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Статті в журналах з теми "Markov chains; interval analysis; sensitivity analysis"
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Liu, Xingliang, Jinliang Xu, Menghui Li, and Jia Peng. "Sensitivity Analysis Based SVM Application on Automatic Incident Detection of Rural Road in China." Mathematical Problems in Engineering 2018 (2018): 1–9. http://dx.doi.org/10.1155/2018/9583285.
Повний текст джерелаАнотація:
Traditional automatic incident detection methods such as artificial neural networks, backpropagation neural network, and Markov chains are not suitable for addressing the incident detection problem of rural roads in China which have a relatively high accident rate and a low reaction speed caused by the character of small traffic volume. This study applies the support vector machine (SVM) and parameter sensitivity analysis methods to build an accident detection algorithm in a rural road condition, based on real-time data collected in a field experiment. The sensitivity of four parameters (speed, front distance, vehicle group time interval, and free driving ratio) is analyzed, and the data sets of two parameters with a significant sensitivity are chosen to form the traffic state feature vector. The SVM and k-fold cross validation (K-CV) methods are used to build the accident detection algorithm, which shows an excellent performance in detection accuracy (98.15% of the training data set and 87.5% of the testing data set). Therefore, the problem of low incident reaction speed of rural roads in China could be solved to some extent.
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Elmesmari, Nasir, Farag Hamad, and Abdelbaset Abdalla. "Parameters Estimation Sensitivity of the Linear Mixed Model To Alternative Prior Distribution Specifications." Scholars Journal of Physics, Mathematics and Statistics 8, no. 9 (November 11, 2021): 166–70. http://dx.doi.org/10.36347/sjpms.2021.v08i09.001.
Повний текст джерелаАнотація:
Markov chain Monte Carlo (MCMC) is the most widely used method for estimating joint posterior distributions in Bayesian analysis. The Markov chain Monte Carlo technique has been used in order to estimate the model parameters based on the different prior distributions. MCMC simulations were carried out in order to evaluate the linear mixed model using different parameters of the prior distribution. In this paper, we established the linear mixed model with different types of variables. The proposed parameters of the prior distribution are different from the traditional parameters of the prior distribution. We assumed special parameters for the prior distribution based on some background or information about the data science. This work aims to estimate the parameters using a point estimator or find a confidence interval (credible interval) for the unknown parameters. Also, a specific hypothesis about these parameters can be tested using a random sample from the posterior distribution. The performance of each prior is measured based on the effective sample size (ESS) for the estimated model. The results showed that the estimated linear mixed model with proposed parameters of the prior distribution performed very well in comparison with the standard or traditional prior (inverse-Wishart prior for random effect component). Based on the scale reduction factors, the estimated model with proposed parameters performed better in comparison with scale reduction factors for the traditional model.
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Weedon-Fekjær, Harald, Lars J. Vatten, Odd O. Aalen, Bo Lindqvist, and Steinar Tretli. "Estimating mean sojourn time and screening test sensitivity in breast cancer mammography screening: new results." Journal of Medical Screening 12, no. 4 (December 1, 2005): 172–78. http://dx.doi.org/10.1258/096914105775220732.
Повний текст джерелаАнотація:
Objective: To assess if new screening techniques, increased use of hormone replacement therapy, or the transition from breast cancer screening trials to large scale screening programmes may influence the average time in preclinical screening detectable phase (mean sojourn time [MST]) or screening test sensitivity (STS). Setting: Screening and interval data for 395,188 women participating in the Norwegian Breast Cancer Screening Programme (NBCSP). Methods: Weighted non-linear least-square regression estimates using a tree step Markov chain model, and a sensitivity analysis of the possible impact by opportunistic screening between ordinary breast cancer screening rounds. Results: MST was estimated to 6.1 (95% confidence interval [CI] 5.1–7.0) years for women aged 50–59 years, and 7.9 (95% CI 6.0–7.9) years for those aged 60–69 years. Correspondingly, STS was estimated to 58% (95% CI 52–64 %) and 73 % (67–78 %), respectively. Simulations revealed that opportunistic screening may give a moderate estimation bias towards higher MST and lower STS. Assuming a probable 21% higher background incidence, due to increased hormone replacement therapy use, MST estimates decreased to 3.9 and 5.0 years for the two age groups, and STS increased to 75 and 85%. Conclusions: The new estimates indicate that screening detectable phase is longer than that found in previous mammography trials/programmes, but also that the sensitivity of the screening test is lower. Overall, the NBCSP detects more cancer cases than most previous trials/programmes.
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Sharma, Tarang, Peter Gøtzsche, and Oliver Kuss. "VP26 Comparing Statistical Methods For Meta-Analysis Of Rare Event Data." International Journal of Technology Assessment in Health Care 33, S1 (2017): 158–59. http://dx.doi.org/10.1017/s0266462317003166.
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INTRODUCTION:We aimed to identify the validity and robustness of effect estimates for serious rare adverse events in clinical study reports of antidepressant trials, across different meta-analysis methods for rare binary events data (1,2).METHODS:Four serious rare adverse events (all-cause mortality, suicidality, aggressive behaviour and akathisia) were meta-analyzed using different methods (3). The Yusuf-Peto odds ratio (OR), which ignores studies with no events in the treatment arms, was compared with the alternative approaches of generalized linear mixed models (GLMM), conditional logistic regression, a Bayesian approach using Markov Chain Monte Carlo (MCMC) and a beta-binomial regression model.RESULTS:Though the estimates for the four outcomes did not change substantially across the different analysis methods, the Yusuf-Peto method underestimated the treatment harm and overstimated its precision, especially when the estimated odds ratio (OR) deviated greatly from 1. For example the OR for suicidality for children and adolescents was 2.39 (95 percent Confidence Interval, CI 1.32 to 4.33, using the Yusuf-Peto method), but increased to 2.64 (95 percent CI 1.33 to 5.26) using conditional logistic regression, to 2.69 (95 percent CI 1.19 to 6.09) using beta-binomial, to 2.73 (95 percent CI 1.37 to 5.42) using the GLMM and finally to 2.87 (95 percent CI 1.42 to 5.98) using the MCMC approach.CONCLUSIONS:The method used for meta-analysis of rare events data influences the estimates obtained and the exclusion of double zero-event studies can give misleading results. To ensure reduction of bias and erroneous inferences, sensitivity analyses should be performed using different methods and we recommend that the Yusuf-Peto approach should no longer be used. Other methods, in particular the beta-binomial method that was shown to be superior, should be considered instead.
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Xu, Jie, Zhengyang Zhao, Qian Ma, Ming Liu, and Giuseppe Lacidogna. "Damage Diagnosis of Single-Layer Latticed Shell Based on Temperature-Induced Strain under Bayesian Framework." Sensors 22, no. 11 (June 2, 2022): 4251. http://dx.doi.org/10.3390/s22114251.
Повний текст джерелаАнотація:
Under the framework of Bayesian theory, a probabilistic method for damage diagnosis of latticed shell structures based on temperature-induced strain is proposed. First, a new damage diagnosis index is proposed based on the correlation between temperature-induced strain and structural parameters. Then, Markov Chain Monte Carlo is adopted to analyze the newly proposed diagnosis index, based on which the frequency distribution histogram for the posterior probability of the diagnosis index is obtained. Finally, the confidence interval of the damage diagnosis is determined by the posterior distribution of the initial state (baseline condition). The damage probability of the unknown state is also calculated. The proposed method was validated by applying it to a latticed shell structure with finite element developed, where the rod damage and bearing failure were diagnosed based on importance analysis and temperature sensitivity analysis of the rod. The analysis results show that the proposed method can successfully consider uncertainties in the strain response monitoring process and effectively diagnose the failure of important rods in radial and annular directions, as well as horizontal (x- and y-direction) bearings of the latticed shell structure.
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ACHIM, Luminiţa-Georgiana, Elena MITOI, Valentin MOLDOVEANU, and Codrut-Ioan TURLEA. "Credit Scoring – General Approach in the IFRS 9 Context." Audit Financiar 19, no. 162 (May 20, 2021): 384–96. http://dx.doi.org/10.20869/auditf/2021/162/014.
Повний текст джерелаАнотація:
With the coming into force of the standard IFRS 9 – Financial Instruments, in January 2018, financial institutions passed from an incurred loss model to a forward-looking model for the computation of impairment losses. As such, the IFRS 9 models use point-in-time, estimates of Probability of Default and Loss Given Default and provide a more faithful representation of the credit risk at a given as they are based on past experiences as well as the most recent and forecasted economic conditions. However, given the short-term fluctuations in the macroeconomic conditions, the final outcome of the Expected credit loss models is highly volatile due to their sensitivity to the business cycle. With regard to Probability of Default estimation under IFRS 9, the most commonly methods are: Markov Chains, Survival Analysis and single-factor models (Vasicek and Z-Shift). The development of the score-cards is still the same as in the case of the Internal Ratings Based Probability of Default models, encouraging institutions to use the already available credit rating systems and perform adjustment to the calibration. This paper outlines a non-exhaustive list of quantitative validation tests would satisfy the requirements of the IFRS 9 standard.
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Cassandras, C. G., and S. G. Strickland. "On-line sensitivity analysis of Markov chains." IEEE Transactions on Automatic Control 34, no. 1 (1989): 76–86. http://dx.doi.org/10.1109/9.8651.
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Lasserre, J. B. "Exact formula for sensitivity analysis of Markov chains." Journal of Optimization Theory and Applications 71, no. 2 (November 1991): 407–13. http://dx.doi.org/10.1007/bf00939928.
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Heidergott, Bernd, Haralambie Leahu, Andreas Löpker, and Georg Pflug. "Perturbation analysis of inhomogeneous finite Markov chains." Advances in Applied Probability 48, no. 1 (March 2016): 255–73. http://dx.doi.org/10.1017/apr.2015.16.
Повний текст джерелаАнотація:
Abstract In this paper we provide a perturbation analysis of finite time-inhomogeneous Markov processes. We derive closed-form representations for the derivative of the transition probability at time t, with t > 0. Elaborating on this result, we derive simple gradient estimators for transient performance characteristics either taken at some fixed point in time t, or for the integrated performance over a time interval [0 , t]. Bounds for transient performance sensitivities are presented as well. Eventually, we identify a structural property of the derivative of the generator matrix of a Markov chain that leads to a significant simplification of the estimators.
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Rahimi, Ebrahim, Seyed Saeed Hashemi Nazari, Yaser Mokhayeri, Asaad Sharhani, and Rasool Mohammadi. "Nine-month Trend of Time-Varying Reproduction Numbers of COVID-19 in West of Iran." Journal of Research in Health Sciences 21, no. 2 (June 28, 2021): e00517-e00517. http://dx.doi.org/10.34172/jrhs.2021.54.
Повний текст джерелаАнотація:
Background: The basic reproduction number (R0) is an important concept in infectious disease epidemiology and the most important parameter to determine the transmissibility of a pathogen. This study aimed to estimate the nine-month trend of time-varying R of COVID-19 epidemic using the serial interval (SI) and Markov Chain Monte Carlo in Lorestan, west of Iran. Study design: Descriptive study. Methods: This study was conducted based on a cross-sectional method. The SI distribution was extracted from data and log-normal, Weibull, and Gamma models were fitted. The estimation of time-varying R0, a likelihood-based model was applied, which uses pairs of cases to estimate relative likelihood. Results: In this study, Rt was estimated for SI 7-day and 14-day time-lapses from 27 February-14 November 2020. To check the robustness of the R0 estimations, sensitivity analysis was performed using different SI distributions to estimate the reproduction number in 7-day and 14-day time-lapses. The R0 ranged from 0.56 to 4.97 and 0.76 to 2.47 for 7-day and 14-day time-lapses. The doubling time was estimated to be 75.51 days (95% CI: 70.41, 81.41). Conclusions: Low R0 of COVID-19 in some periods in Lorestan, west of Iran, could be an indication of preventive interventions, namely quarantine and isolation. To control the spread of the disease, the reproduction number should be reduced by decreasing the transmission and contact rates and shortening the infectious period.
Дисертації з теми "Markov chains; interval analysis; sensitivity analysis"
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de, Souza Matos Júnior Rubens. "An automated approach for systems performance and dependability improvement through sensitivity analysis of Markov chains." Universidade Federal de Pernambuco, 2011. https://repositorio.ufpe.br/handle/123456789/2451.
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Previous issue date: 2011Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
Sistemas computacionais estão em constante evolução para satisfazer crescimentos na demanda, ou novas exigências dos usuários. A administração desses sistemas requer decisões que sejam capazes de prover o nível mais alto nas métricas de desempenho e dependabilidade, com mudanças mínimas `a configuração existente. É comum realizar análises de desempenho, confiabilidade, disponibilidade e performabilidade de sistemas através de modelos analíticos, e as cadeias de Markov representam um dos formalismos matemáticos mais utilizados, permitindo estimar algumas métricas de interesse, dado um conjunto de parâmetros de entrada. No entanto, a análise de sensibilidade, quando feita, é executada simplesmente variando o conjunto de parâmetros dentro de suas faixas de valores e resolvendo repetidamente o modelo escolhido. A análise de sensibilidade diferencial permite a quem está modelando encontrar gargalos de uma maneira mais sistemática e eficiente. Este trabalho apresenta uma abordagem automatizada para análise de sensibilidade, e almeja guiar a melhoria de sistemas computacionais. A abordagem proposta é capaz de acelerar o processo de tomada de decisão, no que se refere a optimização de ajustes de hardware e software, além da aquisição e substituição de componentes. Tal metodologia usa as cadeias de Markov como técnica de modelagem formal, e a análise de sensibilidade desses modelos, preenchendo algumas lacunas encontradas na literatura sobre análise de sensibilidade. Por fim, a análise de sensibilidade de alguns sistemas distribuídos selecionados, conduzida neste trabalho, destaca gargalos nestes sistemas e fornece exemplos da acurácia da metodologia proposta, assim como ilustra sua aplicabilidade
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Balan, Iulian. "Adjoint sensitivity analysis procedure of Markov chains with application on reliability of IFMIF accelerator system facilities." Karlsruhe : FZKA, 2005. http://bibliothek.fzk.de/zb/berichte/FZKA7080.pdf.
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Balan, Iulian [Verfasser]. "Adjoint sensitivity analysis procedure of Markov chains with application on reliability of IFMIF accelerator system facilities / Forschungszentrum Karlsruhe GmbH, Karlsruhe. Iulian Balan." Karlsruhe : FZKA, 2005. http://d-nb.info/976405784/34.
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MATOS, JÚNIOR Rubens de Souza. "Identification of Availability and Performance Bottlenecks in Cloud Computing Systems: an approach based on hierarchical models and sensitivity analysis." Universidade Federal de Pernambuco, 2016. https://repositorio.ufpe.br/handle/123456789/18702.
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CAPES
Cloud computing paradigm is able to reduce costs of acquisition and maintenance of computer systems, and enables the balanced management of resources according to the demand. Hierarchical and composite analytical models are suitable for describing performance and dependability of cloud computing systems in a concise manner, dealing with the huge number of components which constitute such kind of system. That approach uses distinct sub-models for each system level and the measures obtained in each sub-model are integrated to compute the measures for the whole system. Identification of bottlenecks in hierarchical models might be difficult yet, due to the large number of parameters and their distribution among distinct modeling levels and formalisms. This thesis proposes methods for evaluation and detection of bottlenecks of cloud computing systems. The methodology is based on hierarchical modeling and parametric sensitivity analysis techniques tailored for such a scenario. This research introduces methods to build unified sensitivity rankings when distinct modeling formalisms are combined. These methods are embedded in the Mercury software tool, providing an automated sensitivity analysis framework for supporting the process. Distinct case studies helped in testing the methodology, encompassing hardware and software aspects of cloud systems, from basic infrastructure level to applications that are hosted in private clouds. The case studies showed that the proposed approach is helpful for guiding cloud systems designers and administrators in the decision-making process, especially for tune-up and architectural improvements. It is possible to employ the methodology through an optimization algorithm proposed here, called Sensitive GRASP. This algorithm aims at optimizing performance and dependability of computing systems that cannot stand the exploration of all architectural and configuration possibilities to find the best quality of service. This is especially useful for cloud-hosted services and their complex underlying infrastructures.
O paradigma de computação em nuvem é capaz de reduzir os custos de aquisição e manutenção de sistemas computacionais e permitir uma gestão equilibrada dos recursos de acordo com a demanda. Modelos analíticos hierárquicos e compostos são adequados para descrever de forma concisa o desempenho e a confiabilidade de sistemas de computação em nuvem, lidando com o grande número de componentes que constituem esse tipo de sistema. Esta abordagem usa sub-modelos distintos para cada nível do sistema e as medidas obtidas em cada sub-modelo são usadas para calcular as métricas desejadas para o sistema como um todo. A identificação de gargalos em modelos hierárquicos pode ser difícil, no entanto, devido ao grande número de parâmetros e sua distribuição entre os distintos formalismos e níveis de modelagem. Esta tese propõe métodos para a avaliação e detecção de gargalos de sistemas de computação em nuvem. A abordagem baseia-se na modelagem hierárquica e técnicas de análise de sensibilidade paramétrica adaptadas para tal cenário. Esta pesquisa apresenta métodos para construir rankings unificados de sensibilidade quando formalismos de modelagem distintos são combinados. Estes métodos são incorporados no software Mercury, fornecendo uma estrutura automatizada de apoio ao processo. Uma metodologia de suporte a essa abordagem foi proposta e testada ao longo de estudos de casos distintos, abrangendo aspectos de hardware e software de sistemas IaaS (Infraestrutura como um serviço), desde o nível de infraestrutura básica até os aplicativos hospedados em nuvens privadas. Os estudos de caso mostraram que a abordagem proposta é útil para orientar os projetistas e administradores de infraestruturas de nuvem no processo de tomada de decisões, especialmente para ajustes eventuais e melhorias arquiteturais. A metodologia também pode ser aplicada por meio de um algoritmo de otimização proposto aqui, chamado Sensitive GRASP. Este algoritmo tem o objetivo de otimizar o desempenho e a confiabilidade de sistemas em cenários onde não é possível explorar todas as possibilidades arquiteturais e de configuração para encontrar a melhor qualidade de serviço. Isto é especialmente útil para os serviços hospedados na nuvem e suas complexas
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Teo, Mingmei. "Interval Markov chains: performance measures and sensitivity analysis." Thesis, 2013. http://hdl.handle.net/2440/84424.
Повний текст джерелаАнотація:
There is a vast literature on Markov chains where point estimates of transition and initial probabilities are used to calculate various performance measures. However, using these point estimates does not account for the associated uncertainty in estimate. If these point estimates are used, then the best outcome possible would be an approximate solution. Hence, it would be beneficial if there was a way to allow for some uncertainty in the parameters and to carry this through the calculations. One method of incorporating variation is to place bounds on the parameters and use these intervals rather than a single point estimate. By considering the intervals that contain point estimates, it is possible to control the amount of variation allowed. When these intervals are used in calculations, the results obtained are also intervals containing the true solution. Hence, allowing for an approximation of the result as well as a margin of error to be obtained. One of the objectives of this thesis is to develop and investigate different methods of calculating intervals for various performance measures (for example, mean hitting times and expected total costs) for Markov chains when intervals are given for the parameters instead of point estimates. We develop a numerical method for obtaining intervals for the performance measures for general unstructured interval Markov chains through the use of optimisation techniques. During this development, we found a connection between interval Markov chains and Markov decision processes and exploited it to obtain a form for our solution. Further, we also considered structured interval Markov chains, such as interval birth and death processes, and obtained analytic results for the classes of processes considered. Following from the idea of structured Markov chains, we considered the Markovian SIR (susceptible-infectious-recovered) epidemic model and looked to extend the concepts developed for the unstructured interval Markov chains. Two important performance measures, namely the mean final epidemic size and mean epidemic duration, were of interest to us and we were able to prove analytic results for the mean final epidemic size. For the mean epidemic duration, we modified the numerical method for general unstructured interval Markov chains to calculate bounds on this performance measure. The other objective of this thesis was to investigate if it was possible to use interval analysis as an alternative to sensitivity analysis. We explored this in the context of the SIR model, where the true value of the parameters of the model may not be known. Hence, if one were to be careful when using point estimates, one would consider using sensitivity analysis which explores the parameter space around the chosen estimates. We considered a distribution on the parameter estimates and used the methods developed in the early chapters of the thesis, to calculate intervals for performance measures. Using these intervals, we developed a method to obtain an approximate cumulative distribution function of the performance measure. This approximate cumulative distribution function was found to very closely resemble the cumulative distribution function obtained from extensive simulations.Thesis (M.Phil.) -- University of Adelaide, School of Mathematical Sciences, 2013
Частини книг з теми "Markov chains; interval analysis; sensitivity analysis"
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Bacci, Giovanni, Benoît Delahaye, Kim G. Larsen, and Anders Mariegaard. "Quantitative Analysis of Interval Markov Chains." In Model Checking, Synthesis, and Learning, 57–77. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-91384-7_4.
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Caswell, Hal. "Sensitivity Analysis of Discrete Markov Chains." In Sensitivity Analysis: Matrix Methods in Demography and Ecology, 255–80. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-10534-1_11.
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Caswell, Hal. "Sensitivity Analysis of Continuous Markov Chains." In Sensitivity Analysis: Matrix Methods in Demography and Ecology, 281–99. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-10534-1_12.
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Benedikt, Michael, Rastislav Lenhardt, and James Worrell. "LTL Model Checking of Interval Markov Chains." In Tools and Algorithms for the Construction and Analysis of Systems, 32–46. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-36742-7_3.
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Seneta, E. "Sensitivity Analysis, Ergodicity Coefficients, and Rank-One Updates for Finite Markov Chains." In Numerical Solution of Markov Chains, 121–29. Boca Raton: CRC Press, 2021. http://dx.doi.org/10.1201/9781003210160-7.
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Crossen, Dennis M. "Student Retention Performance Using Absorbing Markov Chains." In Advances in Business Information Systems and Analytics, 293–323. IGI Global, 2017. http://dx.doi.org/10.4018/978-1-5225-0654-6.ch015.
Повний текст джерелаАнотація:
Performance models are well established in the literature. More specifically, student performance has been of growing concern at all levels. To confront the challenges, researchers have collected data, monitored performance criterion, developed quantitative models, and analyzed patterns to formulate theories and adaptive measures. At the university level, many students' performance deficiencies are keenly noticed and actualized for a variety of reasons. Some reasons may include transition from a home-reporting educational environment to an autonomous setting; lack of a friendly support system; or a host of behavioral circumstances which exacerbate latent academic deficits. One such technique for reviewing student performance can be employed and analyzed using absorbing Markov chains. The use of Markov Chains can provide quantitative information such the characterization potential delays (latency points) within and throughout the system, prediction of probabilistic metrics which define transitions between each stage of a defined state, and adaptability options for enrollment outcomes for use by school administrators. Furthermore, Markov chains can be employed to determine the impact on system resources such as limitations in faculty schedules, classroom assignments, and technology availability. Managers, administrators and advisors may find this information useful when notified of such limitations. This paper is of value to a broad audience such as researchers, managers, and administrators since it augments standard approaches of the Markov model. The blend of stochastic mathematics, applications of stochastic methods and retention theory, as well as the inclusion of adaptive sensitivity analysis are effective performance measures. Therefore, applications in Markov chains and subsequent forecasting models are of contemporary values in educational performance. Each of these concepts and methods contribute to a broader consideration of Markov properties in a branch of mathematics known as Markov Decision Processes (MDP). These types of processes allow researchers the ability to adjust parameters based on rewards, sets of actions, and discount factors. The cases outlined in this paper may be helpful when considering reductions in recidivism rates, improving policies to diminish recidivism, and increasing enrollment options using Markov analysis.
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Pinheiro, Thiago, Danilo Oliveira, Rubens Matos, Bruno Silva, Paulo Pereira, Carlos Melo, Felipe Oliveira, Eduardo Tavares, Jamilson Dantas, and Paulo Maciel. "The Mercury Environment: A Modeling Tool for Performance and Dependability Evaluation." In Intelligent Environments 2021. IOS Press, 2021. http://dx.doi.org/10.3233/aise210075.
Повний текст джерелаАнотація:
It is important to be able to judge the performance or dependability metrics of a system and often we do so by using abstract models even when the system is in the conceptual phase. Evaluating a system by performing measurements can have a high temporal and/or financial cost, which may not be feasible. Mathematical models can provide estimates about system behavior and we need tools supporting different types of formalisms in order to compute desired metrics. The Mercury tool enables a range of models to be created and evaluated for supporting performance and dependability evaluations, such as reliability block diagrams (RBDs), dynamic RBDs (DRBDs), fault trees (FTs), stochastic Petri nets (SPNs), continuous and discrete-time Markov chains (CTMCs and DTMCs), as well as energy flow models (EFMs). In this paper, we introduce recent enhancements to Mercury, namely new SPN simulators, support to prioritized timed transitions, sensitivity analysis evaluation, several improvements to the usability of the tool, and support to DTMC and FT formalisms.
Тези доповідей конференцій з теми "Markov chains; interval analysis; sensitivity analysis"
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Wang, Yan. "Solving Interval Master Equation in Simulation of Jump Processes Under Uncertainties." In ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/detc2013-12740.
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Two types of uncertainty are generally recognized in modeling and simulation, including variability caused by inherent randomness and incertitude due to the lack of perfect knowledge. Generalized interval probability is able to model both uncertainty components simultaneously, where epistemic uncertainty is quantified by the generalized interval in addition to the probabilistic measure. With the conditioning, independence, and Markovian property uniquely defined, the calculus structures in generalized interval probability resembles those in the classical probability theory. An imprecise Markov chain model is proposed with the ease of computation. A Krylov subspace projection method is developed to solve the interval master equation to simulate jump processes with finite state transitions under uncertainties. The state transitions with interval-valued probabilities can be simulated, which provides the lower and upper bound information of evolving distributions as an alternative to the traditional sensitivity analysis.
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Merletti, German, Michael Rabinovich, Salim Al Hajri, William Dawson, Russell Farmer, Joaquin Ambia, and Carlos Torres-Verdín. "New Iterative Resistivity Modelling Workflow Reduces Uncertainty in the Assessment of Water Saturation in Deeply-Invaded Reservoirs." In 2022 SPWLA 63rd Annual Symposium. Society of Petrophysicists and Well Log Analysts, 2022. http://dx.doi.org/10.30632/spwla-2022-0057.
Повний текст джерелаАнотація:
A new iterative modelling workflow has been designed to reduce uncertainty of water saturation (Sw) calculations in the tight Barik sandstone in the Sultanate of Oman. Results from this case study indicate that Sw can be overestimated by up-to twenty saturation units if the as-acquired deep resistivity is used in volumetric calculations. Overbalanced drilling causes deep invasion of water-based mud (WBM) filtrate into porous and permeable rocks, leading to radial displacement of in-situ saturating fluids away from the wellbore. In low-porosity reservoirs drilled with WBM the inability of the filtration process to quickly build impermeable mudcake translates into long radial transition zones. Under certain reservoir and drilling conditions, deep resistivity logs cannot reliably measure true formation resistivity and are therefore unable to provide an accurate assessment of hydrocarbon saturation. The effect of mud-filtrate invasion on resistivity logs has been extensively documented; processing techniques utilize resistivity inversion and tool-specific forward modeling to provide uninvaded formation resistivity logs which are much better suited for in-place resource volume assessment. However, sensitivity analysis shows that the accuracy of invasion-corrected logs dramatically decreases as the depth of invasion increases whereby the inversion process needs to be further constrained. The new workflow is designed to reduce the non-uniqueness of true formation resistivity models, so that they honor multiple and independent petrophysical data. The inversion routine utilizes a Bayesian algorithm coupled with Markov-Chain Monte Carlo (MCMC) sampling. Inversion results are iteratively modified based upon two rock property models: one derived from rock-core data (helium expansion porosity and Dean- Stark saturations), and the other using an equivalent log interpretation of thick reservoir intervals from oil-based mud (OBM) wells. Simulated borehole-resistivity are compared to field logs after each validation loop against rock property models. The new inversion-based workflow is extensively tested in the unconventional tight Barik formation across water-free hydrocarbon and perched water intervals and inversion-derived Sw models are independently validated by capillary pressure-derived saturation-height models and fluid inflow rate from production logs.