Towards Nonlinear Multimaterial Topology Optimization using Machine Learning and Metamodel-based Optimization Kai Liu Purdue University Andrés Tovar.

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Presentation transcript:

Towards Nonlinear Multimaterial Topology Optimization using Machine Learning and Metamodel-based Optimization Kai Liu Purdue University Andrés Tovar Indiana Univ. - Purdue Univ. Indianapolis Emily NutWell Honda R&D Americas Duane Detwiler Honda R&D Americas

Three Stages Design Optimization Systematic Design Optimization Approach Conceptual Design Generating conceptual design using structural optimization Continuous design distribution Design Parameterization Parameterizing conceptual design using machine learning Simple and efficient Parametric Optimization Utilizing parametric optimization with reduced number of design variables Further improves performances and manufacturability

Conceptual Design Generalized Structural optimization problem The resulting is a distribution of up to n materials within the structure. This is preliminary result. Can we manufacture this result? Can we further improve the performance?

Design Parameterization Generalized Structural optimization problem K-means clustering is a simple widely used unsupervised machine learning technique. K-means This is preliminary result. Can we manufacture this result? Can we further improve the performance?

Design Parameterization K-means clustering Objective Given a set of objects, K-means clustering aims to partition the n objects into K sets so as to minimize the within-cluster sum of squares:

Design Parameterization K-means clustering Algorithm Step 1. Given n objects, initialize k cluster centers Step 2. Assign each object to its closest cluster center Step 3. Update the center for each cluster Step 4. Repeat 2 and 3 until no change in cluster centers

Parametric Optimization Problem statement The parametric optimization problem can be posted with reduced number of variables. To find the material parameters that extremize a set of objective functions, subject to a set of functional constraints.

Parametric Optimization Metamodel-based multi-objective optimization The set of objectives may involve nonlinear and computationally expensive functions. To solve such problems, we proposed a metamodel-based multi-objective optimization algorithm.

Examples Minimum compliance Compliant mechanism Crashworthiness design MBB-Beam Compliant mechanism Force Inverter Crashworthiness design S-rail tubular component

Examples Conceptual Design Minimum Compliance elements: 60x20 Q4 objective: min compliance mass fraction: 0.5 material: E = 1.0, nu = 0.3 optimization problem:

Examples Design Parameterization Cluster Number K Minimum Compliance Using Kmeans to cluster conceptual design into 2 groups Cluster Number K The bigger value of K, the closer clustered solution to the conceptual design.

Examples Parametric Optimization Minimum Compliance Minimum compliance with reduced number of design variables Optimization problem:

Examples Minimum Compliance Conceptual Design Design Parameterization Objective: 164.41 xmin: 0.001 xmax: 1.000 # values: 890 Design Parameterization Objective: 170.831 xmin: 0.300 xmax: 0.971 # values: 2 Parametric Optimization Objective: 168.964 xmin: 0.290 xmax: 1.000 # values: 2

Examples Clustered Multimaterial[1] Minimum Compliance - comparison of multimaterial topology optimization solutions Clustered Multimaterial[1] 16 Topology + 1 Kmeans + 7 SQP 236 Outer + 708 Inner Topology Iterations 167.35 169.35 Objective 1.00 0.25 0.45 1.00 0.25 0.45 0.29 0.53 0.18 0.29 0.53 0.18 3 986 # distinct values

Examples Conceptual Design Compliant Mechanism elements: 150x75 Q4 objective: max output displacement mass fraction: 0.35 material: E = 1.0, nu = 0.3 optimization problem:

Examples Design Parameterization Parametric Optimization Compliant Mechanism Design Parameterization Using Kmeans to cluster conceptual design into 2 groups Parametric Optimization Maximize output displacement with reduced number of design variables

Examples Minimum Compliance Conceptual Design Design Parameterization Parametric Optimization Objective: -1.02 xmin: 0.001 xmax: 1.00 # values: 3027 Objective: 0.133 xmin: 0.042 xmax: 0.940 # values: 2 Objective: -0.614 xmin: 0.011 xmax: 1.000 # values: 2

Examples Clustered Multimaterial[1] Compliant Mechanism - comparison of multimaterial topology optimization solutions. Clustered Multimaterial[1] 200 Outer + 600 Inner Topology Iterations 153 Topology + 1 Kmeans + 2 SQP -0.713 -0.674 Objective 1.000 0.001 0.590 1.000 0.001 0.590 0.298 0.615 0.087 0.298 0.615 0.087 3 3070 # distinct values

Examples Conceptual Design Crashworthiness Design Geometry Initial Design

Examples Crashworthiness Design Conceptual Design Optimization Problem

Examples Design Parameterization Crashworthiness Design Using Kmeans to cluster conceptual design into 11 groups[2]

Examples Parametric Optimization Crashworthiness Design Maximize crashworthiness Optimization problem specific energy absorption, peak crushing force

Pareto Fronts

Summary 1 Conceptual 1 2 Param. 2 3 3 Optimization Three Stages Design Optimization 1 Conceptual structural optimization thousands variables good performance 1 2 Param. Kmeans clustering reduced variables worst performance Design Cycle 2 3 3 Optimization multiobjective optimization sequential metamodel update improved performance improved manufacturability

References Acknowledgement Tavakoli, R., and Mohseni, S. M., 2014. “Alternating active-phase algorithm for multimaterial topology optimization problems: A 115-line MATLAB implementation”, Struct Multidisc Optim, 49(4), pp. 621–642. Liu, K., Tovar, A., Nutwell, E., and Detwiler, D., “Thin-walled compliant mechanism component design assisted by machine learning and multiple surrogates”, SAE Technical Paper 2015-01-1369, 2015. Acknowledgement Honda R&D Americas supported this research effort. Any opinions, findings, conclusions, and recommendations expressed in this investigation are those of the writers and do not necessarily reflect the views of the sponsors.