decision View, Distributed Decision-Making, Framework.

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Authors: Zina Benouaret, Djamil Aissani

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In this work, we introduce the qualitative and quantitative concept of the strong stability method in the risk process modeling two lines of business of the same insurance company or an insurance and re-insurance companies that divide between them both claims and premiums with a certain proportion. The approach proposed is based on the identification of the ruin probability associate to the model considered, with a stationary distribution of a Markov random process called a reversed process. Our objective, after clarifying the condition and the perturbation domain of parameters, is to obtain the stability inequality of the ruin probability which is applied to estimate the approximation error of a model with disturbance parameters by the considered model. In the stability bound obtained, all constants are explicitly written.

Keywords: Markov chain, risk models, ruin probabilities, strong stability analysis.

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