Confidence-Driven Design Optimization Using Gaussian Process Metamodeling With Insufficient Data

2018 ◽  
Vol 140 (12) ◽  
Author(s):  
Mingyang Li ◽  
Zequn Wang
Keyword(s):  
Gaussian Process ◽  
Design Optimization ◽  
Confidence Level ◽  
Model Uncertainty ◽  
Surrogate Model ◽  
Computational Cost ◽  
Training Data ◽  
Design Variables ◽  
Sensitivity Analysis Method ◽  
Mean And Variance

To reduce the computational cost, surrogate models have been widely used to replace expensive simulations in design under uncertainty. However, most existing methods may introduce significant errors when the training data is limited. This paper presents a confidence-driven design optimization (CDDO) framework to manage surrogate model uncertainty for probabilistic design optimization. In this study, a confidence-based Gaussian process (GP) modeling technique is developed to handle the surrogate model uncertainty in system performance predictions by taking both the prediction mean and variance into account. With a target confidence level, the confidence-based GP models are used to reduce the probability of underestimating the probability of failure in reliability assessment. In addition, a new sensitivity analysis method is proposed to approximate the sensitivity of the reliability at the target confidence level with respect to design variables, and thus facilitate the CDDO framework. Three case studies are introduced to demonstrate the effectiveness of the proposed approach.

Confidence-Based Design Optimization for a More Conservative Optimum Under Surrogate Model Uncertainty Caused by Gaussian Process

2021 ◽  
Vol 143 (9) ◽  
Author(s):  
Yongsu Jung ◽  
Kyeonghwan Kang ◽  
Hyunkyoo Cho ◽  
Ikjin Lee
Keyword(s):  
Gaussian Process ◽  
Design Optimization ◽  
Model Uncertainty ◽  
Surrogate Model ◽  
Confidence Estimation ◽  
Mathematical Functions ◽  
Element Analysis ◽  
Computational Burden ◽  
Reliability Based Design ◽  
Stochastic Sensitivity Analysis

Abstract Even though many efforts have been devoted to effective strategies to build accurate surrogate models, surrogate model uncertainty is inevitable due to a limited number of available simulation samples. Therefore, the surrogate model uncertainty, one of the epistemic uncertainties in reliability-based design optimization (RBDO), has to be considered during the design process to prevent unexpected failure of a system that stems from an inaccurate surrogate model. However, there have been limited attempts to obtain a reliable optimum taking into account the surrogate model uncertainty due to its complexity and computational burden. Thus, this paper proposes a confidence-based design optimization (CBDO) under surrogate model uncertainty to find a conservative optimum despite an insufficient number of simulation samples. To compensate the surrogate model uncertainty in reliability analysis, the confidence of reliability is brought to describe the uncertainty of reliability. The proposed method employs the Gaussian process modeling to explicitly quantify the uncertainty of a surrogate model. Thus, metamodel-based importance sampling and expansion optimal linear estimation are exploited to reduce the computational burden on confidence estimation. In addition, stochastic sensitivity analysis of the confidence is developed for CBDO, which is formulated to find a conservative optimum than an RBDO optimum at a specific confidence level. Numerical examples using mathematical functions and finite element analysis show that the proposed confidence analysis and CBDO can prevent overestimation of reliability caused by an inaccurate surrogate model.

scholarly journals Reliability-Based Robust Design Optimization of Structures Considering Uncertainty in Design Variables

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Shujuan Wang ◽  
Qiuyang Li ◽  
Gordon J. Savage
Keyword(s):  
Sensitivity Analysis ◽  
Design Optimization ◽  
Robust Design ◽  
Structural Reliability ◽  
Computational Cost ◽  
Optimization Process ◽  
Robust Design Optimization ◽  
Global Approximation ◽  
Design Variables ◽  
Uncertainty In Design

This paper investigates the structural design optimization to cover both the reliability and robustness under uncertainty in design variables. The main objective is to improve the efficiency of the optimization process. To address this problem, a hybrid reliability-based robust design optimization (RRDO) method is proposed. Prior to the design optimization, the Sobol sensitivity analysis is used for selecting key design variables and providing response variance as well, resulting in significantly reduced computational complexity. The single-loop algorithm is employed to guarantee the structural reliability, allowing fast optimization process. In the case of robust design, the weighting factor balances the response performance and variance with respect to the uncertainty in design variables. The main contribution of this paper is that the proposed method applies the RRDO strategy with the usage of global approximation and the Sobol sensitivity analysis, leading to the reduced computational cost. A structural example is given to illustrate the performance of the proposed method.

scholarly journals Brass Instruments Design Using Physics-Based Sound Simulation Models and Surrogate-Assisted Derivative-Free Optimization

2016 ◽  
Author(s):  
Robin Tournemenne ◽  
Jean-François Petiot ◽  
Bastien Talgorn ◽  
Michael Kokkolaras
Keyword(s):  
Design Optimization ◽  
Search Algorithm ◽  
Rank Order ◽  
Computational Cost ◽  
Simulation Models ◽  
Function Evaluation ◽  
Brass Instruments ◽  
Design Variables ◽  
Direct Search Algorithm ◽  
Sound Simulation

This paper presents a method for design optimization of brass wind instruments. The shape of a trumpet’s bore is optimized to improve intonation using a physics-based sound simulation model. This physics-based model consists of an acoustic model of the resonator (input impedance), a mechanical model of the excitator (the lips of a virtual musician) and a model of the coupling between the excitator and the resonator. The harmonic balance technique allows the computation of sounds in a permanent regime, representative of the shape of the resonator according to control parameters of the virtual musician. An optimization problem is formulated, in which the objective function to be minimized is the overall quality of the intonation of the different notes played by the instrument (deviation from the equal-tempered scale). The design variables are the physical dimensions of the resonator. Given the computationally expensive function evaluation and the unavailability of gradients, a surrogate-assisted optimization framework is implemented using the mesh adaptive direct search algorithm (MADS). Surrogate models are used both to obtain promising candidates in the search step of MADS and to rank-order additional candidates generated by the poll step of MADS. The physics-based model is then used to determine the next design iterate. Two examples (with two and five design optimization variables, respectively) are presented to demonstrate the approach. Results show that significant improvement of intonation can be achieved at reasonable computational cost. The implementation of this method for computer-aided instrument design is discussed, considering different objective functions or constraints based on intonation but also on the timbre of the instrument.

scholarly journals Surrogate based aeroelastic design optimization of tip extensions on a modern 10MW wind turbine

2020 ◽  
Author(s):  
Thanasis Barlas ◽  
Néstor Ramos-García ◽  
Georg Raimund Pirrung ◽  
Sergio González Horcas
Keyword(s):  
Wind Turbine ◽  
Design Optimization ◽  
Surrogate Model ◽  
Bending Moment ◽  
Vortex Method ◽  
Optimized Design ◽  
Near Wake ◽  
Direct Optimization ◽  
Design Variables ◽  
Aeroelastic Simulations

Abstract. Advanced aeroelastically optimized tip extensions are among rotor innovation concepts which could contribute to higher performance and lower cost of wind turbines. A novel design optimization framework for wind turbine blade tip extensions, based on surrogate aeroelastic modeling is presented. An academic wind turbine is modelled in an aeroelastic code equipped with a near wake aerodynamic module, and tip extensions with complex shapes are parametrized using 11 design variables. The design space is explored via full aeroelastic simulations in extreme turbulence and a surrogate model is fitted to the data. Direct optimization is performed based on the surrogate model, seeking to maximize the power of the retrofitted turbine within the ultimate load constraints. The presented optimized design achieves a load neutral gain of up to 6 % in annual energy production. Its performance is further evaluated in detail by means of the near wake model used for the generation of the surrogate model, and compared with a higher fidelity aerodynamic module comprising a hybrid filament-particle-mesh vortex method with a lifting-line implementation. A good agreement between the solvers is obtained at low turbulence levels, while differences in predicted power and flap-wise blade root bending moment grow with increasing turbulence intensity.

Design of a Probabilistic Health Monitoring System Using Embedded Piezoelectric Patch Sensors

2019 ◽  
Author(s):  
Amin Toghi Eshghi ◽  
Soobum Lee ◽  
HyunJun Jung ◽  
Pingfeng Wang
Keyword(s):  
Design Optimization ◽  
Health Monitoring ◽  
Failure Modes ◽  
Computational Cost ◽  
Failure Detection ◽  
Training Data ◽  
Failure Diagnosis ◽  
Geometrical Parameters ◽  
Sensor Output ◽  
Vibration Pattern

Abstract This paper proposes a probabilistic model for the placement of sensors that considers uncertain factors in the sensing system to find the best arrangement of sensor locations. Traditional procedures for structural health monitoring (SHM) usually rely on simplified behavior and deterministic factors from structure’s response. Incorporating the sources of uncertainty (e.g., loading condition, material properties, and geometrical parameters) in the design of sensor network will enhance the safety and extend the useful life of the complex mechanical systems. The proposed method is defined in a reliability-based design optimization framework to search for the sufficient number of sensors for failure detection using Genetic Algorithm. The optimal arrangement is found as the one that minimizes the number and size of sensor patches and maximizes the expected probability for failure detection. This design concept involves a new failure diagnosis indicator, named detectability, formulated based on the Mahalanobis Distance (MD). MD distribution is used as a measure of the quality of the obtained sensor configuration suitable for many sensing/actuation SHM processes, while considering the uncertainties such as those from structure properties and operation condition. The MD classifier categorizes large sets of testing data by comparing the distances of the mean with the distribution of available training data sets. Statistical evaluation of failure detectability can be obtained by comparing the distribution of MD for different failure modes. Kriging modeling, used for metamodel-based design optimization, is applied for surrogate modeling of the stochastic performance of system to reduce computational cost. The surrogate model is constructed by correlating the sensor output to the vibration pattern of the structure and sensor variable inputs (e.g., size and location). Direct finite element analysis (FEA) evaluates the sensor output with respect to the input variables. Consequently, the constructed kriging model enables the estimation of sensor output for any arbitrary sensor arrays. As a case study, a rectangular panel with a size of 40 cm × 30 cm is considered that is fastened using eight screw joints. The harmonic vibration force is applied to the center of the plate and its varied vibration pattern is used to detect the joint failure. Eight different combinations of join failure are defined as health statuses (failure modes), and different size and layouts of the piezoelectric sensors are considered to detect the health status. The results verify the capabilities of the new method for failure diagnosis of screw joints in a panel with high sensitivity of fault detection.

A Sequential Algorithm for Possibility-Based Design Optimization

2006 ◽  
Author(s):  
Jun Zhou ◽  
Zissimos P. Mourelatos
Keyword(s):  
Design Optimization ◽  
Optimization Algorithm ◽  
Computational Cost ◽  
Possibility Theory ◽  
Sequential Optimization ◽  
Sequential Algorithm ◽  
Computationally Efficient ◽  
Worst Case ◽  
Reliability Based Design ◽  
Design Variables

Deterministic optimal designs that are obtained without taking into account uncertainty/variation are usually unreliable. Although reliability-based design optimization accounts for variation, it assumes that statistical information is available in the form of fully defined probabilistic distributions. This is not true for a variety of engineering problems where uncertainty is usually given in terms of interval ranges. In this case, interval analysis or possibility theory can be used instead of probability theory. This paper shows how possibility theory can be used in design and presents a computationally efficient sequential optimization algorithm. After, the fundamentals of possibility theory and fuzzy measures are described, a double-loop, possibility-based design optimization algorithm is presented where all design constraints are expressed possibilistically. The algorithm handles problems with only uncertain or a combination of random and uncertain design variables and parameters. In order to reduce the high computational cost, a sequential algorithm for possibility-based design optimization is presented. It consists of a sequence of cycles composed of a deterministic design optimization followed by a set of worst-case reliability evaluation loops. Two examples demonstrate the accuracy and efficiency of the proposed sequential algorithm.

Aerodynamic optimization to tandem stators by using sweep and dihedral

2020 ◽  
Vol 234 (6) ◽  
pp. 1225-1236
Author(s):  
Jinouwen Zhang ◽  
Haowan Zhuang ◽  
Jinfang Teng ◽  
Mingmin Zhu ◽  
Xiaoqing Qiang
Keyword(s):  
Gaussian Process ◽  
Surrogate Model ◽  
Aerodynamic Performance ◽  
High Dimensional ◽  
Two Dimensional ◽  
Multi Objective Optimization ◽  
Optimization Scheme ◽  
Multi Objective ◽  
Design Variables ◽  
Dimensional Optimization

In the modern aerodynamic design of turbomachinery blades, the geometries of blades often need to be reshaped to achieve better aerodynamic performance by introducing extra parametric design variables. A higher variable dimension will lead to a larger sampling range as well as a sparser sample distribution, which challenges the effectiveness and stability of optimization schemes based on surrogate model by making the model prediction quality even poorer. In this paper, a multi-objective optimization based on Gaussian process model was carried out for a high dimensional design space. Based on the previous two-dimensional optimization, tandem stators of a modern compressor were optimized by the design of sweep and dihedral. The purpose of the study is to improve the aerodynamic performance of the compressor tandem stators as well as to provide an effective optimization scheme for high dimensional multi-objective optimization problems. The design of sweep and dihedral for reshaping the tandem stators consists of a total of 18 design variables. An improvement in total pressure recovery coefficient of at least 0.7% at positive incidence and at least 0.3% at negative incidence was obtained, much larger than that in the previous two-dimensional optimization. The optimization process shows that, by using Gaussian process as the surrogate model and a special sampling strategy, this optimization scheme is effective and efficient to handle this high dimensional space. The aerodynamic influences of design parameters of tandem blades were analyzed in detail and the superiority of sweep and dihedral in reducing aerodynamic loss was confirmed.

scholarly journals Self-Directed Online Machine Learning for Topology Optimization

2021 ◽  
Author(s):  
Changyu Deng ◽  
Yizhou Wang ◽  
Can Qin ◽  
Wei Lu
Keyword(s):  
Topology Optimization ◽  
Optimization Problems ◽  
State Of The Art ◽  
Computational Cost ◽  
Region Of Interest ◽  
Global Optimum ◽  
Training Data ◽  
Computational Time ◽  
Minimization Problems ◽  
Design Variables

Abstract Topology optimization by optimally distributing materials in a given domain requires gradient-free optimizers to solve highly complicated problems. However, with hundreds of design variables or more involved, solving such problems would require millions of Finite Element Method (FEM) calculations whose computational cost is huge and impractical. Here we report a Self-directed Online Learning Optimization (SOLO) which integrates Deep Neural Network (DNN) with FEM calculations. A DNN learns and substitutes the objective as a function of design variables. A small number of training data is generated dynamically based on the DNN's prediction of the global optimum. The DNN adapts to the new training data and gives better prediction in the region of interest until convergence. Our algorithm was tested by compliance minimization problems and fluid-structure optimization problems. It reduced the computational time by 2 ~ 5 orders of magnitude compared with directly using heuristic methods, and outperformed all state-of-the-art algorithms tested in our experiments. This approach enables solving large multi-dimensional optimization problems.

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