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Uncertainty and Reliability Analysis for Engineering Systems

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A special issue of Applied Sciences (ISSN 2076-3417). This special issue belongs to the section "Applied Industrial Technologies".

Deadline for manuscript submissions: 30 December 2025 | Viewed by 10871

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Special Issue Editors

Dr. Guijie Li

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Guest Editor

School of Aeronautics and Astronautics, Dalian University of Technology, Dalian 116024, China
Interests: uncertainty quantification; system reliability design; structural reliability analysis
Special Issues, Collections and Topics in MDPI journals

Dr. Feng Zhang

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Guest Editor

School of Mechanics, Civil Engineering and Architecture, Northwestern Polytechnical University, Xi’an 710129, China
Interests: uncertainty quantification; aircraft reliability engineering
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Dr. Xiaobo Zhang

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Guest Editor

School of Mechanical Engineering, Hefei University of Technology (HFUT), Hefei, China
Interests: structural reliability analysis; uncertainty-based design optimization; sensitivity analysis

Special Issue Information

Dear Colleagues,

Reliability is one of the core performance indexes of products, which has attracted increasingly more attention in recent years. For complex engineering systems, the uncertainties of geometric dimensions, material properties, and loads are more prominent. To ensure the realization of the high-reliability requirements of engineering systems, the above uncertainties must be fully considered in the design, manufacturing, and experimental process. However, due to the complexity of the problem, there are still a large number of challenging problems that need to be studied.

In this regard, this Special Issue focuses on reporting the recent advances related to uncertainty quantification, high-dimensional reliability analysis, sensitivity analysis, reliability-based multidisciplinary design optimization, reliability-based design optimization, and their practical applications in complex engineering systems.

Topics for potential contributions include but are not limited to the following:

Uncertainty quantification;
Advanced uncertainty propagation methodologies, g., metamodel methods and artificial intelligence algorithms;
Sensitivity analysis techniques and efficient algorithms;
Reliability-based design optimization;
Reliability-based multidisciplinary design optimization;
Reliability assessment for engineering systems;
Emerging tools for reliability design analysis and optimization;
Practical applications in engineering systems.

Dr. Guijie Li
Dr. Feng Zhang
Dr. Xiaobo Zhang
Guest Editors

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Keywords

uncertainty quantification
reliability analysis
reliability-based design
reliability-based optimization
sensitivity analysis

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Published Papers (9 papers)

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Research

27 pages, 1008 KB

Open AccessArticle

Efficient Reliability Block Diagram Evaluation Through Improved Algorithms and Parallel Computing

by Gloria Gori, Marco Papini and Alessandro Fantechi

Appl. Sci. 2025, 15(21), 11397; https://doi.org/10.3390/app152111397 (registering DOI) - 24 Oct 2025

Abstract

Quantitative reliability evaluation is essential for optimizing control policies and maintenance strategies in complex industrial systems. While Reliability Block Diagrams (RBDs) are a natural formalism for modeling these hierarchical systems, modern applications require highly efficient, online reliability assessment on resource-constrained embedded hardware. This demand presents two fundamental challenges: developing algorithmically efficient RBD evaluation methods that can handle diverse custom distributions while preserving numerical accuracy, and ensuring platform-agnostic performance across diverse multicore architectures. This paper investigates these issues by developing a new version of the librbd open-source RBD library. This version includes advances in efficiency of evaluation algorithms, as well as restructured computation sequences, cache-aware data structures to minimize memory overhead, and an adaptive parallelization framework that scales automatically from embedded processors to high-performance systems. Comprehensive validation demonstrates that these advances significantly reduce computational complexity and improve performance over the original implementation, enabling real-time analysis of substantially larger systems. Full article

(This article belongs to the Special Issue Uncertainty and Reliability Analysis for Engineering Systems)

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30 pages, 3350 KB

Open AccessArticle

A Unified Modelling Framework Combining FTA, RBD, and BowTie for Reliability Improvement

by Mohamad Afiq Amiruddin Parnon, Kassandra A. Papadopoulou and Jyoti K. Sinha

Appl. Sci. 2025, 15(20), 10902; https://doi.org/10.3390/app152010902 - 10 Oct 2025

Viewed by 286

Abstract

Ensuring reliability and safety is essential in complex energy systems such as wind turbines, where failures can trigger unexpected downtimes, severe incidents, and significant costs. This study proposes a hybrid BowTie-based reliability framework that integrates Fault Tree Analysis, Reliability Block Diagrams, and BowTie methodology to quantify risk and evaluate the effectiveness of safety barriers. The framework employs key reliability metrics including availability, probability of failure on demand, and probability of failure per hour, and supports scenario-based sensitivity analyses to explore redesign options. A simulation-based case study of a wind turbine generator subsystem is presented, using parameter values drawn from published reliability data. Results highlight that protective relays and automatic trip systems represent critical single points of defence, while improvements such as enhanced oil analysis and redundant dashboards reduce consequence frequency from 2.912 × 10⁻¹⁷ to 8.257 × 10⁻¹⁹ failures/h (a 97.16% reduction, nearly two orders of magnitude). Compared to conventional models, the proposed framework introduces explicit defence in depth modelling, improves computational compactness, and provides a practical decision support tool for asset managers by balancing safety and reliability. At this stage, the study should be regarded as a proof of concept that demonstrates feasibility and sets a foundation for future research and application to larger, more complex infrastructures. Full article

(This article belongs to the Special Issue Uncertainty and Reliability Analysis for Engineering Systems)

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34 pages, 7241 KB

Open AccessArticle

An Efficient Uncertainty Quantification Approach for Robust Design of Tuned Mass Dampers in Linear Structural Dynamics

by Thomas Most, Volkmar Zabel, Rohan Raj Das and Abridhi Khadka

Appl. Sci. 2025, 15(17), 9329; https://doi.org/10.3390/app15179329 - 25 Aug 2025

Viewed by 725

Abstract

The application of tuned mass dampers (TMDs) to high-rise buildings or slender bridges can significantly decrease the dynamical vibrations due to external excitation, such as wind or earthquake loads. However, the individual properties of a TMD such as mass, stiffness and damping have to be designed carefully with respect to the dynamical properties of the investigated structure. In real-world structures, the influence of uncertain system properties might be critical for the performance of a TMD and thus the whole structure. Therefore, the design under uncertainty of such systems is an important issue, which is addressed in the current paper. For our investigations, we consider linear single-degree-of-freedom (SDOF) systems, where analytical formulas for the deterministic design already exist, and linear multi-degree-of-freedom (MDOF) systems, where a time integration and numerical optimization algorithms are usually applied to obtain the optimal TMD parameters. If the numerical optimization should be coupled with a sampling-based uncertainty quantification method, such as Monte Carlo sampling, the design procedure would require the evaluation of a coupled double-loop approach, which is very demanding from the computation point of view. Therefore, we focus the following paper on an efficient analytical uncertainty quantification approach, which estimates the mean and scatter from a Taylor series expansion. Additionally, we introduce an efficient mode decomposition approach for MDOF systems with multiple TMDs, which estimates the maximum displacements using a modal analysis instead of a demanding time integration. Different optimal design problems are formulated as single- or multi-objective optimization tasks, where the statistical properties of the maximum displacements are considered as safety margins in the optimization goal functions. The application of numerical optimization algorithms is straightforward and not limited to specific algorithms. As numerical examples, we investigate an SDOF system with single TMD and a multi-story frame with multiple TMDs. The presented procedure might be interesting for the design process of structures, where the dynamical vibrations reach a critical threshold. Full article

(This article belongs to the Special Issue Uncertainty and Reliability Analysis for Engineering Systems)

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22 pages, 7239 KB

Open AccessArticle

A Reliability-Oriented Framework for the Preservation of Historical Railway Assets Under Regulatory and Material Uncertainty

by Thomas Wailes, Muhammad Khan and Feiyang He

Appl. Sci. 2025, 15(9), 4705; https://doi.org/10.3390/app15094705 - 24 Apr 2025

Viewed by 741

Abstract

Preserving historical railway assets presents a complex systems challenge, in which uncertainties in material performance, structural degradation, and regulatory requirements directly impact long-term reliability and operational continuity. Traditional maintenance practices often limit the use of modern materials, introducing inefficiencies, increased lifecycle costs, and higher failure risk due to material ageing and environmental exposure. This study proposes a reliability-informed preservation framework that supports the integration of contemporary materials into historical railway infrastructure while accounting for legal, material, and procedural uncertainties. The framework is validated through two industrial case studies, each reflecting different regulatory and operational constraints. The first case demonstrates the successful substitution of timber with certified PVC cladding on a non-listed signal box, achieving improved durability, reduced maintenance intervals, and enhanced system reliability. The second case explores an unsuccessful attempt to replace decayed timber gables with aluminium, in which late-stage planning misalignment, underestimated risks, and uncertainty in approval outcomes led to a significant cost increase and reduced reliability regarding delivery. By systematically applying and evaluating the framework under real-world conditions, this research contributes to engineering asset management by introducing a structured method for mitigating regulatory and material uncertainties. Full article

(This article belongs to the Special Issue Uncertainty and Reliability Analysis for Engineering Systems)

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11 pages, 1224 KB

Open AccessCommunication

Measurement Uncertainty and Compliance Evaluation Applied to Natural Gas Moisture

by Rosana Medeiros Moreira, Cesar Luís Biazon and Elcio Cruz de Oliveira

Appl. Sci. 2025, 15(5), 2482; https://doi.org/10.3390/app15052482 - 25 Feb 2025

Cited by 1 | Viewed by 1055

Abstract

The reliability of natural gas moisture measurements is crucial in preventing corrosion in pipelines and equipment, ensuring burning efficiency and mitigating operational risks, and is often mandated by standards and regulations. An important quality parameter that aids in conformity assessment, particularly in risk assessment, is measurement uncertainty. The assessment of measurement uncertainty, based on the Law of Uncertainty Propagation, depends on the mathematical model used to calculate this physicochemical property. This study aimed to compare different algorithms for calculating moisture content in natural gas, estimate and validate the measurement uncertainty based on the algorithms implemented in the Portable Moisture Analyzer (PM880) equipment, a portable hygrometer manufactured by Panametrics in Wilmington, NC, USA, and evaluate compliance with Brazilian legislation using guard bands as a decision rule. The moisture results in natural gas varied by a maximum of 1% among the three approaches presented. Furthermore, based on the dew point and pressure results, the expanded uncertainties of moisture were about 20%, which did not compromise the risk assessment for the consumer, as the moisture results were well below the specification value. Consequently, the upper tolerance limit of 58.4 ppmv H₂O was established. Full article

(This article belongs to the Special Issue Uncertainty and Reliability Analysis for Engineering Systems)

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14 pages, 3425 KB

Open AccessArticle

Prediction of Wind Turbine Blade Stiffness Degradation Based on Improved Neural Basis Expansion Analysis

by Shuai Yang, Jianxiong Gao, Yiping Yuan, Jianxing Zhou and Lingchao Meng

Appl. Sci. 2025, 15(4), 1884; https://doi.org/10.3390/app15041884 - 12 Feb 2025

Viewed by 935

Abstract

To reduce the significant time and cost associated with wind turbine blade fatigue testing, the applicability of the deep learning model Neural Basis Expansion Analysis (N-BEATS) for modeling the stiffness degradation of wind turbine blades was investigated. First, on the basis of a traditional blade stiffness degradation model, the stiffness data were expanded to meet the data volume requirements of N-BEATS. Second, the basic block structure of N-BEATS was improved (by treating the sequence-to-sequence prediction problem as a nonlinear multivariate regression problem) to meet the specific prediction requirements of this task, and the Pinball Mean Absolute Percentage Error (Pinball-MAPE) loss function was adopted to further reduce bias during the prediction process. Additionally, two data augmentation methods—time series combination and random noise injection—were applied to mitigate the risk of model overfitting and improve prediction accuracy. Experimental results demonstrated that the model can effectively learn underlying patterns in the stiffness data and successfully predict the remaining stiffness. Full article

(This article belongs to the Special Issue Uncertainty and Reliability Analysis for Engineering Systems)

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20 pages, 6801 KB

Open AccessArticle

Uncertainty Quantification in Shear Wave Velocity Predictions: Integrating Explainable Machine Learning and Bayesian Inference

by Ayele Tesema Chala and Richard Ray

Appl. Sci. 2025, 15(3), 1409; https://doi.org/10.3390/app15031409 - 30 Jan 2025

Cited by 4 | Viewed by 1517

Abstract

The accurate prediction of shear wave velocity (Vs) is critical for earthquake engineering applications. However, the prediction is inevitably influenced by geotechnical variability and various sources of uncertainty. This paper investigates the effectiveness of integrating explainable machine learning (ML) model and Bayesian generalized linear model (GLM) to enhance both predictive accuracy and uncertainty quantification in Vs prediction. The study utilizes an Extreme Gradient Boosting (XGBoost) algorithm coupled with Shapley Additive Explanations (SHAPs) and partial dependency analysis to identify key geotechnical parameters influencing Vs predictions. Additionally, a Bayesian GLM is developed to explicitly account for uncertainties arising from geotechnical variability. The effectiveness and predictive performance of the proposed models were validated through comparison with real case scenarios. The results highlight the unique advantages of each model. The XGBoost model demonstrates good predictive performance, achieving high coefficient of determination (

R^{2}

), index of agreement (IA), Kling–Gupta efficiency (KGE) values, and low error values while effectively explaining the impact of input parameters on Vs. In contrast, the Bayesian GLM provides probabilistic predictions with 95% credible intervals, capturing the uncertainty associated with the predictions. The integration of these two approaches creates a comprehensive framework that combines the strengths of high-accuracy ML predictions with the uncertainty quantification of Bayesian inference. This hybrid methodology offers a powerful and interpretable tool for Vs prediction, providing engineers with the confidence to make informed decisions. Full article

(This article belongs to the Special Issue Uncertainty and Reliability Analysis for Engineering Systems)

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12 pages, 3407 KB

Open AccessArticle

Research on the Effect of Working Memory Training on the Prevention of Situation Awareness Failure in Shearer Monitoring Operations

by Xiaofang Yuan, Ruyi Song and Linhui Sun

Appl. Sci. 2024, 14(24), 11876; https://doi.org/10.3390/app142411876 - 19 Dec 2024

Cited by 1 | Viewed by 1468

Abstract

The digitization of the instrument control system in monitoring operations makes the problem of the operator’s situational awareness failure more prominent. In order to better prevent this occurrence, this paper explores the failure of situational awareness from the perspective of cognitive function. The subjects were randomly divided into two groups: a working memory training group and a control group. Working memory measurements and coal mining machine monitoring simulation system operation tasks were performed before and after training, and the task performance, situational awareness scale, and EEG index data were recorded. The results showed that, after the training, there was a significant improvement in the task performance of the monitoring operation and the scores of the situational awareness scale, and there were different degrees of activation in the θ, α₂, and β₁ frequency bands. It was demonstrated that working memory training could help to improve the rapid reaction and decision-making abilities of operators in complex or emergency situations, thus preventing the failure of situational awareness. This study provides a new direction for research on the prevention of situational awareness failure. Full article

(This article belongs to the Special Issue Uncertainty and Reliability Analysis for Engineering Systems)

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13 pages, 1785 KB

Open AccessArticle

Reliability Analysis of Complex Structures Under Multi-Failure Mode Utilizing an Adaptive AdaBoost Algorithm

by Feng Zhang, Zijie Qiao, Yuxiang Tian, Mingying Wu and Xiayu Xu

Appl. Sci. 2024, 14(22), 10098; https://doi.org/10.3390/app142210098 - 5 Nov 2024

Cited by 3 | Viewed by 2322

Abstract

A reliability analysis can become intricate when addressing issues related to nonlinear implicit models of complex structures. To improve the accuracy and efficiency of such reliability analyses, this paper presents a surrogate model based on an adaptive AdaBoost algorithm. This model employs an adaptive method to determine the optimal training sample set, ensuring it is as evenly distributed as possible on both sides of the failure curve and fully contains the information it represents. Subsequently, with the integration and iterative characteristics of the AdaBoost algorithm, a simple binary classifier is iteratively applied to build a high-precision alternative model for complex structural fault diagnosis to cope with multiple failure modes. Then, the Monte Carlo simulation technique is employed to meticulously assess the failure probability. The accuracy and stability of the proposed method’s iterative convergence process are validated through three numerical examples. The findings of the study illuminate that the proposed method is not only remarkably precise but also exceptionally efficient, capable of addressing the challenges related to the reliability evaluation of complex structures under multi-failure mode. The method proposed in this paper enhances the application of mechanical structures and facilitates the utilization of complex mechanical designs. Full article

(This article belongs to the Special Issue Uncertainty and Reliability Analysis for Engineering Systems)

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