Fuzzy Bayesian Inference Research Articles

Fuzzy Bayesian inference for under-five mortality data

Under-five mortality remains a significant global health challenge, with millions of children dying before their fifth birthday each year. This study explores the application of fuzzy Bayesian inference for under-five mortality data using Tanzania as a case study. Fuzzy Bayesian inference has emerged as a promising technique that combines the flexibility of fuzzy set theory with the probabilistic framework of Bayesian inference. The study employs fuzzy sets and membership functions to represent the linguistic terms and their degrees of membership, along with the Poisson distribution to model the mortality rate. The results demonstrate the potential of fuzzy Bayesian inference for analyzing under-five mortality rates. This approach provides a more nuanced understanding of the complex mortality patterns.

A New Fuzzy Bayesian Inference Approach for Risk Assessments

Bayesian network (BN) inference is an important statistical tool with additive symmetry. However, BN inference cannot deal with the uncertain, fuzzy, random, and conflicting information from experts’ knowledge in the process of conducting a risk assessment. To tackle this issue, a new fuzzy BN inference approach for risk assessments was proposed based on cloud model (CM), interval type-2 fuzzy set (IT2 FS), interval type-2 fuzzy logic system (IT2 FLS), modified Dempster–Shafer (D-S) evidence theory (ET), and Latin hypercube sampling (LHS) methods along the following lines. Firstly, CM was integrated into IT2 FS, and CM-based IT2 FS (CM-IT2 FS) was defined in the IT2 FLS. Secondly, modified D-S ET was utilized to determine the CM-IT2 FS-based a priori probabilities, and the CM-IT2 FS-based BN model was established. Thirdly, the CM-IT2 FS-based a priori probabilities were reduced to the CM-IT1 FS-based ones using a type reducer in the IT2 FLS, LHS was applied to propose a new fuzzy BN inference algorithm, and then, the new algorithm was used in a typical case to perform the fuzzy BN positive inference for risk prediction and the fuzzy BN reverse inference for risk sensitivity analysis. Finally, the BN inference results were analyzed using the proposed algorithm and the two common BN inference algorithms, and the effectiveness of the proposed approach was validated. It can be concluded that the proposed approach was both accurate and promising.

An Integrated Quantitative Risk Assessment Method for Underground Engineering Fires

Fires are one of the main disasters in underground engineering. In order to comprehensively describe and evaluate the risk of underground engineering fires, this study proposes a UEF risk assessment method based on EPB-FBN. Firstly, based on the EPB model, the static and dynamic information of the fire, such as the cause, occurrence, hazard, product, consequence, and emergency rescue, was analyzed. An EPB model of underground engineering fires was established, and the EPB model was transformed into a BN structure through the conversion rules. Secondly, a fuzzy number was used to describe the state of UEF variable nodes, and a fuzzy conditional probability table was established to describe the uncertain logical relationship between UEF nodes. In order to make full use of the expert knowledge and empirical data, the probability was divided into intervals, and a triangulated fuzzy number was used to represent the linguistic variables judged by experts. The α-weighted valuation method was used for de-fuzzification, and the exact conditional probability table parameters were obtained. Through fuzzy Bayesian inference, the key risk factors can be identified, the sensitivity value of key factors can be calculated, and the maximum risk chain can be found in the case of known evidence. Finally, the method was applied to the deductive analysis of three scenarios. The results show that the model can provide realistic analysis ideas for fire safety evaluation and emergency management of underground engineering. The proposed EPB risk assessment model provides a new perspective for the analysis of UEF accidents and contributes to the ongoing development of UEF research.

Quantitative Risk Analysis of Disconnect Operations in a Marine Nuclear Power Platform Using Fuzzy Bayesian Network

Marine nuclear power platforms can continuously supply electricity and fresh water for marine resource exploration and surrounding islands. China’s first marine nuclear power platform uses a soft yoke multi-joint connect mode as the mooring positioning device. When the marine nuclear power platform needs repair, maintenance, nuclear fuel replacement, or a different operation area, a mooring disconnect operation must be carried out. The traditional mooring disconnect process consists of four stages: cable limiting, yoke offloading, yoke dropping, and equipment recovery stages. The entire disconnect process is a high-risk nuclear-related operation that could result in a collision accident between the yoke and hull structure, resulting in nuclear fuel leaks and casualties. Therefore, it is necessary to evaluate the risk factors of the disconnect process and to assess the risk level together with the consequence of each risk. In this paper, a quantitative risk analysis of nuclear power platform disconnect operations is carried out based on a fuzzy Bayesian network approach for risk events in each stage of the disconnect operations. Based on the forward fuzzy Bayesian inference, the criticality of each risk event to the disconnect process is evaluated and compared. The main risk factors that may cause a disconnect accident are then determined based on the reverse Bayesian inference rule. The results indicate that human error is the most likely factor leading to the failure of the disconnect process, requiring strict control of personnel operation procedures during this process. The yoke colliding with the hull and stern antifriction chain-breaking are the most significant hazards caused by the disconnect failing. Thus, the distance between the yoke and hull, stern tug tensile force, and maintenance of the antifriction chain should receive particular attention.

Diagnosing with a hybrid fuzzy–Bayesian inference approach

A diagnosis based on Bayesian theory requires knowledge of the a priori and conditional probabilities of the states of the system being diagnosed. The a priori probabilities are frequently provided nowadays by the manufacturers of these systems. In turn, the probabilities of conditional observations are, as a rule, not available. The question arises as to whether and under what conditions it is possible to substitute conditional probabilities with some aggregate obtainable on the grounds of fuzzy logic. This article responds to this question by proposing a hybrid approach with novelty characteristics in both theoretical and practical terms. In the initial phase of the deliberations, it was concluded that the fundamental difference between Bayesian and fuzzy approaches is that the fuzzy approach considers the uncertainty and lack of precision of observations but overlooks the frequency of observations, and the opposite is true of the Bayesian approach. It therefore seems reasonable to seek the hybridization of both methods so that the Bayesian approach carrying the information regarding the subjective probabilities of faults can be applied in practice. To this end, it has been shown that the probability of a conditional observation can be estimated by calculating the degree of truth of the premise for that observation in the state-specific fuzzy rule. The reminder is devoted to presenting numerical and simulation examples illustrating and verifying the proposed approach.

A failure probability evaluation method for collapse of drill-and-blast tunnels based on multistate fuzzy Bayesian network

Collapse is one of the main hazards during tunnel construction by the drill-and-blast method. In order to evaluate the collapse risk and provide a basis for risk control, a failure probability evaluation method for collapse of drill-and-blast tunnels based on the multistate fuzzy Bayesian network is proposed in this paper. First, the typical tunnel collapse cases are analyzed statistically based on the risk breakdown structure method, a fault tree model is built for drill-and-blast tunnel collapses and the causal relationships between the tunnel collapse and the influential factors, such as natural conditions, engineering geology and construction etc., are revealed. Secondly, the multiple fault states of nodes, including rock mass grade and groundwater, are described by the fuzzy numbers. The fuzzy subsets are utilized to describe the failure probability of nodes and the uncertain logic relationship between nodes described by the multistate fuzzy conditional probability table is established. In order to ensure the reliability of the survey data when evaluating the possibility intervals of the multistate fuzzy conditional probability tables and the fuzzy failure probability of root nodes, as well as taking the expert judgment ability level and subjective reliability level into consideration, an expert investigation method based on the confidence indicator is proposed. Finally, in order to fully exploit expert knowledge and empirical data, the α-weighted valuation method is adopted for defuzzification so as to obtain precise parameters for the conditional probability tables. The 3σ criterion is employed to calculate the characteristic values of triangular fuzzy numbers so as to determine the prior fuzzy failure probability of root nodes. By means of the fuzzy Bayesian inference, the proposed method is capable of calculating the probability distribution of tunnel collapse and identifying the critical risk factors under both prior knowledge and given evidence circumstances. Taking the collapse failure probability evaluation for the Xiucun Tunnel passing through the fault F18 as an example, the application results demonstrated the feasibility and efficiency of the proposed method and it can be utilized as a decision-making tool for safety risk management during tunnel construction.

Collapse Risk Analysis of Deep Foundation Pits in Metro Stations Using a Fuzzy Bayesian Network and a Fuzzy AHP

Collapse risk analysis is of great significance for ensuring construction safety in foundation pits. This study proposes a comprehensive methodology for dynamic risk analysis of foundation pit collapse during construction based on a fuzzy Bayesian network (FBN) and a fuzzy analytical hierarchy process (FAHP). Firstly, the potential risk factors contributing to foundation pit collapse are identified based on the results of statistical analysis of foundation pit collapse cases, expert inquiry, and fault tree analysis. Then, a FAHP and improved expert elicitation considering a confidence index are adopted to elicit the probability parameters of the BN. On this basis, quantitative risk reasoning and sensitivity analysis of foundation pit collapse are achieved by means of fuzzy Bayesian inference. Finally, an actual deep foundation pit in a metro station was used to illustrate a specific application of this approach, and the results were in accordance with the field observations and numerical simulation results. The proposed approach can provide effective decision-making support for planners and engineers, which is vital to the prevention and control of the occurrence of the foundation pit collapse accidents.

Data Fusion through Fuzzy-Bayesian Networks for Belief Generation in Cognitive Agents

Situation Awareness provides a theory for agents decision making to allow perception and comprehension of his environment. However, the transformation of the sensory stimulus in beliefs to favor the BDI reasoning cycle is still an unexplored subject. Autonomous agent projects often require the use of multiple sensors to capture environmental aspects. The natural variability of the physical world and the imprecision contained in linguistic concepts used by humans mean that sensory data contain different types of uncertainty in their measurements. Thus, to obtain the Situational Awareness for Agents with physical sensors, it is necessary to define a data fusion process to perform uncertainty treatment. This paper presents a model to beliefs generation using fuzzy-bayesian inference. An example in robotics navigation and location is used to illustrate the proposal.

Risk Assessment of Water Penetration for Shield Tunnel Construction in Coastal Area

In the process of assessing the risk of flooding during the construction of shield tunnel in coastal area, the basic probability of accidents is often difficult to be expressed by an exact numerical value due to the fact that the actual statistical data of accidents are too few or missing. In order to solve this problem, this paper, with the factors by combining the fuzzy Bayesian network inference advantages and the advantages of the fuzzy set theory to deal with fuzzy information, using a risk assessment method based on fuzzy Bayesian network method, established the waterfront subway shield tunnel construction risk decision model and predicted the subway shield tunnel flooded the area of probability; at the same time, the sensitivity of each basic event was calculated according to the fuzzy significance to identify the key risk factors, and the applicability and accuracy of this method were verified by combining with the regional engineering of Hujing station ∼ Wanshou station of Fuzhou Metro Line 6.

Efficiency of Fuzzy Bayesian Inference in Predicting the Frequency of PDO Crashes on Urban Highways

Efficiency of Fuzzy Bayesian Inference in Predicting the Frequency of PDO Crashes on Urban Highways

Habfuzz: A tool to calculate the instream hydraulic habitat suitability using fuzzy logic and fuzzy Bayesian inference

Theodoropoulos et al, (2016), Habfuzz: A tool to calculate the instream hydraulic habitat suitability using fuzzy logic and fuzzy Bayesian inference, Journal of Open Source Software, 1(6), 82, doi:10.21105/joss.00082

A fuzzy Bayesian approach to flood frequency estimation with imprecise historical information.

This paper presents a novel framework that links imprecision (through a fuzzy approach) and stochastic uncertainty (through a Bayesian approach) in estimating flood probabilities from historical flood information and systematic flood discharge data. The method exploits the linguistic characteristics of historical source material to construct membership functions, which may be wider or narrower, depending on the vagueness of the statements. The membership functions are either included in the prior distribution or the likelihood function to obtain a fuzzy version of the flood frequency curve. The viability of the approach is demonstrated by three case studies that differ in terms of their hydromorphological conditions (from an Alpine river with bedrock profile to a flat lowland river with extensive flood plains) and historical source material (including narratives, town and county meeting protocols, flood marks and damage accounts). The case studies are presented in order of increasing fuzziness (the Rhine at Basel, Switzerland; the Werra at Meiningen, Germany; and the Tisza at Szeged, Hungary). Incorporating imprecise historical information is found to reduce the range between the 5% and 95% Bayesian credibility bounds of the 100 year floods by 45% and 61% for the Rhine and Werra case studies, respectively. The strengths and limitations of the framework are discussed relative to alternative (non‐fuzzy) methods. The fuzzy Bayesian inference framework provides a flexible methodology that fits the imprecise nature of linguistic information on historical floods as available in historical written documentation.

Selection methodology for screening evaluation of EOR methods

ABSTRACTThe choice of enhanced oil recovery (EOR) methods for specific reservoir conditions is one of the most difficult tasks for a reservoir engineer. Taber (Taber, 1980; Taber et al., 1997a,b) gave informative overview of EOR research history. He also offered technical screening guides for EOR nowadays known as Taber's tables. It should be noted that the approach recommended by Taber could not be taken as strong mathematical ranking of EOR methods. The authors propose an approach for EOR methods selection, based on fuzzy logic, possibility theory, and Bayesian inference mechanisms. Rankings were made by way of best EOR method selection for every criteria using fuzzy intervals comparison. Final correction of each EOR selection coefficient was performed by the generalized Bayesian inference mechanism. Application of this methodology for reservoir conditions of Alberta oil field, as well as the offshore field “Guneshli,” allowed for choosing the most effective EOR method, confirming the accuracy and feasibility of the proposed approach. Simple calculation (not more than five iterations) allows the automation of the process of selecting the most effective EOR method for a particular field.

Fuzzy Bayesian Inference for Gompertz Distribution

Objectives: Fuzzy Bayesian approach is implemented to enrich the probability updating process with fuzzy facts. Methods: In this paper, different methods of estimation are discussed for the parameters of Gompertz distribution when the available data are in the form of fuzzy numbers. Bayes estimators of the parameters are studied under different symmetric and asymmetric loss functions. The estimation procedures are discussed in details and compared via Monte Carlo simulations. Finally, a real data set which shows the TB affected people of the thirty districts of Tamil Nadu in the year 2009 to 2011 is investigated to explain the applicability of the proposed methods. Findings: Among all the loss functions which are provided here, Linear Exponential loss function is more preferable as compared to all other loss functions.

Efficient fuzzy Bayesian inference algorithms for incorporating expert knowledge in parameter estimation

Summary Bayesian inference has traditionally been conceived as the proper framework for the formal incorporation of expert knowledge in parameter estimation of groundwater models. However, conventional Bayesian inference is incapable of taking into account the imprecision essentially embedded in expert provided information. In order to solve this problem, a number of extensions to conventional Bayesian inference have been introduced in recent years. One of these extensions is ‘fuzzy Bayesian inference’ which is the result of integrating fuzzy techniques into Bayesian statistics. Fuzzy Bayesian inference has a number of desirable features which makes it an attractive approach for incorporating expert knowledge in the parameter estimation process of groundwater models: (1) it is well adapted to the nature of expert provided information, (2) it allows to distinguishably model both uncertainty and imprecision, and (3) it presents a framework for fusing expert provided information regarding the various inputs of the Bayesian inference algorithm. However an important obstacle in employing fuzzy Bayesian inference in groundwater numerical modeling applications is the computational burden, as the required number of numerical model simulations often becomes extremely exhaustive and often computationally infeasible. In this paper, a novel approach of accelerating the fuzzy Bayesian inference algorithm is proposed which is based on using approximate posterior distributions derived from surrogate modeling, as a screening tool in the computations. The proposed approach is first applied to a synthetic test case of seawater intrusion (SWI) in a coastal aquifer. It is shown that for this synthetic test case, the proposed approach decreases the number of required numerical simulations by an order of magnitude. Then the proposed approach is applied to a real-world test case involving three-dimensional numerical modeling of SWI in Kish Island, located in the Persian Gulf. An expert elicitation methodology is developed and applied to the real-world test case in order to provide a road map for the use of fuzzy Bayesian inference in groundwater modeling applications.

Data-driven fault detection and isolation scheme for a wind turbine benchmark

This paper investigates a new scheme for fault detection and isolation based on time series and data analysis. This scheme is applied in wind turbines which are used to tap the potential of renewable energy. The proposed scheme is performed in two steps and it is based on process data without using any kind of physical modeling. The first step, the fault detection, is based on an alternative method based on the Gibbs sampling algorithm in which the occurrence of a sensor fault is modeled as a change point detection in a time series. The second step, the fault isolation, is handled via a Fuzzy/Bayesian network scheme classifying the kind of fault. The proposed fault detection and isolation (FDI) strategy offers as main contribution the independence from any kind of dynamical modeling and the unprecedented usage of the Gibbs sampling. Furthermore, this work offers a novel data driven FDI approach based on Fuzzy-Bayesian inference and suitable for the wind turbines systems. This approach presents a good performance for detection and diagnostics of sensor faults in a standard wind turbine benchmark.

Towards a Fuzzy Bayesian Network Based Approach for Safety Risk Analysis of Tunnel-Induced Pipeline Damage.

Tunneling excavation is bound to produce significant disturbances to surrounding environments, and the tunnel-induced damage to adjacent underground buried pipelines is of considerable importance for geotechnical practice. A fuzzy Bayesian networks (FBNs) based approach for safety risk analysis is developed in this article with detailed step-by-step procedures, consisting of risk mechanism analysis, the FBN model establishment, fuzzification, FBN-based inference, defuzzification, and decision making. In accordance with the failure mechanism analysis, a tunnel-induced pipeline damage model is proposed to reveal the cause-effect relationships between the pipeline damage and its influential variables. In terms of the fuzzification process, an expert confidence indicator is proposed to reveal the reliability of the data when determining the fuzzy probability of occurrence of basic events, with both the judgment ability level and the subjectivity reliability level taken into account. By means of the fuzzy Bayesian inference, the approach proposed in this article is capable of calculating the probability distribution of potential safety risks and identifying the most likely potential causes of accidents under both prior knowledge and given evidence circumstances. A case concerning the safety analysis of underground buried pipelines adjacent to the construction of the Wuhan Yangtze River Tunnel is presented. The results demonstrate the feasibility of the proposed FBN approach and its application potential. The proposed approach can be used as a decision tool to provide support for safety assurance and management in tunnel construction, and thus increase the likelihood of a successful project in a complex project environment.

Enhancing Security Gaps in Smart Grid Communication

In order to develop smart grid communications infrastructure, a high level of interconnectivity and reliability among its nodes is required. Sensors, advanced metering devices, electrical appliances, and monitoring devices, just to mention a few, will be highly interconnected allowing for the seamless flow of data. Reliability and security in this flow of data between nodes is crucial due to the low latency and cyber-attacks resilience requirements of the Smart Grid. In particular, Artificial Intelligence techniques such as Fuzzy Logic, Bayesian Inference, Neural Networks, and other methods can be employed to enhance the security gaps in conventional IDSs. A distributed FPGA-based network with adaptive and cooperative capabilities can be used to study several security and communication aspects of the smart grid infrastructure both from the attackers and defensive point of view. In this paper, the vital issue of security in the smart grid is discussed, along with a possible approach to achieve this by employing FPGA based Radial Basis Function (RBF) network intrusion.

System reliability for non-repairable multi-state series–parallel system using fuzzy Bayesian inference based on prior interval probabilities

In this article, the fuzzy concepts are applied in analysis of the system reliability problem. The fuzzy number is used to construct the fuzzy reliability of the non-repairable multi-state series–parallel system (NMSS). The fuzzy failure rate function is represented by an exponential fuzzy number. By using this innovative approach, the fuzzy system reliability of NMSS is created. In order to analyse this fuzzy system reliability, the fuzzy Bayesian point estimate of fuzzy system reliability is made by the conventional Bayesian formula. And, the posterior fuzzy system reliability of NMSS is developed by Bayesian inference with fuzzy probabilities. Finally, the performance of the method is measured by the mean square error of fuzzy Bayesian point estimate for the fuzzy system reliability of NMSS.

Fuzzy Bayesian inference

In standard Bayesian inference, a-priori distributions are assumed to be classical probability distributions. This is a topic of critical discussions because, in reality, a-priori information is usually more or less non-precise, i.e. fuzzy. Hence, a more general form of a-priori distributions (so-called fuzzy a-priori densities) is more suitable to model such a-priori information. Moreover, data from continuous quantities are always more or less fuzzy. As a result, Bayes’ theorem has to be generalized to capture this situation. This is possible and will be explained in the paper. In addition, the concepts of HPD-regions and predictive distributions are generalized to the situation of fuzzy a-priori information and fuzzy data.