Mode-Pursuing Sampling Method Using Discriminative Coordinate Perturbation for High-Dimensional Expensive Black-Box Optimization

This article presents a novel mode-pursuing sampling method using discriminative coordinate perturbation (MPS-DCP) to further improve the convergence performance of solving high-dimensional, expensive, and black-box (HEB) problems. In MPS-DCP, a discriminative coordinate perturbation strategy is integrated into the original mode-pursuing sampling (MPS) framework for sequential sampling. During optimization, the importance of variables is defined by approximated global sensitivities, while the perturbation probabilities of variables are dynamically adjusted according to the number of optimization stalling iterations. Expensive points considering both optimality and space-filling property are selected from cheap points generated by perturbing the current best point, which balances between global exploration and local exploitation. The convergence property of MPS-DCP is theoretically analyzed. The performance of MPS-DCP is tested on several numerical benchmarks and compared with state-of-the-art metamodel-based design optimization methods for HEB problems. The results indicate that MPS-DCP generally outperforms the competitive methods regarding convergence and robustness performances. Finally, the proposed MPS-DCP is applied to a stepped cantilever beam design optimization problem and an all-electric satellite multidisciplinary design optimization (MDO) problem. The results demonstrate that MPS-DCP can find better feasible optima with the same or less computational cost than the competitive methods, which demonstrates its effectiveness and practicality in solving real-world engineering problems.

Perturbation Approach to Hydrodynamic Lubrication Theory

Three perturbation approaches that apply for regular hydrodynamic lubrication problems are discussed: a cross-film coordinate perturbation, an iterative scheme, and a regular perturbation in terms of the film aspect ratio. The methods are used to derive higher order terms for a driven corner flow with a Newtonian lubricant of constant properties. Reasons for preferring the regular perturbation scheme are presented, and this method is used to obtain the correct curvature correction in an infinitely long journal bearing. Criteria for identifying singular geometries in hydrodynamic lubrication are set fourth.

On asymptotic forms of reactive-diffusive runaway

Different aspects of reactive-diffusive runaway are discussed in this paper. It is shown that a wide range of reactive nonlinearities can be analysed in essentially the same way, leading to the conclusion that there appear to be only two distinct non-singular, self-similar or approximately self-similar forms of description for non-homogeneous blowup. These exactly self-similar and asymptotically self-similar descriptions have previously been recognized, but are examined here in some detail for many different types of nonlinearity using asymptotic and numerical techniques. It is confirmed that exactly self-similar descriptions only behave non-pathologically in fairly extreme, discrete cases that are very close to a reactive-diffusive (or steady-state) balance under three or more dimensions of symmetry. Quantitative identification of these cases indicates that they may be of dubious practical relevance. It is then shown that only one class of non-singular, asymptotically self-similar descriptions can be found using coordinate perturbation techniques. Resulting solutions are derived to a high asymptotic order and are found to reveal a fairly universal structure for symmetric blowup. A simple analysis reveals that non-symmetric blowup also fits in with this structure, at least to leading order.

Coordinate perturbation and multiple scale in gasdynamics

Usually, the application of the coordinate perturbation technique consists in transforming the equations to perturbed coordinates, and determining from the transformed equations the amount of coordinate straining appropriate to obtain a uniformly valid expansion. However, the transformed equations may become unwieldy with increasing order of the system, number of variables, and order of the approximation. There exists a much simpler way of applying the technique, which bypasses the transformed equations and provides the appropriate coordinate stretching by simple algebraic manipulations on the nonuniformly valid expansion obtained by straightforward expansion from the original equations. Interesting results are obtained by applying the procedure to two gasdynamical problems. In the first the flow field around a supersonic two-dimensional wing is determined up to third order, including a uniformly valid representation of the front shock shape, valid even when the shock does not start at the leading edge. The second problem concerns the oscillations in a closed tube following an arbitrary initial disturbance, both when the two ends are closed, and when one of the two ends contains an oscillating piston (the inviscid Chester problem). In both problems the uniformly valid expansions are substantially simpler than the non-uniformly valid. But most interesting is the result that the uniformly valid expansions cannot be obtained without supplementing the coordinate perturbation technique by the multiple scale technique.

Dynamics of Moving Gas Bubbles in Injection Cooling

This paper presents a study of the growth or collapse of a spherical gas bubble being injected into a quiescent liquid of different compositions. The influence of translatory bubble velocity is given particular attention. Consideration is given to the case in which the bubble dynamics is governed by heat and mass transfer between the bubble and the liquid. By approximating the flow around the bubble as irrotational, two asymptotic solutions, valid for small and large times, respectively, are obtained for the thermal boundary layer over the bubble through the use of a coordinate perturbation technique. The bubble behavior in the two time domains is satisfactorily joined at a certain time interval. It is disclosed that the transient bubble size, interfacial temperature, and interfacial gas composition are governed by four dimensionless parameters. Translatory bubble motion is shown to cause a significant increase in the growth rate, an effect also provided by an increase in the Jakob number. Experimental results are cited and a favorable comparison with the theory is obtained.