Probabilistic Bayesian Network Research Articles

Probabilistic deep learning approach for fatigue crack width estimation and prognosis in lap joint using acoustic waves

Abstract Accurate fatigue crack width estimation is crucial for aircraft safety, however, limited research exists on (i) the direct relationship between fatigue crack width and Lamb wave signatures and (ii) probabilistic artificial intelligence (AI) approach for automated analysis using acoustic emission waveforms. This paper presents a probabilistic deep learning approach for fatigue crack width estimation, employing an automated wavelet feature extractor and probabilistic Bayesian neural network. A dataset constituting the fatigue experiment on aluminum lap-joint specimens is considered, in which Lamb wave signals were recorded at several time instants for each specimen. Signals acquired from the piezo actuator-receiver sensor pairs are related to the optically measured surface crack length. The sensitive features are automatically extracted from the signals using decomposition techniques called maximal overlap discrete wavelet transform (MODWT). The extracted features are then mapped through the deep learning model, which incorporates Bayesian inference to account for both aleatoric as well as epistemic uncertainty, that provides outcomes in the form of providing probabilistic estimates of crack width with uncertainty quantification. Thus, employing an automated wavelet feature extractor (MODWT) on a dataset of fatigue experiments, the framework learns the relationship between Lamb wave signals and crack width. Validation on unseen in-situ data demonstrates the efficacy of the approach for practical implementation, paving the way for more reliable fatigue life prognosis.

CYBER SECURITY ATTACK DETECTION MODEL USING SEMI-SUPERVISED LEARNING

The increasing digitalization of our society has brought about numerous benefits, enabling seamless communication, convenient transactions, and efficient operations. However, with this growing reliance on interconnected systems and information technology, the risk of cyber-attacks has also surged. Cyber threats, such as data breaches, ransomware, and sophisticated malware, have become more prevalent, threatening the confidentiality, integrity, and availability of critical data and services. Organizations across industries face the daunting challenge of defending against a wide array of cyber-attacks that continue to evolve in complexity and stealth. In response to this ever-changing cyber threat landscape, Cyber Security Risk Management (CSRM) and attack detection have become critical components of any comprehensive cybersecurity strategy. The ability to identify and mitigate cyber risks and swiftly detect malicious activities is paramount for safeguarding sensitive information, preserving business continuity, and maintaining the trust of customers and stakeholders. A novel approach to Cyber Security Risk Management through an Attack Detection Model that utilizes Semi-Supervised Learning Auto-Encoders in conjunction with Probabilistic Bayesian Networks. The study compares the performance of Multi Connect Variational Auto-Encoder (MC-VAE), Probabilistic Bayesian Networks (PBN), and a combined model of MC-VAE and PBN. The study employs the NUSW-NB15_GT dataset for training and evaluation purposes. Notably, the Semi-Supervised Learning with Probabilistic Bayesian Networks (SSL-PBN) model demonstrates exceptional results, achieving a precision rate of 94% and a recall rate of 90%. The F1 score of 0.9191 highlights the SSL-PBN model's efficacy in achieving a balanced trade-off between precision and recall, critical for minimizing false positives and false negatives...

Creating synthetic populations in transplantation: A Bayesian approach enabling simulation without registry re-sampling.

Computer simulation has played a pivotal role in analyzing alternative organ allocation strategies in transplantation. The current approach to producing cohorts of organ donors and candidates for individual-level simulation requires directly re-sampling retrospective data from a transplant registry. This historical data may reflect outmoded policies and practices as well as systemic inequities in candidate listing, limiting contemporary applicability of simulation results. We describe the development of an alternative approach for generating synthetic donors and candidates using hierarchical Bayesian network probability models. We developed two Bayesian networks to model dependencies among 10 donor and 36 candidate characteristics relevant to waitlist survival, donor-candidate matching, and post-transplant survival. We estimated parameters for each model using Scientific Registry of Transplant Recipients (SRTR) data. For 100 donor and 100 candidate synthetic populations generated, proportions for each categorical donor or candidate attribute, respectively, fell within one percentage point of observed values; the interquartile ranges (IQRs) of each continuous variable contained the corresponding SRTR observed median. Comparisons of synthetic to observed stratified distributions demonstrated the ability of the method to capture complex joint variability among multiple characteristics. We also demonstrated how changing two upstream population parameters can exert cascading effects on multiple relevant clinical variables in a synthetic population. Generating synthetic donor and candidate populations in transplant simulation may help overcome critical limitations related to the re-sampling of historical data, allowing developers and decision makers to customize the parameters of these populations to reflect realistic or hypothetical future states.

Balancing observational data and experiential knowledge in environmental flows modeling

Environmental flow (e-flow) decision making relies on flow-ecology models to predict ecological outcomes under different flow regimes. While expert knowledge has traditionally informed these models, there is increasing use of data-driven approaches. We investigated data integration for Bayesian conditional probability networks (CPNs) developed through expert elicitation in an e-flows assessment in Victoria, Australia. Using synthetic datasets based on monitoring data, we assessed the impact of varying data characteristics on model outcomes. Incorporating 10 years of data had the greatest influence on model predictions compared to the expert-based models, with diminishing additional effect for longer records. Notably, the expert model based on the most non-conforming expert opinion was more sensitive to data integration than a model based on harnessing the opinion of all experts, highlighting the importance of considering diverse experiential knowledge. We provide recommendations on leveraging limited datasets and models to guide efficient monitoring and management.

Impact of disease outcomes on the Assessment of SpondyloArthritis International Society Health Index (ASAS HI): a Bayesian network analysis of the DESIR cohort

ObjectiveThe objective of this study is to build a structural model visualising and quantifying the interrelationships of different disease outcomes with the Assessment of SpondyloArthritis International Society Health Index (ASAS...

A Bayesian Deep Reinforcement Learning-Based Resilient Control for Multi-Energy Micro-Gird

Aiming at a cleaner future power system, many regimes in the world have proposed their ambitious decarboniz-ing plan, with increasing penetration of renewable energy sources (RES) playing an alternative role to conventional energy. As a re-sult, power system tends to have less backup capacity and operate near their designed limit, thus exacerbating system vulnerability against extreme events. Under this reality, resilient control for the multi-energy micro-grid is facing the following challenges, which are: 1) <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">the effect from the stochastic uncertainties of</i> RES; 2) <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">the need for a model-free and fast-reacting control scheme under extreme events; and</i> 3) <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">efficient exploration and robust performance with limited extreme events data</i> . <p xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">To deal with the aforementioned challenges, this paper pro-poses a novel Bayesian Deep Reinforcement Learning-based resilient control approach for multi-energy micro-grid. In partic-ular, the proposed approach replaces the deterministic network in traditional Reinforcement Learning with a Bayesian probabilistic network in order to obtain an approximation of the value function distribution, which effectively solves the Q-value overestimation issue. Compared with the naive Deep Deterministic Policy Gra-dient (DDPG) method and optimization method, the effectiveness and importance of employing the Bayesian Reinforcement Learn-ing approach are investigated and illustrated across different operating scenarios. Case studies have shown that by using the Monte Carlo posterior mean of the Bayesian value function distribution instead of a deterministic estimation, the proposed Bayesian Deep Deterministic Policy Gradient (BDDPG) method achieves a near-optimum policy in a more stable process, which verifies the robustness and the practicability of the proposed approach.

Incremental evolution of modeling a prognosis for polar bears in a rapidly changing Arctic

Updating predictions of the response of high-profile, at-risk species to climate change and anthropogenic stressors is vital for informing effective conservation action. Here, we review two prior generations of Bayesian network probability models predicting changes in global polar bear (Ursus maritimus) population status, and provide a contemporary update based on recent research findings and sea-ice projections by newer climate models. We compare predictions of polar bear population response from all 3 models among four circumpolar Arctic ecoregions, using sea ice projections based on three IPCC greenhouse gas emissions scenarios (SSP2.6, 4.5, 8.5). Consistent with the previous two model generations, polar bears will continue to experience increasing probability of declining or greatly declining populations throughout the 21st century, varying by emission scenario. Populations within the Polar Basin Divergent Ice Ecoregion have the highest predicted probability of declines, but predictions were slightly less dire relative to the previous model generation. Most of the influence, denoted by model sensitivity analysis, is from expected degradation and loss of sea ice and reduced access to marine prey. The lack of terrestrial prey adequate to substitute for loss of access to marine prey, as well as human-caused bear mortality associated with hunting and defense of life and property encountered when polar bears are increasingly forced ashore also contributed to predicted declines. Although some tidewater glacial fjords and other localized onshore resources may provide local refugia, their benefit is transient. Our findings continue to inform priorities for inventory, monitoring, and research needs, and suggest that similar updates to models of other at-risk species can capitalize on the comparison framework we present here.

A Dynamic Bayesian Network Probability Framework for Typhoon Risk Analysis in the Land-sea Regions

The life cycle of a typhoon is mainly divided into three stages: far away from the coast, offshore, and on land. The disaster bodies and typhoons affected are different at every stage. The traditional assessment methods could not consider the risk from the complete typhoon life cycle to cover the effects of both land and sea. This paper proposes a Bayesian network risk assessment model to evaluate the navigational ship risk and damage risk of coastal structures during the different typhoon life cycles. The disaster memory database of the typhoon is also constructed in this paper, which deconstructs the typhoon risk factors and forms a unified description semantics.

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.

Deep Boosted Molecular Dynamics: Accelerating Molecular Simulations with Gaussian Boost Potentials Generated Using Probabilistic Bayesian Deep Neural Network.

We have developed a new deep boosted molecular dynamics (DBMD) method. Probabilistic Bayesian neural network models were implemented to construct boost potentials that exhibit Gaussian distribution with minimized anharmonicity, thereby allowing for accurate energetic reweighting and enhanced sampling of molecular simulations. DBMD was demonstrated on model systems of alanine dipeptide and the fast-folding protein and RNA structures. For alanine dipeptide, 30 ns DBMD simulations captured up to 83-125 times more backbone dihedral transitions than 1 μs conventional molecular dynamics (cMD) simulations and were able to accurately reproduce the original free energy profiles. Moreover, DBMD sampled multiple folding and unfolding events within 300 ns simulations of the chignolin model protein and identified low-energy conformational states comparable to previous simulation findings. Finally, DBMD captured a general folding pathway of three hairpin RNAs with the GCAA, GAAA, and UUCG tetraloops. Based on a deep learning neural network, DBMD provides a powerful and generally applicable approach to boosting biomolecular simulations. DBMD is available with open source in OpenMM at https://github.com/MiaoLab20/DBMD/.

Evaluating Bicycling Environments with Trajectory Data on Shared Bikes: A Case Study of Beijing

A detailed evaluation of the riding environment can help the government master the urban riding environment, identify problematic road sections, and improve riding quality. However, the current evaluation of riding environment is mainly subjective, lacking big data (e.g., shared bicycle trajectory data) as a data-driven objective evaluation system. The emergence of shared bicycle data has provided data support for data-driven riding environment evaluation, but there are few studies using shared bicycle data for riding evaluation at present. First, according to the characteristics of the data and the riding environment, a boxplot method and Bayesian probabilistic network model are used to exclude abnormal data and to match trajectories to road sections. Second, this paper proposes a data-driven evaluation framework based on riding influencing factors. An evaluation framework, which is composed of node-, link-, and block-level evaluation indicators, was constructed, using an evaluation model combining TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) and KNN (K-Nearest Neighbors). The evaluation results can identify parking issues, intersection difficulties, and lane occupancy issues on bicycle sections, and visually reflect the riding environment. The significance of this article is to create an objective evaluation system based on a data-driven technology to accurately identify sections and causes of riding quality problems. The research results can be applied in the future to evaluate the cycling environment around the railway stations for bicycle parking planning and determine the foothold for traffic management.

Exploratory analysis of machine learning techniques in the Nevada geothermal play fairway analysis

Play fairway analysis (PFA) is commonly used to generate geothermal potential maps and guide exploration studies, with a particular focus on locating and characterizing blind geothermal systems. This study evaluates the application of machine learning techniques to PFA in the Great Basin region of Nevada. Following the evaluation of various techniques, we identified two approaches to PFA that produced promising results, 1) supervised Bayesian probabilistic neural networks to generate geothermal potential maps with confidence intervals, and 2) unsupervised principal component analysis paired with k-means clustering to generate both cluster maps to help identify spatial patterns, as well as new combined feature inputs. We applied these techniques to perform a comparative analysis between two principal sets of geological and geophysical features related to permeability and heat and a set of positive (known geothermal resources) and negative training sites (known drill sites with unsuitable geothermal conditions). We found that these methods constrain previously unrecognized feature controls on geothermal favorability, many of which are spatially organized within the extent of cluster groups and the major structural-hydrologic domains of the study area. Furthermore, we utilized exploratory unsupervised modeling to highlight spatial relationships between input data and predictive output results of our supervised modeling. Finally, we demonstrate how our models compare to the previous Nevada PFA and how the rapid insights these machine learning techniques offer may support future assessments of both known and undiscovered blind geothermal systems in the Great Basin region of Nevada and beyond.

Optimized Monitoring and Conservation of Farmland Bird Species through Bayesian Modelling: The Montagu’s Harrier Circus pygargus Population in Central Italy

The Montagu’s harrier Circus pygargus is considered a rare species at the Italian level, and vulnerable at the European level. The main threat for these farmland birds is represented by agricultural practices; in fact, it nests on the ground in agricultural environments; therefore, at harvest time nests are often destroyed (with the eggs and chicks) by farm machinery. We examined the reproductive traits (clutch size, laying date, hatching, and fledging date and success) of the Montagu’s harrier population in central Italy (about 10% of its population in Italy) where nest protection has been implemented through electric fences and metallic meshes. By using a Bayesian probabilistic network, we modeled the sequence of events that determine its reproductive success (percentages of eggs hatched and chicks fledged) and simulated the effects of different environmental and management scenarios. Our model explained the hatching and fledging success with 90.20% and 95.12% accuracies, respectively. We found that crop type and height, laying date, type and delay of nest protection have specific effects on the reproductive success of this population. Our findings demonstrate that it is possible to optimize the monitoring of this population and significantly increase its reproductive success by acting selectively upon the environmental and management attributes of the breeding area. Our decision tool allowed us to produce several rules for the optimized monitoring and conservation of the Montagu’s harrier population in central Italy. The methodological approach proposed here is suitable for application to any farmland bird population on a local scale.

Application of Probabilistic Models for Multitone Electromagnetic Immunity Analysis

The operational environment of modern electronic systems may include multiple frequency electromagnetic disturbances. However, immunity measurements usually employ single-frequency continuous waveforms (i.e., <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">single-tones</i> ). The performances of two oscillator circuits with different topologies (one simulated and one measured) were used as case studies to investigate immunity to simultaneous single-tone disturbances (i.e., <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">multitones</i> ) using probabilistic Bayesian network models. For the multitone analysis, the noisy-OR model was first used to identify the type of causal interactions between simultaneously occurring single-tones. Probabilistic theories derived from the recursive noisy-OR model, which inherits the independence assumptions of the noisy-OR and any known causal dependence between simultaneously occurring single-tones, were then used to predict the probability of higher order multitone failures. For the two case studies, the probability of three-tone failures was estimated using the single-tone and two-tone failure probability values. An improved adaptive recursive noisy-OR model was also proposed to overcome the practical difficulties of obtaining multitone failure probabilities, from either simulations or measurements.

Rock burst monitoring and early warning under uncertainty based on multi-information fusion approach

Rock burst monitoring and early warning is known as a challenging problem in underground engineering. Existing research mainly focuses on forecast the rock burst using single geophysical signal, which is found limited in characterising the hazard under changeable geological conditions. This paper proposes a novel Bayesian network-based rock burst early warning approach. A multi-index system is firstly constructed for rock burst early warning by extracting characteristic parameters of multiple geophysical signals. Redundant indices are then eliminated to decrease the inconsistency of multiple information. The probabilistically causalities between rock burst and multiple indices and its quantisation are respectively described by directed acyclic graph and conditional probabilities in Bayesian network, and the occurrence probability of rock burst is forecasted by fusing multiple geophysical signals. The study case of LW 1208, Hongyang coal mine, China illustrates the advantages of the proposed approach on rock burst hazard early warning in the presence of uncertainties.

A Bayesian approach for remote sensing of chlorophyll-a and associated retrieval uncertainty in oligotrophic and mesotrophic lakes

Satellite remote sensing of chlorophyll-a concentration (chla) in oligotrophic and mesotrophic lakes faces uncertainties from sources such as atmospheric correction, complex inherent optical property compositions, and imperfect algorithmic retrieval. To improve chla estimation in oligo- and mesotrophic lakes, we developed Bayesian probabilistic neural networks (BNNs) for the Sentinel-3 Ocean and Land Cover Instrument (OLCI) and Sentinel-2 MultiSpectral Imager (MSI). The BNNs were built using an in situ dataset of oligo- and mesotrophic water bodies (1755 observations from 178 systems; median chla: 5.11 mg m−3, standard deviation: 10.76 mg m−3) and provide a per-pixel uncertainty percentage associated with retrieved chla. Shifts of oligo- and mesotrophic systems into the eutrophic regime, characterised by higher biomass levels, are widespread. To account for phytoplankton biomass fluctuation, a set of eutrophic lakes (167 observations from 31 systems) were included in this study (maximum chla 68 mg m−3). The BNNs were evaluated through five assessments including single day and time series match-ups with OLCI and MSI. OLCI BNN accuracy gains of >25% and MSI BNN accuracy gains of >15% were achieved in the assessments when compared to chla reference algorithms for oligotrophic waters (chla ≤ 8 mg m−3). In comparison to the reference algorithms, the accuracy gains of the BNNs decreased as chla and trophic levels increased. To measure the quality of the provided BNN uncertainty estimate, we calculated the prediction interval coverage probability (PICP), Sharpness and mean absolute calibration difference (MACD) metrics. The associated BNN chla uncertainty estimate included the reference in situ chla values for most observations (PICP ≥ 75%) across the different performance assessments. Further analysis showed that the BNN chla uncertainty estimate was not constantly well-calibrated across different evaluation strategies (Sharpness 1.7–6, MACD 0.04–0.25). BNN uncertainties were used to test two chla improvement strategies: 1) identifying and filtering uncertain chla estimates using scene-specific thresholds, and 2) selecting the most accurate prior atmospheric correction algorithm per individual satellite observation to retain chla with the lowest BNN uncertainty. Both strategies increased the quality of the chla result and demonstrated the significance of uncertainty estimation. This study serves as research on Bayesian machine learning for the estimation and visualisation of chla and associated retrieval uncertainty to develop harmonised products across OLCI and MSI for small and large oligo- and mesotrophic lakes.

Spatiotemporal variation in irrigation water requirements in the China–Pakistan Economic Corridor

Agricultural irrigation consumes most of the fresh water in the China–Pakistan Economic Corridor (CPEC), directly affecting water resource management and allocation. Irrigation water demand is a key component of regional water resources management. We analyzed spatiotemporal variation in irrigation water requirement, irrigation demand index (IDI), and the proposed regional optimization of irrigation water use based on the Bayesian probability network. Results showed that: (1) The IDI in the study area increased slightly (trend slope = 0.028 a−1) as the effective precipitation increased by 63% during this period, and total irrigation water requirement (IR) decreased from 277.61 km3 in 2000 to 240 km3 in 2015. (2) Cotton had the highest crop IDI, followed by maize and wheat. (3) According to the comprehensive scenario analysis, improving the crop planting structure (by moderately increasing the planting proportion of maize in the CPEC) is conducive to improving regional water and food security by enhancing the grain yield (+ 9%), reducing the malnourished proportion of the population (low state + 7.2%), and bolstering water-saving irrigation technologies in Pakistan as well as water conveyance systems in Pakistan. Our results form an important baseline in determining the way forward on sustainable water resource utilization management in the CPEC.

Stochastic ground motion models to NGA‐West2 and NGA‐Sub databases using Bayesian neural network

AbstractGround motion models (GMMs) are traditionally developed from a frequentist approach. The Bayesian framework has received recent attention in developing nonergodic models, measuring uncertainty, or updating the model with additional data. However, no neural networks are developed to date in this framework to predict ground motion parameters or spectra. Hence, the present work develops a probabilistic Bayesian neural network (PBNN) to next‐generation attenuation – West2 and Subduction databases using variational inference with mean‐field assumption. Network inputs are magnitude, rupture distance, hypocentral depth, shear wave velocity, style of faulting, and region flags; outputs are peak ground values and response spectra. Both models have two hidden layers with seven neurons in each hidden layer. The models are verified for potential overfit, and their performance is validated through the parametric study by varying inputs. The output of a deterministic model is a point estimate. Considering probabilistic layers in hidden and output layers enables the model to capture within‐model epistemic uncertainty and aleatory variability. Obtained aleatory standard deviations are consistent with other models. Mean epistemic uncertainty and aleatory variability are in the range 0.07–0.10 and 0.62–0.78 (ln units) for NGA‐West2 and 0.09–0.16 and 0.67–0.95 for NGA‐Sub models, respectively. The correlation coefficients between recorded and overall mean predictions ranged from 0.94 to 0.97 for NGA‐the West2 model and from 0.91 to 0.95 for the NGA‐Sub models. Network performance for out‐of‐training inputs showed increased epistemic deviations with no effect on aleatory deviations.

Influence-Based Consequence Assessment of Subsea Pipeline Failure under Stochastic Degradation

The complexity of corrosion mechanisms in harsh offshore environments poses safety and integrity challenges to oil and gas operations. Exploring the unstable interactions and complex mechanisms required an advanced probabilistic model. The current study presents the development of a probabilistic approach for a consequence-based assessment of subsea pipelines exposed to complex corrosion mechanisms. The Bayesian Probabilistic Network (BPN) is applied to structurally learn the propagation and interactions among under-deposit corrosion and microbial corrosion for the failure state prediction of the asset. A two-step consequences analysis is inferred from the failure state to establish the failure impact on the environment, lives, and economic losses. The essence is to understand how the interactions between the under-deposit and microbial corrosion mechanisms’ nodes influence the likely number of spills on the environment. The associated cost of failure consequences is predicted using the expected utility decision theory. The proposed approach is tested on a corroding subsea pipeline (API X60) to predict the degree of impact of the failed state on the asset’s likely consequences. At the worst degradation state, the failure consequence expected utility gives 1.0822×108 USD. The influence-based model provides a prognostic tool for proactive integrity management planning for subsea systems exposed to stochastic degradation in harsh offshore environments.

An uncertainty-informed framework for trustworthy fault diagnosis in safety-critical applications

Deep learning-based models, while highly effective for prognostics and health management, fail to reliably detect the data unknown in the training stage, referred to as out-of-distribution (OOD) data. This restricts their use in safety-critical assets, where unknowns may impose significant risks and cause serious consequences. To address this issue, we propose to leverage predictive uncertainty as a sign of trustworthiness that aids decision-makers in comprehending fault diagnostic results. A novel probabilistic Bayesian convolutional neural network (PBCNN) is presented to quantify predictive uncertainty instead of deterministic deep learning, so as to develop a trustworthy fault diagnosis framework. Then, a predictive risk-aware strategy is proposed to guide the fault diagnosis model to make predictions within tolerable risk limits and otherwise to request the assistance of human experts. The proposed method is capable of not only achieving accurate results, but also improving the trustworthiness of deep learning-based fault diagnosis in safety-critical applications. The proposed framework is demonstrated by fault diagnosis of bearings using three types of OOD data. The results show that the proposed framework has high accuracy in handling a mix of irrelevant data, and also maintains good performance when dealing with a mix of sensor faults and unknown faults, respectively.