Data-driven design of mechanical metamaterials is an increasingly popular method to combat costly... more Data-driven design of mechanical metamaterials is an increasingly popular method to combat costly physical simulations and immense, often intractable, geometrical design spaces. Using a precomputed dataset of unit cells, a multiscale structure can be quickly filled via combinatorial search algorithms, and machine learning models can be trained to accelerate the process. However, the dependence on data induces a unique challenge: an imbalanced dataset containing more of certain shapes or physical properties can be detrimental to the efficacy of data-driven approaches. In answer, we posit that a smaller yet diverse set of unit cells leads to scalable search and unbiased learning. To select such subsets, we propose METASET, a methodology that (1) uses similarity metrics and positive semi-definite kernels to jointly measure the closeness of unit cells in both shape and property spaces and (2) incorporates Determinantal Point Processes for efficient subset selection. Moreover, METASET al...
Dynamic stability is a key performance metric of motor vehicles and has a direct impact on passen... more Dynamic stability is a key performance metric of motor vehicles and has a direct impact on passenger experience and customer satisfaction. The desired vehicle dynamics behavior can be achieved by optimizing the design of vehicle suspensions. Two challenges are associated with this design optimization task. The first one arises from the large number (e.g., 40 or 50) of design variables in modern suspension systems. Such multitude of variables not only makes it expensive to build a training dataset for metamodeling purposes, but also renders accurate surrogate modeling extremely difficult. The second challenge is a lack of guideline for choosing a proper multidisciplinary design optimization (MDO) method for a single MDO problem such as one for vehicle suspension design. In this paper, an enhanced Gaussian process (GP) metamodeling technique is developed and several versions of the collaborative optimization (CO) method are compared via a vehicle suspension design problem. In our enha...
We introduce a novel method for Gaussian process (GP) modeling of massive datasets called globall... more We introduce a novel method for Gaussian process (GP) modeling of massive datasets called globally approximate Gaussian process (GAGP). Unlike most large-scale supervised learners such as neural networks and trees, GAGP is easy to fit and can interpret the model behavior, making it particularly useful in engineering design with big data. The key idea of GAGP is to build a collection of independent GPs that use the same hyperparameters but randomly distribute the entire training dataset among themselves. This is based on our observation that the GP hyperparameter approximations change negligibly as the size of the training data exceeds a certain level, which can be estimated systematically. For inference, the predictions from all GPs in the collection are pooled, allowing the entire training dataset to be efficiently exploited for prediction. Through analytical examples, we demonstrate that GAGP achieves very high predictive power matching (and in some cases exceeding) that of state-...
Predicting the mechanical properties of additively manufactured parts is often a tedious process,... more Predicting the mechanical properties of additively manufactured parts is often a tedious process, requiring the integration of multiple stand-alone and expensive simulations. Furthermore, as properties are highly location-dependent due to repeated heating and cooling cycles, the properties prediction models must be run for multiple locations before the part-level performance can be analyzed for certification, compounding the computational expense. This work has proposed a rapid prediction framework that replaces the physics-based mechanistic models with Gaussian process metamodels, a type of machine learning model for statistical inference with limited data. The metamodels can predict the varying properties within an entire part in a fraction of the time while providing uncertainty quantification. The framework was demonstrated with the prediction of the tensile yield strength of Ferrium ® PH48S maraging stainless steel fabricated by additive manufacturing. Impressive agreement was found between the metamodels and the mechanistic models, and the computation was dramatically decreased from hours of physics-based simulations to less than a second with metamodels. This method can be extended to predict various materials properties in different alloy systems whose processstructure-property-performance interrelationships are linked by mechanistic models. It is powerful for rapidly identifying the spatial properties of a part with compositional and processing parameter variations, and can support part certification by providing a fast interface between materials models and part-level thermal and performance simulations.
Enabled by advancements in multi-material additive manufacturing, lightweight lattice structures ... more Enabled by advancements in multi-material additive manufacturing, lightweight lattice structures consisting of networks of periodic unit cells have gained popularity due to their extraordinary performance and wide array of functions. This work proposes a density-based robust topology optimization method for meso-or macroscale multi-material lattice structures under any combination of material and load uncertainties. The method utilizes a new generalized material interpolation scheme for an arbitrary number of materials, and employs univariate dimension reduction and Gauss-type quadrature to quantify and propagate uncertainty. By formulating the objective function as a weighted sum of the mean and standard deviation of compliance, the tradeoff between optimality and robustness can be studied and controlled. Examples of a cantilever beam lattice structure under various material and load uncertainty cases exhibit the efficiency and flexibility of the approach. The accuracy of univariate dimension reduction is validated by comparing the results to the Monte Carlo approach.
Data-driven design of mechanical metamaterials is an increasingly popular method to combat costly... more Data-driven design of mechanical metamaterials is an increasingly popular method to combat costly physical simulations and immense, often intractable, geometrical design spaces. Using a precomputed dataset of unit cells, a multiscale structure can be quickly filled via combinatorial search algorithms, and machine learning models can be trained to accelerate the process. However, the dependence on data induces a unique challenge: an imbalanced dataset containing more of certain shapes or physical properties can be detrimental to the efficacy of data-driven approaches. In answer, we posit that a smaller yet diverse set of unit cells leads to scalable search and unbiased learning. To select such subsets, we propose METASET, a methodology that (1) uses similarity metrics and positive semi-definite kernels to jointly measure the closeness of unit cells in both shape and property spaces and (2) incorporates Determinantal Point Processes for efficient subset selection. Moreover, METASET al...
Dynamic stability is a key performance metric of motor vehicles and has a direct impact on passen... more Dynamic stability is a key performance metric of motor vehicles and has a direct impact on passenger experience and customer satisfaction. The desired vehicle dynamics behavior can be achieved by optimizing the design of vehicle suspensions. Two challenges are associated with this design optimization task. The first one arises from the large number (e.g., 40 or 50) of design variables in modern suspension systems. Such multitude of variables not only makes it expensive to build a training dataset for metamodeling purposes, but also renders accurate surrogate modeling extremely difficult. The second challenge is a lack of guideline for choosing a proper multidisciplinary design optimization (MDO) method for a single MDO problem such as one for vehicle suspension design. In this paper, an enhanced Gaussian process (GP) metamodeling technique is developed and several versions of the collaborative optimization (CO) method are compared via a vehicle suspension design problem. In our enha...
We introduce a novel method for Gaussian process (GP) modeling of massive datasets called globall... more We introduce a novel method for Gaussian process (GP) modeling of massive datasets called globally approximate Gaussian process (GAGP). Unlike most large-scale supervised learners such as neural networks and trees, GAGP is easy to fit and can interpret the model behavior, making it particularly useful in engineering design with big data. The key idea of GAGP is to build a collection of independent GPs that use the same hyperparameters but randomly distribute the entire training dataset among themselves. This is based on our observation that the GP hyperparameter approximations change negligibly as the size of the training data exceeds a certain level, which can be estimated systematically. For inference, the predictions from all GPs in the collection are pooled, allowing the entire training dataset to be efficiently exploited for prediction. Through analytical examples, we demonstrate that GAGP achieves very high predictive power matching (and in some cases exceeding) that of state-...
Predicting the mechanical properties of additively manufactured parts is often a tedious process,... more Predicting the mechanical properties of additively manufactured parts is often a tedious process, requiring the integration of multiple stand-alone and expensive simulations. Furthermore, as properties are highly location-dependent due to repeated heating and cooling cycles, the properties prediction models must be run for multiple locations before the part-level performance can be analyzed for certification, compounding the computational expense. This work has proposed a rapid prediction framework that replaces the physics-based mechanistic models with Gaussian process metamodels, a type of machine learning model for statistical inference with limited data. The metamodels can predict the varying properties within an entire part in a fraction of the time while providing uncertainty quantification. The framework was demonstrated with the prediction of the tensile yield strength of Ferrium ® PH48S maraging stainless steel fabricated by additive manufacturing. Impressive agreement was found between the metamodels and the mechanistic models, and the computation was dramatically decreased from hours of physics-based simulations to less than a second with metamodels. This method can be extended to predict various materials properties in different alloy systems whose processstructure-property-performance interrelationships are linked by mechanistic models. It is powerful for rapidly identifying the spatial properties of a part with compositional and processing parameter variations, and can support part certification by providing a fast interface between materials models and part-level thermal and performance simulations.
Enabled by advancements in multi-material additive manufacturing, lightweight lattice structures ... more Enabled by advancements in multi-material additive manufacturing, lightweight lattice structures consisting of networks of periodic unit cells have gained popularity due to their extraordinary performance and wide array of functions. This work proposes a density-based robust topology optimization method for meso-or macroscale multi-material lattice structures under any combination of material and load uncertainties. The method utilizes a new generalized material interpolation scheme for an arbitrary number of materials, and employs univariate dimension reduction and Gauss-type quadrature to quantify and propagate uncertainty. By formulating the objective function as a weighted sum of the mean and standard deviation of compliance, the tradeoff between optimality and robustness can be studied and controlled. Examples of a cantilever beam lattice structure under various material and load uncertainty cases exhibit the efficiency and flexibility of the approach. The accuracy of univariate dimension reduction is validated by comparing the results to the Monte Carlo approach.
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Papers by Yu-Chin Chan