Reliability Analysis Framework Research Articles

Physics-informed neural network classification framework for reliability analysis

Reliability analysis is crucial for quantitatively evaluating structural safety amidst uncertainties, laying the foundation for reliability-based design optimization aimed at augmenting structural reliability and reducing economic expenditures, thereby offering substantial engineering benefits. However, performing reliability analysis on intricate structures, especially those requiring time-intensive finite element models, presents a formidable challenge. This study develops an innovative physics-informed neural network classification (PINNC) model to tackle this issue. In the PINNC model, the loss associated with the structural output state (i.e., safety or failed state) is defined as classification loss. Additionally, the structural output value (i.e., actual structural response) is treated as critical physical information, with its associated loss termed as physical loss. To facilitate a separate calculation of physical loss and classification loss, a parametric sigmoid activation function is used, establishing a link between the structural output value and the structural output state. The total loss is calculated as a weighted sum of both physical and classification losses. Unlike conventional neural network classification models that solely focus on classification loss, the PINNC model integrates both physical and classification losses, markedly improving the model’s efficacy in structural reliability analysis. Moreover, an adaptive framework is developed to incrementally include samples proximal to the limit state surface as new training data, thereby reinforcing the PINNC model’s computational precision. The effectiveness of the proposed PINNC framework in overcoming reliability analysis challenges is demonstrated through various applications.

A Statistical Model of Hazard Rate Change Caused by a Random Shock

In the framework of statistical reliability analysis, we propose a model describing the change of reliability of a technical component after certain event, as for instance a shock, or the failure and maintenance. Two kinds of failure rate changes are considered, namely a shift of virtual age of analyzed component and the acceleration of its subjective time. The objective is to estimate both the baseline lifetime probability distribution and the magnitude of these changes. The estimation procedure is based on the maximum likelihood method, both parametric and nonparametric distributions of lifetime are considered. Further, a graphical method of the goodness-of-fit test is proposed. The method is then checked on artificial examples, finally a real data problem is solved.

Development of a human reliability analysis framework for nominal human error probability estimate of the TRIGA research reactor in Thailand

Human reliability analysis (HRA) of nuclear research reactors often encounters a lack of human performance data, a challenge that is also faced by the TRIGA reactor of Thailand having no specific full method or human error database for HRA. To overcome this challenge, in 2023, HRA teams from the Korea Atomic Energy Research Institute (KAERI) and the Thailand Institute of Nuclear Technology (TINT) jointly developed an HRA framework for the TRIGA reactor. In the HRA framework development, the HRA practitioners applied KAERI's three main HRA tools, namely 1) the EMpirical data-Based crew Reliability Assessment and Cognitive Error analysis (EMBRACE) method, 2) the Human Reliability data EXtraction (HuREX) database, and 3) the TAsk COMplexity (TACOM) method. The HRA framework covers the overall process including the classification of documents and human error types as well as nominal human error extraction for estimating nominal human error probabilities. According to the results of the first use of the HRA framework on the TRIGA reactor in Thailand, the HRA framework provided an effective way to improve the procedures and systematically identify nominal human errors of actions in the emergency procedures.

Robust active learning framework for structural reliability analysis using uncertainty quantification and flexible meta-model

Achieving highly accurate results in assessing structural reliability with reduced time complexity is an active and challenging engineering topic, especially when working with complex real-world structures. One of the most prominent methods addressing this issue is AK-MCS, which adaptively updates the Kriging-based surrogate model for forecasting structures’ behavior. While the Kriging model’s performance may be limited compared to multiple new machine learning models, it remains dominant in reliability analysis thanks to its distinctive ability to assess uncertainty along with prediction results. This ability is necessary to determine the potential candidate sample in the active learning procedure. This study proposes a novel method, dubbed AUQ-meta, that allows us to leverage the recent powerful machine learning models while still being able to produce uncertainty quantification. The AUQ-meta method consists of three main components: a machine learning-based predictor, a quantile regression module for uncertainty assessment, and an adaptive reliability analysis process. The effectiveness and efficiency of the proposed method are consistently validated through six examples with high dimensionality, nonlinearity, and time-varying elements. In addition, comparison and sensitivity studies are carried out, providing further insights into the AUQ-meta method’s operational mechanism.

The Latency Performance Analysis and Effective Relay Selection for Visible Light Networks.

In visible light communication (VLC), the precise latency evaluation of wireless access networks and the efficient forwarding strategy of core networks are the crux for end-to-end reliability provisioning. Leveraging martingale theory, an elegant latency-bounded reliability analysis framework is studied for the VLC network. Considering the characteristic that VLC links are easy to block, the martingale of the service process is constructed. Based on the time shift features, the martingale process related to latency is proposed for the VLC system, which models the influence of entanglement between aggregate arrivals and random service on latency. A stopping time event about latency is defined. Renting the stopping time theory, a tight upper bound of the unreliability with regard to latency is derived. In the core network, a dynamic forward backhaul framework is proposed, which uses the relay selection algorithm based on back-pressure theory to improve data transmission quality. The theoretical latency-bounded reliability matches the simulation results well, which verifies the effectiveness of the proposed analysis framework, and the proposed relay selection algorithm can also improve network performance under data-intensive transmission.

Time-dependent seismic reliability analysis of rocking cold-formed steel frame based on improved HOMM

Cold-formed steel structures are particularly sensitive to seismic loads due to their relatively low ductility and limited energy dissipation capacity. Moreover, the small thickness of cold-formed steel structures makes them more susceptible to environmental influences, leading to corrosion and material degradation. Therefore, it is essential to quantitatively assess the seismic reliability of cold-formed steel structures from a lifecycle perspective. Current structural reliability design standards often focus on the ultimate strength at the component level while neglecting the global safety of structures. Additionally, it tends to neglect the time-variant characteristic of structural resistance due to the corrosion and degradation of materials. Therefore, the time-dependent seismic reliability analysis framework was proposed at the global structural level based on an improved high-order moment method (HOMM). It directly addresses the objective failure probabilities at the global structural level and takes into account the resistance degradation of structures in the design reference period. A comparative analysis of the time-dependent seismic reliability between rocking cold-formed steel frames and rigid cold-formed steel frames is conducted, focusing on load-bearing capacity limit states and deformation capacity limit states. The investigation indicates that the differences between time-dependent and time-independent seismic reliability indexes are substantial. For cold-formed steel structures subjected to prolonged exposure to the corrosive environment, it is recommended to consider the time-dependent degradation of structures.

Strength reduction factor based on probabilistic analysis for hybrid reinforced concrete beams

The American Concrete Institute (ACI) developed ACI-318 and ACI-440 codes, providing design guidelines for concrete beams subject to flexure and reinforced with steel or Fiber-Reinforced Polymer (FRP) bars, respectively. Although using a hybrid reinforcing system that combines steel bars and FRP bars has gained significant attention, ACI codes have no design guidelines for this concept. The main objective of this study is to determine the appropriate strength reduction factor for hybrid steel/FRP RC beams (i.e., concrete beams reinforced with a hybrid system of FRP and steel bars) by conducting a comprehensive probabilistic analysis over a wide range of hybrid steel/FRP RC beams dataset. This factor is a crucial component of the design standards outlined by the American Concrete Institute (ACI). The reliability index of the beams dataset under consideration is determined within the framework of reliability analysis using the First Order Reliability Method (FORM). Furthermore, a sectional analysis is employed as a mechanical model initially verified using an experimental dataset of 95 specimens. This model is utilized to forecast the flexural capacity of beams.The study's findings indicate a substantial correlation between the strength reduction factor and the reinforcement and live-to-dead load ratios. For the objective of conservative design, a strength reduction factor of 0.65 is suggested.

Meta-model based sequential importance sampling method for structural reliability analysis under high dimensional small failure probability

Reliability analysis poses a significant challenge for complex structures with stringent reliability requirements. While Sequential Importance Sampling (SIS) and Subset Simulation (SUS) have proven highly effective in addressing high-dimensional problems with small failure probabilities, the computational burden of mechanical simulations remains substantial due to the time-consuming nature of numerical simulation processes. Consequently, this paper introduces a novel approach, denoted as AK-SIS, which combines SIS with Kriging metamodeling specifically designed to address computational challenges associated with small failure probabilities. The fundamental principle of this approach involves utilizing AK-MCS technology (Echard et al., 2011) [1] as a precursor to the SIS approach to initially generate metamodels. These metamodels are then employed in lieu of performance functions in subsequent steps, significantly reducing the number of function calls required to simulate complex engineering problems when applying SIS techniques directly. By inheriting the advantages of SIS, AK-SIS has demonstrated its suitability for reliability analysis in scenarios involving high-dimensional spaces and small fault probabilities. Furthermore, AK-SIS is not limited by the shape of the failure domain, eliminates the need to solve the design point, and is particularly well-suited for analyzing reliability in cases of discontinuous failure domains, multiple failure domains, as well as complex failure domains and rare events. The efficacy of AK-SIS is substantiated through rigorous evaluation encompassing nonlinear, high-dimensional examples, and an engineering application. These empirical validations collectively contribute to a robust methodological framework for reliability analysis of intricate structures characterized by stringent reliability requirements.

Seismic Reliability Analysis of an Excavation Slope Based on Direct Probability Integral Method

China, situated in the circum-Pacific seismic belt, experiences frequent seismic activity and faces diverse geological conditions, making structural stability of paramount importance, especially under seismic conditions. The majority of current earthquake generation methods do not consider the nonstationary nature of earthquakes. This paper introduces a spectral representation-random function model for generating nonstationary earthquakes, effectively simulating stochastic seismic ground motion. Furthermore, traditional slope stability analysis methods are deterministic and incapable of providing probabilistic assessments of slope instability. Therefore, this paper proposes a unified framework for static and dynamic structural reliability analysis based on the direct probability integration method, quantifying the impact of stochastic seismic ground motion on the dynamic reliability of slope stability. Finally, the proposed methods are applied to an excavation slope in Nanjing, using sliding displacement and safety factors as evaluation criteria to study the reliability of the slope under the influence of stochastic seismic events.

A reliability analysis and optimization method for a turbine shaft under combined high and low cycle fatigue loading

AbstractThe combined high and low cycle fatigue (CCF) loading condition and random uncertainty exert a considerable impact on the design of turbine shafts. To enhance the fatigue life and reliability, this research proposes a CCF reliability analysis and optimization method for turbine shafts. A CCF fatigue reliability analysis framework is established, which focuses on the quantification of CCF loading characteristics and random uncertainty. The consideration of CCF loading characteristics contain the loading frequency ratio of high cycle fatigue (HCF) to low cycle fatigue (LCF), the stress amplitude ratio of HCF to LCF, as well as their interaction. The consideration of random uncertainty contains material, geometry and load, and a surrogate model‐based method is introduced to improve the quantification efficiency. Through the validation by comparing with experimental data and traditional methods, the proposed method is with higher accuracy and efficiency. By integrating the proposed fatigue reliability analysis method with design optimization, optimal design values for the turbine shaft were identified. This method theoretically extends the shaft's CCF life and provides practical engineering guidance for its reliability analysis and design.

Seismic collaborative reliability analysis for a slope considering spatial variability base on optimized subset simulation

Seismic reliability analysis of actual slopes considering the spatial variability of soil materials is crucial. However, for the discretization of large-scale random fields, high-precision finite element analysis and analysis of small failure probability events, the random analysis of slopes under seismic loads is inefficient. To address this situation, this study proposes a collaborative reliability analysis framework based on the modified linear estimation method (MLEM) and optimized subset simulation (OSS). First, the random field of the uncertain parameters of the Jinping-I left bank slope model is efficiently discretized by the MLEM, and a sensitivity analysis is carried out. Then, considering the adoption of different degrees of cross-correlation of the sensitive random parameters, the OSS method is used to perform random finite element analysis on the coarse mesh model. Finally, the fine mesh samples are obtained according to the response conditioning method (RCM). The MLEM is used to ensure the consistency of the two sets of random fields, and the seismic failure probability and reliability index of the slope under different cross-correlation coefficients of uncertain parameters are obtained. The results suggest that the degree of cross-correlation of parameters has a great influence on the seismic reliability of the slope. Considering that the shear strength parameters of geotechnical materials are often negatively correlated, the fine analysis based on a fine model is necessary.

Metamodeling-based reliability analysis framework for activated sludge processes

The reliability of activated sludge processes will be adversely affected by alterations in wastewater production and pollutant loading foreseen due to population growth, urbanization, and climate change, as well as the tendency to amend environmental regulations to mandate stricter effluent quality standards to alleviate water pollution. Until now, there was no framework capable of effectively managing these multifaceted challenges in reliability analysis. Previous attempts conducted a low number of simulations leading to insufficient statistical significance to properly validate reliability quantification. A metamodeling-based reliability analysis framework for the activated sludge process is introduced to cope with alterations in wastewater production and pollutant loading, assesses the reliability under different effluent regulations, and leverages metamodels to conduct extensive simulation work, to estimate the reliability. All metamodels produced high-resolution results, enabling reliability estimation after 100 000 simulations. The framework effectively assessed the annual failure rates of various activated sludge facility designs under four regulations, demonstrating the impact of stricter effluent quality standards. Integrating metamodels for reliability analysis greatly lowers computational costs, making the framework a time and resource-efficient choice for quick decision-making in facility design.

Sustainable solar energy in urban areas: A novel framework for uncertainty, reliability, and 7E analysis

Nowadays, access to clean, reliable, and sustainable energy is essential for urban cities. Solar energy, a widely available renewable energy source (RES), is present in abundance throughout the world. Nonetheless, using this energy has challenges such as uncertainty and reliability. The present study proposes a novel two phase framework based on a multi-criteria analysis of solar plants in urban cities in terms of uncertainty and reliability to address this issue. In phase-1, solar plants were evaluated using multi criteria decision-making from technical, economic, environmental, social, political, and risk aspects based on Z-number theory. Different methods such as Z-EDAS, Z-TOPSIS, Z-ARAS, Z-COPRAS, Z-SAW, and Z-MABAC were used for robust assessment. In phase-2, a 10 MW solar plant was examined from seven indicators (energy, exergy, economic, environmental, energoeconomic, exergoeconomic, and enviroeconomic as 7E analysis). The 7E analysis showed the solar photovoltaic plant can generate annually 12.3 GWh of electricity, with an energy and exergy efficiency of 13.85 % and 14.9 %, respectively. Additionally, the Levelized cost of electricity (LCOE) was 57$/MWh. Furthermore, the proposed framework based on Z-number theory effectively consider uncertainty and reliability in solar site assessment in urban cities and can be used in future studies for RES and sustainable urban planning.

Cross-Scale Reliability Analysis Framework for LNG Storage Tanks Considering Concrete Material Uncertainty

The reliability of liquefied natural gas (LNG) storage tanks is an important factor that must be considered in their structural design. Concrete is a core component of LNG storage tanks, and the geometric uncertainty of concrete aggregate material has a significant impact on their reliability. However, owing to the significant size difference between the concrete aggregate compared to the LNG storage tank, structural analysis using an accurate finite element model that includes all the geometric characteristics of the aggregate incurs significant analytical costs. In particular, for reliability analysis requiring a large number of samples, the computational costs incurred by finite element models are infeasible. Therefore, a dual acceleration strategy based on the asymptotic homogenization method and surrogate model technology is proposed to improve the efficiency of LNG storage tank reliability analysis. In the cross-scale analysis of a LNG storage tank based on asymptotic homogenization, order reduction of the LNG storage tank analysis model was realized. Based on this, a surrogate model construction method with the aggregate fraction and mass moment as inputs was proposed to further accelerate the reliability analysis of LNG storage tanks. Subsequently, a Monte Carlo method was used to perform a reliability analysis of the LNG storage tank considering the uncertainty of the concrete aggregate geometry and distribution under the action of liquid weight and wind load. The analysis showed that the wind load has a significant influence on the safety of the design of the roof of a LNG storage tank. The directionality of the wind load has a significant impact on the distribution of the sample point response for reliability analysis and the failure mode of the LNG storage tank. Owing to the directionality of the wind load, the response distributions of the maximum displacement and maximum stress of LNG were more concentrated, and the reliability of the LNG storage tank decreased after considering the wind load. In particular, the stress reliability of the tank decreased by 5.86%. When only the liquid load was considered, the maximum displacement and stress exhibited asynchronous failure, and the two almost never occurred simultaneously. When the wind load was considered, the failure mode of the LNG storage tank was dominated by the maximum stress. Moreover, the numerical example also demonstrated that the degree of freedom involved in structural analysis, as well as the time of structural analysis can be significantly reduced. So, the proposed cross-scale analysis framework can significantly improve the efficiency of reliability analysis. The conclusions established in this study provide theoretical and methodological guidance for the reliable design of LNG storage tanks.

Selective transmit modeling framework of complex system reliability analysis considering failure correlation

To improve the efficiency and accuracy of complex system reliability analysis considering failure correlation, a selective transmit modeling framework (STMF) is proposed by integrating multi-stage selective modeling (MSM) strategy with multi-failure transmit modeling (MTM) architecture. In MSM, the modeling quality of multi-learner is discussed to establish the optimal functional relationship between multi-variable and multi-response by considering the suitability of modeling samples, and the fitting performance of copula functions is quantified to construct the optimal correlation model between multi-failure through distance measure. For MTM, the correlation sequence measurement structure of multiple modes is established to construct the joint reliability analysis model of complex structure by updating iteratively the margin distribution functions with the strongest correlation. Taking the turbine bladed disk as study object, the validation of the proposed STMF is verified by comparing with other methods. The analytical results of study case can be expressed as that (i) STMF holds the superior performance in modeling accuracy and time-consuming, at 2.6308 × 10-2 and 0.4638 s respectively; (ii) STMF also has the best property in simulation, separately at 2.2123 s in simulation efficiency and at 99.9899 % in simulation precision; (iii) the reliability 0.9876 of study case obtained by STMF is higher than the reliability 0.9855 that depends on the mutual independence assumption. The effort of this work is prominent to promote effectively the quantification of multi-failure correlation and the improvement of reliability analysis performance for complex systems.

A novel hybrid adaptive framework for support vector machine-based reliability analysis: A comparative study

This study presents an innovative hybrid Adaptive Support Vector Machine - Monte Carlo Simulation (ASVM-MCS) framework for reliability analysis in complex engineering structures. These structures often involve highly nonlinear implicit functions, making traditional gradient-based first or second order reliability algorithms and Monte Carlo Simulation (MCS) time-consuming. The application of surrogate models has proven effective in addressing computational challenges associated with a large number of simulations. Support Vector Machine (SVM), as an emerging machine learning method suitable for small-sample scenarios, offers a well-established theoretical foundation and presents an effective model substitution approach for reliability analysis in engineering structures. However, the existing literature lacks a comprehensive and thorough comparative analysis of SVM's hybrid adaptive modeling approach, encompassing initial sampling methods and learning functions, with regards to both computational efficiency and accuracy. Additionally, there is a gap in adaptive modeling methods capable of accommodating diverse types of input uncertainty, the nonlinearity of limit state functions, and various application scenarios. In response to these gaps, this article introduces the ASVM-MCS framework, which addresses these challenges by considering different types of input variables and various failure modes. Moreover, this study provides a comprehensive evaluation of the ASVM-MCS framework's performance, including its initial sampling methods and learning functions, across a range of application scenarios, such as scenarios involving only random variables, mixed variables, and the reliability of series-parallel systems.

Integrated reliability analysis procedure for spatially variable soil slopes using recursive FORM algorithm enhanced by importance sampling: Abaqus via Python implementations

ABSTRACT This paper proposes an efficient geotechnical reliability analysis framework that integrates the advantages of the first-order reliability method (FORM) and the Karhunen-Loève expansion (KL) to evaluate the reliability of spatially variable soil slopes. The improved Hasofer-Lind-Rackwitz-Fiessler (iHLRF) recursive algorithm is adopted to implement the FORM procedure when coupled with finite element codes for slope stability analysis, and the KL is used to reduce the dimension of random variables representing the soil random fields. To enhance the accuracy of the failure probability estimated by KL-iHLRF, the importance sampling (IS) is also conducted in this study, resulting in an innovative slope reliability analysis framework, KL-iHLRF-IS. It is found that although the FORM analysis by itself may not be able to confidently estimate the failure probability of spatially variable soil slopes because of the very high dimension of random variables and the strong nonlinearity of the limit state function, it provides useful information on the design point values for KL-iHLRF-IS to rapidly compute the failure probability. The efficiency of KL-iHLRF-IS for slope reliability analysis is illustrated by three example slope case studies. The proposed framework is particularly useful when fast yet accurate slope reliability analysis using the finite element method is needed.

Fault logic and data-driven model for operation reliability analysis of the flap deflection angle.

To effectively perform the reliability analysis of the flap deflection angle, the reliability analysis framework is developed by introducing fault logic and a data-driven model. Herein, the fault logic analysis is used to study the fault mechanism and filter out the characteristic fault parameters that can be used to collect input data for data-driven modelling; the data-driven modelling is employed to establish a reliability analysis model with a small amount of input data. Under this proposed framework, the improved dung beetle optimization algorithm for back propagation (IDBO-BP) method is developed to perform the reliability modelling of the flap deflection angle. To validate the effectiveness of the proposed framework, we study the fault logic of flap symmetry and establish a surrogate model of flap deflection based on the fault parameters and the IDBO-BP algorithm. According to the predicted results of the flap deflection angle, the reliability model based on the fault mechanism can reflect the actual flap motion. At the same time, the proposed IDBO-BP algorithm has excellent modelling and simulation property by comparing with other optimization algorithms. Thus, the efforts of this study provide a new solution to the problem of reliable analysis with uncertain fault parameters. This article is part of the theme issue 'Physics-informed machine learning and its structural integrity applications (Part 1)'.

Data-driven time-variant reliability assessment of bridge girders based on deep learning

This article presents a new data-driven reliability analysis framework through combining the sample convolution and interaction network (SCINet) with Bayesian probability recursion to predict the time-variant reliability of bridge girders. The structural response predicted by SCINet and the state parameter (i.e., the variance of normal distribution) estimated by Bayesian dynamic linear model (BDLM) are used to form the limit state function to predict time-variant reliability. The results with a practical bridge show that the proposed method can predict future structural responses and time-variant reliability more accurately than BDLM, long short-term memory (LSTM), and long- and short-term time-series network (LSTNet) methods.

A two-stage uncertainty quantification framework for reliability and sensitivity analysis of structures using the probability density evolution method integrated with the Fréchet-derivative-based method

In this work, a novel Fréchet-derivative-based global sensitivity analysis is incorporated into the probability density evolution method for the simultaneous reliability and sensitivity analysis of structures. The two methods are synthesized and realized under a two-stage uncertainty quantification framework. Fundamental and numerical algorithms of the method are described, which is validated by a benchmark problem with theoretical solutions. Then it is applied on studying stochastic seismic responses of a real-world reinforced concrete structure of 288 m high. Results demonstrate that the response characteristics of the structure will be greatly changed when both uncertainties from the ground motions and structural parameters are considered, e.g., the failure probability will be enlarged by 1∼2 orders of magnitude. Besides, contrary to the popular opinion that the uncertainty of structural parameters is trivial compared to that of parameters in the ground-motion model, the importance measures of the structural parameters can be greater than those of the parameters in the ground-motion model by a factor of 2. when the coupling effect of randomness and nonlinearity of structural materials becomes dramatic. Some issues to be further outlined are also discussed.