Two of the primary and well-known HDMR-based methods are univariate dimension reduction (UDR) and bivariate dimension reduction (BDR), which get their names on the basis of whether the performance function is decomposed into first- or second-order component functions. Numerical experiments showed that HDMR-based methods are promising for simulation-based design of high-dimensional systems. HDMR was initially applied for efficient multivariate representations in chemical system modeling. In most practical applications, the response of an engineered system can be largely determined by the low-order interactions among the input variables, which makes HDMR an attractive option in these applications. The HDMR-based methods simplify the construction of the surrogate model by decomposing a high-dimensional performance function into several low-dimensional functions (or low-order component functions). The performance of the proposed method is tested through three mathematical examples and a real world problem, the results of which suggest that the method can achieve an accurate and computationally efficient estimation of reliability even when the performance function exhibits high dimensionality, high nonlinearity, and strong interactions among variables. The HDRA method has three advantages: (i) alleviating the curse of dimensionality and adaptively detecting important dimensions (ii) capturing the interactive effects among variables on the performance function and (iii) flexibility in choosing the locations of sample points. Then, the sequential explorationвЂ“exploitation with dynamic trade-off (SEEDT) method is utilized to locally refine the surrogate model by identifying additional sample points that are close to the critical region (i.e., the limit-state function (LSF)) with high prediction uncertainty. HDRA first employs the adaptive univariate dimension reduction (AUDR) method to construct a global surrogate model by adaptively tracking the important dimensions or regions. In this paper, we tackle this problem by proposing a new method, high-dimensional reliability analysis (HDRA), in which a surrogate model is built to approximate a performance function that is high dimensional, computationally expensive, implicit, and unknown to the user. Reliability analysis involving high-dimensional, computationally expensive, highly nonlinear performance functions is a notoriously challenging problem in simulation-based design under uncertainty.

Journal of Verification, Validation and Uncertainty Quantification.

Journal of Thermal Science and Engineering Applications.

Journal of Offshore Mechanics and Arctic Engineering.Journal of Nuclear Engineering and Radiation Science.Journal of Nondestructive Evaluation, Diagnostics and Prognostics of Engineering Systems.Journal of Nanotechnology in Engineering and Medicine.Journal of Micro and Nano-Manufacturing.Journal of Manufacturing Science and Engineering.Journal of Engineering Materials and Technology.Journal of Engineering for Sustainable Buildings and Cities.Journal of Engineering for Gas Turbines and Power.Journal of Engineering and Science in Medical Diagnostics and Therapy.Journal of Electrochemical Energy Conversion and Storage.Journal of Dynamic Systems, Measurement, and Control.Journal of Computing and Information Science in Engineering.Journal of Computational and Nonlinear Dynamics.

Journal of Autonomous Vehicles and Systems.

ASME Letters in Dynamic Systems and Control.ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part B: Mechanical Engineering.Mechanical Engineering Magazine Select Articles.High-dimensional covariance and precision matrix estimation.Each of the techniques listed under the previous heading can be used for this purpose, and are sometimes combined with ideas such as subsampling through Stability Selection. In addition to estimating the underlying parameter in regression models, another important topic is to seek to identify the non-zero coefficients, as these correspond to variables that are needed in a final model. The Fused lasso, which regularises the difference between nearby coefficients when the regression coefficients reflect spatial or temporal relationships, so as to enforce a piecewise constant structure.The Group Lasso, which allows predefined groups of covariates to be selected jointly.Illustration of the linear model in high-dimensions: a data set consists of a response vector Y в€€ R n regularisation of ridge regression to allow highly correlated covariates to be simultaneously selected with similar regression coefficients.

High dimensional data analysis methods