Markov Chain Model Helps Predict Pitting Corrosion Depth and Rate in Underground Pipelines

A continuous-time, non-homogenous pure birth Markov chain serves to model external pitting corrosion in buried pipelines. The analytical solution of Kolmogorov’s forward equations for this type of Markov process gives the transition probability function in a discrete space of pit depths. The transition probability function can be completely identified by making a correlation between the stochastic pit depth mean and the deterministic mean obtained experimentally. Previously reported Monte Carlo simulations have been used for the prediction of the evolution of the pit depth distribution mean value with time for different soil types. The simulated pit depth distributions are used to develop a stochastic model based on Markov chains to predict the progression of pitting corrosion depth and rate distributions from the observed soil properties and pipeline coating characteristics. The proposed model can also be applied to pitting corrosion data from repeated in-line pipeline inspections. Real-life case studies presented in this work show how pipeline inspection and maintenance planning can be improved through the use of the proposed Markovian model for pitting corrosion.

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Markov Chain Models for the Stochastic Modeling of Pitting Corrosion

Mathematical Problems in Engineering ◽

10.1155/2013/108386 ◽

2013 ◽

Vol 2013 ◽

pp. 1-13 ◽

Cited By ~ 30

Author(s):

A. Valor ◽

F. Caleyo ◽

L. Alfonso ◽

J. C. Velázquez ◽

J. M. Hallen

Keyword(s):

Markov Process ◽

Pitting Corrosion ◽

Probability Function ◽

Transition Probabilities ◽

Transition Probability ◽

Closed Form Solution ◽

Form Solution ◽

Extreme Value Statistics ◽

Pit Depth ◽

Transition Probability Function

The stochastic nature of pitting corrosion of metallic structures has been widely recognized. It is assumed that this kind of deterioration retains no memory of the past, so only the current state of the damage influences its future development. This characteristic allows pitting corrosion to be categorized as a Markov process. In this paper, two different models of pitting corrosion, developed using Markov chains, are presented. Firstly, a continuous-time, nonhomogeneous linear growth (pure birth) Markov process is used to model external pitting corrosion in underground pipelines. A closed-form solution of the system of Kolmogorov's forward equations is used to describe the transition probability function in a discrete pit depth space. The transition probability function is identified by correlating the stochastic pit depth mean with the empirical deterministic mean. In the second model, the distribution of maximum pit depths in a pitting experiment is successfully modeled after the combination of two stochastic processes: pit initiation and pit growth. Pit generation is modeled as a nonhomogeneous Poisson process, in which induction time is simulated as the realization of a Weibull process. Pit growth is simulated using a nonhomogeneous Markov process. An analytical solution of Kolmogorov's system of equations is also found for the transition probabilities from the first Markov state. Extreme value statistics is employed to find the distribution of maximum pit depths.

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Multiple repair scenario of life cycle cost of RCC girder bridge using Markov chain model

Challenge Journal of Concrete Research Letters ◽

10.20528/cjcrl.2019.04.001 ◽

2019 ◽

Vol 10 (4) ◽

pp. 75

Author(s):

Md. Shafiqul Islam ◽

Shayla Sharmin ◽

Jebunnesa Islam

Keyword(s):

Markov Chain ◽

Life Cycle ◽

Life Cycle Cost ◽

Markov Chain Model ◽

Transition Probability ◽

Chloride Concentration ◽

Chain Model ◽

Actual Performance ◽

Girder Bridge ◽

Inspection Data

At present, many road authorities in the world face challenges in condition monitoring diagnosis of distress and forecasting deterioration, strengthening and convalescence of aging bridge structures. The accurate prediction of the future condition is crucial for optimizing the maintenance activities. It is very tough to predict the actual performance scenario or actual in–situ structures without carrying out inspection. Limited availability of detailed inspection data is considered as one of the major drawbacks in developing deterioration models. In State Based Markov deterioration (SNMD) modelling, the main job is to estimate transition probability matrixes (TPMs). In this paper, Markov Chain Monte Carlo (MCMC) is used to estimate TPMs. In Markov Chain Model, future conditions depend on only present bridge inspection data. Multiple repair options are adopted in order to optimize life cycle cost. Repairs are needed when the critical chloride concentration exceeds 0.2. Three distinct types of cost corresponding to each repair option is considered. The objective of this paper is to minimize the life cycle cost considering appropriate repair timings of mixed repair methods. Variation of life cycle cost of five different concretes (stronger to weaker) using three different repair option is shown in this paper. For specific normalized condition of concrete’s failure probability (0.3) and specific type of concrete, variation of life cycle cost using multiple repair options is also shown in this paper.

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Vehicle Driving Risk Prediction Based on Markov Chain Model

Discrete Dynamics in Nature and Society ◽

10.1155/2018/4954621 ◽

2018 ◽

Vol 2018 ◽

pp. 1-12 ◽

Cited By ~ 2

Author(s):

Xiaoxia Xiong ◽

Long Chen ◽

Jun Liang

Keyword(s):

Markov Chain ◽

Markov Chain Model ◽

Transition Probability ◽

False Positive Rate ◽

Estimation Method ◽

Prediction Algorithm ◽

Chain Model ◽

Risk Status ◽

Risk Levels ◽

Driving Risk

A driving risk status prediction algorithm based on Markov chain is presented. Driving risk states are classified using clustering techniques based on feature variables describing the instantaneous risk levels within time windows, where instantaneous risk levels are determined in time-to-collision and time-headway two-dimension plane. Multinomial Logistic models with recursive feature variable estimation method are developed to improve the traditional state transition probability estimation, which also takes into account the comprehensive effects of driving behavior, traffic, and road environment factors on the evolution of driving risk status. The “100-car” natural driving data from Virginia Tech is employed for the training and validation of the prediction model. The results show that, under the 5% false positive rate, the prediction algorithm could have high prediction accuracy rate for future medium-to-high driving risks and could meet the timeliness requirement of collision avoidance warning. The algorithm could contribute to timely warning or auxiliary correction to drivers in the approaching-danger state.

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MARKOV CHAIN MODELING AND ANALYSIS OF COMPLICATED PHENOMENA IN COUPLED CHAOTIC OSCILLATORS

Journal of Circuits System and Computers ◽

10.1142/s0218126610006451 ◽

2010 ◽

Vol 19 (04) ◽

pp. 801-818 ◽

Cited By ~ 4

Author(s):

YOSHIFUMI NISHIO ◽

YUTA KOMATSU ◽

YOKO UWATE ◽

MARTIN HASLER

Keyword(s):

Markov Chain ◽

Markov Chain Model ◽

Transition Probability ◽

Transition Probability Matrix ◽

Chain Model ◽

Chaotic Oscillators ◽

Modeling And Analysis ◽

Markov Chain Models ◽

Simulation Results ◽

Markov Chain Modeling

In this paper, we propose a Markov chain modeling of complicated phenomena observed from coupled chaotic oscillators. Once we obtain the transition probability matrix from computer simulation results, various statistical quantities can be easily calculated from the model. It is shown that various statistical quantities are easily calculated by using the Markov chain model. Various features derived from the Markov chain models of chaotic wandering of synchronization states and switching of clustering states are compared with those obtained from computer simulations of original circuit equations.

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Degradation modelling and life expectancy using Markov chain model for carriageway

International Journal of Quality & Reliability Management ◽

10.1108/ijqrm-06-2017-0116 ◽

2018 ◽

Vol 35 (6) ◽

pp. 1268-1288 ◽

Cited By ~ 1

Author(s):

Kong Fah Tee ◽

Ejiroghene Ekpiwhre ◽

Zhang Yi

Keyword(s):

Markov Chain ◽

Life Expectancy ◽

Transition Probabilities ◽

Markov Chain Model ◽

Transition Probability ◽

Condition Assessment ◽

Cumulative Distribution ◽

Chain Model ◽

Content Type ◽

Pairwise Correlation

PurposeAutomated condition surveys have been recently introduced for condition assessment of highway infrastructures worldwide. Accurate predictions of the current state, median life (ML) and future state of highway infrastructures are crucial for developing appropriate inspection and maintenance strategies for newly created as well as existing aging highway infrastructures. The paper aims to discuss these issues.Design/methodology/approachThis paper proposes Markov Chain based deterioration modelling using a linear transition probability (LTP) matrix method and a median life expectancy (MLE) algorithm. The proposed method is applied and evaluated using condition improvement between the two successive inspections from the Surface Condition Assessment of National Network of Roads survey of the UK Pavement Management System.FindingsThe proposed LTP matrix model utilises better insight than the generic or decoupling linear approach used in estimating transition probabilities formulated in the past. The simulated LTP predicted conditions are portrayed in a deterioration profile and a pairwise correlation. The MLs are computed statistically with a cumulative distribution function plot.Originality/valueThe paper concludes that MLE is ideal for projecting half asset life, and the LTP matrix approach presents a feasible approach for new maintenance regime when more certain deterioration data become available.

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STBS-Stega: Coverless text steganography based on state transition-binary sequence

International Journal of Distributed Sensor Networks ◽

10.1177/1550147720914257 ◽

2020 ◽

Vol 16 (3) ◽

pp. 155014772091425

Author(s):

Ning Wu ◽

Zhongliang Yang ◽

Yi Yang ◽

Lian Li ◽

Poli Shang ◽

...

Keyword(s):

Markov Chain ◽

State Transition ◽

Markov Chain Model ◽

Transition Probability ◽

Binary Sequence ◽

Chain Model ◽

Sequence Diagrams ◽

Hide Information ◽

Proposed Model ◽

Text Steganography

Information-hiding technology has recently developed into an area of significant interest in the field of information security. As one of the primary carriers in steganography, it is difficult to hide information in texts because there is insufficient information redundancy. Traditional text steganography methods are generally not robust or secure. Based on the Markov chain model, a new text steganography approach is proposed that focuses on transition probability, one of the most important concepts of the Markov chain model. We created a state transition-binary sequence diagrams based on the aforementioned concepts and used them to guide the generation of new texts with embedded secret information. Compared to other related works, the proposed method exploits the use of the transition probability in the process of steganographic text generation. The associated developed algorithm also encrypts the serial number of the state transition-binary sequence diagram needed by the receiver to extract the information, which further enhances the security of the steganography information. Experiments were designed to evaluate the proposed model. The results revealed that the model had higher concealment and hidden capacity compared to previous methods.

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Metode Markov Chain untuk Menghitung Premi Asuransi pada Pasien Penderita Penyakit Demam Berdarah Dengue

Al-Khwarizmi Jurnal Pendidikan Matematika dan Ilmu Pengetahuan Alam ◽

10.24256/jpmipa.v7i2.1251 ◽

2020 ◽

Vol 7 (2) ◽

pp. 151-160

Author(s):

Irwan Kasse ◽

Didiharyono Didiharyono ◽

Maulidina Maulidina

Keyword(s):

Markov Chain ◽

Dengue Hemorrhagic Fever ◽

Markov Chain Model ◽

Transition Probability ◽

Probability Model ◽

Hemorrhagic Fever ◽

Insurance Premium ◽

The State ◽

Chain Model ◽

Insurance Premiums

Abstract:This paper discusses the Markov Chain method in calculating insurance premiums for patients with dengue hemorrhagic fever (DHF) at Labuang Baji Hospital. The Markov Chain Model is a method that studies the characteristics of a variable in the present that depends on its properties in the past in an attempt to estimate the properties of these variables in the future. This paper aims to determine the transition probability model for each circumstance using the Markov multistate model and to determine insurance premiums using the Markov Method. Based on the results of research and discussion, obtained a probability transition model matrix with the order 5 x 5. Next calculate the transition rate matrix, calculate the transition opportunity, calculate the density function, and calculate the premium of each event. With a large one-year term life insurance premium paid to patients with Dengue Hemorrhagic Fever (DHF) at each transition opportunity adjusted to the state of each gradient I, II, and III, with the maximum value of the premium paid that is at the state of the gradient I that moves to die with the value Ax.a|04=Rp.1.372.500.. Abstrak:Tulisan ini membahas tentang metode Markov Chain dalam menghitung premi asuransi pada penderita penyakit demam berdarah dengue (DBD) di Rumah Sakit Labuang Baji. Model Markov Chain merupakan salah satu metode yang mengkaji sifat-sifat suatu variabel saat sekarang bergantung pada sifat-sifat variabel di masa terdahulu untuk mengestimasi sifat-sifat variabel tersebut untuk keperluan di masa mendatang. Tulisan ini bertujuan untuk mengetahui model probabilitas transisi dari setiap keadaan dengan menggunakan model multistatus Markov dan untuk menentukan premi Asuransi menggunakan Metode Markov. Berdasarkan hasil penelitian diperoleh model matriks probabilitas transisi berordo 5 x 5 . Selanjutnya menghitung matriks laju transisi, menghitung peluang transisi, menghitung fungsi densitas, dan menghitung premi dari setiap kejadian. Dengan Besar premi asuransi jiwa berjangka satu tahun yang dibayarkan pada pasien Demam Berdarah Dengue (DBD) pada setiap peluang transisi disesuaikan dengan keadaan masing-masing gradiasi I, II, dan III, dengan nilai maksimal premi yang di bayarkan yaitu pada keadaan gradiasi I yang berpindah ke meninggal dengan nilai Ax.a|04=Rp.1.372.500..

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Object Trajectory Information for Robotic Service in Intelligent Space

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.490-491.1172 ◽

2014 ◽

Vol 490-491 ◽

pp. 1172-1176

Author(s):

Weerachai Skulkittiyut ◽

Toru Yamaguchi ◽

Makoto Mizukawa

Keyword(s):

Markov Chain ◽

Transition Probabilities ◽

Markov Chain Model ◽

Transition Probability ◽

Basic Knowledge ◽

Chain Model ◽

Object Knowledge ◽

Individual Object ◽

Intelligent Space

Implementation of robotic service is needed extremely enormous of information including environment, place, user and object knowledge. It is extremely difficult for a robot to do tasks ordered by a human without having some basic knowledge or information. This paper proposes a method to create object knowledge focusing on an object and objects place relationship for the robotic service namely tidy-up service, in which a robot is asked to take objects such as books, cups, dishes on a table to appropriate places automatically. In details, as the first phase, we conduct a questionnaire to collect the trajectories in term of places of individual object from the participants. Based on the collected object trajectory information, we are able to build Markov chain model of the object which the states are possible places and transition probabilities are the probability that the object moved from one place to other places. In final, we are able to use the transition probability including the Markov chain model to predict and provide the next appropriate place. The result showed that the proposed approach is efficient in creating object trajectory as knowledge, hence, helping the robots to and to provide intuitive service.

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Detecting Intra-Urban Housing Market Spillover through a Spatial Markov Chain Model

ISPRS International Journal of Geo-Information ◽

10.3390/ijgi9010056 ◽

2020 ◽

Vol 9 (1) ◽

pp. 56 ◽

Cited By ~ 1

Author(s):

Daijun Zhang ◽

Xiaoqi Zhang ◽

Yanqiao Zheng ◽

Xinyue Ye ◽

Shengwen Li ◽

...

Keyword(s):

Markov Chain ◽

Markov Chain Model ◽

Transition Probability ◽

Spillover Effect ◽

Urban Housing ◽

Chain Model ◽

Urban Core ◽

Urban Level ◽

Housing Submarkets ◽

The Impact

This study analyzed the spillovers among intra-urban housing submarkets in Beijing, China. Intra-urban spillover imposes a methodological challenge for housing studies from the spatial and temporal perspectives. Unlike the inter-urban spillover, the range of every submarket is not naturally defined; therefore, it is impossible to evaluate the intra-urban spillover by standard time-series models. Instead, we formulated the spillover effect as a Markov chain procedure. The constrained clustering technique was applied to identify the submarkets as the hidden states of Markov chain and estimate the transition matrix. Using a day-by-day transaction dataset of second-hand apartments in Beijing during 2011–2017, we detected 16 submarkets/regions and the spillover effect among these regions. The highest transition probability appeared in the overlapped region of urban core and Tongzhou district. This observation reflects the impact of urban planning proposal initiated since early 2012. In addition to the policy consequences, we analyzed a variety of spillover “types” through regression analysis. The latter showed that the “ripple” form of spillover is not dominant at the intra-urban level. Other types, such as the spillover due to the existence of price depressed regions, play major roles. This observation reveals the complexity of intra-urban spillover dynamics and its distinct driving-force compared to the inter-urban spillover.

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