quasi-Monte Carlo Simulation Method Research Articles

Research on uncertainties in fuel centrifugal pump based on prediction and reconstruction of internal flow field

Geometric machining errors in the blade profile and variable operating conditions in the extreme operating environment are primary factors leading to the uncertainties in pump performance. This paper presents an analysis of uncertainties of fuel centrifugal pumps by modeling the geometry uncertainty in blade machining based on the Karhunen–Loève (KL) expansion and using a polynomial chaos expansion (PCE) model. First, the geometric uncertainty in the blade machining is described by the KL expansion in three sections and a stochastic simulation of the blade geometry is performed. Then, a PCE surrogate model is trained based on the least angle regression method and validated by the bootstrap method to quantify the uncertainties of performance indices. Finally, the influence mechanism and relative importance of each input uncertainty parameter are investigated using a quasi-Monte Carlo simulation method. The results show that the KL expansion of the blade profile uses the random vector perturbation superposition of three stream surface, achieving the dimensional reduction in the blade machining error. The PCE surrogate model, trained with a dataset of 3 × 106 sample points, exhibits excellent fit, and the R-squared and adjusted R-squared for head coefficient and efficiency are both above 80%. The variance of parameter control points of the reconstructed flow field is less than 0.002. The uncertainties in both operating conditions and parameters have an influence on the distribution of the global flow field, while the influence of the uncertainty in machining error on the global flow field mainly concentrates on the power-generating positions of the blade.

Calibration of a (6 + 3)-DOF kinematically redundant parallel mechanism based on hybrid identification algorithm and two-step compensation strategy

To improve both the absolute accuracy and pose repeatability of a (6 + 3)-DOF kinematically redundant parallel mechanism (KRPM), a novel kinematic calibration method based on hybrid identification algorithm and two-step compensation strategy is proposed. Firstly, the error model is established, and the joint clearances are treated equivalently. On this basis, the global sensitivity index (GSI) is introduced to analyze the influence of parameter errors. Secondly, the absolute accuracy and pose repeatability are evaluated with the quasi-Monte Carlo simulation method (QMCSM) and the three-dimensional ellipsoidal error probability method (ESEPM). Thirdly, a hybrid identification algorithm combining Levenberg-Marquardt (LM) algorithm and adaptive differential evolution (ADE) algorithm is proposed to ensure the identification speed and accuracy. Finally, the error compensation is carried out by two steps. The experimental results show that the absolute accuracy and pose repeatability of the KRPM are improved by at least 52.8 % and 12.5 % respectively based on the novel method.

Error modelling and motion reliability analysis of a multi-DOF redundant parallel mechanism with hybrid uncertainties

Accuracy is one of the most important properties of mechanisms. However, the inherent uncertainties will cause an error between the actual motion and the desired motion, leading to a motion reliability problem. The error model and motion reliability of a type of multi-DOF (degrees of freedom) redundant parallel mechanism (MDRPM) with hybrid uncertainties are studied. Firstly, the error model of the mechanism is established and verified. Then, the motion inside the joints is analyzed, and the joint clearance is regarded as an interval variable, while the other variables are treated as random variables. On this basis, a hybrid motion reliability method based on the quasi-Monte Carlo simulation method (QMCSM) is developed for a mechanism with hybrid uncertainties. Compared with the traditional simulation method, the amount of computation required by the QMCSM is significantly reduced, and it is more suitable for solving the large-scale motion reliability problem of the MDRPM. A numerical simulation and experiments are performed. The simulation results show that the feasibility and adaptability of the motion reliability method in this paper are different. The experimental results demonstrate that the error model is effective, so the motion reliability analysis based on the error model is reliable.

Time-dependent non-linear buckling of 3D CFST arch structures with hybrid random interval uncertainties

Limit point and bifurcation buckling loads are critical concerns in structural stability design. With the inevitable viscoelastic effects of creep and shrinkage in concrete, such critical buckling points may vary due to the time-dependent change of equilibrium configuration. Furthermore, the intrinsic uncertainty and natural randomness in the geometry and material characteristics would affect the structural stability performance significantly. The present study provides a new robust method, called the generalized Chebyshev surrogate model-based sampling approach, in assessing the time-dependent nonlinear buckling behaviour of 3D concrete-filled steel tubular (CFST) arch structures when both random and interval uncertainties are involved. In the proposed approach, the relationships between the uncertain parameters and the critical nonlinear limit and bifurcation buckling loads are formulated using Chebyshev surrogate model strategy combined with finite element method. The extreme bounds of the statistical features, including means, standard deviations, of the critical nonlinear buckling loads are furnished by using Monte Carlo method and Quasi Monte Carlo simulation method. Finally, the applicability and the validity of the proposed approach are illustrated with a series of numerical investigations.

Development of alternative stochastic frontier models for estimating time-space prism vertices

This paper develops alternative stochastic frontier models (ASFM) for estimating time-space prism vertices with different distributional assumptions for the inefficiency term that takes a non-negative value. The traditional stochastic frontier model (SFM) assumes that the inefficiency term follows a half-normal or exponential distribution. Under those assumptions, most travelers’ home departure/arrival time will be close to prism vertices, which is not necessarily consistent with actual travel behaviors. To avoid this potential problem, the ASFM adopt alternative distributions for the inefficiency term whose density values can decrease monotonously or vary non-monotonously. Quasi-Monte Carlo simulation method is employed to estimate the ASFM without closed-form likelihood expressions. Simulation experiment results show that SFM needs a substantially greater number of Halton draws for consistent estimators than a typical mixed logit model does. The ASFM are estimated based on the travel data of 1454 Shanghai commuters and 2964 Houston commuters. It is found that models with inefficiency term following a half-normal distribution tend to underestimate the origin vertex of morning prism and overestimate the terminal vertex of evening prism over 50 and 30 min for Shanghai and Houston samples, respectively. The empirical results show the importance of choosing an appropriate distributional assumption for the inefficiency term in the SFM for better understanding the relation between individuals’ departure/arrival time and time-space prism vertices. The SFM based on an appropriate distributional assumption can be applied in activity-based models for big cities to better reflect tighter temporal constraints on metropolitan residents and narrower time-space prisms for outdoor activity arrangement.

Simulation error in maximum likelihood estimation of discrete choice models

Maximum simulated likelihood is the preferred estimator of most researchers who deal with discrete choice. It allows estimation of models such as mixed multinomial logit (MXL), generalized multinomial logit, or hybrid choice models, which have now become the state-of-practice in the microeconometric analysis of discrete choice data. All these models require simulation-based solving of multidimensional integrals, which can lead to several numerical problems. In this study, we focus on one of these problems – utilizing from 100 to 1,000,000 draws, we investigate the extent of the simulation bias resulting from using several different types of draws: (1) pseudo random numbers, (2) modified Latin hypercube sampling, (3) randomized scrambled Halton sequence, and (4) randomized scrambled Sobol sequence. Each estimation is repeated up to 1 000 times. The simulations use several artificial datasets based on an MXL data generating process with different numbers of individuals (400, 800, 1 200), different numbers of choice tasks per respondent (4, 8, 12), different number of attributes (5, 10), and different experimental designs (D-optimal, D-efficient for the MNL and D-efficient for the MXL model). Our large-scale simulation study allows for comparisons and drawing conclusions with respect to (1) how efficient different types of quasi Monte Carlo simulation methods are and (2) how many draws one should use to make sure the results are of “satisfying” quality – under different experimental conditions. Our study is the first to date to offer such a comprehensive comparison. Overall, we find that the number of the best-performing Sobol draws required for the desired precision exceeds 2 000 in some of the 5-attribute settings, and 20,000 in the case of some 10-attribute settings considered.

A Modified Nataf Transformation-based Extended Quasi-Monte Carlo Simulation Method for Solving Probabilistic Load Flow

Compared to conventional probabilistic load flow analysis, the extended probabilistic load flow can be stopped by itself when the error restriction satisfied, which is more suitable in practical use. Since the power flow results already obtained can be retained, the computational burdens of extended probabilistic load flow largely depend on the extension of samples. Much of the literature suggests that the quasi-Monte Carlo simulation method is more efficient than Latin hypercube sampling. In this article, the extended technique for quasi-Monte Carlo simulation is proposed. After that, spline reconstruction is utilized to modify the conventional Nataf transformation to obtain correlated samples by the first several orders of moments. Based on the above two techniques, a modified Nataf transformation-based extended quasi-Monte Carlo simulation method is proposed to solve probabilistic load flow problems. Compared to extended Latin hypercube sampling, the proposed method not only has higher computational efficiency but can also extend the samples by arbitrary steps. The results also show that both temporal and spatial correlations can be managed by the proposed method.

Dynamic analysis and reliability assessment of structures with uncertain-but-bounded parameters under stochastic process excitations

This paper presents the non-deterministic dynamic analysis and reliability assessment of structures with uncertain-but-bounded parameters under stochastic process excitations. Random ground acceleration from earthquake motion is adopted to illustrate the stochastic process force. The exact change ranges of natural frequencies, random vibration displacement and stress responses of structures are investigated under the interval analysis framework. Formulations for structural reliability are developed considering the safe boundary and structural random vibration responses as interval parameters. An improved particle swarm optimization algorithm, namely randomised lower sequence initialized high-order nonlinear particle swarm optimization algorithm, is employed to capture the better bounds of structural dynamic characteristics, random vibration responses and reliability. Three numerical examples are used to demonstrate the presented method for interval random vibration analysis and reliability assessment of structures. The accuracy of the results obtained by the presented method is verified by the randomised Quasi-Monte Carlo simulation method (QMCSM) and direct Monte Carlo simulation method (MCSM).

Seismic Reliability Analysis of Wood Shear Walls Using Different Methods

AbstractSeismic reliability analysis of wood structures has to take into consideration the uncertainties from many sources. This paper presented three methods to deal with the uncertainties from ground motion records, intensity measure, and resistance. The application of the methods in analyzing wood shear walls was also discussed. The traditional method calculates the exceeding probability of drift demand from conditional distributions given intensity levels. The second method determines the exceeding probability of drift demand from conditional distributions given ground motion records. The second method is computationally efficient and relatively accurate by using the mean of conditional exceeding probabilities. The third method is the quasi-Monte Carlo simulation method. Sequence numbers can be used to improve the efficiency of simulation analysis. These methods were used to analyze three wood shear walls. The shear wall model is a mechanics-based nail analogue with parameters validated by test result...

Path-Dependent Options Pricing: A Quasi Monte Carlo Simulation Approach with MATLAB

This paper presents a tailor-made discrete-time simulation model for valuing path-dependent options, such as lookback option, barrier option and Asian option. In the context of a real-life application that is interest to many students, we illustrate the option pricing by using Quasi Monte Carlo simulation methods. We give an Asian option pricing which relies heavily on the underlying asset path as a case study with the implementation of MATLAB code.

Time Series Simulation with Quasi Monte Carlo Methods

This paper compares quasi Monte Carlo methods, in particular so-called (t, m, s)-nets, with classical Monte Carlo approaches for simulating econometric time-series models. Quasi Monte Carlo methods have found successful application in many fields, such as physics, image processing, and the evaluation of finance derivatives. However, they are rarely used in econometrics. Here, we apply both traditional and quasi Monte Carlo simulation methods to time-series models that typically arise in macroeconometrics. The numerical experiments demonstrate that quasi Monte Carlo methods outperform traditional ones for all models we investigate.

Random polar sampling technique for the reliability analysis of submarine pressure hull

Reliability analysis is essential to reduce the structural system failures to an acceptance level. In this paper, a quasi-Monte Carlo Simulation method called ‘Random Polar Sampling Technique' (RPST) has been described for the reliability analysis of ring stiffened shell structure, in which the combinations of variates are obtained using a polar sampling of Latin hypercube sampled values. An efficient computer program coded in C++ has been developed for use with the RPST. Reliability analysis of internally ring stiffened submarine pressure hull has been described as an illustration and the results are compared with those given by First Order Second Moment method (FOSM), Advanced First Order Second Moment method (AFOSM) and Monte-Carlo Simulation methods. Keywords: Random Polar Sampling Technique, Reliability, Ring stiffened shells, Submarine pressure hull, Latin Hypercube Samples.  doi: 10.3329/jname.v1i1.2036 Journal of Naval Architecture and Marine Engineering 1(2004) 26-34