Expected Improvement in Efficient Global Optimization Through Bootstrapped Kriging - Replaces CentER DP 2010-62

This article uses a sequentialized experimental design to select simulation input com- binations for global optimization, based on Kriging (also called Gaussian process or spatial correlation modeling); this Kriging is used to analyze the input/output data of the simulation model (computer code). This design and analysis adapt the clas- sic "expected improvement" (EI) in "efficient global optimization" (EGO) through the introduction of an unbiased estimator of the Kriging predictor variance; this estimator uses parametric bootstrapping. Classic EI and bootstrapped EI are com- pared through various test functions, including the six-hump camel-back and several Hartmann functions. These empirical results demonstrate that in some applications bootstrapped EI finds the global optimum faster than classic EI does; in general, however, the classic EI may be considered to be a robust global optimizer.Simulation;Optimization;Kriging;Bootstrap

Identification of quasi-optimal regions in the design space using surrogate modeling

The use of Surrogate Based Optimization (SBO) is widely spread in engineering design to find optimal performance characteristics of expensive simulations (forward analysis: from input to optimal output). However, often the practitioner knows a priori the desired performance and is interested in finding the associated input parameters (reverse analysis: from desired output to input). A popular method to solve such reverse (inverse) problems is to minimize the error between the simulated performance and the desired goal. However, there might be multiple quasi-optimal solutions to the problem. In this paper, the authors propose a novel method to efficiently solve inverse problems and to sample Quasi-Optimal Regions (QORs) in the input (design) space more densely. The development of this technique, based on the probability of improvement criterion and kriging models, is driven by a real-life problem from bio-mechanics, i.e., determining the elasticity of the (rabbit) tympanic membrane, a membrane that converts acoustic sound wave into vibrations of the middle ear ossicular bones

구조물 물성치 MCMC 기반 간접 추정의 정확도 향상을 위한 관측 위치 순차적 최적화 기법

학위논문 (석사)-- 서울대학교 대학원 : 공과대학 건설환경공학부, 2019. 2. 송준호.Structures deteriorate naturally when they are used for a long time. Therefore, it is essential to accurately check the degree of deterioration of a structure in order to prevent accidents such as collapse. However, numerical values to detect the degree of deterioration such as the effective thickness are often difficult to measure directly. Thus, it is required to indirectly estimate values associated with deterioration by using direct observations such as strain or displacement obtained from a loading test. In this case, if the number of measurable direct observation is limited due to external factors, it is desirable to choose direct observation locations that can improve the accuracy of indirect estimations under a small number of direct observations. This study proposes a sequential measurement location optimization method to improve the accuracy of an effective thickness indirect estimation of a structure when the number of strain observations is limited. For this goal, the effective thickness distribution of the structure is approximated first by using Karhunen-Loève expansion. Second, system identification based on Bayesian updating using Markov chain Monte Carlo simulation is performed to estimate mean and standard deviation of the effective thickness under given strain measurements. Third, three sequential direct observation selection methods are proposed using the estimated mean and standard deviation of the effective thickness. This study compares the accuracy of the sequentially selected observation locations with simultaneously selected observation locations by applied to the structure. The accuracy of the three sequential measurement location selection methods is also compared. Through the proposed methods, it is possible to determine the next strain measurement location, which can effectively improve the accuracy of the effective thickness estimation, and can maximize the accuracy of the effective thickness estimation under a small number of strain observation locations. It is expected that the proposed methods can be applied to improve the accuracy of estimation of various properties related to the structural deterioration, which can be estimated indirectly.구조물은 사용 기간이 오래될수록 자연히 열화되므로, 구조물 붕괴 등의 사고를 미연에 방지하기 위해서는 구조물의 열화 정도를 정확히 파악하는 것이 필수적이다. 그러나, 열화 정도를 파악할 수 있는 유효 두께 등의 수치들은 직접 측정이 힘든 경우가 많으므로 하중 재하 시험 등에서 얻을 수 있는 변형도나 변위 등의 역학적인 관측값을 이용하여 간접적으로 추정해야 한다. 이 때, 외부 요인으로 인하여 가능한 직접 측정 위치 개수가 한정되어 있다면, 한정된 개수의 관측값 하에서 가능한 간접 추정 정확도를 향상시킬 수 있는 직접 측정 위치 선정을 필요로 한다. 본 연구에서는 변형도 측정 위치 개수가 제한되어 있을 때 구조물의 유효두께 간접 추정의 정확도를 향상시키기 위해 순차적 측정 위치 최적화 방식을 제시한다. 먼저 구조물의 유효 두께 분포를 Karhunen- Loève 모델을 사용하여 근사적으로 표현한 뒤, 마르코프 연쇄 몬테카를로를 사용하는 베이즈 추론을 기반으로 한 역해석을 수행하여 주어진 변형도 측정값 하에서 구조물 전체의 유효두께의 추정값과 편차를 추정한다. 다음으로 추정된 유효두께의 추정값과 편차를 이용하여 관측 위치를 선정하는 세 가지의 관측 위치 선정 방법을 제안한다. 마지막으로, 제안된 방법들을 실제로 구조물에 적용해서 관측 위치 선정 방법들의 정확도를 비교하고, 또한 동시에 관측 위치를 선정한 경우와 정확도를 비교한다. 제안된 방법들을 통하여 유효두께 추정값의 정확도를 효과적으로 향상시킬 수 있는 다음 변위 측정 위치를 결정할 수 있으며, 이를 통해 한정된 관측 위치 개수 하 에서 유효두께 추정의 정확도를 최대화할 수 있다. 제안된 방식은 유효두께뿐만 아니라, 샘플링을 통하여 간접적으로 추론해낼 수 있는 다양한 구조물 열화 관련 물성치 추정의 정확도 향상에도 적용될 수 있을 것으로 기대된다.Chapter 1. Introduction 1 1.1. Research Background 1 1.2. Research Objectives 4 1.3. Outline 6 Chapter 2. System Identification of Structures by Physical Measurements 7 2.1. Karhunen-Loève Expansion 7 2.2. Obtain Samples of KL Random Variables by Bayesian Inference and Markov Chain Monte Carlo 9 2.3. Estimate Distribution of the Effective Thickness 11 Chapter 3. Sequential Selection Technique of Measurement Locations 17 3.1. Goal of Measurement Locations Selection 17 3.2. Methods to Generate Sample Effective Thickness 19 3.2.1. Scheme 1: Sampling specific effective thickness 19 3.2.2. Scheme 2: Sampling whole effective thickness 22 3.2.3. Scheme 3: Sampling random variables of K-L expansion 23 3.2.4. Comparison between sample effective thickness generation methods 26 3.3. Methods to Determine Additional Measurement Location Using Samples 27 Chapter 4. Numerical Example 33 4.1. Structure Overview 33 4.2. Numerical Example 1: Use the Sum of Two SSVs 40 4.3. Numerical Example 2: Use Two SSVs Respectively 45 Chapter 5. Conclusion 51 References 53 초록 56Maste

Robust optimal design of FOPID controller for five bar linkage robot in a cyber-physical system: a new simulation-optimization approach

This paper aims to further increase the reliability of optimal results by setting the simulation conditions to be as close as possible to the real or actual operation to create a Cyber-Physical System (CPS) view for the installation of the Fractional-Order PID (FOPID) controller. For this purpose, we consider two different sources of variability in such a CPS control model. The first source refers to the changeability of a target of the control model (multiple setpoints) because of environmental noise factors and the second source refers to an anomaly in sensors that is raised in a feedback loop. We develop a new approach to optimize two objective functions under uncertainty including signal energy control and response error control while obtaining the robustness among the source of variability with the lowest computational cost. A new hybrid surrogate-metaheuristic approach is developed using Particle Swarm Optimization (PSO) to update the Gaussian Process (GP) surrogate for a sequential improvement of the robust optimal result. The application of efficient global optimization is extended to estimate surrogate prediction error with less computational cost using a jackknife leave-one-out estimator. This paper examines the challenges of such a robust multi-objective optimization for FOPID control of a five-bar linkage robot manipulator. The results show the applicability and effectiveness of our proposed method in obtaining robustness and reliability in a CPS control system by tackling required computational efforts