Probability Of Failure Research Articles

River quality management: Integrating uncertainty, failure probability, and assimilation capacity

Managing river water quality is challenging due to uncertainties in hydraulic and hydrologic parameters. This study integrates the symmetric exponential function (SEF) approach for solving the advection-dispersion equation with the Monte Carlo method in MATLAB. This combination allows us to explore the river's assimilation capacity and the failure probability (Pf) of maintaining desired water quality standards. Here, Pf represents the likelihood of pollutant concentrations exceeding acceptable limits under varying river conditions. A key contribution of this study is the introduction of a novel equation, developed using the Genetic Programming (GP) soft computing tool, to calculate assimilation capacity considering the failure probability of water quality provision. This equation provides a valuable tool for risk assessment in water resource management by quantifying pollutant assimilation dynamics. Its robustness is validated through high Coefficient of Determination (R2) and Overall Index (OI) values near 1, along with low Root Mean Square Error (RMSE) and Mean Absolute Error (MAE). The study identifies critical river characteristics, such as flow velocity and pollutant load, significantly influencing the reliability index (β). By outlining how adjustments in these parameters can achieve a target reliability index (β=4.526), our study offers a practical approach to safeguarding river ecosystems. For example, increasing flow velocity by 76 % can shift the river from a safe state (Pf=3×10−5) to a hazardous state (Pf=1), while a 44 % decrease in velocity allows for 57 % more pollutant assimilation. These findings highlight the importance of flow control as a cost-effective strategy for mitigating high pollutant concentrations and ensuring sustainable water quality management. By integrating numerical approaches with reliability sampling methods and soft computing techniques, this study enhances understanding of river system dynamics and supports informed decision-making for protecting water resources.

Incorporation of machine learning into multiple stripe seismic fragility analysis of reinforced concrete wall structures

This study proposes a novel procedure that incorporates machine learning (ML) into the multiple stripe analysis (MSA) approach to efficiently produce seismic fragility curves for reinforced concrete (R/C) shear walls in building frame systems. The proposed procedure aims to mitigate computational challenges associated with the original MSA approach. In this context, ML models were developed for predicting the failure probability of R/C walls subjected to ground motions based on a specified threshold of maximum interstory drift ratio (MIDR). Specifically, the result of each numerical analysis, taken as the output variable of the ML models, was classified as either “B” (Below) or “E” (Exceeding) to indicate whether the MIDR of R/C walls was below or exceeding the specified threshold. This binary categorization was then used to calculate the failure probability points, which are necessary to derive fragility curves per the MSA approach. Data for training and testing the ML models were generated from nonlinear time history analyses of 46 distinct R/C walls subjected to 1000 ground motions. The R/C walls varied in height from four to 40 stories, and the ground motions included far-field, near-field pulse, and near-field no-pulse types. Four well-established ML methods, including random forest (RF), extreme gradient boosting, light gradient boosting machine, and categorical boosting, were considered. The performances of the ML models were compared using a confusion matrix. Based on this comparison, the RF model was selected and incorporated into the proposed procedure. Subsequently, the proposed approach was demonstrated to create the seismic fragility function of a new R/C wall structure. This study highlights the potential of ML applications in optimization problems within the earthquake engineering domain.

Enhancing subset simulation through Bayesian inference

Analyzing and reducing uncertainty in estimating failure probability has always been a crucial part of reliability analysis using Monte Carlo simulation. This paper employs Bayesian inference to capture uncertainty within Subset Simulation (SuS), with a specific emphasis on constructing the posterior distribution of failure probability. Two types of Bayesian models are discussed. The first type is based on the distribution form of the failure probability estimator from the SuS, where the Log-normal and Beta distributions are compared and analyzed. The second type is based on the distribution of statistics in Bernoulli trials in SuS, involving models such as the Beta-Binomial and Uniform-Bernoulli trials with Sequential Dependence. After evaluating all models among two types, the Log-normal distribution-based model was selected as the optimal solution due to its consideration of sample correlation and closed form of Maximum A Posteriori (MAP). Further exploration of this model reveals that its MAP estimation can provide less bias and deviation compared to mean estimation when SuS is run multiple times. Additionally, when compared to the point estimation of failure probability in conventional SuS, the posterior distribution of failure probability provides a more comprehensive overview, capturing the effects of sample size and MCMC algorithms.

Theoretical model for predicting survival of quantity surveying firms in Nigeria

Firms are susceptible to environmental changes like national economic instability, which affects their survival. Consequently, firms need to ascertain their tendency to survive the challenges of the environment. Therefore, this study investigated the factors influencing the failure of quantity surveying consultancy firms and proposes a survival tendency model that allows decision-makers to assess their propensity to withstand economic downturns. Through observational research, QS firms were studied for 10 years (2010 to 2020) which typifies the economic contraction phase in Nigeria. Archival and qualitative data were obtained from 130 QS firms and Cox regression was adopted to analyse the data. The results revealed that 43% of QS firms failed during the economic downturn due to external loans obtained for their operations. Furthermore, purchasing new software/technologies and employing more staff increases the probability of failure while research and development, diversification, and maintaining the number of partners reduce likelihood of failure. A model was proposed for QS firms to ascertain their survival during economic downturns using the significant predictor (i.e. method of financing). This study, thus, recommends that managers of QS firms should finance their operations using savings from professional fees and profits. They should also decide on strategies that can be implemented to survive economic crises.

Novel Bayesian updating based interpolation method for estimating failure probability function in the presence of random-interval uncertainty

Under random-interval uncertainty, the failure probability function (FPF) represents the failure probability variation as a function of the random input distribution parameter. To quickly capture the effect of the distribution parameters on failure probability and decouple the reliability-based design optimization, a novel Bayesian updating method is proposed to efficiently estimate the FPF. In the proposed method, the prior augmented failure probability (AFP) is first estimated in the space spanned by random input and distribution parameter vectors. Subsequently, by treating the distribution parameter realization as an observation, the FPF can be estimated using posterior AFP based on Bayesian updating. The main novelty of this study is the elaborate treatment of the distribution parameter realization as an observation, whereby the FPF is transformed into the posterior AFP based on Bayesian updating, and can be obtained by sharing the prior AFP simulation samples. The computational cost of the proposed method is the same as that of estimating the prior AFP. To improve the efficiency of recognizing the sample state, and improve AFP and in turn FPF estimation, the adaptive Kriging model for random-interval uncertainty was inserted into the proposed method. The feasibility and novelty of the proposed method were verified on several examples.

Enhancing the Minimum Awareness Failure Distance in V2X Communications: A Deep Reinforcement Learning Approach.

Vehicle-to-everything (V2X) communication is pivotal in enhancing cooperative awareness in vehicular networks. Typically, awareness is viewed as a vehicle's ability to perceive and share real-time kinematic information. We present a novel definition of awareness in V2X communications, conceptualizing it as a multi-faceted concept involving vehicle detection, tracking, and maintaining their safety distances. To enhance this awareness, we propose a deep reinforcement learning framework for the joint control of beacon rate and transmit power (DRL-JCBRTP). Our DRL-JCBRTP framework integrates LSTM-based actor networks and MLP-based critic networks within the Soft Actor-Critic (SAC) algorithm to effectively learn optimal policies. Leveraging local state information, the DRL-JCBRTP scheme uses an innovative reward function to increase the minimum awareness failure distance. Our SLMLab-Gym-VEINS simulations show that the DRL-JCBRTP scheme outperforms existing beaconing schemes in minimizing awareness failure probability and maximizing awareness distance, ultimately improving driving safety.

Assessing the Reliability of Truss Structures Based on the Bound Method and Collectively Exhaustive Events

Damage to long-span truss structures may cause structural deformation, load-capacity reduction, and even collapse. The design service life of truss structures is usually 50 years, so evaluating their reliability is of the utmost importance. Reliability considers the probability of failure as an analysis index. In calculating the probability of structural failure, important components are first selected to form a failure path, and then the failure probability corresponding to the failure path is calculated. A truss structure has many important components and failure paths, so calculating this probability requires extensive and thorough work. As a result, we propose selecting the important components via the approximation method to reduce the influence of the threshold of approximation. Collectively exhaustive events were established using the differential equivalent recursive algorithm to calculate the probability of structural failure. This process was considerably simplified, and validity was verified via a reliability analysis involving a three-bar truss structure, a plane truss structure, and a square pyramid truss structure. This method is suitable for selecting important components of regular flat truss structures.

P-graph and Monte Carlo simulation approach for sustainable and risk-managed CDR portfolios

Negative emission technologies (NETs) that perform carbon dioxide removal (CDR) are now part of the decarbonization strategies to reach net-zero emissions. However, NETs will consume resources that will compete with other societal priorities. Thus, NET portfolios that provide a technology mix are better for sustainability and risk management. This study proposes a two-step approach to optimize and check the robustness of NET portfolios, particularly for industrial-scale applications where resource availability fluctuates due to variations in energy, water, and fertilizer supply. The first step involves the process graph (P-graph) framework to generate optimal and near-optimal solution structures at minimum cost. The second step measures the probability of failure of these solutions against resource availability variations through Monte Carlo simulation. By comparing the cost and probability of failure, decision-makers can select a recommended solution that strikes a balance between robustness and cost. The proposed approach is demonstrated in two case studies involving NET portfolios. The first case study investigates the performance of optimal and near-optimal solutions of NET portfolios, while the second case study focuses on bioenergy with carbon capture and storage portfolios using different feedstocks. In both cases, the results show that near-optimal solutions with higher costs but lower probabilities of failure exist, enabling decision-makers to weigh robustness against cost. This study contributes to developing and analyzing robust decarbonization decision support models, addressing the critical need for sustainable and risk-managed NET portfolios.

Seismic vulnerability analysis of hospitals and school buildings considering the Gaussian regression algorithm

This study combines the Gaussian regression algorithm to propose a nonlinear regression model that can be used to evaluate the seismic vulnerability of regional hospitals and school buildings. The failure features and disaster mechanisms of hospital and school buildings affected by the Jishishan (JSS) earthquake on December 18, 2023, and the Wenchuan (WC) earthquake on May 12, 2008, were reported. The samples of 252 damaged buildings (37 hospitals and 215 schools) in Dujiangyan city affected by the Wenchuan earthquake for which the author participated in the survey were collected and counted. Hospitals and school buildings were classified according to the types of reinforced concrete (RC) and masonry structures, and earthquake vulnerability probability matrices for hospital and school building clusters were established considering the actual failure probabilities. A total of 2103,213 acceleration records (from the Wenchuan earthquake) monitored by 12 real stations were selected. Using dynamic time history and response spectrum analysis methods, time history and spectrum curves were generated, considering the influence of different seismic directions. Using the developed Gaussian regression model, vulnerability comparison curves and parameter matrices considering multiple regression algorithms were generated. This paper considers the effects of the construction year and number of floors on the seismic vulnerability of hospital and school buildings. Seismic vulnerability curves and failure probability matrices were generated and established on the basis of actual structural failure probabilities. According to regression and vulnerability surface analysis, the evaluation results of the proposed model are highly consistent with actual field observations.

Failure Analysis of Ni-8YSZ Electrode under Reoxidation Based on the Real Microstructure.

During the operation of solid oxide fuel cells (SOFCs), the Ni-8YSZ anodes are subjected to thermal mismatch and reoxidation, accompanied by the risk of damage and failure. These damages and failures are generally induced by small defects at the microscopic level, leading to the degradation of the structural bearing capacity. Therefore, the distribution and quantification of the stresses in the real microstructure of Ni-8YSZ electrodes is essential. In this study, the real Ni-8YSZ microstructure was reconstructed based on nano-computed tomography, and the stress distribution of the real microstructure was analyzed based on the finite element method under reoxidation and different operating temperatures. The failure probability of 8YSZ at different degrees of reoxidation was evaluated according to the Weibull method, and the amount of damaged 8YSZ elements was statistically counted. The study results indicate a high level of stress in the thin necks and relatively sharp areas of the microstructure. The 8YSZ has a high failure probability at a reoxidation extent of 5-10%.

Failure Probability-Based Optimal Seismic Design of Reinforced Concrete Structures Using Genetic Algorithms

Artificial intelligence (AI) has enabled several optimization techniques for structural design, including machine learning, evolutionary algorithms, as in the case of genetic algorithms, reinforced learning, deep learning, etc. Although the use of AI for weight optimization in steel and concrete buildings has been extensively studied in recent decades, multi-objective optimization for reinforced concrete (RC) and steel buildings remains challenging due to the difficulty in establishing independent objective functions and obtaining Pareto fronts. The well-known Non-Dominated Sorting Genetic Algorithm II (NSGA-II) is an efficient genetic algorithm approach for multi-objective optimization. In this work, the NSGA-II approach is considered for the multi-objective structural optimization of three-dimensional RC buildings subjected to earthquakes. For the objective of this study, two function objectives are considered: minimizing total cost and the probability of structural failure, which are obtained via several nonlinear seismic analyses of the RC buildings. Beams and columns’ cross-sectional dimensions are selected as design variables, and the Mexican Building Code (MBC) specifications are imposed as design constraints. Pareto fronts are obtained for two RC-framed buildings located in Mexico City (soft soil sites), which demonstrate the efficiency and accuracy of NSGA-II for structural optimization.

Dynamic Fault Tree Generation and Quantitative Analysis of System Reliability for Embedded Systems Based on SysML Models.

As embedded systems become increasingly complex, traditional reliability analysis methods based on text alone are no longer adequate for meeting the requirements of rapid and accurate quantitative analysis of system reliability. This article proposes a method for automatically generating and quantitatively analyzing dynamic fault trees based on an improved system model with consideration for temporal characteristics and redundancy. Firstly, an "anti-semantic" approach is employed to automatically explore the generation of fault modes and effects analysis (FMEA) from SysML models. The evaluation results are used to promptly modify the system design to meet requirements. Secondly, the Profile extension mechanism is used to expand the SysML block definition diagram, enabling it to describe fault semantics. This is combined with SysML activity diagrams to generate dynamic fault trees using traversal algorithms. Subsequently, parametric diagrams are employed to represent the operational rules of logic gates in the fault tree. The quantitative analysis of dynamic fault trees based on probabilistic models is conducted within the internal block diagram of SysML. Finally, through the design and simulation of the power battery management system, the failure probability of the top event was obtained to be 0.11981. This verifies that the design of the battery management system meets safety requirements and demonstrates the feasibility of the method.

Morphological Prediction of CPAP Associated Acute Respiratory Instability.

Multiple mechanisms are involved in the pathogenesis of obstructive sleep apnea (OSA). Elevated loop gain is a key target for precision OSA care and may be associated with treatment intolerance when the upper airway is the sole therapeutic target. Morphological or computational estimation of LG is not yet widely available or fully validated - there is a need for improved phenotyping/endotyping of apnea to advance its therapy and prognosis. This study proposes a new algorithm to assess self-similarity as a signature of elevated loop gain using respiratory effort signals and presents its use to predict the probability of acute failure (high residual event counts) of continuous positive airway pressure (CPAP) therapy. Effort signals from 2145 split-night polysomnography studies from the Massachusetts General Hospital were analyzed for SS and used to predict acute CPAP therapy effectiveness. Logistic regression models were trained and evaluated using 5-fold cross-validation. Receiver operating characteristic (ROC) and precision-recall (PR) curves with AUC values of 0.82 and 0.84, respectively, were obtained. Self-similarity combined with the central apnea index (CAI) and hypoxic burden outperformed CAI alone. Even in those with a low CAI by conventional scoring criteria or only mild desaturation, SS was related to poor therapy outcomes. The proposed algorithm for assessing SS as a measure of expressed high loop gain is accurate, non-invasive, and has the potential to improve phenotyping/endotyping of apnea, leading to more precise sleep apnea treatment strategies.

Integrated optimization for X-bar control chart, preventive maintenance and production rate

There are close relationships among statistical process control, maintenance, and production that have not fully explored in existing studies. In this study, we propose an economic model for jointly optimizing the X-bar control chart, preventive maintenance, and production rate. Unlike conventional studies relying on known failure rate functions, we employ a Gamma process to describe the system's deterioration. This approach allows us to consider not only the relationship between the production rate and the deterioration rate but also a broad range of deterioration scenarios and failure modes in the integrated optimization. After calculating the failure probability at each time point, we propose a recursive method to derive the production revenue, process control costs, and quality losses. This approach explores the close inner relationship between the production rate, deterioration, process monitoring and maintenance. Subsequently, we establish an optimization model aimed at maximizing the profit rate within a renewal cycle. The decision variables of this model include the production rate, control chart coefficient, sample size, length of the first sampling interval, and number of sampling intervals. Finally, we use a case study to illustrate the effectiveness and validity of our proposed model by identifying and explaining the interactions between production rate, deterioration, process control and maintenance.

Structural reliability analysis with parametric p-box uncertainties via a Bayesian updating BDRM

The parametric probability-box model, often abbreviated as “p-box” is frequently used to characterize epistemic uncertainties. However, structural reliability analysis with p-box uncertainties can often be computationally intensive. This paper presents an efficient method to accurately compute the bounds of failure probabilities within this context. The method’s key innovation lies in its ability to achieve high efficiency with only a single round of model evaluations. First, the Fractional Exponential Moments-based Maximum Entropy Method (FEM-MEM) with Bivariate Dimension Reduction Method (BDRM) is employed for precise reliability assessment, where a single-round of model evaluations are carried out. Subsequently, Bayesian Updating (BU) is applied to adjust the weights obtained from BDRM in response to changes in input variables, while ensuring the invariance of integration points. Following this adjustment, the FEM-MEM is once again employed to compute the failure probability after the information change, without necessitating additional model evaluations. To compute the bounds of failure probabilities, a Kriging model is employed to construct a surrogate relationship between the interval variables and failure probabilities. The accuracy and efficiency of the proposed method are demonstrated through numerical examples, with comparisons made against pertinent double-loop method.

Evaluating the Contribution of Model Complexity in Predicting Robustness in Synthetic Genetic Circuits.

The design-build-test-learn workflow is pivotal in synthetic biology as it seeks to broaden access to diverse levels of expertise and enhance circuit complexity through recent advancements in automation. The design of complex circuits depends on developing precise models and parameter values for predicting the circuit performance and noise resilience. However, obtaining characterized parameters under diverse experimental conditions is a significant challenge, often requiring substantial time, funding, and expertise. This work compares five computational models of three different genetic circuit implementations of the same logic function to evaluate their relative predictive capabilities. The primary focus is on determining whether simpler models can yield conclusions similar to those of more complex ones and whether certain models offer greater analytical benefits. These models explore the influence of noise, parametrization, and model complexity on predictions of synthetic circuit performance through simulation. The findings suggest that when developing a new circuit without characterized parts or an existing design, any model can effectively predict the optimal implementation by facilitating qualitative comparison of designs' failure probabilities (e.g., higher or lower). However, when characterized parts are available and accurate quantitative differences in failure probabilities are desired, employing a more precise model with characterized parts becomes necessary, albeit requiring additional effort.

Durability fragility curves for service life prediction of concrete with various supplementary cementitious materials subjected to natural carbonation

This study estimates the service life of concretes containing supplementary cementitious materials (SCM) subjected to carbonation from a probabilistic and reliability-based perspective. The aim is to enhance understanding of the risks associated with degradation and to propose an alternative approach for estimating the durability of reinforced concrete (RC) structures. The inclusion of supplementary cementitious materials (SCMs) is crucial for making concrete more sustainable, as these materials can reduce the carbon footprint of concrete production and improve its durability. Using available natural carbonation data from the literature on samples containing SCM, computational codes were developed for reliability analyses via the Monte Carlo Simulation method. The results indicated that all concrete samples exhibited a 100% probability of failure for coverages of 20 mm and 25 mm at an age of 100 years. For a coverage of 30 mm, all samples maintained a failure probability of over 98% within the same period. Notably, concretes incorporating metakaolin showed a substantial reduction in failure probability across all evaluated time periods, indicating superior durability compared to other samples. These findings significantly contribute to a deeper understanding of concrete degradation processes and provide valuable insights for the design and maintenance of RC structures, particularly in the context of using SCM. By adopting a probabilistic approach, the study underscores the importance of considering variability and uncertainties in predicting concrete durability, ultimately aiding in the development of more resilient and long-lasting infrastructure.

Experimental study on bending fatigue performance of ambient-cured ultra-high-performance concrete thin plate with embedded steel wire mesh

Ambient-cured ultra-high-performance concrete (ACUHPC) with embedded steel wire mesh (SWM) was studied experimentally. ACUHPC-SWM thin plates having different SWM wire ratios and fatigue load stress levels were tested to clarify the effects of SWM on static and fatigue bending behavior. Subsequently, the fatigue equations for ACUHPC-SWM materials (with different failure probabilities) and reinforcement efficiency of the SWM were proposed. Finally, the reinforcement mechanism of the SWM was revealed by comparing it with ACUHPC thin plates. The results show that the inclusion of wire mesh significantly improved the cracking strength, ultimate static strength, energy dissipation performance, and fatigue ultimate strength of ACUHPC, with maximum increases of 23.63 %, 260.32 %, 940.42 %, and 196.34 %, respectively. As the wire mesh ratio increased, the improvement in fatigue ultimate strength initially increased and then decreased once the wire mesh ratio exceeded 1.884 %. The mechanism according to which SWM enhances ACUHPC involves the action of the mesh as a bridge to delay crack development and increase toughness.

Efficient finite element reliability analysis employing sequentially-updated surrogate model for fragility curve derivation

As the threat of natural disasters to structures intensifies, risk assessment of infrastructure has gained much importance. Fragility curves are essential tools in predicting disaster-related losses and making disaster mitigation decisions. In this paper, we propose a new method to efficiently derive accurate fragility curves for structures with high levels of nonlinearity or complexity, addressing the computational challenges of conventional finite element reliability analysis (FERA). To reduce the computational cost for calculating probability of failure in FERA, the proposed method utilizes the first-order reliability method (FORM). However, even with this approach, the computational cost of deriving the fragility curve may remain high; therefore, a surrogate model is used to further reduce costs. By training the surrogate model using the initial structural damage probabilities for a few hazard intensities, an optimal starting point can be calculated for the subsequent FORM analysis. During the fragility analysis, the surrogate model can be updated sequentially to increase the efficiency of FORM analysis continuously. In particular, the training process of the surrogate model requires no separate or additional finite element analysis because it is constructed using previous FERA results. The accuracy and efficiency of the proposed method are tested using conventional FERA and Monte Carlo simulations through a hypothetical short-column example. In addition, fragility curves are derived through a bridge flood fragility assessment considering the scour and seismic vulnerability assessment of a buried gas pipeline considering soil-structure interactions. The derived fragility curves closely match those derived using the conventional FERA, and the computational costs are reduced by 36.54 % and 52.38 %, respectively, compared with the conventional FERA, confirming its cost-effectiveness.

An improved sequential importance sampling method for structural reliability analysis of high dimensional problems

Reliability analysis for rare events has proven to be a significant challenge, particularly in non-linear and complex scenarios. Despite the effectiveness of Sequential Importance Sampling (SIS) and Subset Simulation (SUS) in addressing high-dimensional small failure probability problems, the computational burden associated with mechanical simulations for complex structures remains substantial. To address this issue, this paper introduces a novel approach referred to as SIS and Kriging Metamodel Integration (SISAK), designed for computing small failure probabilities in high dimensions. This method involves generating a small number of samples from the original distribution to construct an adaptive metamodel, which is then iteratively optimized using a series of intermediate distributions introduced by SIS. By substituting the function for intermediate distributions with a continuously optimized metamodel, the enhanced approach significantly reduces the computational load associated with mechanical model evaluations compared to the direct use of SIS. This approach does not depend on determining the most probable failure point and does not require consideration of the failure domain shape. Additionally, it inherits the advantages of SIS in addressing high-dimensional small failure probabilities, making it well-suited for structural reliability analysis of nonlinear systems, discontinuous failure domains, cascading functions, and high-dimensional problems.