Probability Distributions Of Variables Research Articles

Probabilistic model for fatigue damage estimation of wind turbines with hidden markov model and neural network

The growing demand for sustainable and affordable energy sources has led to rapid development in wind energy systems. Ensuring the long-term performance and reliability of wind turbines requires accurate estimation of fatigue damage under diverse environmental conditions. By incorporating probabilistic methods, this paper presents a comprehensive framework for long-term fatigue damage evaluation for wind turbines with high accuracy and efficiency. The proposed framework adopts the multivariate kernel density estimation to construct the high-dimensional joint probability distribution of environmental variables. A hidden Markov model serves as the driver to build the connection between historical records and future events. The short-term fatigue damage is estimated by the deep neural network based on future environmental parameters. The long-term fatigue damage is then achieved by accumulating the short-term fatigue damage evaluations with sufficient event instances. To demonstrate the applicability and effectiveness of the proposed framework, a case study is conducted with a wind turbine in the North Sea region. The fatigue damage analysis results highlight the necessity of regular inspections and maintenance for wind turbines to ensure their long-term service life and optimal performance. The framework is capable of considering a wide range of environmental factors and accounting for the inherent uncertainties and stochastic nature, providing a robust and comprehensive approach for estimating fatigue damage of wind turbines as well as other structures under long-term environmental conditions.

Quantum model regression for generating fuzzy numbers in adiabatic quantum computing

This paper addresses the problem of inherent fuzziness in real-world data, arising from uncertainties, complexities, and limitations of traditional statistical methods. We introduce a pioneering method leveraging Adiabatic Quantum Computing (AQC), based on an adiabatic quantum regression model, to generate fuzzy numbers—ideal tools owing to their extension of real numbers and robust arithmetic properties. This innovative approach overcomes challenges in Quantum Machine Learning (QML) and limitations of Noisy Intermediate-Scale Quantum (NISQ) computers, providing a solution superior to conventional statistical methods and addressing the crucial issue of exponential power increase. Unique to this work, we offer rare closed-form expressions to produce fuzzy numbers through AQC and emphasise the integration of random variables and fuzzy numbers to encapsulate uncertainty fully. We propose a novel transformation of the Cumulative Distribution Function (CDF) into triangular and trapezoidal fuzzy numbers using AQC, enabling a comprehensive description of probability distributions of random variables. Experimental results are detailed, demonstrating the significant applicability and breakthroughs of this research in addressing data fuzziness.

Causal Structure Learning with Conditional and Unique Information Groups-Decomposition Inequalities.

The causal structure of a system imposes constraints on the joint probability distribution of variables that can be generated by the system. Archetypal constraints consist of conditional independencies between variables. However, particularly in the presence of hidden variables, many causal structures are compatible with the same set of independencies inferred from the marginal distributions of observed variables. Additional constraints allow further testing for the compatibility of data with specific causal structures. An existing family of causally informative inequalities compares the information about a set of target variables contained in a collection of variables, with a sum of the information contained in different groups defined as subsets of that collection. While procedures to identify the form of these groups-decomposition inequalities have been previously derived, we substantially enlarge the applicability of the framework. We derive groups-decomposition inequalities subject to weaker independence conditions, with weaker requirements in the configuration of the groups, and additionally allowing for conditioning sets. Furthermore, we show how constraints with higher inferential power may be derived with collections that include hidden variables, and then converted into testable constraints using data processing inequalities. For this purpose, we apply the standard data processing inequality of conditional mutual information and derive an analogous property for a measure of conditional unique information recently introduced to separate redundant, synergistic, and unique contributions to the information that a set of variables has about a target.

An adaptive data-driven subspace polynomial dimensional decomposition for high-dimensional uncertainty quantification based on maximum entropy method and sparse Bayesian learning

Polynomial dimensional decomposition (PDD) is a surrogate method originated from the ANOVA (analysis of variance) decomposition, and has shown powerful performance in uncertainty quantification (UQ) accuracy and convergence recently. However, complex high-dimensional problems result in a large number of polynomial basis functions, leading to heavy computational burden, and the probability distributions of the input random variables are indispensable for PDD modeling and UQ, which may be unavailable in practical engineering. This study establishes an adaptive data-driven subspace PDD (ADDSPDD) for high-dimensional UQ, which employs two types of data for modeling the PDD basis function and the low-dimensional subspace directly, namely, the data of input random variables and the input-response samples. Firstly, we propose a data-driven zero-entropy criterion-based maximum entropy method for reconstructing the probability density functions (PDF) of input variables. Then, with the aid of the established PDFs, a data-driven subspace PDD (DDSPDD) is proposed based on the whitening transformation. To recover the subspace of the function of interest accurately and efficiently, we put forward an approximate active subspace method (AAS) based on the Taylor expansion under some mild premises. Finally, we integrate an adaptive learning algorithm into the DDSPDD framework based on the sparse Bayesian learning theory, obtaining our ADDSPDD; thus, the real subspace and the significant PDD basis functions can be identified with limited computational budget. We validate the proposed method by using four examples, and systematically compare four existing dimension-reduction methods with the AAS. Results show that the proposed framework is effective and the AAS is a good choice when the corresponding assumptions are satisfied.

Aftershock probabilistic seismic hazard analysis based on enhanced Bayesian network considering frequency information

AbstractBayesian network (BN) is an important tool in probabilistic seismic risk analysis (PSRA) due to its holistic nature and powerful probabilistic inference capabilities. However, while the information that can be stored by BN includes variable values, probability distributions, and relationships between variables, it does not involve event quantities. The results obtained from PSRA and probabilistic seismic hazard analysis (PSHA) are commonly frequency‐related (the number of occurrences per unit time), fundamentally describing event numbers. BN assumes a fixed event number relationship between nodes, but the aftershock counts vary for different mainshock magnitudes. This limitation further restricts its effectiveness in lifespan PSRA for structures. Therefore, this study aims to propose an enhanced BN (EBN) for modeling aftershock PSHA (APSHA) considering frequency information. This paper first introduces the modeling method using BN, including PSHA and a simplified model of APSHA using Båth's law. Next, an EBN that can effectively address frequency issues between the mainshock and aftershocks is presented for modeling APSHA considering the modified Omori's law, while the mathematical principles of both forward and backward inferences for the EBN are elaborated in detail. Then, the article carefully analyzes the utilization of the EBN for APSHA modeling under different scenarios where the information regarding the mainshock is known to varying extents, followed by the extension of the EBN in a time domain to obtain time‐dependent aftershock hazard. Finally, an example of APSHA in a specific location in China is illustrated.

Multi-period descriptive sampling for scenario generation applied to the stochastic capacitated lot-sizing problem

Using scenarios to model a stochastic system’s behavior poses a dilemma. While a large(r) set of scenarios usually improves the model’s accuracy, it also causes drastic increases in the model’s size and the computational effort required. Multi-period descriptive sampling (MPDS) is a new way to generate a small(er) set of scenarios that yield a good fit both to the periods’ probability distributions and to the convoluted probability distributions of stochastic variables (e.g., period demands) over time. MPDS uses descriptive sampling to draw a sample of S representative random numbers from a period’s known (demand) distribution. Now, to create a set of S representative scenarios, MPDS heuristically combines these random numbers (period demands) period by period so that a good fit is achieved to the convoluted (demand) distributions up to any period in the planning interval. A further contribution of this paper is an (accuracy) improvement heuristic, called fine-tuning, executed once the fix-and-optimize (FO) heuristic to solve a scenario-based mixed integer programming model has been completed. Fine-tuning uses linear programming (LP) with fixed binary variables (e.g., setup decisions) generated by FO and iteratively adapts production quantities so that compliance with given expected service level constraints is reached. The LP is solved with relatively little computational effort, even for large(r) sets of scenarios. We show the advancements possible with MPDS and fine-tuning by solving numerous test instances of the stochastic capacitated lot-sizing problem under a static uncertainty approach.

Analysis on Probability Mass Function and Probability Density Function

Probability Mass Function (PMF) and Probability Density Function (PDF) are fundamental concepts in probability theory and statistics that play a crucial role in describing the probability distribution of random variables. This abstract provides a comprehensive overview of these concepts, highlighting their definitions, characteristics, and applications. The Probability Mass Function is a concept primarily associated with discrete random variables. It defines the probability of a specific outcome occurring. The PMF assigns probabilities to individual values in the sample space, providing a clear picture of the likelihood of each possible outcome. Commonly denoted as P(X=x), where X is the random variable and x is a specific value, the PMF must satisfy two essential properties: non-negativity and the sum of probabilities over all possible outcomes equals one. On the other hand, the Probability Density Function is a concept applied to continuous random variables. Unlike the PMF, which deals with specific values, the PDF deals with ranges of values. The PDF represents the probability that a continuous random variable falls within a given interval. Denoted as f(x), it is essential to note that the probability of any specific point is zero, and instead, probabilities are defined for intervals. The area under the PDF curve over a given interval corresponds to the probability of the random variable falling within that interval. Understanding the differences and similarities between PMF and PDF is crucial for statistical analysis. While PMF is discrete and deals with specific values, PDF is continuous and provides probabilities for intervals. Both functions are integral to the calculation of various statistical measures, including expected values, variance, and standard deviation. This abstract concludes with a discussion of practical applications in diverse fields, such as finance, engineering, and natural sciences, where a deep understanding of PMF and PDF is essential for making informed decisions and drawing meaningful conclusions from data. The integration of these concepts into statistical models and analyses enhances the accuracy and reliability of predictions, making PMF and PDF indispensable tools in the field of probability and statistics

A deep clustering framework integrating pairwise constraints and a VMF mixture model

<abstract><p>We presented a novel deep generative clustering model called Variational Deep Embedding based on Pairwise constraints and the Von Mises-Fisher mixture model (VDEPV). VDEPV consists of fully connected neural networks capable of learning latent representations from raw data and accurately predicting cluster assignments. Under the assumption of a genuinely non-informative prior, VDEPV adopted a von Mises-Fisher mixture model to depict the hyperspherical interpretation of the data. We defined and established pairwise constraints by employing a random sample mining strategy and applying data augmentation techniques. These constraints enhanced the compactness of intra-cluster samples in the spherical embedding space while improving inter-cluster samples' separability. By minimizing Kullback-Leibler divergence, we formulated a clustering loss function based on pairwise constraints, which regularized the joint probability distribution of latent variables and cluster labels. Comparative experiments with other deep clustering methods demonstrated the excellent performance of VDEPV.</p></abstract>

Law of Probability Distribution Function of The Module of Difference of Discrete Random Variables

The use of the absolute value symbol in theoretical studies often leads to difficulties in analytical operations. However, from a practical point of view, transformations based on absolute differences are the most visual and effective. The article discusses functional transformations, which are modules of the differences of discrete random variables. The concept of the first difference modulus is given. The laws of the probability distribution of random variables obtained as the modulus of the difference of two independent random variables that have the same discrete distribution (Bernoulli or geometric), as well as the distribution laws of new random variables that are the sums of the moduli of the first difference, have been found. The main numerical characteristics of new random variables are calculated.

Systematic framework for handling uncertainty in probabilistic failure analysis of corroded concretes

Due to ambiguous correlations between input random variables and multi-source uncertainties from the electrochemical model, significant differences between deterministic corrosion prediction models and actual measurements are often observed. A systematic framework of quantification of uncertainties is developed for structures with correlated random variables originated from multiple sources, which allows efficiently estimating the failure probability distribution of the steel corrosion over time considering the randomness of the cover depth, the surface chloride concentration, and the chloride diffusion coefficient. After partitioning correlated random variables into different groups based on their uncertain sources, the Morris one-step-at-a-time and Sobol model is established to rank with respect to the importance of each correlated random variable. Based on polynomial chaos expansions and genetic programming methods, a more condensed set of random variables is created to propagate parametric problems. The unknown probability distribution of the input random variables is formulated by the Markov chain Monte Carlo to realize rigorous uncertainty quantification of the structural reliability. The application of the systematic framework to a set of numerical examples of steel corrosion includes experimental validation and uncertainty quantification and propagation of environmental, material and geometric properties. The results show that the framework can be integrated with parametric electrochemical models to allow robustness and reliability of corrosion prediction.

Analysis of statistical properties of variables in log data for advanced anomaly detection in cyber security

Log lines consist of static parts that characterize their structure and enable assignment of event types, and event parameters, i.e., variable parts that provide specific information on system processes, such as host and user names, IP addresses, and file operations. Many detection approaches only focus on anomalous event type occurrences, i.e., they parse log lines to derive unique event identifiers and subsequently detect anomalies in event sequences or event count vectors, but neglect variable parts of log lines entirely during analysis. This is especially problematic, when monitoring strongly structured log data that contains only a small number of distinct event types, for example, logs that consist of strict key value pairs, i.e., parameters that occur consistently throughout all log lines, such as it is case in access and audit logs. Thus, novel approaches are required, which focus on analysis of log lines' variable parts. In this paper, we propose the variable type detector (VTD), a novel unsupervised approach that autonomously analyzes variable log line parts to enable anomaly detection. It assigns data types to each variable, which also include probability distributions for discrete and continuous variables. The VTD raises an alarm if a variable's data type changes. Furthermore, it implements a robust indicator function that reduces false positives by tracking the data type history of each variable and reports only significant data type changes. Additionally, an event indicator enables event-based anomaly detection by taking into account the data types of all variables of a single event type. The evaluation conducted on open-source log data, demonstrates the effectiveness of the VTD compared to conventional anomaly detection approaches, such as time series analysis and PCA. Consequently, the VTD acts as a solution that extends the intrusion detection capabilities of security information and event management (SIEM) and integrates with modern concepts of endpoint detection and response (EDR) and extended detection and responses (XDR), while simultaneously serving as an asset for process monitoring that supports user and entity behavior analytics (UEBA).

Modelo probabilístico para análises de ruído do tráfego urbano usando sinais sonoros reais

Abstract Vehicular traffic is pointed out as a major source of urban noise pollution today. In this paper, we evaluated the precision of a new probabilistic model for urban traffic noise analyses. The proposed model adopts real sound signals and the Monte Carlo method in simulations. Probability distributions of traffic variables were obtained in-situ on two urban roads. The acoustic signals and corresponding energies of single pass-by of vehicles were obtained usingsound signal recordings on test tracks under free-field condition. The model simulates vehicular traffic noise on urban roads in free or in trafficlight controlled flow and considers the influence of bus stops.The proposed model calculates different acoustic descriptors, such as Statistical sound levels (LA10 and LA90), Equivalent continuous sound level (LAeq), Trafficnoise index (TNI) and Noise pollution level (LNP). Furthermore, it allowsthe listening of simulated noise. The experimental results indicate that theproposed model is reliable and accurate for vehicular traffic noise prediction.

Frequency-Control-Aware Probabilistic Load Flow: An Analytical Method

Probabilistic load flow (PLF) calculation, as a fundamental tool to analyze transmission system behavior, has been studied for decades. Despite a variety of available methods, existing PLF approaches rarely take system control into account. However, system control, as an automatic buffer between the fluctuations in random variables and the variations in system variables (e.g., nodal voltages), has a significant impact on the final PLF result. To consider control actions' influence, this paper proposes the first analytical PLF method for the transmission grid that takes into account primary and secondary frequency controls. This method is based on a high-precision linear power flow model, whose precision is even further improved in this paper by an original correction approach. This paper also proves that if the joint probability distribution (JPD) of random variables is expressed by a Gaussian mixture model (GMM), then the JPD of system variables is an infinite GMM. By leveraging this proposition, the proposed method generates the joint PLF of the whole system at the quasi-steady and steady states. The high accuracy and satisfactory efficiency of this method are verified on multiple test systems with different percentages of renewables.

Application of the Monte-Carlo Method to Assess the Operational Reliability of a Household-Constructed Wetland with Vertical Flow: A Case Study in Poland

The objective of this study was to model the operation of a vertical-flow constructed wetland (VF-CW) for domestic wastewater, using Monte-Carlo simulations and selected probability distributions of various random variables. The analysis was based on collected wastewater quality data, including the values of the pollutant indicators BOD5 (biochemical oxygen demand), CODCr (chemical oxygen demand), and TSS (total suspended solids), in the 2017–2020 period. Anderson–Darling (A–D) statistics were applied to assess the fit of the theoretical distributions to the empirical distributions of the random variables under study. The selection of the best-fitting statistical distributions was determined using the percentage deviation (PBIAS) criterion. Based on the analyses that were performed, the best-fitting statistical distributions for the pollution indicators of the raw wastewater were the generalised extreme value distribution for BOD5, the Gaussian distribution for CODCr, and the log-normal distribution for TSS. For treated effluent, the log-normal distribution was the best fit for BOD5 and CODCr; the semi-normal distribution, for TSS. The new data generated using the Monte-Carlo method allowed the reliability of the VF-CW operation to be assessed by determining the reliability indices, i.e., the average efficiency of the removal of pollutants (η), the technological efficiency index (R), the reliability index (CR), and the risk index of the negative control of the sewage treatment plant operation (Re). The obtained results indicate that only in the case of CODCr, the analysed treatment facility may fail to meet the requirements related to the reduction of organic pollutants to the required level, which is evidenced by the values of the indicators CR = 1.10, R = 0.49, and η = 0.82. In addition, the risk index of the negative operation of the facility (Re) assumes a value of 1, which indicates that during the period of its operation, the VF-CW system will not operate with the required efficiency in relation to this indicator. The novelty of this work is the implementation of the indicated mathematical simulation methods for analysing the reliability of the operation of the domestic wastewater treatment facility.

Multivariate probability analysis of wind-wave actions on offshore wind turbine via copula-based analysis

Floating structures in service encounter extreme natural hazards, such as correlated extreme wind-wave loads. This study aims to provide realistic multivariate models of environmental parameters to accurately describe the statistical characteristics of metoceanic conditions, which are essential for the reliability-based design of marine structures. The multiload analysis method includes three major steps: (1) to identify the best-fit univariate marginal distributions of the wind-wave parameters. Mixed models composed of a set of single-mode parametric distributions were found to be more suitable for the measured variables. (2) To construct joint probability distributions of multiple variables using copula-based models, the performance of various models namely, trivariate metaelliptical copulas, Archimedean copulas, and vine copula models. It was observed that joint distributions can be best modelled using vine copula models with considerable flexibility. The final process involves establishing environmental surfaces and contours based on the inverse first-order reliability method. The most unfavourable combination of extreme design conditions can be defined on the environmental surface which is useful for evaluating the response characteristics of offshore wind turbines. These expressions provide a preliminary assessment of wind-wave loads on offshore structures.

Day-ahead optimal peer-to-peer energy trading strategy for multi-microgrids based on Nash bargaining game with data-driven chance constraints

This paper proposes an optimization model to obtain the day-ahead optimal peer-to-peer (P2P) trading strategy for multi-microgrids (MMG). Firstly, a joint economic energy and reserve scheduling model of a microgrid (MG) is established while considering specific network constraints. Then, to mitigate the impact of renewable energy and load forecasting errors, chance constraints are introduced for the reserve capacity and buses voltage limitations of an individual microgrid. Additionally, a versatile distribution method is adopted to capture the probability distribution of uncertain variables in a data-driven manner, avoiding any prior assumptions. Finally, Nash bargaining theory is employed to deal with the P2P energy trading problem among MMG. The problem is equivalently transformed into two sequential subproblems for solving. Moreover, the alternating direction method of multipliers algorithm is used to solve the subproblems in a distributed manner for privacy concerns. The proposed model not only enables effective P2P energy trading for MMG, but also ensures compliance with the internal network constraints of each MG. Furthermore, the scheduling strategy exhibits robustness in handling forecast errors related to renewable energy and load. In case studies, MMG containing three interconnected MGs is constructed based on the IEEE-123 bus distribution network, and simulation results show that the cost of the MMG is reduced by 9.92 % while all the MGs can benefit from P2P trading. In addition, the risk-averse scheduling results of energy and reserve are obtained, and the conservativeness can be controlled by changing the confidence level, which verifies the effectiveness of the proposed model.

REIN: Reliability Estimation via Importance sampling with Normalizing flows

We introduce a novel framework called REIN: Reliability Estimation by learning an Importance sampling (IS) distribution with Normalizing flows (NFs). The NFs learn probability space maps that transform the probability distribution of the input random variables into a quasi-optimal IS distribution. NFs stack together invertible neural networks to construct differentiable bijections with efficiently computed Jacobian determinants. The NF ‘pushes forward’ a realization from the input probability distribution into a realization from the IS distribution, with importance weights calculated using the change of variables formula. We also propose a loss function to learn a NF map that minimizes the reverse Kullback–Leibler divergence between the ‘pushforward’ distribution and a sequentially updated target distribution obtained by modifying the optimal IS distribution. We demonstrate REIN’s efficacy on a set of benchmark problems that feature very low failure rates, multiple failure modes and high dimensionality, while comparing against other variance reduction methods. We also consider two simple applications, the reliability analyses of a thirty-four story building and a cantilever tube, to demonstrate the applicability of REIN to practical problems of interest. As compared to other methods, REIN is shown to be useful for high-dimensional reliability estimation problems with very small failure probabilities.

Contextualized and localized up-to-Date Data Driven Lesson Materials in Statistics and Probability

Statistics and Probability has always been one of the most challenging subjects introduced through a spiral approach in the implementation of K-12 Education Curriculum. A stigma that has been apparent long before the COVID-19 Pandemic. But has become more evident for both the learners and teachers during distance learning. The researcher therefore aims to provide an intervention that is applicable even during situations of mandatory implementation of distance learning modalities. Specifically for schools who have no access to online learning modalities. The researcher used Contextualized and Localized Up-to-Date Data Driven Lesson Materials in Statistics and Probability to Grade 11 GAS learners of San Antonio National High School (SANHS) for SY 2022-2023. The materials were developed by the researcher and includes data from the school. Two materials were used in teaching the following competencies: (a) Calculates the mean and the variance of a discrete random variable M11/12SP-IIIb-2; (b) Interprets the mean and the variance of a discrete random variable M11/12SP-IIIb-3; and (c) Solves problems involving mean and variance of probability distributions M11/12SP-IIIb-4. The study also includes presenting how these Contextualized and Localized Up-to-Date Data Driven Lesson Materials have affected the attitudes of the respondents towards Statistics & Probability using the Survey of Attitudes Toward Statistics – 36 (SATS-36) by Schau, 2003. The conduct of this action research therefore aimed to answer the following research questions: (1) What contextualized and localized up-to-date data driven lesson materials can be used in teaching Statistics & Probability for the following Most Essential Competencies: (a) Calculates the mean and the variance of a discrete random variable. M11/12SP-IIIb-2; (b) Interprets the mean and the variance of a discrete random variable. M11/12SP-IIIb-3; (c) Solves problems involving mean and variance of probability distributions. M11/12SP-IIIb-4. (2) What is the attitude towards Statistics & Probability of Grade-11 GAS students before and after using the developed lesson materials? (3) What are the effects of the developed lessons materials on the students’ academic performance on the chosen competencies? Results of the action research conducted from August – October are as follows: (1) two contextualized and localized up-to-date data driven lesson materials were developed in teaching the following competencies: (a) Calculates the mean and the variance of a discrete random variable M11/12SP-IIIb-2; (b) Interprets the mean and the variance of a discrete random variable M11/12SP-IIIb-3; and (c) Solves problems involving mean and variance of probability distributions M11/12SP-IIIb-4. (2) The Grade 11-GAS learners showed improvement towards their attitudes towards statistics and probability. Specifically in terms of affect, cognitive competence, difficulty, interest, and effort. (3) The developed contextualized and localized up- to-date data driven lesson materials have improved the academic performance of the Grade 11- GAS learners. Specifically, with reference to the administered teacher-made pre/post-test, the respondents showed increase in performance level to each of the three competencies. But such increases performance level was not enough for the respondents to achieve mastery level. Hence, the results suggests that there is a need to further improve the developed materials.

Reliability assessment of civil structures with incomplete probability distribution information

The probability distribution of random variables is usually incomplete owing to a limited amount of data, making it a challenging problem for structural reliability assessments. This paper presents a novel reliability analysis method for civil structures with incomplete data. The probability distributions of the random variables were estimated using an improved Bayesian inference method. In the proposed inference method, the frequencies and mode shapes were selected as the observation data. The likelihood function is replaced by homogeneous chaos, and the computational efficiency of Bayesian inference is improved. The affine invariant ensemble algorithm was used to generate samplers for the posterior distribution. After estimating the probability distribution of the incomplete random variables, a reliability analysis was performed, and the failure probability of the structure was estimated. Numerical studies on a two-span, two-story reinforced concrete building and a five-span bridge are presented. Experimental studies were also performed on an eight-story steel frame structure. The results show that the probability distributions of random variables can be significantly updated using the proposed technique and modal properties. The proposed technique was more efficient than the Gibbs sampling method. The failure probabilities of the structures were estimated using the estimated probability distributions.

An efficient discretization scheme for a dynamic Bayesian network in structural reliability analysis

Using a dynamic Bayesian network (DBN) to estimate the failure risk of a component or system that deteriorates with time has several advantages. A DBN discretizes the probability distribution of variables and thereby increases the efficiency of computing resources and reduces computation time. However, it is important to devise an optimal discretization scheme because the size of the model grows exponentially as the number of discretized intervals increases. In this paper, we propose an optimal discretization scheme for a DBN used to model the time-varying deterioration of a turbine blade component. The results of estimating the reliability indices with the DBN were verified by comparing them with the results of a Monte Carlo simulation. In addition, compared with a log-transformed discretization method, our DBN discretization method shows a significantly increased computation speed.