The research team, led by Zhanpeng Liu and Wensheng Xiao, combined failure mode and effects analysis, Bayesian networks, risk matrices, and fuzzy comprehensive evaluation into one integrated method. Each technique has well-known strengths and blind spots. FMEA can systematically identify potential failure modes but is highly subjective. Bayesian networks excel at quantitative forward and backward inference yet cannot judge how severe a failure’s consequences would be. Risk matrices offer a visual representation of occurrence and severity but cannot assess the risk level of the system as a whole. Fuzzy comprehensive evaluation handles vague, uncertain information but again depends on subjective judgment. By weaving these approaches together, the researchers aimed to let each method compensate for the weaknesses of the others, producing a single assessment that yields both the system failure probability and the risk level of every individual failure mode.

The workflow begins with a fault tree analysis of the motor, in which twenty bottom-event failure modes across six components, the rotor, bearings, windings, permanent magnets, controller, and mechanical seal, are mapped into a Bayesian network. Prior probabilities are derived from historical failure rates in the OREDA offshore reliability database, adjusted upward by expert judgment to reflect the brutal conditions of underground drilling. Bayesian forward inference then computes the overall system failure probability, while backward diagnostic inference produces posterior probabilities revealing which failure modes are most likely responsible when the system fails. In the baseline assessment, the system failure probability came out at 0.428, a strikingly high figure that underscores how punishing the drilling environment is for these machines.

Next comes importance analysis, a mathematical step that quantifies how much each failure mode contributes to system failure. The team calculated three indices: probabilistic importance, which measures the impact of a component’s failure probability on system failure; structural importance, which reflects a component’s position in the system architecture; and critical importance, which combines both failure probability and sensitivity. Because all twenty failure modes feed the system through identical OR-gate logic, their structural importance is equal, but their probabilistic and critical importance diverge dramatically. Rotor breakage, for instance, posted a probabilistic importance of 1.3782, far above its peers, while bearing wear registered a posterior probability of 0.612, the highest of any mode, simply because bearings grind against each other every moment the motor spins.

These quantitative outputs then feed the qualitative side of the framework. The posterior probability of each failure mode determines its occurrence rating on a five-level scale, from improbable to frequent, while the critical importance determines its severity rating, from negligible to catastrophic. The two ratings fuse into a composite risk index called ROS, weighted 0.4 toward occurrence and 0.6 toward severity, a deliberate choice reflecting the safety-critical nature of drilling, where even rare events with devastating consequences demand priority attention. The resulting ROS values map onto a fuzzy evaluation matrix through a parabolic membership function, and the weights of that matrix come directly from the importance analysis rather than from pure expert opinion, reducing the subjectivity that plagues conventional assessments.

The baseline results identified winding phase-to-phase short circuit as the single highest-risk failure mode, with a ROS value of 4.2 placing it firmly in the high-risk category. Rotor dynamic eccentricity and permanent magnet partial demagnetization followed at 3.6 each, classed as medium-high risk. Perhaps more revealing were the failure modes with severe consequences but vanishingly low occurrence, including rotor breakage, bearing breakage, and permanent magnet breakage, all rated medium risk despite being improbable. The framework’s dual weighting captured exactly the kind of nuance that pure probability-based methods miss: a rare failure that destroys the motor deserves as much managerial attention as a common one that merely degrades performance. The fuzzy evaluation concluded that the system sat at medium risk with a membership probability of 0.498, but with a worrying 0.351 probability of medium-high risk.

Armed with this diagnosis, the researchers proposed targeted countermeasures for every failure mode, ranging from corona-resistant enameled wire and vacuum pressure impregnation for the windings to hastelloy springs and fluorocarbon or EPDM elastomers for the seals, matched to oil-based and water-based mud chemistries respectively. For winding faults, they applied weak magnetic current injection, multi-phase redundancy, and winding redundancy, allowing the motor to shed faulty phases gracefully while maintaining partial power. After implementing the improvements, the system failure probability dropped from 0.428 to 0.394, the mean time between failures rose from 1,847 to 2,032 hours, and the medium-high risk membership probability fell from 0.351 to 0.245. The highest-risk failure mode, the winding short circuit, saw its ROS value plunge from 4.2 to 3.2, a 23.8 percent risk reduction.

What distinguishes this study from earlier hybrid approaches is its unusually rigorous treatment of uncertainty and validation. The team ran a Monte Carlo simulation with 10,000 samples, assuming failure rates follow log-normal distributions with a 20 percent coefficient of variation, and found that the 95 percent confidence intervals of key outputs remained narrow, less than 15 percent of their mean values. A perturbation analysis of the weighting coefficients showed that risk rankings stay stable, with Spearman rank correlations above 0.88, as long as severity retains reasonable dominance, confirming the wisdom of the 0.4-0.6 split. The importance-based weights were cross-checked against the entropy weight method and the CRITIC method, with Kendall’s coefficient of concordance reaching 0.82, indicating strong agreement between expert judgment and data-driven weighting. A paired bootstrap test and a Wilcoxon signed-rank test both confirmed that the post-improvement risk reduction was statistically significant, with p below 0.001.

The authors also introduced three methodological innovations that broaden the framework’s reach. A risk coupling coefficient quantifies how strongly each failure mode couples with environmental loads such as vibration, high temperature, current fluctuations, and high-pressure drilling fluid, distilled from a multi-factor coupling matrix that identified twenty high-probability coupled failure modes. An adaptive risk transfer function models nonlinear propagation from component-level risk to system-level risk, capturing synergistic effects that simple OR-gate logic overlooks. And a risk entropy metric measures how dispersed or concentrated the system’s risk profile is; it fell from 1.42 before improvement to 1.24 after, signaling reduced uncertainty in the risk landscape.

The framework is not without limitations, which the authors acknowledge candidly. Integrating four methodologies creates a complex model with substantial computational overhead, and exact Bayesian inference scales exponentially with the number of failure modes, though hierarchical decomposition into sub-networks reduces the complexity from an intractable O(2^100) to a manageable O(10 times 2^10) for a hundred-mode system split across ten components. Prior probabilities still lean on the OREDA database and expert experience, which update infrequently, and the static Bayesian network does not yet ingest real-time sensor data. Future work, the team suggests, will move toward dynamic Bayesian networks fed by live monitoring evidence, adaptive neuro-fuzzy membership functions optimized by backpropagation, and hierarchical architectures spanning failure mode, component, subsystem, and system layers. For now, the study offers drilling engineers something genuinely valuable: a single, statistically validated assessment that tells them not just whether their motor is likely to fail, but exactly which of twenty failure modes deserves their attention first, and how much safer each repair will make it.

Subject of Research: Hybrid fuzzy risk assessment of drilling permanent magnet synchronous motors using FMEA and Bayesian networks

Article Title: An improved fuzzy risk assessment method fusing FMEA and BN for drilling permanent magnet synchronous motors

Article References: Liu, Z., Xiao, W., Cui, J., Wang, H., & Mei, L. (2026). An improved fuzzy risk assessment method fusing FMEA and BN for drilling permanent magnet synchronous motors. Results in Engineering, 32, Article 113047. https://doi.org/10.1016/j.rineng.2026.113047

Image Credits: AI Generated

DOI: 10.1016/j.rineng.2026.113047

Keywords: risk assessment, FMEA, Bayesian network, fuzzy comprehensive evaluation, permanent magnet synchronous motor, drilling motor, reliability engineering, risk matrix, Monte Carlo simulation, importance analysis, oil and gas drilling, failure modes