21.4.1. Background
L.A. Schmit in 1960 was the first to offer a comprehensive statement of the use of numerical optimization techniques to solve the nonlinear-inequality-constrained problem of designing elastic structures under a multiplicity of loading conditions. This work is significant, not only in that it ushered in an era of structural optimization, but also because it offered a new philosophy of engineering design which is only now beginning to be broadly applied.
In 1970 and 1980, design sensitivity analysis methodologies and gradient-based-approximation techniques were rapidly developed in the context of linear FEM process. All these researches contributed the popularization of structural optimization. Today, most of linear FEM software has its’ design optimization modules.
Figure 21.137 Role of design sensitivity and gradient based approximation
Recently, industrial design requires the validation of multi-body dynamics, non-linear FE analysis, and test etc. However, the conventional DSA based approaches cannot be used in these disciplinary. Multi-body dynamics and non-linear FE analysis is very complicated. Thus, their design sensitivity analysis process can be very tedious and difficult. What is worse is that their analysis results can have meanings after low pass filtering process. This represents that analytical design sensitivity is impossible in these areas.
Unlike CAE (computer-aided-engineering) areas, test areas have used DOE (Design of Experiments) methodologies to improve their performances. This classical DOE methods have developed in 1920 ~ #. Fisher first introduced ANOVA to validate the effect analysis result. Box used RSM concept to estimate the performance at the untried points. Since the mid of 1970s, several researches tried to combine the classical DOE methodologies with numerical optimization techniques. Among them, RSM (Response Surface Model), based on CCD and BBD, widely used in their researches.
Figure 21.138 New design approach for MBD and Nonlinear FEM
In the late of 1980s, Bayesian type meta-modeling techniques are newly introduced to overcome the lack of accuracy in the classical RSM. Among them, DACE (Design and Analysis of Computer Experiments), an automation of Kriging method, come into spot the light in the CAE areas. Recently, the RBF (Radial Basis Function) methods are tried to overcome the computational burden of DACE (or Kriging) method in the large scaled model construction.
As meta-model techniques are changed from RSM into Bayesian types, the experimental design methods are newly studied. RSM is a polynomial-type fitting model but Bayesian model is a non-polynomial type interpolation model. Hence, the classical DOE method such as CCD, BBD and alphabetic optimality design (D-optimal design etc.) are not adequate to Bayesian model. All the classical DOE for RSM made much of the rotatibility of samplings to minimize the variance of unknown coefficient vector. However, the Bayesian models require good space filling sampling to cover all design range. In the late of 1970, Mckay and Beckman first introduced a Latin Hypercube design for efficient space filling sampling. Since their approach, many methods have studied for more efficient space filling.
Reference
Schmit, L.A., “Structural Synthesis - Its Genesis and Development”, AIAA Journal, Vol. 19, Oct. 1981, pp. 1249-1263.
Vanderplaats, G.N., “Structural Optimization - Past, Present, and Future”, AIAA Journal, Vol. 20, No. 7, 1982, pp. 992-1000.
Barthelemy, J.-F., “Function Approximation”,(eds Kamat, M.P, Structural Optimization: Status and Promise), Progress in Astronautics and Aeronautics, AIAA,Vol 150, 1992, pp. 51-66
Fleury, C. and Duysinx, P., “Optimization Software: View from Europe”, ,(eds Kamat, M.P, Structural Optimization: Status and Promise), Progress in Astronautics and Aeronautics, AIAA,Vol 150, 1992, pp. 807-847.
Johnson, E.W., “Tools for Structural Optimization”, ,(eds Kamat, M.P, Structural Optimization: Status and Promise), Progress in Astronautics and Aeronautics, AIAA,Vol 150, 1992, pp. 851-862.
Healy, MJ., Kowalik, J.S., and Ransay, J.W., “Airplane Engine Selection by Optimization on Surface Fit Approximations”, Journal of Aircraft, Vol. 12, No. 7, July, 1974, pp. 593-599.
Hurst, T.N., Free,J.C., Brtce, G.R., and Parkinson, A.R., “A Comparison of Regression and Mechanistic Techniques for Estimating Design Sensitive in Solving Constrained, Nonlinear Optimization Problems”, Design Engineering Technical Conference, Columbus, Ohio, Oct. 5-8, 1986, Paper No 86-DET-40.
Free,J.W. etc, “Approximation of Computationally Expensive and Noisy Functions for Constrained Nonlinear Optimization”, Transaction of ASME, Journal of Mechanisms, Transmissions, and Automation in Design, Vol. 109, 1987, pp. 528-532.
Sacks, J., Welcj, W.J., Mitchell, T.J. and Wynn, H.P., “Design and Analysis of Computer Experiments”, Statistical Science, Vol. 4, No.4, 1989, pp. 409-435.
Mckay, M.D., Conover, W.J., and Beckman, R.J., “A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output From a Computer Code”, Technometrics, Vol. 21, pp. 239-245.
Stein, M., “Large Sample Properties of Simulations Using Latin Hypercube Sampling”, Technometrics, Vol. 29, No.2, 1987, pp. 143-151.
Haftka, R.T., Scott, E.P. and Cruz, J.R., “Optimization and Experiments: A Survey”, Applied Mechanics Review, Vol. 51, No. 7, 1998, pp. 435-448.
Simpson, T.W., Peplinski, J.D., Koch, P.N. and Allen, J.K., “Metamodels for Computer-Based Engineering Design: Survey and Recommendations”, Engineering with Computers, Vol. 17, 2001, pp. 129-150.
Saliby, E., “Descriptive Sampling: An Improvement over Latin Hypercube Sampling”, Proceedings of the 1997 Winter Simulation Conference (eds. S. Andradottir, K.J. Healy, D.H. Withers, and B.L. Nelson), pp. 230-233.