Causal reversibility in Bayesian networks

Updating conditional probabilities of Bayesian belief networks by merging expert knowledge and system monitoring data

This article contains highlights of paper SPE 189799, “Self-Learning Probabilistic Detection and Alerting of Drillstring Washout and Pump Failure Incidents During Drilling Operations,” by A. Ambrus, formerly with Intellicess; P. Ashok, D. Ramos, A. Chintapalli, Intellicess; A. Susich, T. Thetford, B. Nelson, M. Shahri, J. McNab, and M. Behounek, Apache Corp., presented at the 2018 IADC/SPE Drilling Conference and Exhibition, Fort Worth, Texas, 6–8 March. https:/doi.org/10.2118/189700-MS Introduction In recent years, detection and alerting systems have been applied to numerous drilling failures, including stuck pipe, fluid influx/loss, and drilling dysfunctions. But the detection of drillstring washout and mud pump failure has been left primarily to traditional methods that rely solely on standpipe pressure and pump rates or on measurement-while-drilling (MWD) sensor data. Drillers commonly use a simple hydraulic coefficient relating standpipe pressure to pump rate to detect drillstring washouts. MWD pressure and mud motor data may improve detection but this approach remains problematic owing to poor-quality sensor data and various factors that affect flow and pressure data. As a result, drillers often do not recognize a crack in the drillstring before it grows into a washout that may cost operators hundreds of thousands of dollars in lost time, equipment replacement, and fishing operations. Drillers also rely on standpipe pressure changes to detect mud pump failures and degradation from damaged pump parts. High-frequency pump pressure data may enhance pump wear detection and accelerometer data may be used to infer valve leaks, but these solutions are impractical in most field applications. To address these shortcomings, a methodology has been introduced using basic rig sensors and contextual information to detect various drilling failure modes. It has applied that same approach to early wash-out and pump failures detection and alerting. Methodology The detection and alerting system uses a Bayesian network, which aggregates key sensor inputs and contextual data and predictions from hydraulic modeling. Cumulatively they are the inputs to a probabilistic belief system. The probabilistic model outputs belief values of between 0 and 1 that are indicative of specific drilling, equipment, and sensor failures. Just as the human brain uses experience to generate beliefs upon which to act and react to the world around it intelligently, the probabilistic model uses past and present trends and artificial intelligence (AI) to generate beliefs about drilling dysfunctions and equipment failures. The model also assesses these trends to increase its accuracy through self-learning and self-calibration that enables it to adjust for poor sensor data, drilling conditions, and model uncertainties. As a consequence, when the value of a belief rises to a specified level and the system triggers an alert, the driller can act upon it with increased certainty that it is not a false alarm. Bayesian networks consist of discrete, or continuous-valued, nodes. Nodes are connected via conditional probability tables (CPTs) and linked by arrows generally representing the direction of causation. Each CPT is assigned a specific weight based on its relative impact on specific outcomes. A Bayesian Network in which the key node is “Unplanned Event” includes several event types and their associated probabilities, or beliefs. This network arrangement can be used to detect a broad variety of incidents related to well control and hydraulics, such as washouts, pump failures, kicks, lost circulation, wellbore breathing, packoff and others to which a probability value is assigned.

The LANL IKE team proposes that the surveillance metrics for several data stream that are used to detect the same failure mode be weighted. Similarly, the failure mode metrics are weighted to obtain a subsystem metric. E.g., if there n data streams (nodes 1-n), the failure mode (node 0) metric is obtained as M{sub 0} = w{sub 1}M{sub 1} + {hor_ellipsis} + w{sub n}M{sub n}, where {Sigma}{sub i=1}{sup n} w{sub i} = 1. This proposal has been implemented with Bayes Nets using the Netica/IKE software by specifying an appropriate conditional probability table (CPT). This CPT is calculated using the same form as (1), where the data stream metrics for the true (T) and false (F) states are replaced by 1 and 0, respectively. Then using this CPT, the failure mode metric calculated by Netica/IKE equals (1). This result has two nice features. First, the rollup Bayes nets is doing can be easily explained. Second, because Bayes Nets can implement this rollup using Netica/IKE, then data marshalling (allocating next year's budget) can be studied. A proof that the claim 'failure mode metric calculated by Netica/IKE equals (1)' for n = 2 and n = 3 follows as well as the sketch of a proof by induction for general n.

Background: Bayesian Belief Network (BBN) is a well-established causal framework that is widely adopted in various domains and has a proven track record of success in research and application areas. However, BBN has weaknesses in causal knowledge elicitation and representation. The representation of the joint probability distribution in the Conditional Probability Table (CPT) has increased the complexity and difficulty for the user either in comprehending the causal knowledge or using it as a front-end modelling tool. Methods: This study aims to propose a simplified version of the BBN ─ Bayesian causal model, which can represent the BBN intuitively and proposes an inference method based on the simplified version of BBN. The CPT in the BBN is replaced with the causal weight in the range of[-1,+1] to indicate the causal influence between the nodes. In addition, an inferential algorithm is proposed to compute and propagate the influence in the causal model. Results: A case study is used to validate the proposed inferential algorithm. The results show that a Bayesian causal model is able to predict and diagnose the increment and decrement as in BBN. Conclusions: The Bayesian causal model that serves as a simplified version of BBN has shown its advantages in modelling and representation, especially from the knowledge engineering perspective.

One problem faced in knowledge engineering for Bayesian networks (BNs) is the exponential growth of the number of parameters in their conditional probability tables (CPTs). The most common practical solution is the application of the so-called canonical gates and, among them, the noisy-OR (or their generalization, the noisy-MAX) gates, which take advantage of the independence of causal interactions and provide a logarithmic reduction of the number of parameters required to specify a CPT. In this paper, we propose an algorithm that fits a noisy-MAX distribution to an existing CPT, and we apply this algorithm to search for noisy-MAX gates in three existing practical BN models: ALARM, HAILFINDER, and HEPAR II. We show that the noisy-MAX gate provides a surprisingly good fit for as many as 50% of CPTs in two of these networks. We observed this in both distributions elicited from experts and those learned from data. The importance of this finding is that it provides an empirical justification for the use of the noisy-MAX gate as a powerful knowledge engineering tool. © 2013 IEEE.

Exact inference in Bayesian networks with nodes having a large parent set is not tractable using standard techniques as are the junction tree method or the variable elimination. However, in many applications, the conditional probability tables of these nodes have certain local structure than can be exploited to make the exact inference tractable. In this paper we combine the CP tensor decomposition of probability tables with probabilistic inference using weighted model counting. The motivation for this combination is to exploit not only the local structure of some conditional probability tables but also other structural information potentialy present in the Baysian network, like determinism or context specific independence. We illustrate the proposed combination on BN2T networks – two-layered Bayesian networks with conditional probability tables representing noisy threshold models.

As a dominant method in evidential reasoning, Bayesian network has been proved powerful in discrete fields. Although Bayesian network performs reliable in continuous variables and interval estimations, it relies on discretizing continuous variables or building an approximate model to conduct, which causes information loss and accuracy reduction. In order to bridge this gap, this paper introduces two inference rules combined with four inference rules proposed by other scholars. Then we propose a concept of uncertain inference network that consists of six basic structures matching inference rules to represent relationships and logic connection among the evidence. Evidence is represented by uncertain sets that can apply to continuous variables using membership functions to represent vague concepts. Furthermore, a numeric experiment for a forensic investigation of fire incidents is given to compare the results of uncertain inference network and Bayesian network. We found three merits in the case study. First, an uncertain inference network has simpler data access for each node because Bayesian network depends on conditional probability tables while uncertain inference network only relies on membership function. Second, an uncertain inference network has a more wide application because it can perform continuous variables with certain mathematical formulas without discretizing or approximating. Third, an uncertain inference network has a more accurate result because Bayesian network gives a point estimation with a 0–1 value while uncertain inference network conducts an interval estimation with a range value.

Bayesian networks (BN) are an excellent tool for classification of a complex inter-correlated data such as medical data. This study is aimed at learning diabetes data using CI Search Algorithm and to determine the factors that cause Type 1 and Type 2 Diabetes. Diabetes dataset was obtained from medical records unit of the Abubakar Tafawa Balewa University Teaching Hospital (ATBUTH) Bauchi, Bauchi State consisting of 569 cases with 8 different variables. To achieved the stated objectives, Bayesian Network (BN) were used i.e. CI Search Algorithm. CI Search Algorithm explored the nature of relationship between the attributes and diabetes type (T1D/T2D). Conditional Probability Tables (CPT) obtained by CI Search Algorithm reveals that a diabetes patient of age between 45.5-72 years is 86% likely to be T2D, a diabetes patient of BMI between 24.6-38.6 is 89% likely to be T2D, a diabetes patient with history of diabetes is 64% likely to be T1D, a diabetes patient without history of diabetes is 66% likely to be T2D.

At present, ecological and environmental problems are becoming increasingly serious. Traditional risk assessment methods are difficult to fully integrate the complex relationships among multiple variables and lack the ability to dynamically analyze uncertainty and conditional dependence, which affects the scientific nature of environmental policies. To address this problem, this paper proposes an ecological risk assessment and environmental policy analysis framework based on Bayesian networks, aiming to effectively quantify ecological risks and provide support for policy decisions. In terms of methodology, first, a Bayesian network structure is constructed with ecosystem elements as nodes and causal relationships as edges; second, the conditional probability table is determined by combining expert knowledge with historical data; then, node sensitivity analysis and scenario simulation are carried out to identify key risk factors and sources of uncertainty; finally, the regulatory effect of policy intervention on risks is evaluated. The study took a typical river basin as an example, and the results showed that driven by pollutant concentrations and land use changes, the river basin ecosystem risk index reached 0.72, among which water quality deterioration and biodiversity decline were the main sources of risk; policy simulation showed that by increasing sewage treatment rate and vegetation coverage rate, the risk index could be reduced to 0.48, a reduction of 33.3%. Studies have shown that Bayesian networks can effectively reveal causal relationships and the impact of policy interventions in complex ecosystems, providing a scientific basis for the precise formulation of environmental policies.

<p>System identification (SI) is a systematic process to estimate structural parameters by minimizing errors between measured and simulated responses of the structure. Existing SI algorithms have been suffering from ill-posedness, a well-known issue in inverse problems. To overcome challenges in SI, this paper investigates the potential use of Bayesian Network (BN) for the purpose of probabilistic identification of structural parameters. The relationships between the nodes in the BN graph are described by the conditional probability tables (CPT) obtained by Monte Carlo simulations of structural analysis. To depict the spatial distribution of deteriorating structural parameter in two-dimension effectively in a BN model, a bi- variate Gaussian function is employed. The performance of the proposed method is tested and demonstrated through comparison with the results by maximum likelihood estimation (MLE) using several assumed scenarios of structural deterioration.</p>

The global threat of deliberate attacks on chemical, process, and energy facilities underscores the urgent need to enhance Security Vulnerability/Risk Assessment (SVA/SRA) approaches. Traditional assessments often use historical data and Exploratory Data Analysis (EDA) to identify reference scenarios. However, EDA lacks a standardized approach to identify and rank the incident chains. A novel methodology based on Bayesian Networks (BN), named BAS2E, was developed to support the systematic identification of reference scenarios from past event datasets. The methodology is based on the development of a static quantified BN, that accurately reflects the causal relationships in incident chains, focusing specifically on those between threats, attack methods, and physical damage scenarios. The BN is quantified by statistical information from the analysis of the incident records and employs the Noisy-OR gate model to manage data gaps in the conditional probability tables (CPTs) specification. The application of the BN sensitivity analysis provides quantification of the reciprocal influence between nodes using a specific derivative-based parameter, allowing for the systematic ranking of the most impactful incident chains to be included as reference scenarios in SVA/SRA. The methodology is demonstrated through its application to a dataset of 109 security incidents that occurred in the offshore Oil&Gas sector.

One difficulty faced in knowledge engineering for Bayesian Network (BN) is the quantification step where the Conditional Probability Tables (CPTs) are determined. The number of parameters included in CPTs increases exponentially with the number of parent variables. The most common solution is the application of the so-called canonical gates. The Noisy-OR (NOR) gate, which takes advantage of the independence of causal interactions, provides a logarithmic reduction of the number of parameters required to specify a CPT. In this paper, an extension of NOR model based on the theory of belief functions, named Belief Noisy-OR (BNOR), is proposed. BNOR is capable of dealing with both aleatory and epistemic uncertainty of the network. Compared with NOR, more rich information which is of great value for making decisions can be got when the available knowledge is uncertain. Specially, when there is no epistemic uncertainty, BNOR degrades into NOR. Additionally, different structures of BNOR are presented in this paper in order to meet various needs of engineers. The application of BNOR model on the reliability evaluation problem of networked systems demonstrates its effectiveness.

<p>Rough estimations in emergency mode are now playing an important role in making key decisions for managing disasters including search and rescue. Most of the studies only paid attention to the earthquakes and ignored the presence of disaster chains and the hazard interactions in earthquakes. Bayesian Networks are ideal tools to explore the causal relationships between events, combine prior knowledge and observed data, and are integrated to solve uncertain problems. In such situations, we present improvements based on a Bayesian Network Model in approaches to estimations of casualties in earthquakes. According to the development of the earthquake disaster chain in literature, the proposed model extracts the key events of earthquakes, considers the hazard interactions, and constructs the Bayesian Networks based on a scenario-based method, to deal with the events in the earthquakes. In the model, lifeline system damages, fires, landslides, and debris flow have been integrated into the networks. The conditional probability tables are encoded by using the collected cases. Validations in the Netica allow the simulation of expected shaking intensity and estimation of the expected casualties by strong earthquakes in emergency mode. Compared to the literature, the method is closer to the fact in the rough estimations, providing important information for our response to earthquakes. Further, rough estimations are started when only seismic intensity or fewer earthquake source parameters are available.</p> <p> </p>

This study develops a probabilistic dynamic risk assessment framework for grounding and collision/contact accidents in narrow waterways by integrating the Human Factors Analysis and Classification System for Passenger Vessels (HFACS-PV) with Bayesian Networks (BN). Marine accident reports from the Dover Strait (2004–2020) were systematically analysed to identify human, organisational, technical, and environmental risk factors, which were subsequently structured into a Bayesian Network to model their interdependencies and dynamic influence on accident occurrence. Conditional probability tables were derived from accident data and supplemented through structured expert elicitation. The resulting model enables real-time inference and predictive risk estimation under evolving operational conditions. Model performance was evaluated using detailed grounding and collision case studies, demonstrating its capability to replicate accident evolution and quantify the contribution of key causal factors. The results indicate that unsafe acts, particularly decision-based and perceptual errors, combined with deficiencies in voyage planning, supervision, and situational awareness, dominate accident causation in the Dover Strait. The proposed framework provides a quantitative decision-support tool for vessel traffic services and maritime operators, supporting proactive risk mitigation and safety optimisation in high-density and constrained navigational environments. • Analysis of Dover Strait grounding and collision accidents using HFACS to identify human and organisational causes. • A novel dynamic risk model enables real-time assessment of collision, contact, and grounding risks for operators. • The model supports risk control measures and optimises best practices to improve safety in narrow waterways.

The increasing frequency and severity of Natech accidents warn us to investigate the occurrence mechanism of these events. Cascading disasters chain magnifies the impact of natural hazards due to its propagation through critical infrastructures and socio-economic networks. In order to manipulate imprecise probabilities of cascading events in Natech scenarios, this work proposes an improved Bayesian network (BN) combining with evidence theory to better deal with epistemic uncertainty in Natech accidents than traditional BNs. Effective inference algorithms have been developed to propagate system faulty in a socio-economic system. The conditional probability table (CPT) of BN in the traditional probability approach is modified by utilizing an OR/AND gate to obtain the belief mass propagation in the framework of evidence theory. Our improved Bayesian network methodology makes it possible to assess the impact and damage of Natech accidents under the environment of complex interdependence among accidents with insufficient data. Finally, a case study of Guangdong province, an area prone to natural disasters, is given. The modified Bayesian network is carried out to analyze this area’s Natech scenario. After diagnostic analysis and sensitivity analysis of human factors and the natural factor, we are able to locate the key nodes in the cascading disaster chain. Findings can provide useful theoretical support for urban managers of industrial cities to enhance disaster prevention and mitigation ability.