Enhanced high‐dimensional model representation for reliability analysis

Based on the high dimensional model representation (HDMR) and Monte Carlo simulation (MCS), this paper presents the improved method used to evaluate the failure probability of the system with multi-failure models. The HDMR is a general set of quantitative model assessment and analysis tools for capturing the high-dimensional relationships between sets of input and output model variables. Once the limit state function is defined by using the HDMR, the failure probability can be obtained by using the MCS without increasing computational efforts. The series and parallel system are considered in this paper, a numerical example is presented to demonstrate the efficiency and the accuracy of the proposed method. It is shown that the efficiency of the HDMR are both high in terms of series system and parallel system, the accuracy can be acceptable with respect to series system, and the accuracy can not be acceptable with respect to parallel system.

High Dimensional Model Representation (HDMR) method does not have the random data partitioning capability because of its nature. This paper focuses on how we can bring the random data partitioning feature to the HDMR method by virtue of the fluctuation free approximation method for the multivariate interpolation problems. The main aim of this work is to construct the universal fluctuation free matrix and to determine the best eigenvalues and the corresponding eigenvectors needed in our new method for partitioning the given multivariate random data through the HDMR method.

A comparative assessment of efficient uncertainty analysis techniques for environmental fate and transport models: application to the FACT model

A new engineering optimization approach using an adaptive metamodeling method is developed and studied. The adaptive metamodels are based on a high-dimensional model representation framework, and the high-dimensional model representation component functions are created using radial basis functions or augmented radial basis functions. The proposed optimization approach starts with an explicit first-order augmented radial basis function–high-dimensional model representation metamodel, before a numerical optimization algorithm is applied. In each subsequent iteration, an additional sample point is found, and a high-order high-dimensional model representation component function is created and added to the first-order augmented radial basis function–high-dimensional model representation metamodel. The accuracy of the augmented radial basis function–high-dimensional model representation metamodel is improved in an adaptive manner, especially in the neighborhood of the optimal design point. Several numerical examples are solved to demonstrate the method, including a practical three-dimensional reinforced concrete high-rise building structure. The proposed approach works well, and the convergence of the optimal solutions for each of the examples is obtained within a few adaptive iterations.

Availability of numerical model providing reliable estimation of the parameters of ablation processes induced by extreme ultraviolet laser pulses in the range of nanosecond and sub-picosecond timescales is highly desirable for recent experimental research as well as for practical purposes. Performance of the one-dimensional thermodynamic code (XUV-ABLATOR) in predicting the relationship of ablation rate and laser fluence is investigated for three reference materials: (i) silicon, (ii) fused silica and (iii) polymethyl methacrylate. The effect of pulse duration and different material properties on the model predictions is studied in the frame of this contribution for the conditions typical for two compact laser systems operating at 46.9 nm. Software implementation of the XUV-ABLATOR code including graphical user's interface and the set of tools for sensitivity analysis was developed. Global sensitivity analysis using high dimensional model representation in combination with quasi-random sampling was applied in order to identify the most critical input data as well as to explore the uncertainty range of model results.

This paper presents an efficient uncertain analysis method for estimating the bounds on the reliability of structural systems in the presence of mixed uncertain variables. The proposed method involves high dimensional model representation (HDMR) for the limit state function approximation, transformation technique to obtain the contribution of the fuzzy variables to the convolution integral and fast Fourier transform for solving the convolution integral. In the proposed method, efforts are required in evaluating conditional responses at a selected input determined by sample points, as compared to full scale simulation methods. Therefore, the proposed technique estimates the failure probability accurately with significantly less computational effort compared to the direct Monte Carlo simulation. The methodology developed is applicable for structural reliability estimation involving any number of fuzzy variables and random variables with any kind of distribution. The accuracy and efficiency of the proposed method is demonstrated through numerical examples.

Hydrate formation temperature (T) is an important parameter for any industrial process that deals with natural gas hydrates. In this study, the Group Method of Data Handling (GMDH) approach is used to predict hydrate formation T in natural gas binary mixtures. A comprehensive database containing 728 data samples is compiled from 46 published experimental works. To find the best combination of input variables, different sets of input variables were assessed. A total of seven models were developed using different sets of input variables. Compared to the correlations proposed in the literature, the developed models in this study performed better and the model developed based on input Set #7 was the most accurate: RMSE values of 1.6381 and 1.5499 for the training and testing datasets, respectively. All models also were evaluated using a blind dataset-that was not included in testing or training-to check model applicability to wider data. Similarly, all GMDH models performed excellently for the external dataset, where the developed model based on input Set #5 showed the best performance: RMSE values of 1.3482. The findings of this study contribute to our understanding of hydrate formation conditions in natural gas binary mixtures. As pure and binary mixtures of natural gas main constituents are studied, the results can be especially useful for purification and energy transport applications.

Digital weld quality assurance systems are increasingly used to capture local geometrical variations that can be detrimental for the fatigue strength of welded components. In this study, a method is proposed to determine the required scanning sampling resolution for proper fatigue assessment. Based on FE analysis of laser-scanned welded joints, fatigue failure probabilities are computed using a Weakest-link fatigue model with experimentally determined parameters. By down-sampling of the scanning data in the FE simulations, it is shown that the uncertainty and error in the fatigue failure probability prediction increases with decreased sampling resolution. The required sampling resolution is thereafter determined by setting an allowable error in the predicted failure probability. A sampling resolution of 200 to 250 μm has been shown to be adequate for the fatigue-loaded welded joints investigated in the current study. The resolution requirements can be directly incorporated in production for continuous quality assurance of welded structures. The proposed probabilistic model used to derive the resolution requirement accurately captures the experimental fatigue strength distribution, with a correlation coefficient of 0.9 between model and experimental failure probabilities. This work therefore brings novelty by deriving sampling resolution requirements based on the influence of stochastic topographical variations on the fatigue strength distribution.

The effects of vibration loads on the reliability of printed circuit boards is gaining importance due to the increasing use in vibration-intensive areas such as the drive train of electric cars. When assessing the reliability of electronic systems, it is important to consider not only the general probability of failures, but also their effects at the system level. Different failure modes present varying degrees of safety risk, which is taken into account in the design process through target values for failure probabilities. However, the occurrence probabilities of specific failure modes are currently assessed mainly qualitatively, or based on literature values and expert estimations. This work presents a simulation-based failure modes and effects analysis (FMEA) to estimate the probability of failure modes depending on external vibration loads. The simulation-based FMEA combines a numerical simulation, a lifetime model and a probabilistic FMEA. The key to reliable estimations of failure probabilities is the quantification of uncertainties that cause variations of the structural dynamic properties and thereby variations of local stresses on the electronic components. Therefore, Bayesian model updating is conducted to find probability distributions representing the scattering of selected parameters. The method is applied to a test printed circuit board and validated with experimental failure data.

Pressure pipeline is the key equipment of oil and gas resource transportation. The prediction technology of pipeline failure probability is a global challenge. However, the industrial field data are scattered and have a less amount, which cause a large prediction error, therefore cannot be applied to the actual production. So, this paper makes use of the advantage of support vector machine (SVM) that adapt to small-scale data, and combines with particle filter algorithm (PSO) to find the best SVM parameters, finally builds the probability prediction model of pressure pipeline failure based on PSO-SVM. In order to prove the effect of the proposed model, this paper uses the industrial field data of the pressure pipeline from the oil platform to verify the PSO-SVM model. The results show that the average relative error of the proposed failure probability prediction model is 3.58%, which proves the high accuracy of the PSO-SVM model.

This paper considers the impact of assumptions made when formulating analytic approaches to deterministic and probabilistic analyses of slope stability. The assumptions reviewed were presented in a paper, Waddell (2023) that presented semi-quantitative stability assessment using survey data, deterministic and probabilistic slope stability analyses of fill embankments constructed from residual soil and weathered bedrock in Western Sydney. A single variable fill strength was adopted, that was obtained from an Infinite Slope analysis assuming fully saturated fill. Rainfall records were used to predict risk of saturation to calculate annual probability of slope failure. The impacts of assumptions used to calculate the strength parameter, factor of safety and predicted failure probability are addressed in this paper. Saturation assumptions, the choice of limit equilibrium model, shape of the probability distribution functions, and spatial correlation of material properties are considered.

Two strongly NP-hard problems of clustering a finite set of points in Euclidean space are considered. In the first problem, given an input set, we need to find a cluster (i.e., a subset) of given size that minimizes the sum of the squared distances between the elements of this cluster and its centroid (geometric center). Every point outside this cluster is considered a singleton cluster. In the second problem, we need to partition a finite set into two clusters minimizing the sum, over both clusters, of weighted intracluster sums of the squared distances between the elements of the clusters and their centers. The center of one of the clusters is unknown and is determined as its centroid, while the center of the other cluster is set at some point of space (without loss of generality, at the origin). The weighting factors for both intracluster sums are the given cluster sizes. Parameterized randomized algorithms are presented for both problems. For given upper bounds on the relative error and the failure probability, the parameter value is defined for which both algorithms find approximation solutions in polynomial time. This running time is linear in the space dimension and the size of the input set. The conditions are found under which the algorithms are asymptotically exact and their time complexity is linear in the space dimension and quadratic in the input set size.

Fatigue life has to be considered in the design of many concrete structures at various stress levels and stress ratios. Many flexural fatigue test results of plain normal-weight concrete are available in the literature and almost every set of test results provides different fatigue equations. It is necessary, though, to have a common fatigue equation to predict the design fatigue life of concrete structures under flexural load with reasonable accuracy. Therefore, a database of flexural fatigue test results was created for concrete with strengths ranging from 25 to 65 MPa; this database was used to derive new fatigue equations (Wöhler fatigue equation and S-N power relationship) for predicting the flexural fatigue life of normal-weight concrete. The concept of equivalent fatigue life was introduced to obtain a fatigue equation using the same stress ratio. A probabilistic analysis was also carried out to develop flexural fatigue equations that incorporate failure probabilities.

Efficient methodology for the probabilistic safety assessment of high-speed railway bridges

Probabilistic methods predict response variations caused by a system’s random design parameters. While it is generally assumed that the parameter statistics are known absolutely, they are usually an estimate taken from a small sample. A sampling distribution is associated with the statistical estimate that quantifies its uncertainty and from which confidence intervals can be determined. The sampling distributions also lead to a distribution and confidence intervals for probabilistically predicted responses such as failure probability. Calculating the failure probability distribution is expensive because each sample can require a full Monte Carlo simulation. This work develops a failure probability approximation method to efficiently quantify the effect of design parameter sampling distributions on failure probability distributions and confidence bounds. First, Response Surface and Kriging approximations are used and then a new failure probability approximation approach is developed. The method is labeled Probabilistic Gradient Kriging (PGK), and is based on an augmented Kriging approach which uses both the function values and analytically calculated probabilistic sensitivities. Fatigue crack growth and a dynamic oscillator demonstration problem are used to compare the traditional response surface method, the Kriging approach, and the new PGK method. Results show that the PGK method can fit surfaces extremely well, reduce approximation error by an order of magnitude, and enable efficient design parameter sample statistic uncertainty propagation. It is also shown that the statistical estimates from small samples can cause large variations in failure probabilites that should be accounted for to ensure system reliability.