Conditional Probability Tables Research Articles

Advanced Bayesian study on inland navigational risk of remotely controlled autonomous ship

The arise of autonomous ships has necessitated the development of new risk assessment techniques and methods. This study proposes a new framework for navigational risk assessment of remotely controlled Maritime Autonomous Surface Ships (MASS). This framework establishes a set of risk influencing factors affecting safety of navigation of a remotely-controlled MASS. Next, model parameters are defined based on the risk factors, and the model structure is developed using Bayesian Networks. To this end, an extensive literature survey is conducted, enhanced with the domain knowledge elicited from the experts and improved by the experimental data obtained during representative MASS model trials carried out in an inland river. Conditional Probability Tables are generated using a new function employing expert feedback regarding Interval Type 2 Fuzzy Sets. The developed Bayesian model yields the expected utilities results representing an accident’s probability and consequence, with the results visualized on a dedicated diagram. Finally, the developed risk assessment model is validated by conducting three axiom tests, extreme scenarios analysis, and sensitivity analysis. Navigational environment, natural environment, traffic complexity, and shore-ship collaboration performance are critical from the probability and consequence perspective for inland navigational accidents to a remotely controlled MASS. Lastly, important nodes to Shore-Ship collaboration performance include autonomy of target ships, cyber risk, and transition from other remote control centers.

Reliability analysis of diesel engine cooling system based on improved Bayesian network

For the benefit of solving the problem of absoluteness of conditional probability distribution and difficulty in obtaining basic event probability in Bayesian networks, this paper studies the reliability of diesel engine cooling systems through leakage noise or gate intuitionistic fuzzy Bayesian network. Firstly, the leakage noise or gate is introduced into the intuitionistic fuzzy Bayesian network, which makes the results more realistic. Secondly, prior probability in the Bayesian network is obtained based on the similarity aggregation method of triangular intuitionistic fuzzy numbers. The results show that the introduction of leakage noise or gate, intuitionistic fuzzy set, and Bayesian network can solve the problem that the probability of basic events in a Bayesian network is difficult to obtain. The conditional probability table corrected by leakage noise or gate is more realistic and greatly reduces the workload. It is determined that the two weakest components of the cooling system are the thermostat and the water pump. The results show that the way in this paper can provide support for the reliability analysis of the complex system.

Оценка безопасности движения большого автономного необитаемого подводного аппарата

The problems of ensuring the safe motion of a large autonomous underwater vehicle (AUV) when it passes through sections with different environmental conditions are considered by the example of the development of the Northern Sea Route. An analysis was made of the influence of various environmental conditions - open and coastal water, fast ice and ice conditions - on the safety of the operation of a large AUV. An approach is proposed to assess the vehicle safety in various environments using a dynamic Bayesian network and conditional probability tables. To test the algorithms for controlling the the vehicle motion and the vehicle itself, a digital test site was developed in the form of a stand for simulating the functioning of the AUV. The development of digital twins in the form of software simulators of the vehicle devices and mechanisms made it possible to test control algorithms on the simulation stand both during normal operation of its systems and in the event of malfunctions due to functioning in various environments. The results obtained on a simulation stand for a large AUV operating on the farthest and most complicated part of the Northern Sea Route - the Vilkitski Strait, helped us to assess the safety of the vehicle operation and outline the ways to improve the safety by upgrading the algorithms for controlling the AUV motion in difficult environmental conditions.

Bayesian networks based hierarchical vulnerability evaluation of long-span structures

Vulnerability analysis of long-span structures explores the weakness regions, which should be concerned during structural design and operation stages. However, the vulnerability analysis procedure under regular loads is conventionally a tough task in virtue of structural complexity and uncertainties. Therefore, a Bayesian networks (BNs) framework has been developed for hierarchical vulnerability evaluation of long-span structures under regular loads. External loads, structural systems and components are defined as network nodes, and mechanical and risk causalities are simultaneously considered during network establishment. The causality strength between two nodes is quantitatively expressed by a conditional probability table. The state probability inference of nodal variables is accomplished after inputting the observed state of a damaged component as the evidence into the established BN. A new component importance coefficient is defined and calculated on the inferred nodal state probabilities. A component vulnerability index is further defined to predict the most likely failure sequence of components. In addition, a system vulnerability measure is proposed for evaluating the safety risk of the system. The proposed method has been verified against an experimental space truss model and an actual cable-stayed bridge. The component importance of the truss members and the cables was well evaluated with the predictions of their most likely failure sequences. The estimated system vulnerability could indicate the safety risk of the long-span structures due to the damaged components

Conditional probability table limit-based quantization for Bayesian networks: model quality, data fidelity and structure score

Bayesian Networks (BN) are robust probabilistic graphical models mainly used with discrete random variables requiring discretization and quantization of continuous data. Quantization is known to affect model accuracy, speed and interpretability, and there are various quantization methods and performance comparisons proposed in literature. Therefore, this paper introduces a novel approach called CPT limit-based quantization (CLBQ) aimed to address the trade-off among model quality, data fidelity and structure score. CLBQ sets CPT size limitation based on how large the dataset is so as to optimize the balance between the structure score of BNs and mean squared error. For such a purpose, a range of quantization values for each variable was evaluated and a Pareto set was designed considering structure score and mean squared error (MSE). A quantization value was selected from the Pareto set in order to balance MSE and structure score, and the method’s effectiveness was tested using different datasets, such as discrete variables with added noise, continuous variables and real continuous data. In all tests, CLBQ was compared to another quantization method known as Dynamic Discretization. Moreover, this study assesses the suitability of CLBQ for the search and score of BN structure learning, in addition to examining the landscape of BN structures while varying dataset sizes and confirming its consistency. It was sought to find the expected structure location through a landscape analysis and optimal BNs on it so as to confirm whether the expected results were actually achieved in the search and score of BN structure learning. Results demonstrate that CLBQ is quite capable of striking a balance between model quality, data fidelity and structure score, in addition to evidencing its potential application in the search and score of BN structure learning, thus further research should explore different structure scores and quantization methods through CLBQ. Furthermore, its code and used datasets have all been made available.

Data and knowledge fusion-driven Bayesian networks for interpretable fault diagnosis of HVAC systems

Timely diagnosis and maintenance of faults in chiller units is beneficial for reducing energy consumption in buildings. In order to improve the diagnostic accuracy and provide reasonable explanations for fault occurrences of the heating, ventilation, and air conditioning (HVAC) systems in buildings, a fusion-driven Bayesian network fault diagnosis method is proposed based on broad learning system and fuzzy expert knowledge. Firstly, from the data-driven perspective, an efficient broad learning system is developed as benchmarking model to build the prior Bayesian network structure. Secondly, from the knowledge-driven perspective, the fuzzy logic system is used to fuzz expert knowledge, which then used to optimize the Bayesian network. Finally, the information obtained by experts on-site is incorporated into the optimized Bayesian network as new evidence nodes to determine the Bayesian network. The parameters of the Bayesian network are learned through Noisy-MAX processing of the conditional probability table. The performance of the proposed method is evaluated based on the fault diagnosis of a chiller system. The results demonstrate that the Bayesian network established through this method combines the advantages of data-driven and knowledge-driven approaches. It not only performs well in terms of diagnostic accuracy, with accuracy rates above 98 % for six typical faults, but also provides effective explanations for the underlying mechanisms of the faults through causal relationship diagrams.

Leverage rule-based Bayesian network on assessing straits/canals resilience performance on a risk coupling analysis perspective

ABSTRACT The maritime transportation system is comprised of several crucial nodes, including straits and canals, which are becoming increasingly susceptible to external emergencies and disturbances. The intricate interactive relationships and non-linear influences among the risk factors pose significant challenges in assessing the resilience performance of these straits and canals. To address these challenges, a four-stage resilience assessment framework was developed to analyze the resilience performance of the straits and canals under uncertain risk coupling scenarios. The framework leverages the advantages of fuzzy logic and Bayesian network, enabling the construction of conditional probability tables and reducing expert judgement inconsistencies. The findings indicate that the Strait of Malacca exhibits higher resilience performance under multi-dimensional risk coupling scenarios. This framework has significant potential in providing valuable insights for risk and resilience management and can be extended to similar industries.

Development of a Bayesian network-based early warning system for storm-driven coastal erosion

Coastal hazards such as flooding and erosion can cause large economic and human losses. Under this threat, early warning systems can be very cost-effective solutions for disaster preparation. The goal of this study was to develop, test, and implement an operational coastal erosion early warning system supported by a particular method of machine learning. Thus, the system combines Bayesian Networks, and state-of-the-art numerical models, such as XBeach and SWAN, to predict storm erosion impacts in urbanized areas. This system was developed in two phases. In the development phase, all information required to apply the machine learning method was generated including the definition of hundreds of oceanic synthetic storms, modeling of the erosion caused by these storms, and characterization of the impact levels according to a newly defined eerosion iimpact index. This adimensional index relates the distance from the edge of the dune/beach scarp to buildings and the height of that scarp. Finally, a Bayesian Network that acted as a surrogate of the previously generated information was built. After the training of the network, the conditional probability tables were created. These tables constituted the ground knowledge to make the predictions in the second phase. This methodology was validated (1) by comparing 6-h predictions obtained with the Bayesian Network and with process-based models, the latest considered as the benchmark, and (2) by assessing the predictive skills of the Bayesian Network through the unbiased iterative k-fold cross-validation procedure. Regarding the first comparison, the analysis considered the entire duration of three large storms whose return periods were 10, 16, and 25 years, and it was observed that the Bayesian Network correctly predicted between 64% and 72% of the impacts during the course of the storms, depending on the area analyzed. Importantly, this method was also able to identify when the hazardous conditions disappeared after predicting potential consequences. Regarding the Regarding the second validation approach, second validation approach, the k-fold cross-validation procedure was applied to the peak of a set of varying storms and it demonstrated that the predictive skills were maximized (63%–72%) when including three nodes as input conditions of the Bayesian Network. In the operational phase, the system was integrated into the architecture of a forecast and early warning system that predicts emergencies in coastal and port zones in Portugal, and the alerts are issued to authorities every day. This study demonstrated that the two-phase approach developed here can provide fast and high-accuracy predictions of erosion impacts. Also, this methodology can be easily implemented on other sandy beaches constituting a powerful tool for disaster management.

Identifying the Causes of Ship Collisions Accident Using Text Mining and Bayesian Networks

Under the backdrop of the robust growth of the global economy, the water transport industry is experiencing rapid development, resulting in an increase in ship collisions and a critical water traffic safety situation. This study uses text mining techniques to gather a corpus of data. The corpus includes human factors, ship factors, natural environmental factors, and management factors, which are used as target data to obtain a high-dimensional sparse original feature vector space set comprising eigenvalues and eigenvalue weight attributes. Chi-square statistics are utilised to reduce dimensionality, resulting in a final set of 33-dimensional text feature items that determine the causal factors of ship collision risk. Taking the four steps involved in the collision process as the primary focus, a Bayesian network structure for ship collision risk is constructed based on the “human-ship-environment-management” system. By incorporating existing ship collision accident/danger reports, conditional probability tables are computed for each node in the Bayesian network structure, enabling the modelling of ship collision risk. The model is validated through an example, revealing that, under relevant conditions, the probability of collision exceeds 90 %. This finding demonstrates the validity of the model and allows one to deduce the primary cause of ship collision accidents.

Reasoning Disaster Chains with Bayesian Network Estimated Under Expert Prior Knowledge

With the acceleration of global climate change and urbanization, disaster chains are always connected to artificial systems like critical infrastructure. The complexity and uncertainty of the disaster chain development process and the severity of the consequences have brought great challenges to emergency decision makers. The Bayesian network (BN) was applied in this study to reason about disaster chain scenarios to support the choice of appropriate response strategies. To capture the interacting relationships among different factors, a scenario representation model of disaster chains was developed, followed by the determination of the BN structure. In deriving the conditional probability tables of the BN model, we found that, due to the lack of data and the significant uncertainty of disaster chains, parameter learning methodologies based on data or expert knowledge alone are insufficient. By integrating both sample data and expert knowledge with the maximum entropy principle, we proposed a parameter estimation algorithm under expert prior knowledge (PEUK). Taking the rainstorm disaster chain as an example, we demonstrated the superiority of the PEUK-built BN model over the traditional maximum a posterior (MAP) algorithm and the direct expert opinion elicitation method. The results also demonstrate the potential of our BN scenario reasoning paradigm to assist real-world disaster decisions.

Innovative Path of Civic Education Management Mode in Colleges and Universities Based on Bayesian Networks

Abstract This paper constructs a Bayesian network structure learning model using both the Bayesian network and the Notears algorithm. Combined with acyclic graph and conditional probability table, the structure and parameters of BN are described respectively. Focusing on the basic methods of Bayesian network structure, the hybrid algorithm based on Notears is chosen as the basic method of structure learning by analyzing the application of the evaluation search method, constraint method and hybrid search algorithm. The results show that the ideal education management method should focus on the integration with real life, so much so that it has a low rate of detachment from reality as well as a low rate of theory, accounting for 0.35 and 0.4, respectively. The traditional way of management of ideology and political education in colleges and universities is more theoretical and detached from the actual situation of education and management, with theoretical management accounting for 0.75, and management is inefficient, with a percentage of 0.6. The research in this paper promotes, to a certain extent, the innovation of the management of the ideological education in colleges and universities, for the management of ideological education in colleges and universities.

Spatial bayesian approach for socio-economic assessment of pumped hydro storage

Pumped hydro energy storage (PHES) is a key enabler for transitioning to 100 % renewable energy sources. However, PHES site selection is multi-faceted and challenging, including from a socio-economic perspective, due to complex economic issues and the heterogeneity of social factors. To overcome this challenge, this study developed a spatial probabilistic decision-making approach to identify and rank the best PHES sites from a shortlisted number of sites determined from a previous techno-environmental assessment. This model was developed in a participatory environment, where both study evidence and experts’ judgements were utilised to determine the key socio-economic factors, develop the Bayesian Network (BN), and populate the conditional probability tables (CPT). The BN parent node data were retrieved from publicly available sources in a high-resolution spatial and statistical format. An ArcGIS 10.3 tool was utilised to process the data with spatial characteristics, whereas GeNIe 2.5 was used to develop the BN model. Forward propagation, sensitivity, and strength analysis were performed to validate the developed BN model. Application of the spatial-BN model to northern Queensland, Australia reduced the fourteen previously determined techno-environmentally suitable PHES sites, to nine sites that are suitable from a socio-economic perspective for future developments. These nine sites could store and generate over 323 TWh of electricity over their life expectancy and at a levelised cost of 0.040–0.274 AU$/kWh. The developed procedure and model streamline the PHES site selection pre-feasibility process, thereby expediting renewable energy transition.

On the causation analysis for hazards involved in the engine room fire-fighting system by integrating STPA and BN

A novel methodology is proposed in this study to investigate the hazards involved in the engine room fire-fighting system. In the proposed methodology, the fuzzy theory is applied to bridge the superiority of the systems theoretic process analysis (STPA) and Bayesian network (BN). The engine room fire-fighting system is initially audited within the framework of STPA qualitatively to identify unsafe control actions, and then, the causations contributing to these actions are determined, which are subsequently considered as the root nodes of the BN. To implementing Bayesian inference, the expert elicitation within fuzzy theory is employed to determine the probability distribution of the root nodes, and the conditional probability tables for intermediate nodes are obtained by leaky Noisy-OR function, based on which the developed BN is simulated. Finally, the results from BN simulation are interpretation from the perspectives of brief propagation analysis, sensitivity analysis and influence strength analysis. The proposed methodology can be applied to audit the integrity of engine room fire-fighting system to eliminate the potential causations contributing to engine room fire.

Temporal noisy-adder of bayesian network for scalable consecutive-k-out-of-n:F system reliability analysis

The Bayesian network(BN) is a powerful tool for modeling and analyzing reliability, safety, and risk in various engineering systems. Although there have been studies that incorporate it into the modeling of Consecutive-k-out-of-n: F systems(C(k,n:F)), these applications are limited to naive mode and cannot tackle scalable systems (e.g., n>2000,k>40). By introducing temporal Noisy-adder structure, named NaCkoon model, the number of nodes in equivalent C(k,n:F) BN model is significantly reduced, and the Conditional Probability Table (CPT) of temporary nodes can be controlled to linear complexity. The correctness of the proposed algorithm is validated by the comparison of literature case. Through numerical experiments, the novel algorithms proposed in this paper were compared with existing ones, including BN construction and inference computation time, was found to be the most optimal solution. Finally, the computable ranges of novel and existing algorithms are obtained through the capability computation. The test results show that NaCkoon model proposed in this paper has great advantages over existing algorithms and proposed NaA+NaO model based BN.

Leverage Bayesian Network and Fault Tree Method on Risk Assessment of LNG Maritime Transport Shipping Routes: Application to the China–Australia Route

The China–Australia Route, which serves as the southern economic corridor of the ‘21st Century Maritime Silk Road’, bears great importance in safeguarding maritime transportation operations. This route plays a crucial role in ensuring the security and efficiency of such activities. To pre-assess the risks of this route, this paper presents a two-stage analytical framework that combines fault tree analysis and Bayesian network for evaluating the occurrence likelihood of risk of transporting liquefied natural gas (LNG) on the China–Australia Route. In the first stage, our study involved the identification of 22 risk influencing factors drawn from a comprehensive review of pertinent literature and an in-depth analysis of accident reports. These identified factors were then utilized as basic events to construct a fault tree. Later, we applied an expert comprehensive evaluation method and fuzzy set theory, and by introducing voting mechanism into expert opinions, the prior probability of basic events was calculated. In the second stage, a fault tree was transformed into a Bayesian network, which overcame the deficiency that the structure and conditional probability table of the Bayesian network find difficult to determine. Consequently, the employment of the Bayesian network architecture was applied to forecast the likelihood of LNG maritime transport along the China–Australia shipping pathway. The probability importance and critical importance of each basic event was calculated through an importance analysis. The development of a risk matrix was achieved by considering the two primary dimensions of frequency and impact, which were subsequently utilized to categorize all relevant risk factors into high, moderate, or low risk categories. This allowed for effective risk mitigation and prevention strategies to be implemented. Finally, assuming that the final risk occurs, we calculated the posterior probability of the basic event to diagnose the risk. The research findings indicate that the primary reasons for the risk of transporting LNG on the China–Australia Route are the impact of natural forces and epidemics, piracy and terrorist attacks, and the risk of LNG explosions. In the final section, we provide suggestions and risk control measures based on the research results to reduce the occurrence of risks.

Automatically Finding the Right Probabilities in Bayesian Networks

This paper presents alternative techniques for inference on classical Bayesian networks in which all probabilities are fixed, and for synthesis problems when conditional probability tables (CPTs) in such networks contain symbolic parameters rather than concrete probabilities. The key idea is to exploit probabilistic model checking as well as its recent extension to parameter synthesis techniques for parametric Markov chains. To enable this, the Bayesian networks are transformed into Markov chains and their objectives are mapped onto probabilistic temporal logic formulas. For exact inference, we compare probabilistic model checking to weighted model counting on various Bayesian network benchmarks. We contrast symbolic model checking using multi-terminal binary (aka: algebraic) decision diagrams to symbolic inference using proba- bilistic sentential decision diagrams, symbolic data structures that are tailored to Bayesian networks. For the parametric setting, we describe how our techniques can be used for various synthesis problems such as computing sensitivity functions (and values), simple and difference parameter tuning and ratio parameter tuning. Our parameter synthesis techniques are applicable to arbitrarily many, possibly dependent, parameters that may occur in multiple CPTs. This lifts restrictions, e.g., on the number of parametrized CPTs, or on parameter dependencies between several CPTs, that exist in the literature. Experiments on several benchmarks show that our parameter synthesis techniques can treat parameter synthesis for Bayesian networks (with hundreds of unknown parameters) that are out of reach for existing techniques.

Risk Analysis of Laboratory Fire Accidents in Chinese Universities by Combining Association Rule Learning and Fuzzy Bayesian Networks

Targeting the challenges in the risk analysis of laboratory fire accidents, particularly considering fire accidents in Chinese universities, an integrated approach is proposed with the combination of association rule learning, a Bayesian network (BN), and fuzzy set theory in this study. The proposed approach has the main advantages of deriving conditional probabilities of BN nodes based on historical accident data and association rules (ARs) and making good use of expert elicitation by using an augmented fuzzy set method. In the proposed approach, prior probabilities of the cause nodes are determined based on expert elicitation with the help of an augmented fuzzy set method. The augmented fuzzy set method enables the effective aggregation of expert opinions and helps to reduce subjective bias in expert elicitations. Additionally, an AR algorithm is applied to determine the probabilistic dependency between the BN nodes based on the historical accident data of Chinese universities and further derive conditional probability tables. Finally, the developed fuzzy Bayesian network (FBN) model was employed to identify critical causal factors with respect to laboratory fire accidents in Chinese universities. The obtained results show that H4 (bad safety awareness), O1 (improper storage of hazardous chemicals), E1 (environment with hazardous materials), and M4 (inadequate safety checks) are the four most critical factors inducing laboratory fire accidents.

Development of a Bayesian networks-based early warning system for wave-induced flooding

Coastal flooding prediction systems can be an efficient risk-reduction instrument. The goal of this study was to design, build, test, and implement a wave-induced flooding early warning system in urban areas fronted by sandy beaches. The system utilizes a novel approach that combines Bayesian Networks and numerical models (SWAN + XBeach) and was developed in two phases. In the development phase, firstly, the learning information was generated including the creation of oceanic conditions, modeling overtopping discharges, the characterization of the associated impacts (no, low, moderate and high) in pedestrians, urban components and buildings, and vehicles, and secondly, the Bayesian Networks were designed that surrogated the previously generated information. After their training, the conditional probability tables were created representing the foundation to make predictions in the operational phase. This methodology was validated for several historical events which hit the study area (Praia de Faro, Portugal), and the system correctly predicted the impact level of around 80% of the cases. Also, the predictive skills varied depending on the level, with the no and high impact levels overcoming the intermediate levels. In terms of efficiency, one simulation (deterministic) of coastal flooding for 72 h by running SWAN + XBeach operationally would take more than two days on a one-logical processor workstation, while the current approach can provide quasi-instantaneously predictions for that period, including probability distributions. Moreover, the two-working phase approach is very flexible enabling the inclusion of additional features such as social components representing a powerful tool for risk reduction in coastal communities.

Structural learning of mixed noisy-OR Bayesian networks

In this paper we discuss learning Bayesian networks whose conditional probability tables are either Noisy-OR models or general conditional probability tables. We refer to these models as Mixed Noisy-OR Bayesian Networks. To learn their structure, we modify the Bayesian Information Criterion used for standard Bayesian networks to reflect the number of parameters of a Noisy-OR model. We prove that the log-likelihood function of a Noisy-OR model has a unique maximum and adapt the EM-learning method for the leaky Noisy-OR model. We propose a structure learning algorithm that learns optimal Mixed Noisy-OR Bayesian Networks. We evaluate the proposed approach on synthetic data, where it performs substantially better than standard Bayesian networks. We perform experiments with Bipartite Noisy-OR Bayesian networks of different complexity to find out when the results of Mixed Noisy-OR Bayesian Networks are significantly better than the results of standard Bayesian networks and when they perform similarly. We also study how different penalties based on the number of model parameters affect the quality of the results. Finally, we apply the suggested approach to a problem from the domain of linguistics. Specifically, we use Mixed Noisy-OR Bayesian Networks to model the spread of loanwords in the South-East Asian Archipelago. We perform numerical experiments in which we compare the prediction ability of standard Bayesian networks with Mixed Noisy-OR Bayesian networks and test different pruning methods to reduce the number of parent sets considered.

A new fusion method to predict coal mine roof accidents

AbstractIn the context that coal remains the main energy source of China now, the safety of coal mine production is still worth our attention. For the factors influencing the roof accident of coal mine roadway have great complexity and uncertainty, a new risk prediction method of coal mine roof accidents integrating T‐S fuzzy fault tree and Bayesian network (BN) is proposed. The constructed method determines the BN and the conditional probability tables according to the established T‐S fuzzy fault tree. The fault state and fuzzy fault rate of root nodes are described according to the fuzzy number. And the forward inference of Bayesian is used to calculate the probability of the accidents on the roadway roof based on the fault probability of the root nodes and actual fault probability during construction respectively, to realize the risk prediction of roof accidents. Finally, practical data are used to verify the new fusion risk evaluation method by taking two mines as cases. The results show that the influencing factors calculated by the new fusion risk prediction method are completely consistent with the actual situation, confirming the effectiveness and reliability of this method, which providing new ideas for the research about the risk prediction of coal mine roof accidents.