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• Bearing failure rules are learned and guided by multi-physical fusion constraints. • Real physical information is ensured by introducing a 15-DOF kinetic physical model. • Self-calibration of sound-vibrational physical-information margins is met by PF. • Dual learning of physical and data features for fault diagnosis is enabled by PFCG. • Model explanability is analyzed by feature visualization and sensitivity analysis. Although current deep learning models for bearing fault diagnosis have achieved excellent accuracy, the lack of constraint-guided learning of the physical mechanisms of real bearing failures and a physically scientific training paradigm leads to low interpretability and unreliability of intelligent fault diagnosis models. In this study, a sound-vibration physical-information fusion constraint-guided (PFCG) deep learning (DL) method is proposed, aiming at weighted fusion of sound and vibration multi-physical information into a deep learning model, to guide the DL model to learn more realistic physical laws of bearing failure. Firstly, a 15-degree-of-freedom nonlinear dynamics model of multi-stage degraded bearing failure mechanism with sound-vibration response is developed, which considers the evolutionary mechanism of bearing failure from healthy state to different stages, and utilizes a particle filtering algorithm for dynamic calibration of hidden parameters. Moreover, a lightweight DL fault diagnosis model is designed to realize the deep interaction between the physical model and the DL model through the weighted fusion of the cross-entropy loss function, physical consistency loss and uncertainty loss. Moreover, the superior diagnostic performance of the proposed sound and vibration PFCG-DL model is verified by comparing the performance fluctuations and parameter attributes of different DL benchmark models before and after being guided by physical information fusion constraints (PFCG). Eventually, the proposed PFCG-Transformer model achieves a diagnostic accuracy of 99.45% while keeping the number of parameters at only 0.62M, which significantly improves the accuracy and reduces the computational complexity by 81.5% compared to the CAME-Transformer model's 3.24 M number of parameters and 95.00% diagnostic accuracy. In addition, the test time of PFCG-Transformer is reduced to 1.02 s, which is 60.2% less than CAME-Transformer, demonstrating higher computational efficiency and real-time performance. Importantly, in terms of interpretability, the engineering interpretability and credibility of the models are further improved by visualizing the feature learning results of the vibration modal and multimodal fusion models and the sensitivity analyses of the sound-vibration response models with internal and external physical hyperparameters. Therefore, this study proposes a physical information-guided deep learning method with strong interpretability and superior performance, which provides an important reference for further research and application in the field of bearing fault diagnosis. [ABSTRACT FROM AUTHOR]

• A quantitative resilience assessment method for FPSO leakage emergency response is proposed. • A hierarchical framework is developed to quantify the system resilience based on the performance variability. • A quantitative FRAM combining Monte Carlo simulation is proposed to quantify the performance variability of functions. • A FRAM model of FPSO leakage emergency response is presented. • The method is illustrated in a case study on the FPSO emergency response process. FPSO production process is prone to leakage, and failure to respond promptly and effectively will lead to accident escalation and serious consequences. However, traditional safety assessment methods cannot handle the nonlinear relationships between human, technology, and organization in emergency response process. This study proposes a quantitative FRAM to evaluate the emergency response resilience of FPSO leakage. This method establishes a resilience evaluation framework including three tiers: function, ability, and system, which can quantify system resilience based on the variability of function. First, identify basic functions according to the four stages of monitoring, response, learning and anticipation in the emergency response process, and establish the FRAM model of FPSO leakage emergency response. Then, the quantitative FRAM and Monte Carlo simulation are combined to calculate the variabilities of functions under different operating conditions. Finally, based on the simulation results, the variabilities of basic functions are aggregated and statistically analyzed to quantify system resilience. The implementation process of this method is illustrated by a case study. The influence of different factors on the system resilience is analyzed by setting various operation scenarios, and critical functions are identified by sensitivity analysis, which can provide reference for improving system resilience and ensuring FPSO safety production. [ABSTRACT FROM AUTHOR]

In the development and deployment of both tethered and autonomous High Altitude Platform Station (HAPS), flight modules such as hexacopter and octocopter with 6 or 8 rotors are most often used. The primary focus of this article is to compute the reliability of tethered HAPS by analyzing the effectiveness of their redundant rotor systems. To measure the performance of such systems, it is convenient to consider mathematical models as k -out-of- n models. Although Markov models have extensively been reported to analyze the reliability of repairable k -out-of- n models, this work introduces an alternative and more thorough methodology. In this work, a semi-Markov model (SMM) is proposed to calculate the probability of rotors being operational after the failure of some rotors in order to analyze system reliability. We emphasize that an SMM model is more appropriate as it provides a more accurate assessment of the probability of system failure over time through non-exponential sojourn time. Further, the efficacy of the proposed SMM is studied through the evaluation of steady-state availability, mean time to failure and reliability. Overall, the findings of this study enhance our comprehension of the reliability of repairable systems and extend the existing knowledge base of HAPS reliability analysis. [Display omitted] • The aim is to compute reliability of tethered HAPS by employing redundant rotors. • A k -out-of- n : G system is proposed to assess the reliability of a HAPS. • A semi-Markov model is proposed to analyze the reliability of k-out-of-n: G system. • An octocopter, 5-out-of-8: G system, is examined for various parameters and factors. [ABSTRACT FROM AUTHOR]

In the health assessment for complex systems, system attributes refer to the indicators or components having an impact on the health state of the system. When assessing the health state of complex systems, the relative importance of system attributes should be accurately modeled, otherwise incorrect results may occur. Especially for some complex systems with small samples, data-driven methods are prone to overfitting. In this article, a new method using belief rule base (BRB) is proposed to model the relative importance of system attributes while assessing the health state. As an interpretable modeling tool, BRB constructs nonlinear mapping relationships between system attributes and health state. A data-knowledge hybrid-driven ensemble feature selection (DKH-EFS) method is developed to calculate the relative importance of the system attributes, namely attribute importance (AM). A random sensitivity analysis (RSA) method of the model output to the input of BRB is proposed to calculate the feature importance (FI) of BRB. A new parameter optimization model considering the consistency between the AM and FI is introduced to improve the modeling ability of BRB for the AM. A case study on the health assessment of the fiber optic gyroscope (FOG) validates the proposed method. [ABSTRACT FROM AUTHOR]

• SCEIS is a time-dependent reliability sensitivity method for rare events. • SCEIS is an extension of the cross entropy-based importance sampling. • Low computation cost to accurately measure the importance of input variables. • SCEIS is performed well on rare events with random variables and random processes. To deal with the time-dependent reliability sensitivity (TDRS) analysis of rare events with both random variables and stochastic processes, a single-loop sampling procedure combined with the cross entropy-based importance sampling strategy (CEIS), namely SCEIS, is derived to lighten the computational burden without loss of precision. Firstly, the TDRS indices are derived to make them implementable by a single-loop importance sampling (IS) procedure. Then, the quasi-optimal IS density is obtained through the extension of the cross-entropy method, which is an adaptive procedure that overcomes the challenges of determining the position and number of design points in traditional IS. Furthermore, the SCEIS can be easily implemented to estimate the TDRS indices for problems with small failure probability. Three examples involving numerical and engineering problems are analyzed to demonstrate the performance of the proposed method. The results obtained from comparing with other existing methods reveal that the proposed method provides satisfactory TDRS analysis for rare events while significantly reducing computational costs. [ABSTRACT FROM AUTHOR]

• A framework combining knowledge graph and DFMEA is presented to identify to-be-evaluated objectives. • An approach of improved DS evidence fusion with comprehensive weights is proposed to fuse multiple evaluations. • We propose a risk classification approach based on risk trade-off VIKOR to determine component risk levels. • The proposed method is validated on the tunnel boring machine, and comparison and sensitivity analyses are performed. With the development of information technology in manufacturing, product lifecycle iteration is accelerating. Efficiently analyzing and identifying component risks is important to ensure the reliability of products. This paper proposes a new method that combines improved design failure mode and effect analysis (DFMEA) with the knowledge graph for component risk analysis of complex products. A risk evaluation knowledge graph is built for the risk identification and knowledge provision in the process of DFMEA. Graph analysis is used to identify to-be-evaluated objectives based on historical maintenance data, which helps designers avoid the heavy task of identification. The graph matrix of the historical evaluations is used to calculate the comprehensive weights. A Dempster-Shafer (DS) evidence fusion method based on comprehensive weight evaluation information is proposed for the effective fusion of evaluation evidence. As an alternative to the exact risk ranking, we offer a risk trade-off VIKOR (VIseKriterijumska Optimizacija I Kompromisno Resenje) method for components classification that classifies components into different risk classes for different risk treatment measures. Finally, the proposed method is validated using a tunnel boring machine as an example, and comparison and sensitivity analyses are performed to demonstrate that the risk value shows a consistent and stable change with expert evaluation. [ABSTRACT FROM AUTHOR]

• Detailed uncertainty analysis on shear capacity for five SFRC beam types. • Assessed SFRC beam probability of failure using FORM and SORM. • Calculated resistance factor for SFRC beams based on different structure risk categories. • Weibull and lognormal distributions found ideal for SFRC shear models. • Conducted sensitivity analyses to prepare for future SFRC database integration. In the field of structural engineering, the exploration of steel fibre reinforced concrete (SFRC) beams has recently intensified, particularly due to their improved tension and shear performance of structure. This study pioneers a novel reliability analysis of shear capacity predictions for SFRC beams, distinctively classifying the datasets into high-strength (HSFRC) and normal-strength (NSFRC) categories. A comprehensive database of 142 HSFRC and 265 NSFRC beams serves as the foundation for this analysis, which critically examines the standard Gaussian distribution in shear design models and proposes the Lognormal and Weibull distributions as more precise alternatives. Employing advanced First-order (FORM) and Second-order Reliability Methods (SORM), the study covers a broad spectrum of load conditions, including dead, live, snow, wind, and seismic loads, to evaluate various empirical, semi-empirical and machine learning proposed shear capacity prediction formulas. One of the key innovations of this research is the development of differentiated resistance coefficients for various risk levels in the reliability analysis, allowing future structural designers to tailor their designs according to specific risk profiles. This approach significantly enhances the balance between economic efficiency and structural safety based on the evolution of different target reliability indexes. The study reveals that existing design equations for SFRC beams generally lean towards conservatism. This study found that formulas derived from machine learning exhibited superior prediction ability compared to traditional theoretically derived regression formulas. When compared the proposed machine learning formulas, the Tarawneh's formula demonstrated better prediction ability than the Kara's formula when applied to larger datasets. However, high predictive power does not necessarily equate to high reliability. Machine learning formulas prioritise predictive accuracy, often at the expense of insufficient redundancy for ensuring safety. Overall, it introduces Kara's formula for NSFRC beams, which stands out with its superior predictive performance, offering an optimal balance of safety and cost-efficiency. Ashour's formula is also identified as a more effective and safer option for HSFRC beams. Complementing these findings, the extensive sensitivity analysis of the collected data not only confirms the robustness of the conclusions but also prepares for the integration of broader datasets in the future. [ABSTRACT FROM AUTHOR]

This paper proposes a maintenance model for a Proton-Exchanged Membrane Fuel Cells system. Two types of failures are considered: non repairable internal failures and possibly repairable external failures. The maintenance involves replacing one or more cells. Therefore the maintenance can be perfect or imperfect. Moreover after each repair, the maintenance operator improves and the down time due to maintenance is reduced. A semi-Markov process is proposed to model the system's lifetime. In this framework, the reliability measures and the remaining useful lifetime are derived. The long run average maintenance cost is studied. A sensitivity analysis of model parameters and maintenance unit costs is performed and a maintenance optimization strategy is proposed. • Semi-Markov process for PEMFC maintenance modeling. • Non perfect repair modeling by geometric process. • Model Sensitivity analysis. [ABSTRACT FROM AUTHOR]

We present an inspection and maintenance model for a two-component lubrication system, filter and bypass valve, with applications to centralized lubrication systems. It presents significant differences from redundant systems in previous studies on cold, warm or hot stand-by components. These are the dissimilarity between the filter and the bypass, as the latter can induce catastrophic damage after a long working period, and the stochastic dependence between the filter and the bypass valve. Inspection and testing is focused on the valve, and only if it fails to open on inspection, or it is found to be open, is the filter inspection triggered. Preventive maintenance is mainly concerned with the filter, which is replaced periodically and also when an inspection detects an open valve or a clogged filter. The sensitivity analysis reveals that the optimum policy depends more on the parameters defining the lifetime of the filter than on those of the valve. • New model of redundant system not covered by assumptions in cold, warm or hot standby units. • Inspection and maintenance of a filter and a bypass valve in centralized lubrication systems. • Random inspection of the filter induced by the outcome of the valve inspection. • Catastrophic damage in the main system due to dry running if the bypass valve fails on demand. • Increasing damage to the main system the longer the bypass works, if it does not fail on demand. [ABSTRACT FROM AUTHOR]

Aeroengines and gas turbines are susceptible to uncertainties during manufacturing and operation, leading to reduced efficiency and dispersed performance. Current engine design system often produces deterministic performance databases that cannot be effectively used to guide the uncertainty analysis and robust design process of turbomachinery. This paper proposes an interpretable dynamic machine learning method for sensitivity analysis and robust optimization of turbomachinery blades. A dynamic extreme gradient boosting (XGBoost) is trained to predict fan aerodynamic performance, and the SHapley additional explanation (SHAP) method is introduced to explain regression model behavior and identify the impact of uncertain variables. On this basis, the Lipschitz-based trust region (MAXLIPO-TR) optimization algorithm is used to obtain the optimal configuration with the best robustness performance. Finally, the method is applied to data mining for design guidelines of robustness performance enhancement of an aeroengine fan. The results show that maximum camber and tangential stacking have major effects on fan performance dispersion. The standard deviation of the isentropic efficiency, pressure ratio and mass flow rate of the optimized configuration are reduced by 42.4%, 35.6% and 22.7% respectively at design conditions. The proposed data mining method has scientific significance and industrial application value in the robust design of advanced turbomachinery. [ABSTRACT FROM AUTHOR]

In this paper, a new rebalancing strategy is proposed by replacing the standby components for a balanced system with a standby pool. The working components are connected in series. All standby components are stored in a standby component pool. When the working components do not fail and the balance degree of the system does not exceed a threshold, the system can operate normally. The balance degree of the system is defined as the maximum state difference of all the working components. If the system becomes unbalanced or fails, a qualified standby component in the standby pool should be selected to replace the working component. The replacement strategy is given in detail. This paper uses the discrete-state continuous-time Markov process to derive the system reliability. Finally, a numerical example and sensitivity analysis are given. Considering the downtime cost and the cost of purchasing standby components, the number of standby components in the standby pool is optimized. [ABSTRACT FROM AUTHOR]

• Proposes a novel method for optimizing industrial robot trajectory accuracy under parametric uncertainties. • Incorporates dynamics with Stribeck friction into sensitivity-based accuracy analysis and reliability-based design. • Constructs a comprehensive simulation framework identifies critical uncertain parameters affecting trajectory accuracy. • Develops a multi-objective optimization design approach balancing cost, quality, and trajectory accuracy reliability. To address the challenges of poor trajectory accuracy in industrial robots, which has emerged as a technological bottleneck hindering further robots' applications in high-precision manufacturing industries, this paper proposes a method for the analysis and reliability-based optimization design for industrial robots' trajectory accuracy considering parametric uncertainties. Firstly, the dynamic equation of an articulated industrial robot with six degrees of freedom is derived, incorporating the Stribeck joint friction model, followed by the uncertain parameter identification of this dynamic model. Subsequently, an uncertainty simulation system for the robot is established based on the constructed dynamic model and the sensitivity of system uncertain parameters to the robot trajectory accuracy is analyzed, where 10 key parameters are obtained among 54 uncertain parameters. Finally, a reliability-based multi-objective optimization design methodology is proposed synthesizing the robot trajectory accuracy, manufacturing cost, and quality loss, to achieve tolerance design of the robot's parameters, and enables minimizing costs and quality losses while ensuring the robot's trajectory accuracy reliability. The performance and practicality of the proposed method were validated using a six-degree-of-freedom rotary joint serial industrial robot as an example. [ABSTRACT FROM AUTHOR]

• Bayesian Network method is proposed to identify reference scenarios from past events. • Noisy-OR gate model is applied to address data gaps in BN quantification. • BN sensitivity analysis is used to systematically rank influence among nodes. • Chains of nodes with higher influences are selected as reference incident chains. • The method is demonstrated on a dataset of 109 incidents occurred in Oil&Gas sector. 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. [ABSTRACT FROM AUTHOR]

In a context of uncertainty quantification, the probabilistic model of a random vector at the input of a computational code is not always known. An identification of the joint distribution on a restricted sample of experimental data can lead to a bad calibration of the model. The quantity of interest estimated at the output of the code is then subject to a bi-level epistemic uncertainty that must be properly quantified. A first level arises from the statistical estimation whilst a second one comes from the identification of the probabilistic model. Each epistemic uncertainty can thus be reduced by an enrichment with new data, either by increasing the size of the estimation sample or by increasing the size of the identification sample. When gathering data is costly, it is then interesting to know which uncertainty source to reduce first, thus introducing a trade-off between simulation and physical experiment. This paper aims at presenting a sensitivity-analysis-guided enrichment procedure in a small data context to improve the estimation quality of a quantity of interest. The proposed methodology is shown to be both low cost and adaptive by introducing importance-sampling-based methods. The performance of the guided enrichment procedure is assessed on three examples. • A nested estimator allows one to consider a bi-level epistemic uncertainty source. • Enrichment in leading source answers the trade-off between simulation and physical experiment. • New data enrichment is driven by a cost-free variance based sensitivity analysis. • Multiple importance sampling allows for data reuse and auxiliary density adaptation. • The number of calls to the black box function induced by the approach is minimized. [ABSTRACT FROM AUTHOR]

The manufacturing and use of aircraft lock mechanisms are characterized by coupling multiple stochastic factors and multiple progressive damage factors that seriously affect the reliability of the mechanism. For a certain type of aircraft drag chute lock mechanism, a reliability degradation analysis method considering the coupling of multiple stochastic factors and multiple progressive damage factors is proposed. Based on the working principle of the drag parachute lock mechanism, the effects of multiple progressive damage factors on the motion accuracy of the mechanism are analyzed by considering the wear and tear over time, the deformation due to impact and the creep of the steel cables. The influence of multiple stochastic factors on the function of the mechanism is investigated, and the multiple stochastic factors include manufacturing and processing errors, changes in material properties, and changes in environmental stresses. A reliability degradation model and sensitivity analysis method based on multiple progressive damage factors under multiple stochastic factors are proposed. The results show that the proposed method can provide guidance for the design, manufacture and utilization of drag chute lock mechanisms as well as the reliability analysis of complex mechanical mechanisms in other aerospace products. [ABSTRACT FROM AUTHOR]

The high-temperature rotating structures (HTRS), e.g., steam turbine rotors, often operate in extremely harsh environments with a flexible load condition during peak shaving of power system. In this work, a damage-driven framework for reliability assessment is developed in terms of the cumulative damage-damage threshold interference (CD-DT) principle, in which the cumulative damage and damage threshold are regarded as two random parameters to address uncertainties. The CD-DT principle is founded on the engineering damage theory and incorporates physics-of-failure into the probabilistic modeling of high-temperature structural reliability. Probabilistic damage analysis, correlation analysis of weak sites, system-level reliability analysis, and sensitivity analysis have been encompassed in this framework. Three numerical examples are used to verify the effectiveness and applicability of the proposed framework. Application to steam turbine rotor involving multiple weak sites with multi-damage modes illustrate the implementation procedures of the framework. Results show that the reliability-based design life of rotor decreases with the increases of start-stop frequency, the implementation of a two-shift operation would pose a threat to meeting the safety requirement of a 30-year design life. Furthermore, sensitivity analysis highlights the critical influences of initial rotor temperature and speed rising rate on rotor reliability, providing insights for operational maintenance and reliability optimization. [ABSTRACT FROM AUTHOR]

• A single-loop estimation method is proposed for PFP-based global sensitivity analysis. • Bayes theorem-based sensitivity estimation formulations are derived. • The calculation of all sensitivity measures needs only one set of functional evaluations. • Adaptive Kriging model is embedded to enhance the computational efficiency. The existing predictive failure probability (PFP)-based global sensitivity analysis methods may get stuck in practical application due to the large amount of calculation or insufficient precision. Therefore, a novel single-loop estimation method is proposed in this paper to effectively estimate PFP-based global sensitivity measures. Firstly, by introducing standard normal auxiliary variables and equivalent probability transformation, the overall uncertainty of each input variable is decomposed into its inherent uncertainty and distribution parameter uncertainty. Then, Bayes theorem-based formulations are derived for three PFP-based global sensitivity measures, where only the unconditional PFP and the conditional marginal and joint distributions of standard normal auxiliary variables and distribution parameters need to be known. These items can be evaluated simultaneously using only one set of functional calls. Finally, adaptive Kriging model is embedded into the proposed method in place of the time-demanding performance function to further enhance computational efficiency. The effectiveness of the proposed methods is validated through four benchmark reliability problems asnd one engineering problem. [ABSTRACT FROM AUTHOR]

• An ensemble polynomial chaos expansion (EPCE) method is proposed. • An active learning hybrid criterion is proposed to update the accuracy of EPCE for Sobol index estimation. • The model correlation and sensitivity pursuit criteria are developed to improve the local accuracy of EPCE. • The performance of the proposed method is validated by four benchmark functions and an engineering example. Global sensitivity analysis (GSA) techniques, especially Sobol indices, have gained prominence in assessing the impact of uncertainty across all input variables on the variation of model response. However, GSA can incur intensive computational costs, particularly when dealing with time-consuming models. To address this issue, an ensemble polynomial chaos expansion (EPCE) surrogate model based on an active learning hybrid (ALH) criterion is proposed. The proposed method integrates a weighted combination of multiple sparse PCE surrogate models to formulate the EPCE method. To enhance the performance, the ALH criterion, which balances local exploitation and global exploration, is developed to sequentially select samples for updating the EPCE model. In terms of local exploitation, the model correlation and sensitivity pursuit criteria are derived to identify the local region displaying both the largest discrepancy among multiple sparse PCE methods and the most substantial contribution to the total variance. The ALH criterion also incorporates a minimum distance-based measure for global exploration. The performance of the proposed method is evaluated by four benchmark functions and an engineering application. The numerical studies demonstrate that the proposed method exhibits favorable performance for conducting GSA. [ABSTRACT FROM AUTHOR]

This paper addresses the challenge of optimizing maintenance for systems with varying degradation characteristics in dynamic environment. The focus is on repairable systems, where degradation is characterized by a Wiener process that incorporates the dynamic influence of the environment. We investigate a condition-based maintenance model aiming at minimizing the expected cost over a finite and infinite horizon. Firstly, the model considers the evolution of environment as a Markov process, which influences the drift parameter in the Wiener process. The choice between a corrective and preventive replacement rests on the periodic inspections on the system and environment. Subsequently, the maintenance model is formulated in the framework of Markov decision process. Meanwhile, the backward dynamic programming algorithm and value iteration algorithm are employed to gain the optimal maintenance policies over the finite and the infinite planning horizons, respectively. Finally, the proposed model is further explained with concrete examples and a comprehensive sensitivity analysis. Numerical results clearly demonstrate notable variations in the optimal maintenance strategies in different periods and underscore the importance of taking proactive maintenance measures in harsh environmental conditions, even if the degradation level of the system is relatively low. • Develop CBM model for degrading system considering environmental impact. • Integrate impact to aid maintenance decisions in dynamic environment. • Analyze maintenance policies using MDP for finite and infinite horizons. • Explore structural properties of optimal policy. • Numerical results demand proactive maintenance in harsh environments. [ABSTRACT FROM AUTHOR]

• Service vulnerability of high-speed rail networks is refined with service adjustments. • Service vulnerability metrics in terms of passengers carried are proposed. • Cancelation and rerouting strategies are simulated under various disruptions. • Critical stations and critical cities in China's high-speed train network are studied. • Vulnerability assessment without service adjustments may lead to overestimation. This study proposes a simulation approach to assess the service vulnerability of a high-speed railway (HSR) at the network scale. The service vulnerability assessment is defined with train service adjustments, including cancelations, detour arrangements, and changes in departure or arrival station. Service vulnerability metrics in terms of passengers carried are proposed by quantifying the percentage change in the network-wide performance. Using actual passenger flow data generated from the ticket-booking system, a simulation is conducted to evaluate the service vulnerability of China's HSR network under various disruptions. Sensitivity analysis is conducted to emphasize the impact of train service adjustments during disruptions. The results of the critical station and critical city identification show the significance of the Beijing–Shanghai HSR line, as stations located along this line present considerable vulnerability. Nanjing South, the HSR station with the largest passenger volume, was also the most critical station in China's HSR train network in 2016. A comparative analysis of vulnerability assessments with and without adjustments demonstrates the necessity of examining service vulnerability. The findings have insightful management implications for mitigating HSR service network vulnerability and preparing emergency response plans for operators and administrators. [ABSTRACT FROM AUTHOR]

We present an application of design-of-experiment (DoE) based history matching as an approach to reduce and investigate parameter uncertainties in finite-element models for repositories of high-level radioactive waste. We combine experimental data from the FE-experiment at the Mont Terri underground research laboratory in Switzerland with thermo-hydro-mechanical modeling using the open-source package OpenGeoSys. Uncertainties were reduced by an initial parameter screening to find heavy hitters and an experiment-matching procedure using Monte-Carlo sampling on a Gaussian proxy model to fit the error between modeling response and the experiment. Furthermore, we performed a global sensitivity analysis based on the proxy model, demonstrating the spatial impact of parameter sensitivities. Very good agreement between the experimental data and the model was found for the temperature response, whereas the pressure match hints at a significant remaining gap in the physical models and/or structure. This gap could not be filled within the scope of our contribution and needs further investigation. • DoE-based history-matching for UQ of evolution of radioactive waste repositories. • Uses Gaussian Process regression to accelerate MC sampling. • Non-isothermal Richards flow model used as full forward model. • Forward model incorporates an effective description of mechanical effects. • Data from FE-experiment at Mont Terri rock laboratory used as application case. [ABSTRACT FROM AUTHOR]

• Propose of a realistic performance assessment method for nuclear fuel under accident scenario. • Application of the proposed method to HPR-1000 LBLOCA with FeCrAl-UN/U 3 Si 2 fuel. • Uncertainty and sensitivity analysis of the fuel models and related parameters on the PCT. The rigorous safety requirements in the nuclear industry have necessitated the development of accident tolerant fuels, with FeCrAl-UN/U 3 Si 2 being one of the latest innovations in this field. To comprehensively evaluate the performance of this fuel type under accident scenarios, the best estimate plus uncertainty method is employed to conduct a realistic safety assessment of a large break loss-of-coolant accident in the HPR-1000 nuclear power plant using FeCrAl-UN/U 3 Si 2 fuel. The peak cladding temperature and peak pellet temperature are selected as figures of merit, while the uncertainties of key performance models for the FeCrAl cladding and UN/U 3 Si 2 pellet are quantified. The upper tolerance limits of the two figures of merit are determined through uncertainty propagation calculations, and the key influencing parameters are also identified based on the sensitivity analysis. Results demonstrate that the FeCrAl-UN/U 3 Si 2 fuel type owns larger safety margin than the conventional Zr-UO 2 fuel type and effectively reduces the cladding temperature while significantly reducing oxidation and hydrogen production during the accident. [ABSTRACT FROM AUTHOR]

• We propose a sensitivity analysis-based method for unsupervised fault diagnostics. • The method does not require the use of labelled data from abnormal conditions. • The method relies on the Differential Importance Measure (DIM). • Method validated on data from a wind turbine simulator and from a real gas turbine. Fault diagnostic approaches based on supervised classifiers are difficult to apply to safety-critical or new design systems, because they require the availability of labelled data collected when the systems operate abnormally, which is a rare situation. To address this challenge, we develop a novel unsupervised method for fault diagnostics based on a fault detection module and on sensitivity analysis. Specifically, the Differential Importance Measure (DIM) is originally used to quantify how much a signal is, or a set of signals are, responsible for the variation of the system health state. The proposed method is tested on simulated data from a wind turbine and on real data from a gas turbine. The advantages of the proposed fault diagnostic method are: (1) it can be developed using only normal condition data (2) it allows identifying the component responsible for the abnormality by quantifying the contribution of groups of signals to the variation of the system health state; (3) it is capable of distinguishing the abnormalities caused by changes in external conditions from those caused by components malfunctions; (4) it can be used in combination with any fault detection technique. [ABSTRACT FROM AUTHOR]

As a novel supporting approach, performance-based contracting (PBC) ties the service supplier's compensation to the performance outcome of the system owned by the customer. It enables the service supplier to implement an effective maintenance and spare parts inventory policy so as to improve system performance. In this paper, we propose a principal–agent modeling framework for deteriorating production systems operating under PBC, with the objective of maximizing the expected utilities of both stakeholders. The customer (principal) offers PBC with a fixed payment plus performance incentive form to the service supplier (agent), who in turn implements a condition-based maintenance (CBM) policy based on the system prognostic condition at periodic inspections, and sets an investment level of spare parts inventory. Considering the partial observability of the service supplier's actions, the optimal combination of performance incentive in PBC provided by the customer, and the joint CBM and spare parts inventory policy implemented by the service supplier, are determined through a two-stage and heuristic approach. Finally, a numerical example and sensitivity analysis based on a real-world scenario are presented to illustrate and verify the applicability of the proposed model. • Investigate the performance-based contracting (PBC) for degrading production systems. • Analyze condition-based maintenance (CBM) and spare parts inventory policy. • Propose a principal–agent model and a two-stage solution approach. • Determine optimal PBC incentive, joint CBM and spare parts inventory policy. • Verify the applicability of the proposed model. [ABSTRACT FROM AUTHOR]

The use of sensitivity analysis is essential in model development for the purposes of calibration, verification, factor prioritization, and mechanism reduction. While most contributions to sensitivity methods focus on the average model response, this paper proposes a new sensitivity method focusing on the extreme response and structural limit states, which combines an extreme-oriented sensitivity method with polynomial chaos expansion. This enables engineers to perform sensitivity analysis near given limit states and visualize the relevance of input factors to different design criteria and corresponding thresholds. The polynomial chaos expansion is used to approximate the model output and alleviate the computational cost in sensitivity analysis, which features sparsity and adaptivity to enhance efficiency. The accuracy and efficiency of the method are verified in a truss structure, which is then illustrated on a dynamic train–track–bridge system. The role of the input factors in response variability is clarified, which differs in terms of the design criteria chosen for sensitivity analysis. The method incorporates multi-scenarios and can thus be useful to support decision-making in design and management of engineering structures. • New sensitivity method focusing on the extreme response and structural limit states. • High computational efficiency through the use of sparse polynomial chaos expansion. • Ranking the relevance of input factors to different design criteria and the corresponding thresholds. • Visualization of the structural performance around the limit states. • Demonstration on a stochastic dynamic train–track–bridge system including track irregularities. [ABSTRACT FROM AUTHOR]

• The inherent information in conditional samples in Subset Simulation is leveraged. • The reasoning of the first order indices is extended to the higher order. • Partition scheme is optimized considering coefficient of variation of the indices. This paper presents a novel reliability-oriented global sensitivity analysis method using the Subset Simulation (SS) method and the Space Partition (SP) scheme. It can exploit the inherent information of uncertainty within all the conditional samples in each simulation level of SS along the spirit of the SP scheme. The reasoning of the first order indices is firstly provided, followed by a heuristic study on the influence of parametric settings upon the statistical properties of the indices. By extending the calculation process to the higher order indices and formally optimizing the partition scheme considering the coefficient of variation of all the indices, the framework of the proposed reliability-oriented global sensitivity for arbitrary order of indices can be formed. The performance of the direct Monte Carlo method, the Quasi-Monte Carlo method, SP and the proposed method is compared through three numerical examples and two engineering applications, to demonstrate the merits of the proposed one. [ABSTRACT FROM AUTHOR]

• A multi-state balanced system with standby components switching mechanism is proposed. • A general degree balance function is proposed. • In case 1, system balance degree is defined based on all components states. • In case 2, system balance degree is defined based on symmetrical components states. • Finite Markov chain imbedding approach is used to get reliability indexes. An increasing attention has been paid to the reliability analysis of balanced system. In previous studies, there were three rebalancing strategies for balanced systems: forcing down the unbalanced pair of subsystems, restarting components that have been shut down, and dynamically adjusting the state of the working components. In this paper, a new rebalancing strategy is proposed by switching the standby components for a multi-state balanced system. The system consists of m subsystems, each with one working component and n -1 standby components. The system is balanced when the working components do not fail and the system's balanced degree doesn't exceed a threshold. Two cases of system balance conditions are considered: one is based on component states and the other is based on symmetric component states. If the system is imbalanced or fails, the system needs to adjust the state of the working component by switching switches to let the system operate normally. The switching rules for each case are given separately. In this paper, the finite Markov chain imbedding approach (FMCIA) is used to derive the system reliability. Finally, numerical examples and sensitivity analysis are given. [ABSTRACT FROM AUTHOR]

• Proposing a self-separation demarcation method for sUAVs in structured airspace. • Developing a collision risk model considering 3-D maneuverability characteristics. • Analyzing the sensitivity of collision shape, trajectory error and crossing angle. • Presenting a multi-layer separation framework for UAV transportation system. Maintaining safe separations is essential to achieve reliable operations for unmanned aerial vehicles (UAV). Given the escalating severity of collision risks associated with UAVs, separation criteria have emerged as foundational to both airspace design and collision avoidance strategies. However, without adequate consideration of the characteristics of small-UAV (sUAV) encounters and airspace structure, most of the existing models focus on assessing uniform separation volume with manned aircraft. This paper proposes a demarcation method of safety separation for sUAVs based on collision risk estimation. Firstly, five collision zones are developed for collision determination by considering the shape characteristics. Then, the collision risk model is established from the 3-D probability density function (PDF) with the supremum of total system error (TSE). Finally, the minimum safe separations for different encountering scenarios are demarcated by setting the threshold of risk. Simulation results testify that the selection of the collision zones and crossing angles affect the collision risk apparently. The results also demonstrate the effectiveness of separation criteria demarcated by 'Equivalent Level of Safety' (ELoS). Statistical analysis for 100 sampled environments shows the reliability of the proposed method, which captured the characteristics of sUAVs and could be utilized for elaborative separation framework in structured low-altitude airspace. [ABSTRACT FROM AUTHOR]

• Morris' extension method was applied to evaluate the combined actions of model inputs. • Study of three types of convergence of combined actions results using formal criteria. • New Morris' extension indices was proposed to achieve convergent results at lower cost. • Morris' extension method and total interaction Sobol indices provide the same results. • Convergence of screening and ranking can be reached before sensitivity indices stabilize. This work aims at studying Morris' extension method to evaluate the contribution of combined variations of inputs to variations of a model output. There is a lack of studies on the Morris' extension method concerning crucial choices of the adequate number of trajectories to distinguish influential and non-influential groups of pairs of inputs, rank pairs of inputs according to their relative importance and reach out the stability of sensitivity indices values. The Morris' extension method was studied regarding the three previous issues via applications on simple and complex models, in comparison with total interaction indices of Sobol. Formal criteria were implemented to assess the convergence of sensitivity analysis results. Sensitivity indices based on the median of mixed elementary effects (MEE) were investigated and found to be competing with classical ones based on the mean of MEE, to achieve convergent results. [ABSTRACT FROM AUTHOR]

• We look at the most important system elements for improving resilience in interdependent CIs. • We distinguish the individual contributions to system resilience from both the mitigation and recovery viewpoints. • We perform sensitivity analysis supported by importance measures to identify the most relevant system parameters. • We resort to two different strategies based on ANNs and an ensemble-based method to reduce the computational burden of the analysis. In interdependent critical infrastructures (ICIs), a disruptive event can affect multiple system elements and system resilience is greatly dependent on uncertain factors, related to system protection and restoration strategies. In this paper, we perform sensitivity analysis (SA) supported by importance measures to identify the most relevant system parameters. Since a large number of simulations is required for accurate SA under different failure scenarios, the computational burden associated with the analysis may be impractical. To tackle this computational issue, we resort to two different approaches. In the first one, we replace the long-running dynamic equations with a fast-running Artificial Neural Network (ANN) regression model, optimally trained to approximate the response of the original system dynamic equations. In the second approach, we apply an ensemble-based method that aggregates three alternative SA indicators, which allows reducing the number of simulations required by a SA based on only one indicator. The methods are implemented into a case study consisting of interconnected gas and electric power networks. The effectiveness of these two approaches is compared with those obtained by a given data estimation SA approach. The outcomes of the analysis can provide useful insights to the shareholders and decision-makers on how to improve system resilience. [ABSTRACT FROM AUTHOR]

• System with nonhomogeneous pure birth process under warranty with maintenance. • A new way to model the effect of repair on failure rate, worse than minimal repair. • Deriving the optimal preventive maintenance scheme under the free-repair warranty. • Offer an important analytical tool for marketing managers to design warranty. This investigation focuses on deriving an optimal preventive maintenance (PM) scheme for a system under the free-repair warranty (FRW). We utilize a Non-Homogeneous Pure Birth Process (NHPBP) to model the process of more general failures and repairs during the coverage period of FRW, propose a type of PM model for such a NHPBP repairable system, and develop the expected cost function. Under the special case of failure intensity, we first prove that there exists a unique optimal PM schedule for FRW with a finite number of PMs and then compute the optimal number of PMs and their implementation times for a given FRW coverage period. Numerical computation and sensitivity analysis are conducted to gain more insights about the NHPBP repairable system under FRW with and without PMs. Our results offer an important analytical tool for marketing managers to design more competitive and cost minimal warranty policies for durable and complex systems with a more general failure process and 'worse-than-minimal repair'. [ABSTRACT FROM AUTHOR]

• A manufacturing system constructed by multi-state manufacturing network (MSMN). • Manufacturing network with joint buffers is considered. • A simulation approach to estimate system reliability for the MSMN. • Sensitivity analysis to investigate the most potential location to increase buffer volume. This paper proposes a simulation approach to estimate system reliability of a multi-state manufacturing network (MSMN) with joint buffers. The system reliability is an indicator to evaluate the probability that an MSMN can provide sufficient capacity to meet a given demand. From the perspective of industrial and systems engineering, the MSMN is constructed as a network topology in which each node denotes an inspection point and arcs denote workstations. In particular, joint buffers with finite volume are embedded in such a topology. Based on the topology, workload processed by each workstation is derived according to a given demand. Subsequently, a simulation approach is applied to randomly generate the current capacity state for the MSMN and to compute the buffer usage under such a state. System reliability is estimated after several iterations of simulation to check if the generated capacity state is available to process the workload or not. Besides, sensitivity analysis is adopted to investigate the most potential location to increase buffer volume. Two practical examples are adopted to validate the effectiveness of the proposed simulation approach. Experimental results show that using joint buffers is more reliable than using parallel buffers in separated production lines. [ABSTRACT FROM AUTHOR]

• Complex nonlinear models are challenges for common sensitivity analysis methods. • The RS-HDMR performs well and efficiently on a complex repository PA model. • Second- and total-order indices were computed with consistent and plausible results. Sensitivity analysis is considered a useful tool for determining sensitivities and assessing uncertainties of computational models, which is critical for the performance assessment of final repository models. One group of methods of sensitivity analysis is variance-based methods, which can identify sensitivities of individual parameters and parameter interactions. This is done via computation of Sobol' sensitivity indices of first and higher orders. Models describing complex physical systems can behave in a highly nonlinear, non-monotonic or even discontinuous manner. Many methods of sensitivity analysis perform poorly or even fail completely on such models. In former investigations with a model of this kind, we could not identify any method capable of calculating reliably second- or higher-order sensitivity indices. This paper demonstrates that the Random-Sampling High Dimensional Model Representation (RS-HDMR) meta-modelling approach is able to compute efficiently sensitivity indices of the first, second and total orders for a complex, highly nonlinear model describing the long-term behaviour of a final repository for low- and intermediate-level radioactive waste, and that the results are consistent and plausible. The efficiency of the RS-HDMR approach in computing sensitivity indices of the first order is compared to that of two other methods: EASI and the State-Dependent-Parameter (SDP) meta-modelling approach. [ABSTRACT FROM AUTHOR]

• A method to estimate Sobol' indices for sensitivity analysis is proposed. • It relies on a tensorised Bayesian linear model built from Kahrunen–Loève expansions. • Posterior distributions of indices are derived and used to design adapted experiments. We use the Karhunen–Loève expansion of a random-field model to construct a tensorised Bayesian linear model from which Sobol' sensitivity indices can be estimated straightforwardly. The method combines the advantages of models built from families of orthonormal functions, which facilitate computations, and Gaussian-process models, which offer a lot of flexibility. The posterior distribution of the indices can be derived, and its normal approximation can be used to design experiments especially adapted to their estimation. Implementation details are provided, and values of tuning parameters are indicated that yield precise estimation from a small number of function evaluations. Several illustrative examples are included that show the good performance of the method, in particular in comparison with estimation based on polynomial chaos expansion. [ABSTRACT FROM AUTHOR]

• Total support index and first-order support index as new sensitivity measures. • Detection of spaces of input variables for which the output variation is high. • Connected to derivative-based sensitivity measures and Sobol' indices. • Application to Ishigami function and sheet metal forming example. Two new sensitivity indices are presented which give an original solution to the question in sensitivity analysis of how to determine regions within the input space for which the model variation is high. The indices, as functions over the input domain, give insight into the local influence of input variables over the whole domain when the other variables lie in the global domain. They can serve as an informative extension to a standard analysis and in addition are especially helpful in the specification of the input domain, a critical, but often vaguely handled issue in sensitivity analysis. In the usual framework of independent continuous input variables, we present theoretical results that show an asymptotic connection between the presented indices and Sobol' indices, valid for general probability distribution functions. Finally, we show how the indices can be successfully applied on analytical examples and on a real application. [ABSTRACT FROM AUTHOR]

• OA arrays of strength two are proposed for 1st- and 2nd order Sobol indices estimation. • Bootstrap confidence intervals are computed to assess the accuracy of the estimations. • Accurate estimates are obtained with affordable computational cost. • Comparisons of the new approach with existing ones are conducted on several examples. Among practitioners, the importance of inputs to a model output is commonly measured via the computation of Sobol' sensitivity indices. Various estimation strategies exist in the literature, most of them requiring a very high number of model evaluations. Designing methods that compete favorably both in terms of computational cost and accuracy is therefore an issue of crucial importance. In this paper, an efficient replication-based strategy is proposed to estimate the full set of first- and second-order Sobol' indices. It relies on a Sobol' pick-freeze estimation scheme and requires only two replicated designs based on randomized orthogonal arrays of strength two. The precision of this procedure is assessed with bootstrap confidence intervals, presented for the first time in the replication framework. Our developments are compared to known approaches and validated on numerical test cases. A way to estimate the full set of first-, second-order but also total-effect Sobol' indices at a very competitive cost is also described, as a combination of our procedure and the one introduced by Saltelli [1]. [ABSTRACT FROM AUTHOR]

• An efficient and accurate method for estimating sensitivity indices is proposed. • PDF-based and FP-based global sensitivity indices are estimated simultaneously. • Model evaluations only appear in constructing the Gaussian integration grid. • Maximum entropy technique is employed to estimate the PDF. Probability density function (PDF)-based and failure probability (FP)-based moment-independent global sensitivity indices can commendably reflect the influence of model input on the whole distribution and partial distribution (or called FP) of model output respectively, yet how to efficiently and accurately estimate these two indices for guiding the engineering practice still remains an essential and challenging problem. In this paper, a novel PDF estimation based method is proposed, which equivalently transforms the computation of these two indices into that of the unconditional and conditional fractional moments of model output. To estimate them, an efficient and simple way is introduced based on a multiplicative version of the dimensional reduction method. The proposed method remarkably reduces the computational cost and can obtain these two indices simultaneously by reusing the information in the integration grid. Results of three case studies demonstrate the effectiveness of the proposed method and its good engineering application. [ABSTRACT FROM AUTHOR]

• Generalized sensitivity indices (GSIs) using covariance matrices. • Estimators of the first-order and total-effect covariance matrices. • Minimun variance unbiased estimators of the classical GSIs. • Numerical simulations. In uncertainty quantification, multivariate sensitivity analysis (MSA) extends variance-based sensitivity analysis to cope with the multivariate response, and it aims to apportion the variability of the multivariate response into input factors and their interactions. The first-order and total-effect covariance matrices from MSA, which assess the effects of input factors, provide useful information about interactions among input factors, the order of interactions, and the magnitude of interactions over all model outputs. In this paper, first, we propose and study generalized sensitivity indices (GSIs) using the first-order and total-effect covariance matrices. The new GSIs make use of matrix norms when partial orders such as the Loewner ordering on covariance matrices is not possible, and we obtain the classical GSIs using the Frobenius norm. Second, we propose minimum variance unbiased estimators (MVUEs) of the first-order and total-effect covariance matrices, and third, we provide an efficient estimator of the first-order and total (classical) GSIs. We also derive the consistency, the asymptotic normality, and the asymptotic confidence regions of these estimators. Our estimator allows for improving the GSIs estimates. [ABSTRACT FROM AUTHOR]

• Parameter correlations have a strong impact on the sensitivity analysis and should be strictly considered in model-based process design and safety analysis. • Two different measures of global sensitivities are implemented and systematically compared. • An effective implementation strategy is proposed to ensure low computational costs for calculating the sensitivities. • A case study from chemical engineering is presented to illustrate the effect of parameter correlations on the parameter ranking. Parameter uncertainties affect model-based system reliability analysis and may lead to safety issues in model-based process design. Global sensitivity analysis (GSA) is a valuable tool to quantify the influence of parameter uncertainties in the variation of the model output. However, GSA has not been widely employed in the field of chemical engineering, especially for processes with correlated model parameters. Parameter correlations, in turn, are quite common when identifying model parameters with experimental data. Thus, we propose and critically compare (co)variance-based and moment-independent GSA techniques for analyzing chemical processes in the absence and presence of parameter correlations. Technically, polynomial chaos expansion is used to reduce the computational burden for GSA. The proposed methods are demonstrated for a continuous synthesis process. Here, the results show significant differences in the parameter sensitivity rankings when parameter correlations are considered or not while the moment-independent technique provides a universal and easy-to-interpret sensitivity measure. [ABSTRACT FROM AUTHOR]

• A data-driven GSA framework to compute various Sobol' indices. • A new Gaussian mixture copula model. This paper presents a probability model-based global sensitivity analysis (PM-GSA) framework, to compute various Sobol' indices when only input-output data are available. The PM-GSA framework consists of two main elements, namely data extraction and probability model training. The data extraction step extracts data of the variables of interest (VoI) and quantity of interest (QoI) from an input-output data matrix. Following that, a probability model is built to approximate the joint probability density function between the VoI and QoI. The learned probability model is then used to compute various Sobol' indices. The implementation of the PM-GSA framework is investigated through three probability models including Gaussian copula model, Gaussian mixture model, and a new Gaussian mixture copula model. The number of dimensions of the probability model in the PM-GSA framework, is independent of the number of input variables and is always N + 1 (e.g. 2 for the first-order index), where N is the order of the Sobol' index. In addition, the PM-GSA framework is applicable to global sensitivity analysis with not only independent input variables, but also with dependent input variables and for sets of variables. Four numerical examples are used to demonstrate the effectiveness of the proposed method and analyze the advantages and disadvantages of the different probability models. [ABSTRACT FROM AUTHOR]

• A new method for GSA of models with functional inputs is introduced. • Filtering operators are used to perturb the functional inputs. • The response on model outputs is studied with Sobol Indices of boolean variables. • Relationships between Sobol Indices and error due to filtering are established. • The approach is generic and can improve model understanding or input acquisition. We design a method called filter-based global sensitivity analysis (filter-based GSA) to analyze computer models with functional inputs. Understanding the impact of functional inputs is central in many applications like building energy or environmental studies. The present work is a step further in the analysis of the impact of functional inputs signal components onto model responses of interest. To perform filter-based GSA, the functional inputs are modified with filters in order to either enhance or suppress some components in the signal. The influence of filters on the model response is assessed by computing the Sobol' indices of Boolean factors that trigger the filters application. Two relationships between these indices and the error resulting from the filters application are established. The method is illustrated with smoothing filters applied on the climatic inputs of a toy model simulating crop yield. We show that the high frequencies for three out of the four climatic inputs are not important in the tested configuration. The present method does not require any hypotheses on the model or the type of filters used. It seems promising for model understanding, validation or simplification. [ABSTRACT FROM AUTHOR]

• Global sensitivity analysis is extended to the context of imprecise probability theory (parametric p-boxes). • Imprecise Sobol' indices are defined and computed from a sparse polynomial chaos expansion (PCE) of the computational model. • The sparse PCE is built in an augmented space of input parameters and associated hyperparameters. • A smart experimental design using phantom points is devised to reduce the number of runs of the computational model. Global sensitivity analysis aims at determining which uncertain input parameters of a computational model primarily drives the output quantities of interest. Sobol' indices are now routinely applied in this context when the input parameters are modelled by classical probability theory using random variables. In many practical applications however, input parameters are affected by both aleatory and epistemic uncertainty. In this respect, imprecise probability theory have become popular in the last decade. In this paper, we consider that the uncertain input parameters are modelled by parametric probability boxes (p-boxes). We propose interval-valued (so-called imprecise) Sobol' indices as an extension of their classical definition. An original algorithm based on the concepts of augmented space, isoprobabilistic transforms and sparse polynomial chaos expansions is devised to allow for the computation of these imprecise Sobol' indices at extremely low cost. In particular, phantoms points are introduced to build an experimental design in the augmented space (necessary for the calibration of the sparse PCE) which leads to a smart reuse of runs of the original computational model. The approach is applied to three analytical and engineering examples which illustrate the efficiency of the algorithms against brute-force double-loop Monte Carlo simulation. Image, graphical abstract [ABSTRACT FROM AUTHOR]

• Sensitivity Analysis helps to identify the key factors concerning the robustness. • SA of Vehicle Restraint Systems is a way enhance the robustness of the design. • Certification of VRS based on very few crash tests is quite unsatisfactory. • The two most influential parameters are the post thickness and post yield strength. • Combining numerical studies and SA is a way to improve regulations. Restricted by high calculation cost of single engineering model run and large number of model runs for sampling-based Sensitivity Analysis (SA), qualitative SA are used for parameter study of the Vehicle Restraint System (VRS) and quantitative SA of such models has always been a challenge. Sequential approaches are proposed for SA of complex systems and the SA of a VRS is realized: sampling-based SA methods are discussed; SA of a simple three points dynamic bending test model is realized, the aims are to compare different two-level screening methods and put into practice the sequential SA; crash test FE model of a VRS is created and used for SA; influential uncertain parameters of the VRS are identified qualitatively through screening analyses (SA with Two-level screening and Morris Analysis), and Sobol' indices are used to quantify the influence of influential parameters with Kriging metamodeling. The uncertain parameters which contribute the most to robustness of the VRS are identified and their influences are quantified by combining screening analyses and Sobol' Indices. [ABSTRACT FROM AUTHOR]

• The Gaussian process metamodel allows to build a functional risk curve (FRC) with a limited number of computer model runs. • Two sensitivity analysis methods are developed for the functional risk curve as quantity of interest. • Sensitivity analysis can be realized via the aggregated Sobol' indices. • The Perturbed-Law based sensitivity Indices (PLI) give the effect of change of input pdf on the FRC. • An example from the non-destructive control domain illustrates all the proposed methods. A functional risk curve gives the probability of an undesirable event as a function of the value of a critical parameter of a considered physical system. In several applicative situations, this curve is built using phenomenological numerical models which simulate complex physical phenomena. To avoid cpu-time expensive numerical models, we propose to use Gaussian process regression to build functional risk curves. An algorithm is given to provide confidence bounds due to this approximation. Two methods of global sensitivity analysis of the model random input parameters on the functional risk curve are also studied. In particular, the PLI sensitivity indices allow to understand the effect of misjudgment on the input parameters' probability density functions. [ABSTRACT FROM AUTHOR]

Highlights • Preventive strike that can cause random loss of attacking resource is considered. • The trade-off between preventive strike and protection is studied. • The case where false targets can be deployed is also considered. • Both perfect false targets and imperfect false targets are investigated. Abstract Most existing research on system defence is restricted to passive measures such as providing redundancy, protecting system elements, and deploying false elements. Some recent works have considered the launching of preventive strikes, where a preventive strike, if successful, destroys all the attacker's resources. However, in practice, a preventive strike might cause a random loss to the attacker's resources. This paper assumes that the destroyable attacking resources follow a Poisson distribution. Procedures are presented to solve the optimal defence strategies for three cases: (1) where preventive strikes and object protections are the only available defence measures; (2) where false targets can also be deployed, and they are perfect; and (3) where false targets can also be deployed, but they are imperfect. Numerical examples are provided to illustrate the applications, and sensitivity analysis is employed to demonstrate the influence of parameters. [ABSTRACT FROM AUTHOR]

Highlights • Orthogonal augment RBF metamodel based sensitivity analysis method is proposed. • Orthogonal condition of RBF and linear basis is derived. • The influence of polynomial and RBF items are decoupled. • Analytical formulas for OA-RBF based sensitivity indices are derived. Abstract Global sensitivity analysis (GSA) plays an important role in determining how the output behavior is related to the changes in the inputs, which can be utilized to quantify the influence of the inputs and their interactions or eliminate the unessential input parameters. When the computationally expensive analysis model is utilized, the computation of sampling-based GSA is rather a challenging task, and the metamodel based GSA is a promising alternative. This paper proposes an orthogonal augment radial basis function (OA-RBF) method, for estimating a general class of Sobol' indices. To this end, the orthogonal condition of augment RBF is derived first to decouple the impact of polynomial and RBF items. Then analytical formulas for Sobol' indices are obtained based on the proposed OA-RBF metamodel. Five examples are presented to demonstrate the performance of the proposed approach. For all the problems, the proposed approach yields satisfactory results with a significantly reduced computational effort. The results obtained, to some extent, indicate that the approach proposed here can be utilized for GSA of industrial-scale engineering problems. [ABSTRACT FROM AUTHOR]

Highlights • New global sensitivity measures based on quantiles of the output are introduced. • Difference between proposed measures and quantile oriented sensitivity indices is discussed. • It is proven that there is a link between introduced measures and Sobol' main effect sensitivity indices. • It is shown that the double loop reordering approach is much more efficient than the brute force estimator. • Results of numerical calculations show the efficiency of the presented method. Abstract New global sensitivity measures based on quantiles of the output are introduced. Such measures can be used for global sensitivity analysis of problems in which α th quantiles are explicitly the functions of interest and for identification of variables which are the most important in achieving extreme values of the model output. It is proven that there is a link between introduced measures and Sobol' main effect sensitivity indices. Two different Monte Carlo estimators are considered. It is shown that the double loop reordering approach is much more efficient than the brute force estimator. Several test cases and practical case studies related to structural safety are used to illustrate the developed method. Results of numerical calculations show the efficiency of the presented technique. [ABSTRACT FROM AUTHOR]

Highlights • A non-linear piecewise state function is designed to describe maintenance states. • A high-level maintenance planning model for high-speed trains is formulated. • The original model is linearized using a big M method. • Develop a simulated annealing algorithm to solve the relaxation model. • Conduct a real-world case study with 124 trains from the China Shanghai Railroad. Abstract For safety reasons, a high-speed train needs to carry out the preventive maintenance when its accumulated running mileage or time reaches a predefined threshold. This paper formulates the train high-level preventive maintenance planning problem as a 0-1 programming model. A novel state function is designed to describe whether a train is under maintenance or not. By using this function, the constraint for restricting the total number of trains under maintenance can be formulated reasonably well. A linearization technique is also employed to refine the original non-linear state function into a linear one. To handle large-scale instances, a simulated annealing algorithm is proposed for solving the problem and is applied to a real-world case study from Shanghai Railway Bureau (SRB), a regional railway operator under China Railway. The optimized results yield a total cost of 3,619,200 standard train-km in terms of remaining mileage. In addition, sensitivity analyses based on the real-world case study reveal some interesting insights. We have delivered the results to SRB as a useful and efficient decision support tool for their high-level maintenance planning work. [ABSTRACT FROM AUTHOR]

Highlights • We propose the Sobol tensor train, a data structure containing all Sobol indices of a surrogate model compressed using the tensor train decomposition • We show how to extract the proposed tensor from any tensor train surrogate, and how such surrogates can be learned • We derive all total, closed, and superset indices from our representation at very small cost • We are able to answer advanced queries among the set of all sensitivity indices • Our algorithms are demonstrated with two high-dimensional analytical functions and an engineering simulation example Abstract Sobol indices are a widespread quantitative measure for variance-based global sensitivity analysis, but computing and utilizing them remains challenging for high-dimensional systems. We propose the tensor train decomposition (TT) as a unified framework for surrogate modeling and sensitivity analysis via Sobol indices. We first overview several strategies to build a TT surrogate using either an adaptive sampling strategy or a predefined set of samples. Our main contribution is the introduction of the Sobol TT, which compactly represents variance components for all possible joint variable interactions of any order. Our formulation allows efficient aggregation and subselection operations, and we are able to obtain related Sobol indices (closed, total, and superset indices) at negligible cost. Furthermore, we exploit an existing global optimization procedure within the TT framework for variable selection and model analysis tasks. We demonstrate our algorithms with two analytical models and a parallel computing simulation data set. [ABSTRACT FROM AUTHOR]

Highlights • Investigation of adaptive sampling methods for surrogate models. • A novel global adaptive sampling method for least-squares support vector regression. • Useful for the application to global sensitivity analysis. • A faster and more robust global adaptive sampling is enabled. • Especially useful for functions with critical behavior in some specific regions. Abstract In the field of engineering, surrogate models are commonly used for approximating the behavior of a physical phenomenon in order to reduce the computational costs. Generally, a surrogate model is created based on a set of training data, where a typical method for the statistical design is the Latin hypercube sampling (LHS). Even though a space-filling distribution of the training data is reached, the sampling process takes no information on the underlying behavior of the physical phenomenon into account and new data cannot be sampled in the same distribution if the approximation quality is not sufficient. Therefore, in this study we present a novel adaptive sampling method based on a specific surrogate model, the least-squares support vector regression. The adaptive sampling method generates training data based on the uncertainty in local prognosis capabilities of the surrogate model - areas of higher uncertainty require more sample data. The approach offers a cost efficient calculation due to the properties of the least-squares support vector regression. The opportunities of the adaptive sampling method are proven in comparison with the LHS on different analytical examples. Furthermore, the adaptive sampling method is applied to the calculation of global sensitivity values according to Sobol, where it shows faster convergence than the LHS method. With the applications in this paper it is shown that the presented adaptive sampling method improves the estimation of global sensitivity values, hence reducing the overall computational costs visibly. [ABSTRACT FROM AUTHOR]