Jul 2026· PHM Society European Conference· Vol 9, pp. 1-9· 0 citations· 11 references
Abstract
Reliability assessment of rolling element bearings is critical for the predictive maintenance of industrial rotary machinery.This study proposes a Quadratic-Exponential Weighted Model (QEWM) based on Nonlinear Mixed-Effects (NLME) to characterize the degradation process of bearings. Utilizing the IMS Bearing Dataset (Set No. 2), we define the failure threshold based on the latest ISO 20816-3:2022 vibration severity standards, setting the critical RMS limit at 0.4 mm/s for Zone D. Unlike traditional models, the proposed QEWM incorporates a weight function to address heteroscedasticity, which typically intensifies during the rapid degradation phase. Model comparison based on the Akaike Information Criterion (AIC)demonstrates that QEWM significantly outperforms linear and unweighted quadratic models. To quantify the uncertainty ofthe estimation, a parametric bootstrap method with 5,000 replications was employed. The results identify a B10 life (t0.1) of165.3 hours, supported by a precise 95% confidence interval of [162.7, 168.6] hours. This research provides a robust statistical framework for bearing life prediction that aligns with international industrial standards, ensuring high precision inprognostic assessments.
This study presents the development and validation of a machine learning model for predicting the residual life of bronze bearing liners used in the universal spindle of a 1680 rolling mill. The model is based on the Random Forest ensemble algorithm and implemented in the RStudio environment using real industrial obtained from 36 bearing replacement events. The input feature set includes operating time, replacement frequency, failure probability density, and replacement count, enabling the identification of nonlinear relationships between technological parameters and component degradation. Model performance was evaluated using mean squared error (MSE) and mean absolute error (MAE), achieving an MSE of 0.125 and an MAE of 0.32 days on the test data set, with cross‐validation confirming model stability (MSE = 0.130 ± 0.012). Sensitivity analysis demonstrated robustness to input data variations typical for industrial environments. Comparative analysis with linear regression showed significantly lower predictive accuracy of conventional statistical approaches. The obtained results confirm the feasibility of applying ensemble machine learning methods for reliable residual life prediction under small‐sample industrial conditions. The proposed approach enables data‐driven maintenance planning, reduces the risk of unplanned downtime, and supports the implementation of intelligent condition monitoring systems aligned with Industry 4.0 principles.
The reliable estimation of remaining useful life (RUL) of rolling bearings plays a critical role in maintaining the reliability of modern industrial equipment and minimizing machine downtime. However, the conventional vibration-based prognostic methods tend to experience challenges in predicting the remaining useful life of rolling bearings in variable-speed operating environments due to issues with nonstationary signals and the lack of incorporation of physical degradation processes. This paper proposes a physics-informed approach for estimating the remaining useful life of rolling bearings using vibration envelope characteristics and accelerated life testing. The approach starts with the use of order tracking combined with envelope analysis to extract vibration envelope characteristics under variable speed conditions. A health index is constructed to represent the degradation process. The nonlinear degradation process is modelled using a physics-informed exponential degradation model. An ensemble prediction model is proposed for predicting RUL. The results demonstrate that the developed model was significantly more accurate in its predictions, with a maximum of 49% improvement in the RMSE compared to traditional models and consistent results under varied operational conditions. The use of physics-based modelling and envelope analysis increased the clarity and robustness of the model, and the acceleration of the life testing process contributed to better generalizability of the model. Moreover, the introduction of adaptive threshold values improved maintenance time prediction by over 50%, and uncertainty assessment confirmed the validity of the model.
Suleiman Ibrahim Mohammad, A. Vasudevan, Seif Al Bustanji et al.· Sound & Vibration· 0 citations
In practical engineering, mechanical structures are affected by time-dependent uncertainties and by correlated failure modes. This study proposes an enhanced time-variant reliability analysis framework by coupling a mixed Archimedean Copula model with an adaptive Kriging model driven by the maximum expected prediction error (MEPE) learning function. The mixed Copula combines Gumbel, Clayton and Frank components, so that upper-tail, lower-tail and nearly symmetric dependence can be represented in one model. The MEPE function combines Kriging prediction variance and leave-one-out cross-validation error through a dynamic balance factor, which guides early global exploration and later refinement near the most probable point trajectory. For the planar three-bar structure, the mixed-Copula failure probability at t = 7 is 0.4078, close to the direct-MCS benchmark 0.4059, with a relative error of 0.47%; the number of original limit-state evaluations decreases from 1.00 × 106 to 326, corresponding to a 99.97% reduction. For the two-rod parallel structure, the mixed-Copula failure probability at T = 2 is 0.0987, close to the direct-MCS benchmark 0.0992, with a relative error of 0.50%; the number of original limit-state evaluations decreases to 284. The calculated upper- and lower-tail dependence coefficients of the mixed Copula are 0.1345 and 0.2985 for the planar three-bar structure and 0.0003 and 0.3709 for the two-rod parallel structure. These quantitative results show that the proposed framework can describe nonlinear failure dependence more flexibly than a single Copula while retaining high computational efficiency.
Debiao Meng, Huaxi Wu, Muhammad Umar Khan et al.· Mathematics· 0 citations
Gear wear and fatigue often coexist under complex operating conditions. Their coex istence may bias reliability assessment and greatly increase the computational cost of time-varying reliability analysis. To address these issues, this paper proposes a dynamic multi-failure reliability analysis method for tooth surface wear, tooth surface contact fa tigue, and tooth root bending fatigue. First, the dynamic pressure angle is incorporated into the tooth surface wear model. A wear evolution model and a threshold limit-state function are then established by combining Archards wear law with Hertzian contact theory. Second, a Gamma stochastic process is used to describe the random strength degradation associated with contact fatigue and bending fatigue, and the degradation parameters are identified from the material probability-stress-life (P-S-N) curve. Third, Pearson correlation coefficients (PCCs) are introduced to describe the correlations among the basic random variables. Based on the moment information of the performance func tion obtained by second-order expansion, skewness and kurtosis are further used to construct an improved optimal squared approximation (OSA) probability density func tion for time-varying reliability computation. A high-speed stage gear of a belt-conveyor reducer is used as an example. The results show that the proposed method captures the reliability evolution of different failure modes and agrees well with Monte Carlo simulation (MCS) while reducing the computational cost.
Shuzhi Gao, Jiaxin Xu, Yimin Zhang et al.· International Journal of Rel...· 0 citations
With the continuous development of drilling technology, accurately predicting mechanical penetration rates is particularly important for improving operational efficiency and reducing costs. Existing methods often struggle to provide reliable predictions when faced with complex geological conditions and variable drilling environments because they primarily rely on traditional models and fail to adequately consider various influencing factors and their nonlinear relationships. To ad-dress these issues, this paper proposes a mechanical penetration rate prediction model based on committee machines. This model effectively captures the variability characteristics of mechanical penetration rates by integrating multiple expert models while employing wavelet filtering methods to denoise the data to enhance data quality. In the application case, this paper collects relevant drilling parameter data based on a vertical well in a specific block. The evaluation of the model shows that it performs excellently in key indicators such as mean square error, coefficient of determination, root mean square error, and mean absolute error, particularly demonstrating a high predictive capability and stability by explaining 97.19% of data variability. The advantage of the constructed model lies in its strong ensemble learning ability, which not only enhances the prediction accuracy of mechanical penetration rates but also helps to deepen the understanding of the dynamic changes in the drilling process, providing effective support for subsequent drilling optimization and resource development.
Tao Cai, Huai-Yan Qi, Xue-Wu Yang et al.· Journal of Physics, Conferen...· 0 citations
Using reliability assessment methods to calculate failure probability for a product is of vital importance in the design process of the product. The active learning reliability method combining Kriging and Monte Carlo simulation (AK-MCS) is a famous reliability analysis approach for evaluating engineering problems. However, the efficiency of establishing high-precision Kriging models has also been a major obstacle hindering the further employment of the AK-MCS method. This paper proposes an adaptive two-stage framework for AK-MCS to enhance computational efficiency in structural reliability analysis. The core innovation lies in the task decomposition strategy: Stage 1 employs a global exploration criterion to rapidly identify the region containing the true limit-state surface, while Stage 2 switches to a local refinement criterion for precise failure-probability estimation. Comparative studies across six benchmark cases demonstrate that the Two-Stage AK-MCS method reduces the average number of function evaluations by 2.0% to 10.0% compared to the standard AK-MCS method. These results confirm that the proposed two-stage strategy effectively enhances fitting efficiency without compromising accuracy.