Multiple Random Inputs Research Articles

Comparison of the Point-Collocation Non-Intrusive Polynomial (NIPC) and Non-Intrusive Spectral Projection (NISP) Methods for the γ-Rθ Transition Model

In the present work, a comparative study of two major non-intrusive polynomial chaos methods, Point-Collocation Non-Intrusive Polynomial Chaos (NIPC) and Non-Intrusive Spectral Projection (NISP), was conducted for the transitional transitional model. Three multiple model coefficients, Ca2, Ce1, and Ce2 were considered with multiple random inputs with the assumption of uniform distributions with ±10% deviation. The target transitional flows were one around a flat plate and Aerospatiale A-airfoil. Deterministic solutions were obtained by employing the open source software OpenFOAM. The results of two methods were compared to the results of Monte Carlo simulation with 500 runs. The order convergence of the mean value and the standard deviation (STD) were compared in terms of the quantities of interest, drag and lift coefficients. Further, the most effective model coefficient for each transitional flow could be found through the calculation of the Sobol index.

Probabilistic fatigue damage assessment of coastal slender bridges under coupled dynamic loads

With coupled dynamic interactions of vehicle-bridge-wind-wave (VBWW) system, fatigue damage accumulations at complicated weldments of the orthotropic steel deck (OSD) for coastal slender bridges could be critical and might affect structural safety and reliability. Due to the stochastic nature of the environmental loadings including vehicles, wind and waves, it is challenging to include uncertainties for the assessment of the fatigue damage accumulations in the bridge’s life cycle. In the present study, an efficient probabilistic fatigue damage assessment framework for coastal slender bridges is proposed with a machine learning algorithm to include the coupled stochastic dynamic loads in the VBWW system. Firstly, stochastic load models are developed based on the long-term field measurements for realistic modeling of the truck load and the correlated wind and wave load, which serve as the input for the VBWW system to extract the stress time histories at critical structural details using multi-scale finite-element analysis (FEA). After calculating the equivalent stress range and the corresponding number of cycles using the rain-flow counting method, the daily equivalent fatigue damage is obtained using the linear fatigue damage rule. To reduce the calculation cost, a machine learning algorithm is utilized for probabilistic modeling of the daily equivalent fatigue damage by integrating uniform design and support vector regression to link the multiple random inputs of environmental loadings with the single output of the stress time history. The fatigue life of critical structural details, therefore, can be obtained using the established limit-state function with a target reliability index. A prototype cable-stayed bridge in a coastal region is presented to demonstrate the effectiveness of the proposed simulation framework. Finally, the impacts of the traffic growth including the traffic volume and the gross vehicle weight on the fatigue life of three welded joints are investigated and discussed, as well.

Uncertainty propagation of heat conduction problem with multiple random inputs

Uncertainty propagation analysis in engineering systems constitutes a significant challenge. To effectively solve the uncertain heat conduction problem with multiple random inputs, a random collocation method (RCM) and a modified random collocation method (MRCM) are established based on the spectral analysis theory. In both methods, the truncated high-order polynomial series is adopted to approximate the temperature responses with respect to random parameters, and the eventual probabilistic moments are derived by using the orthogonal relationship of polynomial bases. In the pivotal process of calculating the expansion coefficients, RCM evaluates the deterministic solutions directly on full tensor product grids, whereas the Smolyak sparse grids are reconstructed in MRCM to avoid the huge computational cost caused by high dimensions. Comparing the results with traditional Monte Carlo simulation, two numerical examples verify the remarkable accuracy and effectiveness of the proposed methods for random temperature field prediction in engineering.

Probabilistic collocation method for unconfined flow in heterogeneous media

In this study, we make use of the probabilistic collocation method in studying nonlinear flow in heterogeneous unconfined aquifers. In realistic problems there may exist multiple random inputs, nonlinearity, rainfall/evaporation, wells, nonstationary trends and complex boundary conditions. These complications may lead to strong spatial nonstationarity in the flow, which cannot be handled well with most existing approaches. In the present work, a general unconfined problem is explored with the probabilistic collocation method. The stochastic differential equation of flow is reduced into a set of deterministic equations that can be solved with the aid of existing deterministic solvers without any modification. Two types of random inputs are considered, which may be either perfectly correlated or uncorrelated. This approach is demonstrated through some synthetic cases in the presence of rainfall/evaporation, pumping/injection wells, composite mean conductivity fields. The approach can easily combine the proven techniques in deterministic simulations with stochastic treatments and thus provides a practical way for solving stochastic problems with complex fields of hydraulic parameters, nontrivial boundary conditions, and realistic sources/sinks.

A stochastic approach to nonlinear unconfined flow subject to multiple random fields

In this study, the KLME approach, a moment-equation approach based on the Karhunen–Loeve decomposition developed by Zhang and Lu (Comput Phys 194(2):773–794, 2004), is applied to unconfined flow with multiple random inputs. The log-transformed hydraulic conductivity F, the recharge R, the Dirichlet boundary condition H, and the Neumann boundary condition Q are assumed to be Gaussian random fields with known means and covariance functions. The F, R, H and Q are first decomposed into finite series in terms of Gaussian standard random variables by the Karhunen–Loeve expansion. The hydraulic head h is then represented by a perturbation expansion, and each term in the perturbation expansion is written as the products of unknown coefficients and Gaussian standard random variables obtained from the Karhunen–Loeve expansions. A series of deterministic partial differential equations are derived from the stochastic partial differential equations. The resulting equations for uncorrelated and perfectly correlated cases are developed. The equations can be solved sequentially from low to high order by the finite element method. We examine the accuracy of the KLME approach for the groundwater flow subject to uncorrelated or perfectly correlated random inputs and study the capability of the KLME method for predicting the head variance in the presence of various spatially variable parameters. It is shown that the proposed numerical model gives accurate results at a much smaller computational cost than the Monte Carlo simulation.

Determining the von Mises stress power spectral density for frequency domain fatigue analysis including out-of-phase stress components

This paper provides a new formula to take into account phase differences in the determination of an equivalent von Mises stress power spectral density (PSD) from multiple random inputs. The obtained von Mises PSD can subsequently be used for fatigue analysis. The formula was derived for use in the commercial vehicle business and was implemented in combination with Finite Element software to predict and analyse fatigue failure in the frequency domain.

Multiscaled randomness: A possible source of 1/f noise in biology.

We evaluate the possibility that the 1/f fluctuations observed in many biological time series result simply from the fact that biological processes have many inputs with differing time scales. We present a stochastic model whose output is the summation of multiple random inputs (i.e., different regulatory mechanisms). We derive the conditions under which the model reproduces the complex fluctuations and 1/f scaling observed in biological systems. Simulations demonstrate that if model parameters are unconstrained, the likelihood of generating 1/f noise is quite small. Thus, while the model can be used to generate 1/${\mathit{f}}^{\mathrm{\ensuremath{\beta}}}$ noise with various scaling exponents, it is unlikely that the 1/f behavior observed in many biological systems is due only to the fact that these systems are regulated by many different inputs acting on different time scales. \textcopyright{} 1996 The American Physical Society.

Spectral and bispectral analysis for single‐ and multiple‐input nonlinear phreatic aquifer systems

In general, stochastic partial differential equations and/or boundary conditions describing flow in phreatic aquifers are nonlinear. This paper uses second‐order perturbation to approximate the response of a phreatic aquifer system subject to multiple random inputs. The approach is equivalent to assuming quadratic nonlinearities in the original nonlinear phreatic aquifer system. Using frequency domain representations, the resulting model is decomposed into linear and nonlinear (quadratic) frequency response functions (FRF). For Gaussian input, the response of a nonlinear phreatic aquifer system is non‐Gaussian and is typically skewed. Thus the variance spectrum is insufficient to describe the response process. The bispectrum, defined as the Fourier transform of the third‐order cumulant sequence, represents the distribution of skewness with frequency and further serves as a measure of the nonlinearity of the system. Given input processes of aquifer recharge and stream stage fluctuations, the linear and quadratic FRF are used to construct the spectrum and bispectrum of the response process. The role of nonlinearity in a stream‐aquifer system is examined.