An Adaptive Framework for Uncertainty Quantification in the Material Point Method

A sample-efficient deep learning method for multivariate uncertainty qualification of acoustic–vibration interaction problems

This paper proposes an adaptive sparse polynomial chaos expansion(PCE)-based method to quantify the impacts of uncertainties on critical clearing time (CCT) that is an important index in transient stability analysis. The proposed method can not only give fast and accurate estimations for the probabilistic characteristics (e.g., mean, variance, probability density function) of the probabilistic CCT (PCCT), but also provides crucial information about the sensitivity of random inputs with respect to the variance of PCCT. Utilizing the sensitivity information, mitigation measures can be developed for transient stability enhancement. Numerical studies on the WSCC 9-bus system demonstrate the high accuracy and efficiency of the proposed method compared to the Monte Carlo simulation method. The provided sensitivity information and the effectiveness of mitigation measures in transient stability enhancement are also verified.

Sensitivity and reliability analysis of a globe valve using an adaptive sparse polynomial chaos expansion

Electric vehicle (EV) is the core part of future automobile technology, and safe and reliable wireless power transfer (WPT) technology is the key link to improve the intelligent driving technology of EV. In this paper, the uncertainty quantification method is proposed to guide the optimization design of WPT structure, so as to improve the efficiency of WPT. First this paper establishes a surrogate model of WPT efficiency based on the adaptive sparse polynomial chaos expansion, and the uncertainty of EVs WPT transmission efficiency is quantified, the computational efficiency is improved by about 8.4 times. Then the surrogate model is combined with the global sensitivity analysis method to quantify the impact of different variables in WPT on efficiency and screen out the variables with greater impact. Finally, this paper uses the improved marine predators algorithm to optimize the selected WPT system structure parameters. Considering the uncertainty, the average efficiency of the optimized WPT system is increased from 73.43% to 94.64%. Compared with other optimization methods, it proves that the method in this paper can optimize WPT more efficiently, and significantly improve the transmission efficiency.

Isogeometric dual reciprocity BEM for solving non-Fourier transient heat transfer problems in FGMs with uncertainty analysis

With large-scale wind farms integrated into power systems, the computational requirements for reliability evaluation of composite power systems are increasing. This paper introduces a new concept of dynamic orthogonal list, which is a form of multiple failure retrievals to avoid repeatedly calling the optimal power flow (OPF) program in the stage of state evaluation. An existing algorithm of cross-entropy (CE) method was developed to deal with the rare events in sampling. The major contribution of CE is to achieve convergence faster and reduce the number of samples, thus shortening the consuming time in the stage of sampling. This paper proposes a fast reliability evaluation process which combines the CE method with dynamic orthogonal list (CE-DOL), comprehensively improving the computational efficiency of Monte Carlo simulation (MCS). The proposed method is tested on a modified IEEE-RTS 79 system. In addition, for comparison purposes, the efficiencies of MCS, CE, and CE-DOL are estimated in the cases of different system adequacies. It is shown that, in range of certain reliability level, the proposed method is much more efficient compared with the CE method. Finally, the applicability of different methods is analyzed under different system reliability levels.

Variational variance reduction for particle transport eigenvalue calculations using Monte Carlo adjoint simulation

This paper proposes three new advanced techniques for engineering reliability analysis. These are computational tools that interface with the physical behavior model of the system and use the statistical information about the primitive random variables to estimate the reliability. Three types of strategies have been used for such computation: analytical methods, response surface methods, and Monte Carlo simulation. All three strategies are improved for efficiency and accuracy with the proposed techniques. In the case of analytical methods, a multiple linear approximation of the limit state is proposed for the reliability estimation of highly nonlinear problems. For problems with large computational models, response surface approximation may be expensive. An alternative approach based on the kriging technique is proposed to overcome this hurdle. Similarly, the efficiency of Monte Carlo simulation is greatly improved by the use of an adaptive importance sampling technique.

This study explores a hybrid method to enhance the efficiency of Monte Carlo simulations for European option pricing by incorporating neural network models. Traditional Monte Carlo Methods require high computational costs when dealing with high-dimensional financial derivatives due to the increased demand for simulation paths to achieve prediction accuracy. By integrating a feedforward neural network, this research aims to predict future price paths based on intermediate simulations, effectively reducing the number of paths while maintaining pricing accuracy. The proposed model employs residual block, regularization, early stopping, and other techniques to capture the nonlinear relationships between price paths and payoffs. Based on the trained model, the number of simulation paths required is successfully reduced from 10,000 to around 4,000 5,000 without significantly reducing prediction accuracy while achieving a balance in computation costs. The method exhibits stable predictive performance and computational efficiency, providing a potential solution for reducing the overhead of pricing complex financial derivatives. Future work could explore more advanced neural network architectures and hybrid with other techniques to further improve performance and efficiency.

Rare event simulation in the context of queueing networks has been an active area of research for more than two decades. A commonly used technique to increase the efficiency of Monte Carlo simulation is importance sampling. However, there are few rigorous results on the design of efficient or asymptotically optimal importance sampling schemes for queueing networks. Using a recently developed game/subsolution approach, we construct simple and efficient state-dependent importance sampling schemes for simulating buffer overflows in stable open Jackson networks. The sampling distributions do not depend on the particular event of interest, and hence overflow probabilities for different events can be estimated simultaneously. A by-product of the analysis is the identification of the minimizing trajectory for the calculus of variation problem that is associated with the sample-path large deviation rate function.

This chapter develops methods for increasing the efficiency of Monte Carlo simulation by reducing the variance of simulation estimates. These methods draw on two broad strategies for reducing variance: taking advantage of tractable features of a model to adjust or correct simulation outputs, and reducing the variability in simulation inputs. We discuss control variates, antithetic variates, stratified sampling, Latin hypercube sampling, moment matching methods, and importance sampling, and we illustrate these methods through examples. Two themes run through this chapter: The greatest gains in efficiency from variance reduction techniques result from exploiting specific features of a problem, rather than from generic applications of generic methods. Reducing simulation error is often at odds with convenient estimation of the simulation error itself; in order to supplement a reduced-variance estimator with a valid confidence interval, we sometimes need to sacrifice some of the potential variance reduction. KeywordsImportance SamplingVariance ReductionLatin Hypercube SamplingGeometric Brownian MotionUnderlying AssetThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Direct Simulation Monte Carlo (DSMC) solves the Boltzmann equation with large Knudsen number. The Boltzmann equation generally consists of three terms: the force term, the diffusion term and the collision term. While the first two terms of the Boltzmann equation can be discretized by numerical methods such as the finite volume method, the third term can be approximated by DSMC, and DSMC simulates the physical behaviors of gas molecules. However, because of the low sampling efficiency of Monte Carlo Simulation in DSMC, this part usually occupies large portion of computational costs to solve the Boltzmann equation. In this paper, by Markov Chain Monte Carlo (MCMC) and multicore programming, we develop Direct Simulation Multi-Chain Markov Chain Monte Carlo (DSMC3): a fast solver to calculate the numerical solution for the Boltzmann equation. Computational results show that DSMC3 is significantly faster than the conventional method DSMC.

Aiming at the low efficiency of Monte Carlo simulation in power system probability analysis. The paper will use layered important sampling technology in reliability evaluation. The system state space is divided into different levels of subspace according to the important degree and category of system components. It will calculate the optimal multipliers of failure probability in the different layers and optimize the important sampling function gradually. So the later algorithm will have more advantage .It avoids the degeneration phenomenon for conventional sampling in the higher reliability system. The paper compared the method of this paper whit other methods in IEEE-RTS79 and its modified system. The results show the method of this paper not only ensuring calculation accuracy but also improving the calculation speed and efficiency.

Stochastic dynamical response of a gear pair under filtered noise excitation

An evaluation of temporally adaptive transformation approaches for solving Richards' equation