Xiaoqian Chen

Concurrent Subspace Width Optimization Method for RBF Neural Network Modeling

Radial basis function neural networks (RBFNNs) are widely used in nonlinear function approximation. One of the challenges in RBFNN modeling is determining how to effectively optimize width parameters to improve approximation accuracy. To solve this problem, a width optimization method, concurrent subspace width optimization (CSWO), is proposed based on a decomposition and coordination strategy. This method decomposes the large-scale width optimization problem into several subspace optimization (SSO) problems, each of which has a single optimization variable and smaller training and validation data sets so as to greatly simplify optimization complexity. These SSOs can be solved concurrently, thus computational time can be effectively reduced. With top-level system coordination, the optimization of SSOs can converge to a consistent optimum, which is equivalent to the optimum of the original width optimization problem. The proposed method is tested with four mathematical examples and one practical engineering approximation problem. The results demonstrate the efficiency and robustness of CSWO in optimizing width parameters over the traditional width optimization methods.

A surrogate-based optimization method with RBF neural network enhanced by linear interpolation and hybrid infill strategy

In engineering, it is computationally prohibitive to directly employ costly models in optimization. Therefore, surrogate-based optimization is developed to replace the accurate models with cheap surrogates during optimization for efficiency. The two key issues of surrogate-based optimization are how to improve the surrogate accuracy by making the most of the available training samples, and how to sequentially augment the training set with certain infill strategy so as to gradually improve the surrogate accuracy and guarantee the convergence to the real global optimum of the accurate model. To address these two issues, a radial basis function neural network (RBFNN) based optimization method is proposed in this paper. First, a linear interpolation (LI) based RBFNN modelling method, LI-RBFNN, is developed, which can enhance the RBFNN accuracy by enforcing the gradient match between the surrogate and the trend observed from the training samples. Second, a hybrid infill strategy is proposed, which uses the surrogate prediction error based surrogate lower bound as the optimization objective to locate the promising region and meanwhile employs a linear interpolation-based sequential sampling approach to improve the surrogate accuracy globally. Finally, extensive tests are investigated and the effectiveness and efficiency of the proposed methods are demonstrated.

An enhanced unified uncertainty analysis approach based on first order reliability method with single-level optimization

Abstract In engineering, there exist both aleatory uncertainties due to the inherent variation of the physical system and its operational environment, and epistemic uncertainties due to lack of knowledge and which can be reduced with the collection of more data. To analyze the uncertain distribution of the system performance under both aleatory and epistemic uncertainties, combined probability and evidence theory can be employed to quantify the compound effects of the mixed uncertainties. The existing First Order Reliability Method (FORM) based Unified Uncertainty Analysis (UUA) approach nests the optimization based interval analysis in the improved Hasofer–Lind–Rackwitz–Fiessler (iHLRF) algorithm based Most Probable Point (MPP) searching procedure, which is computationally inhibitive for complex systems and may encounter convergence problem as well. Therefore, in this paper it is proposed to use general optimization solvers to search MPP in the outer loop and then reformulate the double-loop optimization problem into an equivalent single-level optimization (SLO) problem, so as to simplify the uncertainty analysis process, improve the robustness of the algorithm, and alleviate the computational complexity. The effectiveness and efficiency of the proposed method is demonstrated with two numerical examples and one practical satellite conceptual design problem.

A Fractionated Spacecraft System Assessment Tool Based on Lifecycle Simulation Under Uncertainty

To comprehensively assess fractionated spacecraft, an assessment tool is developed based on lifecycle simulation under uncertainty driven by modular evolutionary stochastic models. First, fractionated spacecraft nomenclature and architecture are clarified, and assessment criteria are analyzed. The mean and standard deviation of risk adjusted lifecycle cost and net present value (NPV) are defined as assessment metrics. Second, fractionated spacecraft sizing models are briefly described, followed by detailed discussion on risk adjusted lifecycle cost and NPV models. Third, uncertainty sources over fractionated spacecraft lifecycle are analyzed and modeled with probability theory. Then the chronological lifecycle simulation process is expounded, and simulation modules are developed with object oriented methodology to build up the assessment tool. The preceding uncertainty models are integrated in these simulation modules, hence the random object status can be simulated and evolve with lifecycle timeline. A case study to investigate the fractionated spacecraft for a hypothetical earth observation mission is carried out with the proposed assessment tool, and the results show that fractionation degree and launch manifest have great influence on cost and NPV, and generally fractionated spacecraft is more advanced than its monolithic counterpart under uncertainty effect. Finally, some conclusions are given and future research topics are highlighted.

Coordinate Transform Methods Used in Dynamic Simulation of Satellite Separation

Direction cosine matrix, Euler angles and quaternions are the common methods for translating vector equations into scalar equations. These methods used in separation simulation lack systematic discussion and comparison. This article is trying to present a proper coordinate transformation method for dynamic analysis of satellite separation. 321 and 123 rotations of Euler angles are proposed to construct the dynamic equations, which is different from simulation of missiles by the rotation of 321 and 231. Both Euler angles and quaternions are adopted to model the separation process of a small satellite that uses the helical compression springs mechanism. Feasibility and practicability of the approach are proved by comparing the simulation results, which are solved in MATLAB and ADAMS software platforms. It is concluded that the method of quaternions is more accurate and efficient in dynamic simulation of satellite separation.

Chance-Constrained Optimization Approach Based on Density Matching and Active Subspaces

Chance-constrained optimization has recently been receiving much attention from the engineering community. Uncertainties are being incorporated in increasingly large numbers to ensure reliability and robustness. However, the efficiency and accuracy of chance-constrained optimization under multiple uncertainties remains challenging. In this study, a constrained density-matching optimization methodology is established to address these pressing issues in chance-constrained optimization. The methodology employs an alternative objective metric between a designer-given target and system response, enables more uncertainties in design variables and random parameters to be handled, and accommodates multiple chance constraints with an adaptive penalty function. An active subspace identification strategy and a dynamic response surface are given to overcome the curse of uncertainty dimensionality and to guarantee sufficient samples for kernel density estimation in an uncertainty analysis. The efficacy is demonstrated...