Uncertainty and Reliability Analysis of Engineering Systems: Theory, Methods, and Applications

1. Introduction

Uncertainty and reliability analysis constitutes a core pillar in the design, operation, and assessment of engineering systems, directly impacting safety, efficiency, and sustainability. In practical engineering scenarios, uncertain factors—such as material property variations, load fluctuations, environmental disturbances, and human operation differences—are pervasive. Reliability, which is defined as the capacity of a system to stably perform its intended functions under specified conditions for a predetermined period, serves as a fundamental criterion for evaluating the performance of engineering systems. These two concepts are intrinsically linked: uncertainty is the primary source of reliability risks in systems, and scientific reliability analysis must be based on the accurate identification and quantification of uncertainty. Neglecting these critical factors may culminate in catastrophic consequences such as structural failure, equipment malfunction, and decision-making biases. Consequently, uncertainty and reliability analysis has become an essential research priority in the engineering field.

This book presents ten thematic papers centered on “Uncertainty and Reliability Analysis of Engineering Systems”. The contributions cover diverse engineering scenarios and cutting-edge analytical methods, providing a comprehensive overview of recent research advancements in the field.

The selected papers exhibit both theoretical depth and practical value, focusing on three core dimensions: firstly, innovations in fundamental theories and methods, including uncertainty-driven reliability assessment, the optimization of efficient algorithms, and the development of unified modeling frameworks; secondly, practical applications in engineering, specifically uncertainty quantification and reliability assurance in structural vibration control, the preservation of historical infrastructure, and industrial measurement; and thirdly, the integration of cutting-edge interdisciplinary technologies, applying machine learning and Bayesian inference to performance prediction, failure prevention, and multi-mode fault analysis. Each achievement contains innovative theoretical insights and technical solutions. We are honored to present this systematic collection, which integrates research achievements on uncertainty and reliability analysis from multiple engineering fields such as structural and energy engineering, rail transit, and industrial measurement. It not only showcases the latest research trends in this field but also provides rich practical application cases. This book serves as a valuable academic reference and technical resource for researchers, frontline engineering and technical personnel, and graduate students specializing in system reliability and uncertainty analysis.

We hope that this book will promote academic discussions and the exchange of achievements in this field, drive the innovative development of theories and methods for uncertainty and reliability analysis, facilitate their practical application in a wider range of engineering scenarios, and provide strong support for improving the safety, reliability, and durability of engineering systems.

2. Overview of Contributions

The following is a brief overview of the ten contributions included in this book, centered on the core themes of uncertainty quantification and reliability analysis in engineering systems, two interconnected concepts critical to ensuring the safety, efficiency, and sustainability of complex engineering infrastructures. Uncertainty, defined as the lack of complete knowledge about system properties, operating conditions, or measurement outcomes, and reliability, the ability of a system to perform its intended function under specified conditions, are addressed through diverse methodological innovations and practical applications across multiple engineering domains.

In [1], the authors tackle the challenge of reliability assessment for complex engineering systems operating under variable conditions that induce component degradation. They propose a two-level framework integrating Reliability Block Diagrams (RBDs), Fault Tree Analysis (FTA), Importance Measures, and Failure Mode and Effects Analysis (FMEA). By incorporating uncertainty through the statistical parameters of component reliability distributions, the framework identifies critical components via Importance Measures and quantifies dominant failure modes using Risk Priority Numbers (RPN). Applied to a fleet of Solid Waste Collection and Compaction Trucks in Colombia, the approach establishes a probabilistic basis for maintenance prioritization, enhancing the accuracy of critical component and failure mode identification.

To address the challenges of limited reliability evaluation efficiency and the inability to ensure platform-independent performance across different multi-core architectures, which arise when Reliability Block Diagrams are applied to the scenario of efficient online evaluation for resource-constrained embedded hardware, the authors of [2] proposed a solution by developing an enhanced version of the open-source librbd library. This library is equipped with optimized evaluation algorithms, restructured computational sequences, cache-aware data structures, and an adaptive parallelization framework. The verification results demonstrate a significant reduction in computational complexity, enabling real-time analysis of larger-scale systems compared with the original implementation.

To improve the reliability and safety in complex energy systems such as wind turbines, the authors of [3] present a unified hybrid modeling framework integrating FTA, RBD, and BowTie methodology. This framework quantifies risk, evaluates safety barrier effectiveness, and supports scenario-based sensitivity analysis using key metrics including availability and failure probability. A simulation-based case study on a wind turbine generator subsystem shows that critical defense points (e.g., protective relays) are identified, and targeted improvements (e.g., enhanced oil analysis, redundant dashboards) reduce consequence frequency by nearly two orders of magnitude. The approach introduces explicit defense-in-depth modeling, improving computational efficiency and providing a practical decision support tool for asset managers. Focusing similarly on wind turbine systems, the authors of [4] address the high time and cost of wind turbine blade fatigue testing by exploring the application of an improved Neural Basis Expansion Analysis (N-BEATS) deep learning model for stiffness degradation prediction. To optimize the model’s performance, they expand stiffness data to meet model requirements, modify N-BEATS’ basic block structure to treat sequence-to-sequence prediction as a nonlinear multivariate regression problem, and adopt the Pinball Mean Absolute Percentage Error (Pinball-MAPE) loss function to reduce bias. Additionally, two data augmentation techniques (time series combination and random noise injection) mitigate overfitting. Experimental results demonstrate the model’s ability to learn underlying stiffness patterns and accurately predict remaining stiffness, offering a cost-effective alternative to traditional fatigue testing.

In [5], the authors address the robust design of Tuned Mass Dampers (TMDs) in linear structural dynamics. For single-degree-of-freedom (SDOF) and multi-degree-of-freedom (MDOF) systems, the authors propose an efficient analytical uncertainty quantification method based on Taylor series expansion, estimating the mean and scatter of key performance indicators without the computational burden of double-loop sampling approaches. An additional mode decomposition technique for MDOF systems with multiple TMDs replaces time-consuming time integration with modal analysis. Formulated as single- or multi-objective optimization tasks, the approach is validated through numerical examples, offering a practical solution for TMD design in structures prone to critical dynamical vibrations.

How to protect historical railway assets amid uncertainties in material performance, structural degradation, and regulatory requirements? The authors of [6] propose a reliability-oriented preservation framework that systematically accounts for legal, material, and procedural uncertainties. Two industrial case studies validate the framework: the successful substitution of timber with certified PVC cladding in a non-listed signal box (improving durability and reducing maintenance needs) and an unsuccessful timber-to-aluminum gable replacement (attributed to planning misalignment and unestimated approval uncertainties). This research provides a structured method for mitigating uncertainties in the asset management of historical infrastructure.

The authors of [7] investigate measurement uncertainty and compliance evaluation in natural gas moisture analysis, a critical factor in preventing pipeline corrosion and ensuring combustion efficiency. The authors compare multiple algorithms for moisture content calculation, estimate and validate measurement uncertainty using the Panametrics PM880 portable hygrometer, and evaluate compliance with Brazilian legislation via guard bands. The results reveal a maximum variation of 1% in moisture content results across the compared algorithms, with an expanded uncertainty of approximately 20%. Notably, this uncertainty value does not compromise risk assessment, as the measured moisture levels remain well within acceptable ranges below the specified limits, which ultimately leads to the establishment of an upper tolerance limit of 58.4 ppmv H₂O.

In [8], the authors focus on uncertainty quantification in shear wave velocity (Vs) prediction, critical for earthquake engineering applications. Geotechnical variability and inherent uncertainties are addressed through a hybrid framework integrating an explainable machine learning (ML) model and Bayesian inference. The Extreme Gradient Boosting (XGBoost) algorithm, coupled with Shapley Additive Explanations (SHAPs) and partial dependency analysis, identifies key geotechnical parameters and delivers high predictive accuracy. A Bayesian Generalized Linear Model (GLM) complements this by providing probabilistic predictions with 95% credible intervals, explicitly quantifying uncertainty. Validated against real case scenarios, the hybrid approach combines ML’s predictive power with Bayesian inference’s uncertainty quantification, offering an interpretable tool for confident engineering decision-making.

The prevention of situation awareness failure in shearer monitoring operations, an issue that has been exacerbated by the digitization of instrument control systems, is explored from a cognitive function perspective with a focus on the impact of working memory training. In [9], the authors randomly assigned subjects to either a training group or a control group, conducting pre- and post-training assessments that included working memory measurements, simulated shearer monitoring tasks, and recordings of task performance, situational awareness scales, and electroencephalography (EEG) data. The results revealed significant improvements in both monitoring performance and situational awareness scores following training, accompanied by activation in the θ, α₂, and β₁ EEG frequency bands—findings consistent with the established link between these oscillatory bands and cognitive processes underlying working memory and decision-making. The study demonstrates that working memory training enhances operators’ rapid reaction and decision-making abilities in complex or emergency scenarios, thereby providing a new direction for mitigating situation awareness failure in high-stakes monitoring environments.

To enhance the efficiency of reliability analysis for nonlinear implicit models of complex structures under multi-failure modes, the authors of [10] propose a surrogate model based on an adaptive AdaBoost algorithm. An adaptive method selects optimal training samples, ensuring even distribution across failure curve boundaries and comprehensive information retention. Leveraging AdaBoost’s integration and iterative properties, simple binary classifiers are iteratively combined to build a high-precision alternative model for fault diagnosis, with Monte Carlo simulation used to assess failure probability. Validated through three numerical examples, the method exhibits exceptional accuracy and efficiency, overcoming challenges in multi-failure mode reliability evaluation and facilitating the application of complex mechanical designs.

3. Conclusions

The above overview of the ten papers in this book shows that uncertainty and reliability analysis is a crucial issue in various engineering fields. It can be stated that uncertainty and reliability analysis should be properly considered across all domains, in any structural, energy, rail transit, and industrial measurement application. It is my aspiration that this book integrates contributions from various engineering fields, thereby enriching the research landscape with this pivotal topic.