Full-Space Response Surface Method for Analysis of Structural Reliability

In order to improve the computational efficiency of the response surface method (RSM) in analysis of structural reliability, a full-space response surface method (FRSM) is presented in this paper. First, a vector-type response surface is developed by expanding the stochastic nodal displacement vector along the Krylov basis vectors defined by the global stiffness matrix and the force vector. Then the effective collocation points are picked out of the candidate ones according to the linear independence of the combining row vector. Finally, the unknown coefficients of the proposed response surface are determined by means of the regression analysis. Examples show that the proposed FRSM requires much fewer effective collocation points and less times of finite element analysis, achieving much higher computational efficiency by comparing with the traditional RSM.

Disanalogies Between Physical Space and Metaphoric Musical Space: Response to Jonathan Still’s Essay

Jonathan Still&rsquo;s exploration of differences in how dancers and musicians experience and conceptualize beats, rhythm, and meter raises issues that scholars interested in these temporal components of music ought to consider, particularly with respect to the relationship between embodiment, physical gravity, and the notion of &ldquo;musical gravity.&rdquo; This response offers a brief explanation of how the musicians&rsquo; concept of <em>downbeat</em> is motivated by a different reasoning than that which motivates a sense of melodic &ldquo;gravity.&rdquo; It also extends another issue raised by Still concerning the range in the degree of congruence, across various kinds of dancing, between dancers&rsquo; steps and musical rhythm and meter.

A Numerical Method for Solving Bilevel Optimization Based on Moving Space Response Surface

Bilevel programming has great significance in the field of engineering optimization, but for the particularity of the model it is difficult to solve. A numerical method for solving the bilevel programming has variable range constraints only in upper-level model based on Moving Space Response Surface Fitting Optimum Solution Function (MRFOM) is proposed in this paper. Some bilevel programming for the engineering optimization is hard to solve by mathematical method because the lower-level function expressions are hard to get because the lower-level optimizations are performed by specialty optimization software. MRFOM is specially applicable for this condition. Result shows that it has a good computing effect for the application of engineering optimization.