Sampling Of Design Space Research Articles

A data-driven framework to predict fused filament fabrication part properties using surrogate models and multi-objective optimisation

In additive manufacturing (AM), due to large number of process parameters and multiple responses of interest, it is hard for AM designers to attain optimal part performance without a systematic approach. In this research, a data-driven framework is proposed to achieve the desired AM part performance and quality by predicting part properties and optimising AM process parameters effectively and efficiently. The proposed framework encompasses efficient sampling of design space and establishing the initial experiment points. Based on established empirical data, surrogate models are used to characterise the influence of critical process parameters on responses on interest. Furthermore, process maps can be generated for enhancing understanding on the influence of process parameters on responses of interests and AM process characteristics. Subsequently, multi-objective optimisation coupled with a multi criteria decision-making technique is applied to determine an optimal design point, which maximises the identified responses of interest to meet the part functional requirements. A case study is used to validate the proposed framework for optimising an ULTEM™ 9085-fused filament fabrication part to meet its functional requirements of surface roughness and mechanical strength. From the case study, results indicate that the proposed approach is able to achieve good predictive results for responses of interest with a relatively small dataset. Furthermore, process maps generated from the surrogate model provide a visual representation of the influence between responses of interest and critical process parameters for FFF process, which traditionally requires multiple investigations to arrive at similar conclusions.

You only design once (YODO): Gaussian Process-Batch Bayesian optimization framework for mixture design of ultra high performance concrete

Ultra-high-performance concrete (UHPC) has superior strength and durability, and hence it has been primarily favored in a variety of applications in structural engineering. While the open literature presents a series of predictive machine learning (ML) models to predict the strength of UHPC from its constituent materials, the reverse problem of identifying possible concrete mixtures with a targeted (pre-tailored) performance persists to exist. Unlike other works, and in an effort to bridge this knowledge gap, this study proposes a Gaussian process (GP) modeling with batch Bayesian optimization (BBO) framework (GP-BBO) to infer the mixture design of UHPC. In this framework, the GP is used as a predictive surrogate model constructed from experimental measurements. After the GP is trained and validated, BBO is used to infer the plausible formulae for the targeted strength by optimizing an acquisition function that trades off exploitation and exploration based on the optimality and variability of the surrogate model. As such, the proposed framework offers a list of possible UHPC formulae of a targeted strength. To facilitate a wide spread of the proposed framework, The ML code is shared for interested researchers to verify and expand upon. In addition, and to negate arising hurdles associated with GP-BBO programming, also an open-source and coding-free software (App) is created that can be directly deployed by UHPC fabricators. In contrast to the conventional trial-and-error-based mixture design, GP-BBO provides a self-adaptive paradigm for efficient sampling of design space for identifying the optimum sampling points. This framework can be extended to infer formulae that satisfy multiple performance objectives such as strength, workability, and durability.

The Objective Space and the Formulation of Design Requirement in Natural Laminar Flow Optimization

Design requirement is as important in aerodynamic design as in other industries because it sets up the objective for the samples in design space to approach. Natural Laminar Flow (NLF) optimization belongs to the type of aerodynamic design problems featured by the combination of distinct aerodynamic performance, where the design requirement is often formulated in form of summation of laminar-related performance and pressure drag performance with different weight assignment according to different perspectives. However, the formulations are rather experience-oriented and are decided non-quantitatively. Inspired by data manipulation approaches in design space (spanned by design variables of geometrical representation parameters) in many aerodynamic designs, this paper proposes new formulations of design requirement in NLF optimization via consideration of objective space (projection of design space through aerodynamics) and shows the impact of the corresponding formulation of design requirement to the result of NLF optimization in cases of transonic airfoil and aero engine compressor blade design from two perspectives: Pareto front convergence and improving effect of accessory performance. The paper uses Principal Component Analysis (PCA) to obtain the eigenvectors of objective space to extract the intrinsic information about specific problem. The method is realized in two cases with satisfactory result.

Innovative adaptive penalty in surrogate-assisted robust optimization of blade attachments

This paper proposes the combination of the adaptive penalty method based on design space sampling and evolutionary optimization towards the solution of a multi-objective blade attachment robust design problem. An adaptive penalty function based on Latin hypercube sampling was applied to tackle the non-feasible spaces inside the searching domain. Implementing this method provided a reduction in time to convergence. A genetic algorithm (GA) was used as an optimizer to minimize the stress state in critical areas of the attachment. The state of stress was computed using a finite-element model denoted as high-fidelity model. To reduce the call back to the high-fidelity model, a meta-model (also denoted as surrogate model) was developed and embedded in the GA to reduce the computational time. Using the surrogate model instead of the high-fidelity model also provided a reduction in the time needed to find the optimum. Besides, in order to obtain the most robust solution among the optimums given by the Pareto front, the same Kriging surrogate model was employed to perform a global sensitivity analysis.

Deep-learning neural-network architectures and methods: Using component-based models in building-design energy prediction

Increasing sustainability requirements make evaluating different design options for identifying energy-efficient design ever more important. These requirements demand simulation models that are not only accurate but also fast. Machine Learning (ML) enables effective mimicry of Building Performance Simulation (BPS) while generating results much faster than BPS. Component-Based Machine Learning (CBML) enhances the capabilities of the monolithic ML model. Extending monolithic ML approach, the paper presents deep-learning architectures, component development methods and evaluates their suitability for space exploration in building design. Results indicate that deep learning increases the performance of models over simple artificial neural network models. Methods such as transfer learning and Multi-Task Learning make the component development process more efficient. Testing the deep-learning model on 201 new design cases indicates that its cooling energy prediction (R2: 0.983) is similar to BPS, while errors for heating energy predictions (R2: 0.848) are higher than BPS. Higher heating energy prediction error can be resolved by collecting heating data using better design space sampling methods that cover the heating demand distribution effectively. Given that the accuracy of the deep-learning model for heating predictions can be increased, the major advantage of deep-learning models over BPS is their high computation speed. BPS required 1145 s to simulate 201 design cases. Using the deep-learning model, similar results can be obtained in 0.9 s. High computation speed makes deep-learning models suitable for design space exploration.

Adaptive Surrogate-Based Optimization of Vortex Generators for Tiltrotor Geometry

The design of vortex generators on a tiltrotor-aircraft infinite wing is presented using an adaptive surrogate modeling approach. Particular design issues in tiltrotors produce wings that are thick and highly loaded, and so separation and early-onset buffet can be problematic, and vortex generators are commonly used to alleviate these issues. In this work, the design of vortex generators for the elimination of separation is considered using a viscous flowfield simulation. A large design space of rectangular vane-type vortex generators is sampled and simulated, and a radial-basis-function surrogate model is implemented to model the full design space. An efficient adaptive sampling approach for improved design space sampling has also been developed that balances the properties of space filling, curvature capture, and optimum locating. This approach has been tested on the design of a vortex generator on a highly loaded infinite wing, with a representative tiltrotor airfoil section, using a five-dimensional design space. The design of the vortex generators using this approach shows that elimination of the separation is possible while simultaneously reducing the drag of the wing with optimized vortex generators, compared to the clean wing.

Accurate design‐oriented simulation‐driven modeling of miniaturized microwave structures

SummaryOne of the important prerequisites for efficient design optimization of microwave structures is availability of fast yet reliable replacement models (surrogates) so that multiple evaluations of the structure at hand can be executed in reasonable timeframe. Direct utilization of full‐wave electromagnetic (EM) simulations for handling optimization‐related tasks is often prohibitive. A popular approach to construction of fast surrogates is data‐driven modeling. Unfortunately, it normally requires a large number of training samples, and it is virtually infeasible for structures that exhibit highly nonlinear responses (e.g. filters or couplers). In this work, a design‐oriented modeling technique is proposed where good accuracy is achieved by careful non‐uniform design space sampling that accounts for nonlinear relationship between the operating frequency of the structure and its geometry parameters, as well as carrying out the modeling process only for selected characteristic points of the structure responses (those that determine satisfaction/violation of given design specifications). Our approach is demonstrated using a miniaturized microstrip rat‐race coupler modeled in a wide range of geometry parameters and compared to conventional data‐driven modeling using kriging interpolation. Design optimization examples are also provided. Copyright © 2016 John Wiley & Sons, Ltd.

An integrated multidisciplinary design optimization method for computer numerical control machine tool development

Computer numerical control machine tool is a typical complex product related with multidisciplinary fields, complex structure, and high-performance requirements. It is difficult to identify the overall optimal solution of the machine tool structure for their multiple objectives. A new integrated multidisciplinary design optimization method is then proposed by using a Latin hypercube sampling, a Kriging approximate model, and a multi-objective genetic algorithm. Design space and parametric model are built by choosing appropriate design variables and their value ranges. Samples in design space are generated by optimal Latin hypercube method, and design variable contributions for design performance are discussed for aiding the designer’s judgments. The Kriging model is built by using polynomial approximation according to the response outputs of these samples. The multidisciplinary design model is established based on three optimization objectives, that is, setting mass, optimum deformation, and first-order natural frequency, and two constraints, that is, second-order natural frequency and third-order natural frequency. The optimal solution is identified by using a multi-objective genetic algorithm. The proposed method is applied in a multidisciplinary optimization case study for a typical computer numerical control machine tool. In the optimal solution, the mass decreases by 3.35% and the first-order natural frequency increases by 4.34% in contrast to the original solution.

Multi-Objective Optimization of Impact Crusher Rotor Based on Response Surface Methodology

In this study, a method of multi-objective optimization is proposed to improve the quality of crushed materials and vibration performance of the rotor. This method is driven by the first order natural frequency and the radius of the rotor. The Central Composite Design (CCD) experiment method was used to guide the selection of appropriate structure finite element analysis samples in design space. The quadratic polynomials were employed to construct response surface (RS) model based on the response outputs of these samples obtained by analyzing the first order natural frequency, the harmonic and mass with the software ANSYS. Well-distributed samples were generated in the design space by shifted Hamersley sampling method. The prominent points were selected by the weighing method as initial samples. The multiobjective genetic algorithm was used to obtain the Pareto optimal solution set. Through optimization, the first order natural frequency was increased by 5.5%; the radius of the rotor was enlarged by 2.5% and the amplitude of the vibration was decreased by 11% at the position of bearing. At the same time, the rotor mass did not change much. The results show strong engineering practicability of the proposed method.

Structural Optimization of a Machining Center Column Based on Response Surface Method

In order to improve dynamic characteristics of a machining center column, this paper proposes a structural optimization method based on finite element method (FEM) and response surface method (RSM). In order to reduce number of design variables, the finite element analysis samples in design space are selected by using the central composite design (CCD) experiment method. On the basis of FEM results at these experiment samples, quadratic polynomials are employed to establish response surface model, which reflects the relationship between the response (mean frequency of the first four orders) and the design variables (the column structural sizes). The goal of getting maximum mean frequency is reached by using NLPQL algorithm in iSIGHT. Through the optimization, the mean frequency is increased by 8.12%.

"Smart" design space sampling to predict Pareto-optimal solutions

Many high-level synthesis tools offer degrees of freedom in mapping high-level specifications to Register-Transfer Level descriptions. These choices do not affect the functional behavior but span a design space of different cost-performance tradeoffs. In this paper we present a novel machine learning-based approach that efficiently determines the Pareto-optimal designs while only sampling and synthesizing a fraction of the design space. The approach combines three key components: (1) A regression model based on Gaussian processes to predict area and throughput based on synthesis training data. (2) A "smart" sampling strategy, GP-PUCB, to iteratively refine the model by carefully selecting the next design to synthesize to maximize progress. (3) A stopping criterion based on assessing the accuracy of the model without access to complete synthesis data. We demonstrate the effectiveness of our approach using IP generators for discrete Fourier transforms and sorting networks. However, our algorithm is not specific to this application and can be applied to a wide range of Pareto front prediction problems.

Nearly-orthogonal sampling and neural network metamodel driven conceptual design of multistage space launch vehicle

This paper presents a new design methodology for efficient conceptual design of complex systems involving multidisciplinary and computationally intensive analysis with large number of design variables. A nearly-orthogonal sampling of design space is proposed with good space filling properties to extract maximum useful information about system behavior using much lower number of trial designs. This sampled data is then used as training data for artificial neural network, which will act as a metamodel to represent the time consuming disciplinary analyses. A stage-wise interconnection of separate neural networks is also proposed for trajectory metamodel to offset dimensionality curse of neural networks. Genetic Algorithm performs global optimization by utilizing this metamodel and subsequently sequential quadratic programming performs the local optimization utilizing exact analyses. The performance of proposed methodology is investigated in this paper for the conceptual design optimization of multistage solid fueled space launch vehicle. The results show excellent approximation of highly non-linear functions using proposed sampling and drastic reduction in overall design optimization time, due to greatly reduced number of exact disciplinary analyses.