Shuxing Yang

Optimizing Latin hypercube design for sequential sampling of computer experiments

Space-filling and projective properties are desired features in the design of computer experiments to create global metamodels to replace expensive computer simulations in engineering design. The goal in this article is to develop an efficient and effective sequential Quasi-LHD (Latin Hypercube design) sampling method to maintain and balance the two aforementioned properties. The sequential sampling is formulated as an optimization problem, with the objective being the Maximin Distance, a space-filling criterion, and the constraints based on a set of pre-specified minimum one-dimensional distances to achieve the approximate one-dimensional projective property. Through comparative studies on sampling property and metamodel accuracy, the new approach is shown to outperform other sequential sampling methods for global metamodelling and is comparable to the one-stage sampling method while providing more flexibility in a sequential metamodelling procedure.

Stability Limits of Spinning Missiles with Attitude Autopilot

Cr = control moment derivative coefficient, 1=rad C = static moment derivative coefficient, 1=rad C _ = damping moment derivative coefficient, s=rad IP, IQ = roll and lateral moment of inertia, kg m kr = dynamic gain of servo system ks = gain of servo system k! = gain of rate feedback kz = gain of attitude feedback L = reference length, m ncy, ncz = control command along Oy4 and Oz4 Ox5y5z5 = nonspinning velocity coordinate q = dynamic pressure, N=m S = reference area, m Ts = reciprocal of natural frequency of servo system, s = roll angle, rad c = coupling angle of the servo system, rad d = total delay angle of the system, rad l = lead angle of the command, rad m = roll angle measured by feedback element, rad = nutation angle, rad 2, 1 = nutation angle on plane Ox5y5 and plane Ox5z5, rad # = pitch angle, rad s = damping ratio of servo system cz, cy = command of servo in nonspinning body coordinate, rad 1, 2 = control surface angle in nonspinning body coordinate, rad = time delay of control system, s = yaw angle, rad

Enhanced probabilistic analytical target cascading with application to multi-scale design

Probabilistic analytical target cascading (PATC) is an approach for multi-level multi-disciplinary design optimization under uncertainty. In the original PATC approach, only the mean and variance of each interrelated response and linking variable are matched in a multi-level hierarchy. The ignorance of response correlation introduces difficulties in finding optimal solutions especially when the covariance of interrelated responses has a significant impact. In this article, an enhanced PATC (EPATC) approach is proposed. In addition to matching the first two statistical moments, the covariance between the interrelated responses is also considered by applying a modified updating strategy for estimating the statistical performance of an upper-level subsystem. A mathematical example and a multi-scale design problem are used to demonstrate the effectiveness and efficiency of the proposed EPATC approach. This study shows that the EPATC approach outperforms the original PATC by providing more accurate optimal solutions.

A New Weighted Stochastic Response Surface Method for Uncertainty Propagation

Conventional stochastic response surface method (SRSM) based on polynomial chaos expansion (PCE) for uncertainty propagation treats every sample points equally during the regression process and may produce inaccurate coefficient estimations in PCE. A new weighted stochastic response surface method (WSRSM) to overcome such limitation by considering the sample probabilistic weights in regression is studied in this work. Techniques that associate sample probabilistic weights to different sampling approaches such as Gaussian Quadrature point (GQ), Monomial Cubature Rule (MCR) and Latin Hypercube Design (LHD) are developed. The proposed method is demonstrated by several mathematical and engineering examples. Results show that for various sampling techniques, WSRSM can consistently improve the accuracy of uncertainty propagation compared to the conventional SRSM without adding extra computational cost. Insights into the relative accuracy and efficiency of using various sampling techniques in implementation are provided.

A new probabilistic distribution matching PATC formulation using polynomial chaos expansion

In the existing probabilistic hierarchical optimization approaches, such as probabilistic analytical target cascading (PATC), all the stochastic interrelated responses are characterized only by the first two statistical moments. However, due to the high nonlinear relation between the inputs and outputs, the interrelated responses are not necessarily normally distributed. The existing approaches, therefore, may not accurately quantify the probabilistic characteristics of the interrelated responses, and would further prevent achieving the real optimal solution. To overcome this deficiency, a novel PATC approach, named PATC-PCE is developed. By employing the polynomial chaos expansion (PCE) technique, the entire distribution of interrelated response can be characterized by a PCE coefficients vector, and then matched and propagated in the hierarchy. Comparative studies show that PATC-PCE outperforms PATC in terms of yielding more accurate optimal solutions and fewer design cycles when the interrelated response are random non-normal quantities, while at a sacrifice of extra function evaluations.

Robust Hierarchical Multiscale Design Using PATC and PCE

Multiscale design for dealing with 2-scale material and product system is implemented by employing the probabilistic analytical target cascading (PATC) and polynomial chaos expansion (PCE) approaches in this paper. PATC allows design autonomy at each scale subsystem by formulating the multiscale design problem as a hierarchical structure. PCE ensures uncertainties to be propagated within and across each scale accurately and efficiently. In addition, correlation between the random inputs is also considered during uncertainty propagation. Comparative study on a multiscale bracket design problem shows that the results obtained by our strategy are very close to the reference values. It is demonstrated that PATC and PCE are effective and applicable on multiscale design.

A New Sparse Grid Based Method for Uncertainty Propagation

Current methods for uncertainty propagation suffer from their limitations in providing accurate and efficient solutions to high-dimension problems with interactions of random variables. The sparse grid technique, originally invented for numerical integration and interpolation, is extended to uncertainty propagation in this work to overcome the difficulty. The concept of Sparse Grid Numerical Integration (SGNI) is extended for estimating the first two moments of performance in robust design, while the Sparse Grid Interpolation (SGI) is employed to determine failure probability by interpolating the limit-state function at the Most Probable Point (MPP) in reliability analysis. The proposed methods are demonstrated by high-dimension mathematical examples with notable variate interactions and one multidisciplinary rocket design problem. Results show that the use of sparse grid methods works better than popular counterparts. Furthermore, the automatic sampling, special interpolation process, and dimension-adaptivity feature make SGI more flexible and efficient than using the uniform sample based metamodeling techniques.

Quasi-LHD Sequential Sampling Method for Computer Experiments

Space-filling and projective properties are desired features in design of computer experiments to create global metamodels to replace of expensive computer simulations in engineering design. Our goal in this paper is to develop an efficient and effective sequential Quasi-LHD (Latin Hypercube Design) sampling method to maintain and balance the two aforementioned properties. The sequential sampling is formulated as an optimization problem, with the objective being the Maximin distance, a space-filling criterion, and the constraints based on a set of pre-specified minimum one-dimensional distances to achieve the approximate one-dimensional projective (Quasi-LHD) property. Through comparative studies on sampling property and metamodel accuracy, the new approach is shown to outperform other sequential sampling methods for global metamodeling and is comparable to the one-stage sampling method while providing more flexibility in a sequential metamodeling procedure.