Importance Sampling Method Research Articles

AWK-TIS: An Improved AK-IS Based on Whale Optimization Algorithm and燭runcated Importance Sampling for Reliability Analysis

In this work, an improved active kriging method based on the AK-IS and truncated importance sampling (TIS) method is proposed to efficiently evaluate structural reliability. The novel method called AWK-TIS is inspired by AK-IS and RBF-GA previously published in the literature. The innovation of the AWK-TIS is that TIS is adopted to lessen the sample pool size significantly, and the whale optimization algorithm (WOA) is employed to acquire the optimal Kriging model and the most probable point (MPP). To verify the performance of the AWK-TIS method for structural reliability, four numerical cases which are utilized as benchmarks in literature and one real engineering problem about a jet van manipulate mechanism are tested. The results indicate the accuracy and efficiency of the proposed method.

Importance Sampling Method for Discrete Critical State Space

Importance Sampling Method for Discrete Critical State Space

Generative methods for sampling transition paths in molecular dynamics

Molecular systems often remain trapped for long times around some local minimum of the potential energy function, before switching to another one – a behavior known as metastability. Simulating transition paths linking one metastable state to another one is difficult by direct numerical methods. In view of the promises of machine learning techniques, we explore in this work two approaches to more efficiently generate transition paths: sampling methods based on generative models such as variational autoencoders, and importance sampling methods based on reinforcement learning.

Spatiotemporal Learning via Mixture Importance Gaussian Filtering With Sparse Regularization

This letter proposes a novel spatiotemporal learning model via mixture importance Gaussian filtering (MIGF). In the MIGF, we explore the causal mapping between the target's true parameters and the latest measurement, and present an approach for elegantly combining the deterministic Gaussian-Hermite integral with the stochastic importance sampling method. This formulation allows for the use of soft-constrained and sparse regularization to reduce the truncation error and improve the weight adaptivity. We also provide an effective causal invariant updating rule to learn the parameters of this constrained dynamic model with a convergence guarantee. Experimental results show that MIGF can effectively eliminate the constraint uncertainty for the constrained dynamics.

Bayes and Maximum Likelihood Estimation of Uncertainty Measure of the Inverse Weibull Distribution under Generalized Adaptive Progressive Hybrid Censoring

The inverse Weibull distribution (IWD) can be applied to a various situations, including applications in reliability and medicine. In a reliability and medicine test, it is generally known that the results of test units may not be recorded. Recently, the generalized adaptive progressive hybrid censoring (GAPHC) scheme was introduced. In this paper, therefore, we consider the classical estimators (maximum likelihood estimator (MLE) and maximum product spacings estimator (MPSE)) and Bayes estimators (BayEsts) of the uncertainty measure of the IWD under GAPHC scheme. We derive the BayEsts of the uncertainty measure based on flexible (symmetrical and asymmetrical) priors. Additionally, we derive the Bayes estimators using the Tierney and Kadane approximation (TiKa) and importance sampling methods. In particular, the importance sampling method is used to obtain the credible interval for the uncertainty measure of the IWD under the GAPHC scheme. To compare the proposed estimators (classical and BayEsts), the Monte Carlo simulation method is conducted. Finally, the real dataset based on GAPHC scheme is analyzed.

Reliability assessment of cyber-physical power systems considering the impact of predicted cyber vulnerabilities

This paper presents a reliability assessment technique for cyber-physical power systems (CPPSs) that incorporates cybersecurity issues by considering non-normal random variables with non-linear dependencies. Our model uses bidirectional encoder representations from transformers (BERTs) to predict the severity of cyber vulnerabilities by analyzing their textual description. This practical model allows the engineer to manually enter text that describes threats to predict the probability of cyber vulnerability. We use a Bayesian attack graph to simulate the attack paths and a Markov model to demonstrate the consequences of cyber attacks on the CPPS. Furthermore, a hybrid approximate-analytical approach is employed to assess the overall reliability of the CPPS when considering the load and wind generation uncertainties, given their non-linear dependencies. The proposed method is implemented on the modified IEEE Reliability Test System. The results demonstrate that the reliability indices for a simultaneous cyber attack on corporate networks and wind farm control centers are more significant than those obtained for other attack scenarios. The proposed prediction method is highly accurate, and the predicted vulnerability scores align with those provided by the National Vulnerability Database. The results are compared with sequential Monte Carlo simulation, subset simulation, and cross-entropy-based importance sampling methods. The comparison shows that the proposed method outperforms other methods in terms of convergence speed and accuracy.

Robust DRSS Based Localization in Sensor Networks With Generalized Gaussian Noise

This letter addresses the problem of robust differential received signal strength (DRSS) based localization in the presence of generalized Gaussian noise. Instead of transforming the nonlinear equation into a pseudo-linear equation, we develop a maximum likelihood (ML) estimator which is based on the unconstrained <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$l_{p}$ </tex-math></inline-formula> -norm optimization problem for highly nonlinear cost functions. A non-iterative Monte Carlo importance sampling (MCIS) method is proposed to solve the optimization problem. To obtain the global optimal solution using relatively a fair number of random particles, a robust <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$l_{1}$ </tex-math></inline-formula> -norm based estimator for initial position is developed by solving the linear programming problem. The MCIS- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$l_{1}$ </tex-math></inline-formula> method can yield a nearly unbiased estimate and avoid derivation or matrix multiplication operations compared to these algorithms that are based on pseudo-linear measurement equations. Simulation shows that the localization algorithm proposed in this letter achieves significant performance improvement in wireless sensor network localization with generalized Gaussian noise.

An adaptive artificial neural network for reliability analyses of complex engineering systems

Reliability analyses of engineering systems require methods capable of reducing the number of function calls and response variances to calculate the failure probability. This paper is aimed to employ a combination of the Monte Carlo simulation (MCS), artificial neural network (ANN) and control variate technique (CVT) to improve the efficiency and accuracy of the reliability analyses of various engineering systems. The ANN used in this paper is of the multilayer perceptron type. The paper uses the design of experiments (DoE), importance sampling and uniform sampling methods to generate the samples. The combination of the MCS, ANN model, DoEs, and CVT is used for the reliability analyses and significantly improved the results in terms of efficiency. Various numerical examples have shown the superiority of the improved ANN model using CVT in reducing the number of calls of the limit state function and revealed that the obtained results are not sensitive to the number of hidden layer neurons. The reduced number of required simulations and computation costs has enabled the proposed method to be applicable to reliability analyses in complex engineering systems such as structures made by functionally graded materials.

Vehicle-Following Control Based on Deep Reinforcement Learning

Intelligent vehicle-following control presents a great challenge in autonomous driving. In vehicle-intensive roads of city environments, frequent starting and stopping of vehicles is one of the important cause of front-end collision accidents. Therefore, this paper proposes a subsection proximal policy optimization method (Subsection-PPO), which divides the vehicle-following process into the start–stop and steady stages and provides control at different stages with two different actor networks. It improves security in the vehicle-following control using the proximal policy optimization algorithm. To improve the training efficiency and reduce the variance of advantage function, the weighted importance sampling method is employed instead of the importance sampling method to estimate the data distribution. Finally, based on the TORCS simulation engine, the advantages and robustness of the method in vehicle-following control is verified. The results show that compared with other deep learning learning, the Subsection-PPO algorithm has better algorithm efficiency and higher safety than PPO and DDPG in vehicle-following control.

On Subsampling Procedures for Support Vector Machines

Herein, theoretical results are presented to provide insights into the effectiveness of subsampling methods in reducing the amount of instances required in the training stage when applying support vector machines (SVMs) for classification in big data scenarios. Our main theorem states that under some conditions, there exists, with high probability, a feasible solution to the SVM problem for a randomly chosen training subsample, with the corresponding classifier as close as desired (in terms of classification error) to the classifier obtained from training with the complete dataset. The main theorem also reflects the curse of dimensionalityin that the assumptions made for the results are much more restrictive in large dimensions; thus, subsampling methods will perform better in lower dimensions. Additionally, we propose an importance sampling and bagging subsampling method that expands the nearest-neighbors ideas presented in previous work. Using different benchmark examples, the method proposed herein presents a faster solution to the SVM problem (without significant loss in accuracy) compared with the available state-of-the-art techniques.

RSS-based visible light positioning with unknown receiver tilting angle: robust design and experimental demonstration.

In this paper, we consider the received signal strength (RSS)-based indoor visible light positioning (VLP) with unknown receiving angle. A novel VLP scheme is proposed by joint estimation of the receiver coordinate and receiver characteristic vector. We equivalently convert the original estimation problem into the problem that maximizes the projection of the RSS vector on the column space spanned by the measurement matrix. The proposed scheme does not require the prior knowledge of receiving coefficient and receiving angle. To further reduce the computational complexity, we also propose an importance sampling (IS) method for solving the VLP problem. Simulation and experimental results demonstrate the robustness of the proposed scheme to the receiving coefficient and receiving angle. Specifically, experimental results show that the proposed VLP scheme achieves a stable positioning accuracy below 7 cm under different receiver tilting angles in a 60 cm × 60 cm × 150 cm space, and is not sensitive to height perturbation.

Rare event estimation with sequential directional importance sampling

In this paper, we propose a sequential directional importance sampling (SDIS) method for rare event estimation. SDIS expresses a small failure probability in terms of a sequence of auxiliary failure probabilities, defined by magnifying the input variability. The first probability in the sequence is estimated with Monte Carlo simulation in Cartesian coordinates, and all the subsequent ones are computed with directional importance sampling in polar coordinates. Samples from the directional importance sampling densities used to estimate the intermediate probabilities are drawn in a sequential manner through a resample-move scheme. The latter is conveniently performed in Cartesian coordinates and directional samples are obtained through a suitable transformation. For the move step, we discuss two Markov Chain Monte Carlo (MCMC) algorithms for application in low and high-dimensional problems. Finally, an adaptive choice of the parameters defining the intermediate failure probabilities is proposed and the resulting coefficient of variation of the failure probability estimate is analyzed. The proposed SDIS method is tested on five examples in various problem settings, which demonstrate that the method outperforms existing sequential sampling reliability methods.

Reliability Sensitivity Analysis by the Axis Orthogonal Importance Sampling Method Based on the Box-Muller Transformation

The axis orthogonal importance sampling method proves to be one version of efficient importance sampling methods since the quasi-Monte Carlo simulation is its basic ingredient, in which it is now a common practice to transform low-discrepancy sequences from the uniform distribution to the normal distribution by the well-known inverse transformation. As a valid transformation method for low-discrepancy sequences, the Box-Muller transformation is introduced into the axis orthogonal importance sampling method and compared with the inverse transformation in this paper for structural reliability sensitivity analysis. Three representative quasi-random sequences with low discrepancy are presented to generate samples following the target distribution and explore the interaction with the transformation method, which is used as a sample plan along the tangent plane at the most probable failure point in the axial orthogonal importance sampling for structural reliability analysis and reliability sensitivity analysis. The numerical experiments show that the reliability sensitivity analysis method by means of the Box-Muller transformation is a good alternative to the inverse transformation to generate samples from low-discrepancy sequences to the normal distribution. In particular, the scheme of the Box-Muller transformation combined with the Sobol sequence needs fewer samples with more accuracy and is more applicable for solving reliability sensitivity analysis in various nonlinear problems.

Estimating Tail Probabilities of Random Sums of Phase-Type Scale Mixture Random Variables

We consider the problem of estimating tail probabilities of random sums of scale mixture of phase-type distributions—a class of distributions corresponding to random variables which can be represented as a product of a non-negative but otherwise arbitrary random variable with a phase-type random variable. Our motivation arises from applications in risk, queueing problems for estimating ruin probabilities, and waiting time distributions, respectively. Mixtures of distributions are flexible models and can be exploited in modelling non-life insurance loss amounts. Classical rare-event simulation algorithms cannot be implemented in this setting because these methods typically rely on the availability of the cumulative distribution function or the moment generating function, but these are difficult to compute or are not even available for the class of scale mixture of phase-type distributions. The contributions of this paper are that we address these issues by proposing alternative simulation methods for estimating tail probabilities of random sums of scale mixture of phase-type distributions which combine importance sampling and conditional Monte Carlo methods, showing the efficiency of the proposed estimators for a wide class of scaling distributions, and validating the empirical performance of the suggested methods via numerical experimentation.

Computing quantum correlation functions by importance Sampling method based on path integrals

In this paper, an importance sampling method based on the Generalized Feynman–Kac (GFK) method has been used to calculate the mean values of quantum observables from quantum correlation functions for many-body systems with the Born–Oppenheimer approximation in the nonrelativistic limit both at zero and finite temperature. Specifically, the expectation values [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] for the ground state of the lithium and beryllium and the density matrix, the partition function, the internal energy and the specific heat of a system of quantum harmonic oscillators are computed, in good agreement with the best nonrelativistic values for these quantities. Although the initial results are encouraging, more experimentation will be needed to improve the other existing numerical results beyond chemical accuracies specially for the last two properties for lithium and beryllium. Also more work needs to be done to improve the trial functions for finite temperature calculations. Although these results look promising, more work needs to be done to achieve the spectroscopic accuracy at zero temperature and to estimate the finite temperature effects from the non-Born–Oppenheimer calculations. Also more experimentation will be needed to study the convergence criteria for the inverse properties for atoms at zero temperature.

An efficient Kriging model-based importance sampling method for estimating the failure probability-based parameter global sensitivity index with uncertain distribution parameters

The failure probability-based parameter global sensitivity index measures the importance of each uncertain distribution parameter on the uncertainty of failure probability. The crude Monte Carlo simulation for estimating the failure probability-based parameter global sensitivity index involves a complicated nested triple-loop process, and the huge amount of computational burden restricts the application of the failure probability-based parameter global sensitivity. For efficiently analyzing the failure probability-based parameter global sensitivity index, this paper proposes an efficient Kriging model-based importance sampling method. First, the standard normal auxiliary variables are inducted by using the equivalent probability transformation, in which the equivalent limit state function with respect to the uncertain distribution parameters and the standard normal auxiliary variables are constructed, so that the importance sampling samples of uncertain distribution parameters and the standard normal auxiliary variables can be generated based on the equivalent limit state function. Secondly, based on the importance sampling technique, the formula of single-loop method for estimating the failure probability-based parameter global sensitivity index is derived in which the importance sampling samples can be reused to obtain all uncertain distribution parameters' failure probability-based global sensitivity indices. Thirdly, the equivalent probability transformation is used again to transform the importance sampling samples in the high-dimensional space into the relatively low-dimensional input space, and the Kriging model of the original limit state function with relatively low-dimensional input space is adaptively constructed to recognize the states (failure or safety) of all high-dimensional importance sampling samples. Then, the failure probability-based parameter global sensitivity indices can be efficiently estimated. The results of three case studies verify the accuracy and efficiency of the proposed method.

A Kriging-based important region sampling method for efficient reliability analysis

ABSTRACT Reliability analysis methods such as active learning Kriging surrogate model combined with simulation-based methods have been paid much attention in recent years. These techniques can reduce the computational cost to a certain extent. However, the computational burden may still be heavy for complex engineering problems. To address these issues, a Kriging-based important region sampling method is proposed for efficient reliability analysis. The new method is an improvement on the original active learning reliability method combining Kriging and Monte Carlo simulation (AK-MCS), and three strategies are developed to enhance the original method: 1) a new strategy, which is called the key point method, is utilized to define the initial design of experiment (DoE) instead of the Latin hypercube sampling; 2) the concept of dynamic important region/uncertain region and importance factor is proposed to avoid adding useless sample points to the DoE, which have little effect on the accuracy improvement of the Kriging model; 3) the redundant region is introduced to make the distance between the new and existed sample points be larger than a certain value and avoid the information redundancy caused by too close sample points. Five examples are utilized to demonstrate the efficiency and accuracy of this new method.

A novel approach for multi‐output structural system reliability problem with small failure probability

AbstractThe multi‐output structural system with implicit function widely exists in actual engineering, which refers that the multiple output responses of structural system can be obtained by one experiment or finite element simulation. Considering the correlation of multiple output responses and the small failure probability involved in multi‐output structural system, this article proposes a novel active learning Kriging (ALK) based reliability method for multi‐output structural system by combining multiple response Gaussian process (MRGP) and importance sampling (IS). First, due to the Kriging model can only construct the surrogate model under the single‐output variable, the MRGP model is introduced to substitute the Kriging model and thus the correlation in multiple output responses can be efficiently described by a correlation matrix in MRGP model. Second, for the case that the distance information of new iterated sample point is not considered by the commonly used learning functions (U‐function, EFF‐function and H‐function) in ALK, three improved learning functions are correspondingly proposed. Finally, aiming at the problem that the small failure probability leads to the increasing of candidate sample pool and further results in low computational efficiency, the IS method is combined with the MRGP model to efficiently accomplish the reliability analysis for multi‐output structural system. Several examples are also provided to demonstrate the effectiveness of the proposed method.

AK-HMC-IS: A Novel Importance Sampling Method for Efficient Reliability Analysis Based on Active Kriging and Hybrid Monte Carlo Algorithm

Abstract Sampling methods are powerful tools for structural reliability analysis with complex failure domains due to their stability and accuracy. One of the most frequently used sampling methods is the importance sampling (IS) method, which can markedly reduce the sampling variance and computational costs. The pivotal problem in IS method is the determination of the IS probability density function (ISPDF), which influences the accuracy and efficiency of reliability analysis greatly. This study proposes an effective method for constructing the ISPDF, combining the hybrid Monte Carlo algorithm (HMC) with the Gaussian mixture model. The HMC is superior to the common Markov chain Monte Carlo algorithm in convergence, which is helpful in improving sampling efficiency. Our ISPDF is generated adaptively and does not require the most probable failure point (MPFP); therefore, it can also work well for multiple MPFPs and high-nonlinear problems. To release the computational burden further, the performance function is replaced with the Kriging model, and the well-known U criterion is used for its refinement. In the proposed method, the process of the refinement of the Kriging model is coupled with the HMC sampling for constructing the ISPDF, which is the difference between some common methods; thus, no samples are vain. We verify the proposed method using three classical numerical examples and one practical engineering problem. Results show that the proposed method is accurate and superior to common IS methods in efficiency.

Sequential Reliability Analysis for the Adjusting Mechanism of Tail Nozzle Considering Wear Degradation

The adjusting mechanism is an important part of an aero engine, and the wear degradation of clearance is widely present in its hinges. In this work, an adjusting mechanism with hinge clearance is analyzed by dynamic simulation and the wear depth is predicted precisely using a wear model. Based on that, a sequential reliability analysis of motion accuracy is carried out. In order to avoid the expensive computational cost of simulation, the adaptive radial-based importance sampling method combined with the adaptive Kriging model (AK-ARBIS) is employed, which describes the decrease of reliability in the standard normal space sphere by sphere with the updated Kriging model. To further utilize the information about each state of wear degradation, the advanced AK-ARBIS method is investigated. Through analytical examples of two typical mechanisms and the engineering application of the adjustment mechanism, the results show that the calculation cost of the sequential reliability analysis under different states can be effectively reduced.