Optimization of the Vibration Response of a Longitudinal-Transverse Stiffened Conical Shell Based on an Ensemble of Surrogates

2018 ◽  
Author(s):  
Jiachang Qian ◽  
Enen Yu ◽  
Jinlan Zhang ◽  
Dawei Zhan ◽  
Yuansheng Cheng
Keyword(s):  
Conical Shell ◽  
Design Space ◽  
Computational Cost ◽  
Kriging Model ◽  
Surrogate Models ◽  
Vibration Response ◽  
Support Vector ◽  
Conical Shells ◽  
Design Variables ◽  
Ensemble Of Surrogates

The acceleration responses at certain points of the longitudinal-transverse stiffened conical shells in special frequency region are major matters of concern. Because the finite element models of the longitudinal-transverse stiffened conical shells have to be employed to calculate the vibration response of the structure at all frequencies under consideration, it requires a large amount of computational cost when the optimization is conducted. In order to optimize the vibration response of the longitudinal-transverse stiffened conical shell, the surrogate modeling method is used in this study to approximate the frequency-acceleration response function which makes the vibration response optimization affordable. Since different surrogate models often perform differently in different regions of the design space, an ensemble of surrogate models is utilized to maximize the overall accuracy over the whole design space. The ensemble of surrogates is a weighted combination of Kriging model, radial basis function (RBF) and support vector regression (SVR). The weights of the ensemble of surrogates vary in different regions and are determined by the estimated errors of the surrogate models at the study point. The smaller the estimated error is, the higher the weight is. Then the prediction of ensemble of surrogates is compared to the individual surrogate’s, and the results show that the accuracies of the ensemble of surrogates in peak regions are significant higher than its components. Based on the ensemble of surrogates, a vibration optimization of a longitudinal-transverse stiffened conical shell is conducted using genetic algorithm (GA). The design variables of the optimization are the thickness of the longitudinal-transverse stiffened conical shell and the height of stiffened structure. The objective is to minimize the highest acceleration of the shell and the calculations of the peak accelerations are approximated by the built ensemble of the surrogates. The constraints include the weight of the stiffened conical shell and structure size combination. The optimization results show that the proposed approach is efficient in optimization of the vibration response of longitudinal-transverse stiffened conical shells.

Global Sensitivity Analysis for Stay Vane and Casing Design of Reaction Hydraulic Turbine

2019 ◽  
Author(s):  
Hyunkyoo Cho ◽  
Ujjwal Shrestha ◽  
Young-Do Choi ◽  
Jungwan Park
Keyword(s):  
Sensitivity Analysis ◽  
Design Process ◽  
Performance Measures ◽  
Global Sensitivity Analysis ◽  
Computational Cost ◽  
Surrogate Models ◽  
Sensitivity Index ◽  
Global Sensitivity ◽  
Design Variables ◽  
Hydraulic Turbines

Abstract Global sensitivity analysis (GSA) estimates influence of design variables in the entire design domain on performance measures. Hence, using GSA, important design variables could be found for an engineering application with high dimension which require computationally expensive analyses. Then, similar engineering applications could use selected variables to carry out design process with smaller dimension and affordable computational cost. In this study, GSA has been carried out for the performance measures in design of stay vane and casing of reaction hydraulic turbines. Global sensitivity index method is used for GSA because it can fully capture the effect of interaction between the design variables. For efficiency, genetic aggregation surrogate models are constructed using the responses of computational fluid dynamic (CFD) analysis. Global sensitivity indices for the performance measures of stay vane and casing have been evaluated using the surrogate models. It is found that less than three design variables among 12 are effective in the design process of stay vane and casing in reaction hydraulic turbines.

Characterizing Uncertainty Attributable to Surrogate Models

2014 ◽  
Vol 136 (3) ◽  
Author(s):  
Jie Zhang ◽  
Souma Chowdhury ◽  
Ali Mehmani ◽  
Achille Messac
Keyword(s):  
Cross Validation ◽  
System Analysis ◽  
Design Space ◽  
Surrogate Models ◽  
Support Vector ◽  
Test Problems ◽  
Local Error ◽  
Design Domain ◽  
Validation Technique ◽  
Leave One Out

This paper investigates the characterization of the uncertainty in the prediction of surrogate models. In the practice of engineering, where predictive models are pervasively used, the knowledge of the level of modeling error in any region of the design space is uniquely helpful for design exploration and model improvement. The lack of methods that can explore the spatial variation of surrogate error levels in a wide variety of surrogates (i.e., model-independent methods) leaves an important gap in our ability to perform design domain exploration. We develop a novel framework, called domain segmentation based on uncertainty in the surrogate (DSUS) to segregate the design domain based on the level of local errors. The errors in the surrogate estimation are classified into physically meaningful classes based on the user's understanding of the system and/or the accuracy requirements for the concerned system analysis. The leave-one-out cross-validation technique is used to quantity the local errors. Support vector machine (SVM) is implemented to determine the boundaries between error classes, and to classify any new design point into the pertinent error class. We also investigate the effectiveness of the leave-one-out cross-validation technique in providing a local error measure, through comparison with actual local errors. The utility of the DSUS framework is illustrated using two different surrogate modeling methods: (i) the Kriging method and (ii) the adaptive hybrid functions (AHF). The DSUS framework is applied to a series of standard test problems and engineering problems. In these case studies, the DSUS framework is observed to provide reasonable accuracy in classifying the design-space based on error levels. More than 90% of the test points are accurately classified into the appropriate error classes.

Kriging Modeling for Engine Mount Optimization in Motorcycles

2009 ◽  
Author(s):  
Sudhir Kaul ◽  
Anoop K. Dhingra
Keyword(s):  
Correlation Function ◽  
Theoretical Model ◽  
Optimization Problem ◽  
Design Space ◽  
Substantial Reduction ◽  
Kriging Model ◽  
Surrogate Models ◽  
Fractional Factorial ◽  
Engine Mount ◽  
Selection Of

This paper addresses two critical aspects associated with the successful use of a Kriging model for solving the engine mount optimization problem. The two aspects are the selection of an appropriate correlation function and the use of a suitable governing design for sampling within the design space. The selection of a correlation function is critical in building a Kriging model since the function should accurately represent the behavior of the response over the entire design space. Whereas the Gaussian correlation function is most commonly used for building Kriging models, it is generally suitable for only those processes or systems which have a relatively smooth response within the entire design space. The correlation functions that have been evaluated in this paper for building the Kriging models for solving the engine mount optimization problem are as follows: Exponential, Linear Spline, Matern’s 3/2, Matern’s 5/2 and Gaussian. Three types of experimental designs – Fractional Factorial, D-optimal and Latin Hypercube, have been used to select the sampling points for making simulation runs in order to build the Kriging models. A theoretical model that represents the dynamics of the engine mount system in a motorcycle application has been used to build all the surrogate models. The Kriging models are then used to solve the engine mount optimization problem for enhanced vibration isolation with mount stiffness, mount orientation and mount location as the design variables. The optimization results of the Kriging models are compared to the results of the theoretical model. It is found that the D-optimal design in conjunction with Matern’s 3/2 correlation function provides the best results. This can be attributed to the high irregularity of the response function in the design space, especially due to the influence of orientation variables. The use of the surrogate Kriging model simplifies the governing model and leads to a substantial reduction in computational effort for solving the optimization problem. Based on the results, it can be concluded that the Kriging modeling technique can be successfully used to build surrogate models for the engine mount problem for design iterations as well as for design optimization if the correlation function and the governing design are judiciously chosen.

Optimization of Joined Conical Shells Based on Free Vibration

2016 ◽  
Author(s):  
Rayehe Karimi Mahabadi ◽  
Firooz Bakhtiari-Nejad
Keyword(s):  
Genetic Algorithm ◽  
Free Vibration ◽  
Natural Frequency ◽  
Conical Shell ◽  
Fibre Orientation ◽  
Laminated Composite ◽  
Conical Shells ◽  
Design Variables

This work aims at utilizing genetic algorithm (GA) to pursue the optimization of joined conical shells based on free vibration. Semi-vertex angles of cones and fibre orientation of the laminated composite are considered as design variables. First, the model is simulated in ABAQUS, the model is validated by comparing its results to other obtained from the literature. Then the first non-zero natural frequency of isotropic joined conical shell is maximized by changing the two semi-vertex angles of cones. Last the fibre orientation of laminated joined shells are optimized to achieve the maximum natural frequency.

Optimization Framework Using Surrogate Model for Aerodynamically Improved 3D Turbine Blade Design

2014 ◽  
Author(s):  
Sanga Lee ◽  
Saeil Lee ◽  
Kyu-Hong Kim ◽  
Dong-Ho Lee ◽  
Young-Seok Kang ◽  
...  
Keyword(s):  
Surrogate Model ◽  
Design Space ◽  
Computational Cost ◽  
Three Dimensional ◽  
Experimental Point ◽  
Optimized Design ◽  
Kriging Method ◽  
Baseline Design ◽  
Design Variables ◽  
Nonlinear Design

In simple optimization problem, direct searching methods are most accurate and practical enough. However, for more complicated problem which contains many design variables and demands high computational costs, surrogate model methods are recommendable instead of direct searching methods. In this case, surrogate models should have reliability for not only accuracy of the optimum value but also globalness of the solution. In this paper, the Kriging method was used to construct surrogate model for finding aerodynamically improved three dimensional single stage turbine. At first, nozzle was optimized coupled with base rotor blade. And then rotor was optimized with the optimized nozzle vane in order. Kriging method is well known for its good describability of nonlinear design space. For this reason, Kriging method is appropriate for describing the turbine design space, which has complicated physical phenomena and demands many design variables for finding optimum three dimensional blade shapes. To construct airfoil shape, Prichard topology was used. The blade was divided into 3 sections and each section has 9 design variables. Considering computational cost, some design variables were picked up by using sensitivity analysis. For selecting experimental point, D-optimal method, which scatters each experimental points to have maximum dispersion, was used. Model validation was done by comparing estimated values of random points by Kriging model with evaluated values by computation. The constructed surrogate model was refined repeatedly until it reaches convergence criteria, by supplying additional experimental points. When the surrogate model satisfies the reliability condition and developed enough, finding optimum point and its validation was followed by. If any variable was located on the boundary of design space, the design space was shifted in order to avoid the boundary of the design space. This process was also repeated until finding appropriate design space. As a result, the optimized design has more complicated blade shapes than that of the baseline design but has higher aerodynamic efficiency than the baseline turbine stage.

scholarly journals An approximate high-dimensional optimization method using hierarchical design space reduction strategy

2021 ◽  
Vol 39 (2) ◽  
pp. 292-301
Author(s):  
Pengcheng Ye ◽  
Congcong Wang ◽  
Guang Pan
Keyword(s):  
Design Space ◽  
Optimization Method ◽  
Surrogate Models ◽  
Black Box ◽  
High Dimensional ◽  
Hierarchical Design ◽  
Reduction Strategy ◽  
Space Reduction ◽  
Ensemble Of Surrogates ◽  
Dimensional Optimization

To overcome the complicated engineering model and huge computational cost, a hierarchical design space reduction strategy based approximate high-dimensional optimization(HSRAHO) method is proposed to deal with the high-dimensional expensive black-box problems. Three classical surrogate models including polynomial response surfaces, radial basis functions and Kriging are selected as the component surrogate models. The ensemble of surrogates is constructed using the optimized weight factors selection method based on the prediction sum of squares and employed to replace the real high-dimensional black-box models. The hierarchical design space reduction strategy is used to identify the design subspaces according to the known information. And, the new promising sample points are generated in the design subspaces. Thus, the prediction accuracy of ensemble of surrogates in these interesting sub-regions can be gradually improved until the optimization convergence. Testing using several benchmark optimization functions and an airfoil design optimization problem, the newly proposed approximate high-dimensional optimization method HSRAHO shows improved capability in high-dimensional optimization efficiency and identifying the global optimum.

Topology and Sizing Optimization of Micromixers Using Graph-Theoretical Representation and Genetic Algorithm

2017 ◽  
Author(s):  
Mitsuo Yoshimura ◽  
Koji Shimoyama ◽  
Takashi Misaka ◽  
Shigeru Obayashi
Keyword(s):  
Genetic Algorithm ◽  
Topology Optimization ◽  
Optimization Problems ◽  
Computational Cost ◽  
Kriging Model ◽  
Local Optimum ◽  
Sizing Optimization ◽  
Local Optima ◽  
Novel Approach ◽  
Design Variables

This paper proposes a novel approach for fluid topology optimization using genetic algorithm. In this study, the enhancement of mixing in the passive micromixers is considered. The efficient mixing is achieved by the grooves attached on the bottom of the microchannel and the optimal configuration of grooves is investigated. The grooves are represented based on the graph theory. The micromixers are analyzed by a CFD solver and the exploration by genetic algorithm is assisted by the Kriging model in order to reduce the computational cost. Three cases with different constraint and treatment for design variables are considered. In each case, GA found several local optima since the objective function is a multi-modal function and each local optimum revealed the specific characteristic for efficient mixing in micromixers. Moreover, we discuss the validity of the constraint for optimization problems. The results show a novel insight for design of micromixer and fluid topology optimization using genetic algorithm.

Enhanced Multi-Objective Optimization of a Microchannel Heat Sink Using Multiple Surrogates Modeling

2009 ◽  
Author(s):  
Afzal Husain ◽  
Kwang-Yong Kim
Keyword(s):  
Heat Sink ◽  
Design Space ◽  
Surrogate Models ◽  
Pareto Optimal ◽  
Microchannel Heat Sink ◽  
Objective Functions ◽  
Multi Objective Optimization ◽  
Pareto Optimal Front ◽  
Multi Objective ◽  
Design Variables

A liquid flow microchannel heat sink has been studied and optimized with the help of three-dimensional numerical analysis and multiple surrogate methods. Two objective functions, thermal resistance and pumping power have been selected to assess the performance of the microchannel heat sink. The design variables related to the microchannel top and bottom widths, depth and fin width, which contribute to objective functions, have been identified and design space has been explored through some preliminary calculations. Design of experiments was performed and a three-level full factorial design was selected to exploit the design space. The numerical solutions obtained at these design points were utilized to construct surrogate models namely Response Surface Approximations and Kriging. A hybrid multi-objective evolutionary algorithm coupled with surrogate models and a gradient-based search algorithm is applied to find global Pareto-optimal solutions. Since, the surrogate models are highly problem-dependent, the accuracy of the two surrogate models has been discussed in view of their predictions at on- and off-Pareto-optimal front. The trade-off analysis was performed in view of the two competing objectives. The Pareto-optimal sensitivity (change in value along the Pareto-optimal front) of the design variables has been found out to economically compromise with the design variables contributing relatively less to the objective functions. The application of the multiple surrogate methods not only improves quality of multi-objective optimization but also gives the feedback of the fidelity of the model near the optimum region.

A Framework for Parallel Sampling of Design Space With Application to Vehicle Crashworthiness Optimization

2012 ◽  
Author(s):  
Karim Hamza ◽  
Mohammed Shalaby
Keyword(s):  
Design Space ◽  
Kriging Model ◽  
Efficient Global Optimization ◽  
High Quality ◽  
Analytical Functions ◽  
Design Variables ◽  
Crashworthiness Design ◽  
Meta Modeling ◽  
System Output ◽  
Vehicle Crashworthiness

This paper presents a framework for simulation-based design optimization of computationally-expensive problems, where economizing the generation of sample designs is highly desirable. Various meta-modeling schemes are used in practice in order to approximate the input-output relationships in the designed system and suggest candidate locations in the design space where high quality designs are likely to be found. One such popular approach is known as Efficient Global Optimization (EGO), where an initial set of design samples is used to construct a Kriging model, which approximates the system output and provides a prediction of the uncertainty in the approximations. Variations of EGO suggest new sample designs according to various infill criteria that seek to maximize the chance of finding high quality designs. The new samples are then used to update the Kriging model and the process is iterated. This paper attempts to address one of the limitations of EGO, which is the generation of the infill samples often becoming a difficult optimization problem in its own right for a larger number of design variables. This is done by adapting a previously developed approach for locating the optimum of a Kriging model to a modified EGO infill sampling criterion. The new implementation also allows the generation of multiple new samples at a time in order to take advantage of parallel computing. After testing on analytical functions, the algorithm is applied to vehicle crashworthiness design of a full vehicle model of a Geo Metro subject to frontal crash conditions.

Stability and vibration analysis of an axially moving thin walled conical shell

2021 ◽  
pp. 107754632199760
Author(s):  
Hossein Abolhassanpour ◽  
Faramarz Ashenai Ghasemi ◽  
Majid Shahgholi ◽  
Arash Mohamadi
Keyword(s):  
Natural Frequency ◽  
Conical Shell ◽  
Shell Theory ◽  
Cone Angle ◽  
Theory Of Elasticity ◽  
Lower Velocity ◽  
Motion Equations ◽  
Conical Shells ◽  
Divergence Instability ◽  
Axially Moving

This article deals with the analysis of free vibration of an axially moving truncated conical shell. Based on the classical linear theory of elasticity, Donnell shell theory assumptions, Hamilton principle, and Galerkin method, the motion equations of axially moving truncated conical shells are derived. Then, the perturbation method is used to obtain the natural frequency of the system. One of the most important and controversial results in studies of axially moving structures is the velocity detection of critical points. Therefore, the effect of velocity on the creation of divergence instability is investigated. The other important goal in this study is to investigate the effect of the cone angle. As a novelty, our study found that increasing or decreasing the cone angle also affects the critical velocity of the structure in addition to changing the natural frequency, meaning that with increasing the cone angle, the instability occurs at a lower velocity. Also, the effect of other parameters such as aspect ratio and mechanical properties on the frequency and instability points is investigated.

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