APPLICATION OF STOCHASTIC APPROXIMATION IN TECHNICAL DESIGN

Engineers agree with the fact that uncertainty is an important issue to get a better model of real behavior. Uncertainty quantification techniques have been largely developed during the recent years; Stochastic and probabilistic collocation methods are clear examples of recent developments. This work is based on a more traditional uncertainty quantification method, as Monte-Carlo method and its extension to Latin Hypercube sampling techniques. Two definitions of the optimization problem have been analyzed. The first one is the called Stochastic procedure, while the second one is the Robust one. Both of them deal with uncertainty on the input parameters, but they manage the uncertainty effects from two different points of view. Applications to aerodynamics and aero-elastic problems have been described.

Ingenieria e Investigación

Stochastic approximation algorithms are alternative linear search methods for optimising control systems where the functional relationship between the response variable and the controllable factors in a process and its analytical model remain unknown. These algorithms have no criteria for selecting succession measurements ensuring convergence, meaning that, when implemented in practice, they may diverge with consequent waste of resources. The objective of this research was to determine industrial processes' optimum operating conditions by using a modified stochastic approximation algorithm, where its succession measurements were validated by obtaining response variable values for each iteration through simulation. The algorithm is presented in nine stages; its first six describe which are process independent and dependent variables, the type of experimental design selected, the experiments assigned and developed and the second order models obtained. The last three stages describe how the algorithm was developed, and the optimal values of the independent variables obtained. The algorithm was validated in 3 industrial processes which it was shown to be efficient for determining independent variables' optimum operating conditions (temperature and time): the first three iterations were obtained at 66°C in 3 hours 42 minutes for process 1, unlike processes 2 and 3 where the first iteration was obtained at 66°C in 6 hours 06 minutes and 80°C in 5 hours 06 minutes, respectively.

IEEE Transactions on Magnetics, 2001

The problem of obtaining sensitivity analysis information from optimization stochastic methods is addressed in this work. The sensitivity analysis calculation is obtained using the evaluations of the objective function as samples of the behavior of the objective function in the vicinity of the optimum. A linear optimization problem is formulated for the approximation of a contour surface of the objective function in the vicinity of the optimum. The formulation is applied to TEAM benchmark problems 25 and 22. The results, which are in good agreement with the literature, show the applicability of the formulation in practical optimization problems.

International conference KNOWLEDGE-BASED ORGANIZATION

This paper aims to analyze the stage reached in the development and application of stochastic optimization models, highlighting some of the most important moments and achievements in the field. The author tries to identify particular aspects that define the classes of stochastic optimization models, specifying the level reached in certain directions of research and implementation of these models in order to identify possible directions of development of these specific techniques.

2021

We consider steady-state production processes that have feasibility constraints and metrics of cost and throughput that are stochastic functions of process controls. We propose an efficient stochastic optimization algorithm for the problem of finding process controls that minimize the expectation of cost while satisfying deterministic feasibility constraints and stochastic steady state demand for the output product with a given high probability. The proposed algorithm is based on (1) a series of deterministic approximations to produce a candidate set of near-optimal control settings for the production process, and (2) stochastic simulations on the candidate set using optimal simulation budget allocation methods. We demonstrate the proposed algorithm on a use case of a real-world heat-sink production process that involves contract suppliers and manufacturers as well as unit manufacturing processes of shearing, milling, drilling, and machining, and conduct an experimental study that shows that the proposed algorithm significantly outperforms four popular simulation-based stochastic optimization algorithms.

In real case applications within the virtual prototyping process, it is not always possible to reduce the complexity of the physical models and to obtain numerical models which can be solved quickly. Usually, every single numerical simulation takes hours or even days. Although the progresses in numerical methods and high performance computing, in such cases, it is not possible to explore various model configu- rations, hence efficient surrogate models are required. The paper gives an overview about advanced methods of meta-modeling. In addition, some new aspects are introduced to impove the accuracy and predictability of surrogate models, commonly used in numerical models for automotive applications. Whereby, the main topic is reducing the neccessary number of design evaluations, e.g. finite element analysis within global variance-based sensitivity and robustness studies. In addition, the similar approach can be used to perform optimization and stochastic analysis and to create synt...

tucson.ars.ag.gov

Many engineering systems are affected by uncertainty in future demands or inputs. Decisions regarding their design, however, typically must be made in the present. Two-stage stochastic programming can consider this type of problem but, in the past, procedures to fully incorporate the uncertainty have come with a high computational cost.

Proceedings of the Winter Simulation Conference, 2002

In principle, known central limit theorems for stochastic approximation schemes permit the simulationist to provide confidence regions for both the optimum and optimizer of a stochastic optimization problem that is solved by means of such algorithms. Unfortunately, the covariance structure of the limiting normal distribution depends in a complex way on the problem data. In particular, the covariance matrix depends not only on variance constants but also on even more statistically challenging parameters (e.g. the Hessian of the objective function at the optimizer). In this paper, we describe an approach to producing such confidence regions that avoids the necessity of having to explicitly estimate the covariance structure of the limiting normal distribution. This procedure offers an easy way for the simulationist to provide confidence regions in the stochastic optimization setting.

2014

A large number of problems in manufacturing processes, production planning, finance and engineering design require an understanding of potential sources of variations and quantification of the effect of variations on product behavior and performance. Traditionally, in engineering problems uncertainties have been formulated only through coarse safety factors. Such methods often lead to overdesigned products. Different methods exist to describe model uncertainties and to calculate reliability and safety, but they all have a limited area of application. A new adaptive response surface method is introduced to analyse the design reliability with high accuracy and efficiency. Whereby the surrogate model is based on an improved moving least square approximation combined with an adaptive design of experiment. In order to obtain a fast simulation procedure on the response surface an adaptive importance sampling concept is used. Two numerical examples show the applicability of this concept fo...

FAST 2015 - 13th International Conference on Fast Sea Transportation, Washington DC, USA, 2015

Hull-form stochastic optimization methods are developed and evaluated for resistance reduction and operability increase, addressing stochastic sea state and operations. The cost/benefit analysis of the design-optimization procedure is presented, by comparison of four hierarchical problems, from stochastic most general to deterministic least general. The parent hull is a 100 m Delft catamaran, with geometrical constraints for maximum variation of length, beam, draft and displacement. Problem 1 is used as a benchmark for the evaluation of the other problems. It is as a multi-objective stochastic optimization for resistance and operability, considering stochastic sea state and speed, but limited to head waves. Problem 2 is a multi-objective stochastic optimization for resistance and motions at fixed sea state and speed. Problem 3 is a multi-objective deterministic optimization for resistance and motions using a single regular wave at fixed speed. Problem 4 is a single-objective deterministic optimization for calm-water resistance at fixed speed. The design optimization is based on hull modifications by the Karhunen-Loève expansion of a free-form deformation space, URANS simulations, regular wave approximations for irregular wave, metamodels and multi-objective particle swarm. The design optimization achieves an 8.7, 23, 53, and 10% average improvement for problems 1, 2, 3, and 4, respectively. Comparing to problem 1, problem 2, 3, 4 optimized designs have average performances 1, 2.1 and 1.7% worse, respectively. The most efficient problem, from computational cost/benefit analysis, is problem 3. Nevertheless, problem 1 is needed in order to evaluate and compare the stochastic performance of the design, and assess the optimization cost/benefit.