Design Space Optimization Research Articles

Nested loop approach for topology and shape optimization of crash-loaded deep-drawn components using contact forces for the inner loops

In this paper a new method for the optimization of deep-drawn shell components in crash by using substitute load cases in established sensitivity based static optimization is presented. The optimization process is split into an inner and an outer loop. In the outer loop the contact forces during crash are determined. These contact forces are used as substitute load cases in a static topology optimization, which builds the inner loop of the method. The presented method was inspired by the Equivalent Static Loads Method, but differs primarily in two aspects. These are the use of the contact forces as alternative to equivalent static loads in the linear static topology optimization and the extraction of a shell model that represents the voxel result obtained from topology optimization. A manufacturing constraint is applied in the topology optimization so that the results are shell components. This manufacturing constraint is enabling the mentioned extraction of a shell model. Two examples are presented where the method is applied to minimize the intrusion. The first example is a cantilever, the second example is a structure that is twisted. In both examples a rigid body impacts the structure. The method has shown to be numerical stable and suitable for the shown examples when the intrusion is the objective of the optimization. The intrusion was reduced significantly in both examples. The key novelty of the presented method is the ability to perform a static topology optimization of a voxel design space for a non-linear dynamic optimization model with the result being a shell model that can be analyzed for crash.

Data Mining-Based Design Space Exploration and Optimization for Tandem Airfoils

The joined-wing configuration has great technical appeal for the development of next-generation SensorCraft. Research based on the simplified tandem airfoil system can improve understanding of the joined-wing configuration’s aerodynamic characteristics. We combine the adjoint-based aerodynamic shape optimization and self-organizing map- (SOM-) based data mining technology to reveal the flow interactions of tandem airfoils and aerodynamic characteristics from the perspective of the entire aerodynamic design space. The SOM is used to explore the correlation between relative position parameters and aerodynamic force coefficients of tandem airfoil systems. Results show that the drag coefficient at the defined range of lift coefficients has obviously positive linear correlation and greatly dependents on the value of decalage. The tandem airfoils with negative decalage around -2.7° have the smallest drag coefficients. Due to variations in the aerodynamic interaction strength, the drag coefficient of each airfoil changes from a linear law to a nonlinear law as airfoils approach each other. We then perform single-point aerodynamic shape optimization based on two sets of relative position parameters with different aerodynamic interaction strengths, and 1.8% and 1.28% drag reductions are obtained, respectively. Based on optimized airfoils, the SOM is used to reveal the distribution of drag variation in the design space constructed by relative position parameters. Results illustrate that the aerodynamic interference strength between the front and rear airfoils significantly affects the drag reduction mechanism, which results in the different distribution patterns of drag variation in design space.

Design and Additive Manufacturing of a Passive Ankle-Foot Orthosis Incorporating Material Characterization for Fiber-Reinforced PETG-CF15.

The individualization of patient-specific ankle joint orthoses is becoming increasingly important and can be ideally realized by means of additive manufacturing. However, currently, there are no functional additively manufactured fiber-reinforced products that are used in the field of orthopedic treatment. In this paper, an approach as to how additively manufactured orthopedic products can be designed and produced quickly and flexibly in the future is presented. This is demonstrated using the example of a solid ankle-foot orthosis. For this purpose, test results on PETG-CF15, which were determined in a previous work, were integrated into a material map for an FEA simulation. Therewith, the question can be answered as to whether production parameters that were determined at the test specimen level can also be adapted to real, usable components. Furthermore, gait recordings were used as loading conditions to obtain exact results for the final product. In order to perfectly adapt the design of the splint to the user, a 3D scan of a foot was performed to obtain a perfect design space for topology optimization. This resulted in a patient-specific and stiffness-optimized product. Subsequently, it was demonstrated that the orthosis could be manufactured using fused layer modelling. Finally, a comparison between the conventional design and the consideration of AM-specific properties was made. On this basis, it can be stated that the wearing comfort of the patient-specific design is very good, but the tightening of the splint still needs to be improved.

Aerodynamic and structural multidisciplinary optimization design method of fan rotors based on blade curvature constraints

The optimization design of the actual fan/compressor rotors is a multidisciplinary problem. The aerodynamics and strength multidisciplinary optimization design of the fan/compressor rotors can improve the aerodynamic performance of rotors as much as possible under the condition of satisfying the structural strength requirements. However, the conventional multidisciplinary optimization of aerodynamics and structures will significantly increase the amount of computation cost and time period. Thus, it is difficult for conventional multidisciplinary optimization methods to be used in real-world engineering practices. In order to reduce the computational burden and time cost of the multidisciplinary optimization design, this paper firstly proposes a multidisciplinary optimization design method for rotors based on blade curvature constraints. In the optimization, the self-organizing map (SOM) method is applied to analyze and extract the constraint value of the blade curvature. And the blade curvature constraint value is used as a penalty function instead of the time-consuming high-fidelity FEM, which greatly reduces the computational cost and runtime of the multidisciplinary optimization. Besides, the Free-form deformation (FFD) method is adopted to realize the flexible deformation of the three-dimensional blade with the smallest number of design variables and polynomial chaos Kriging is used as a surrogate model for aerodynamic performance prediction in the optimization process. The method verification and mechanism analysis are carried out by studying a fan rotor. Data mining of FEM samples shows that, in the optimization design space, the maximum spanwise curvature of the blade is monotonically related to the maximum stress of the blade. And the maximum streamwise curvature, maximum spanwise slope, maximum streamwise slope, and maximum thickness of the blade have no related relationship with the maximum stress of the blade. Compared with the conventional multidisciplinary optimization design method based on the surrogate models of high-fidelity computational fluid dynamics (CFD) and finite element method (FEM), the time cost of the multidisciplinary optimization design method based on curvature constraints is reduced by 10 times, and the time cost of the multidisciplinary optimization is significantly reduced. The results show that, in terms of structural performance, the maximum stress of the aerodynamic optimization method without blade curvature constraints is 426 MPa, which exceeds the yield limit of aluminum alloy material (420 MPa), and the maximum stress of the multidisciplinary optimization design with blade curvature constraints proposed in this paper is 344 MPa. In terms of aerodynamic performance, the isentropic efficiency of the aerodynamic optimization method without blade curvature constraints and the method proposed in this paper are increased by 2.1% and 1.8%, respectively. Therefore, the proposed method reduces the maximum stress of the blade by 19.5% with little influence on the aerodynamic performance.

Physical design guidelines to minimize area-specific ON-resistance for rated ON-current and breakdown voltage of GaN power HEMTs

In this article, we report on the development of an analytical model to estimate area-specific ON-state resistance (R ds,on) of GaN-based power high electron mobility transistor (HEMT) using rated device specifications—ON-state drain current (I ON) and maximum operating drain-to-source voltage (V DSO)—as input parameters. The rated I ON and V DSO are considered as fractions k and S, of the maximum possible drain current (I DS,max) and breakdown voltage (V BR), respectively, deliverable by the power device. The developed model is utilized to obtain the optimal physical design space parameters for a comb-like power HEMT design. Due consideration has been given to the trade-off between R ds,on and area-specific R ds,on of the transistor, device processing limitations for all the physical device parameters. The developed model has been validated with experimental results of prior literature. Our calculations impose a lower-bound for the best possible R ds,on as well as the area-specific on-resistance product (R ds,on AA) that can be obtained for a given starting channel sheet resistance in the comb architecture for a desired I ON − V DSO rating.

Energy buffer mechanism for heat transfer enhancement in grooved channel cooling with flow intermittency

Driven by the ever-growing heat load in industrial applications such as fast charging electrical vehicle batteries and high-performance processors, advanced cooling technologies for efficient thermal management are urgently needed. This numerical work demonstrates the great potential of flow intermittency in grooved channels for thermal performance improvement at laminar condition, and aims to reveal the underlying mechanism that governs the heat transfer enhancement. The open-source computational fluid dynamics code OpenFOAM is employed to resolve the intermittent channel flow with triangular surface grooves. The time-averaged Reynolds number Re m = 100 and the Strouhal number St = 0.2 are maintained, while the close time ratio γ ranges from 0.1 to 0.9. The thermal performance improvement is attributed to the “energy buffer” mechanism by cavity vortices, which induces strong near-wall reverse flow and promotes effective mainstream-boundary flow mixing. The results indicate that the averaged surface Nusselt number consistently increases with the close time ratio and at γ = 0.9 reaches 1.9 times of the steady-flow value. Particularly the heat transfer performance inside grooves is remarkably improved by a maximum of 175%. This novel concept of synergizing flow intermittency and surface structure achieves notable heat transfer enhancement under constant coolant consumption, and shows ample design space for further optimization.

On the combination of dynamic substructuring and surrogate modeling for the design and study of complex systems

For decades, dynamic substructuring approaches have been successfully utilized for the modeling and simulation of complex systems. More recently, surrogate modeling methods have emerged as a way to reduce the computational cost of simulating for design. This talk will introduce a paradigm in which these two techniques may be combined for the design and study of complex systems. For illustration, a simple example is put forward in which a mass-spring system is broken into subsystems and parameterized. The open-source Python package SMT (Surrogate Modeling Toolbox) developed and maintained by Bouhel et al. is used to construct surrogate models for each subsystem in which the component parameters are taken as inputs and the frequency response functions (FRFs) of the interface degrees of freedom are output. These FRFs are then used to construct the response of the fully coupled system by utilizing a dual Frequency Based Substructuring technique. In many real-world applications, this manner of calculating the effect of varying design parameters on the system response is likely more practical and computationally feasible than the alternative of directly simulating the coupled system response for many parameter sets and training a surrogate model from that output for further design space exploration and optimization. [Work supported by the Office of Naval Research]

Suggestions for solution space exploration in the early stage of architectural design based on a literature review

Early design decisions have higher potential to influence building performance compared with the decisions made at later design stages. Performance simulation and optimization algorithms have been integrated to assist early design in reducing carbon emissions, improving indoor thermal comfort, etc. However, early decision making within a limited time frame is still challenging due to the large number of design options, the lack of decision-making guidance, and the trade-offs among various requirements. Selecting appropriate methods to explore design space is the key to find an ideal solution. This paper reviewed the challenges and identified the key questions to access the ability of existing decision-making methods to cope with different challenges. It is concluded that the interactive exploration of design space could be more effective and efficient by (1) combining the surrogate models and the automated optimization algorithms to improve the efficiency of the building performance calculation and the optimal design space position; and by (2) extending the optimal design space to increase the solution diversity, and (3) filtering the near optimal design space with consideration of the stakeholders’ preferences and values. Further integration of tools for building performance simulation, diversity description and decision-making guidance is needed to support the decision -making process.

Structural optimization of the wing box for a hybrid-electric commuter aircraft

Hybrid-electric commuter aircraft segment is playing a significant role in the electrification of air transportation. Towards the achievement of efficient and robust transportation, design and optimization processes are necessary to evaluate the different aircraft components. Within this context, the current work investigates the impact of the positioning of the propulsion system and spars on the structural integrity of a hybrid-electric commuter aircraft. The proposed approach is based on an in-house aircraft sizing tool, along with geometry generation and high-fidelity structural evaluation models. These tools are tailored in an automated computational pipeline, that includes pre-processing, model evaluation and post-processing tasks, able to perform design space exploration and optimization over different loading conditions of a selected mission envelope. This work focuses on the assessment of the impact of the additional non-structural weight e.g., batteries, fuel, and propulsion components, inside the wing box, on the stress, deformation and spanwise thickness distribution of the structure. The effect of spars and propulsion system positioning on the available storage space, maximum stress and displacement is discussed, with the aft spar having the greatest impact. Finally, the structural model is optimized to minimize the mass, resulting in a 29% weight reduction, compared to the initial design.

Response surface methodology for design of gas turbine combustor

• Automated design space exploration with CFD quantifies combustor performance. • SST - kω turbulence model with partially premixed FGM combustion model used. • Removing blow-off design points improves response surface prediction accuracy by 57.2% • Pareto fronts from multi objective optimization used for trade-off decisions. • Six sigma DOE analysis quantifies uncertainty in combustor performance. Gas turbine combustor design is a complex multi-objective problem. In the present study, parametric design space study and optimization of a gas turbine combustor using computational fluid dynamics (CFD) simulations is presented. Baseline case validation, automated workflow setup for geometry modification, meshing, boundary condition specification, CFD solution and output parameter calculations are discussed. Response surface methodology is used to study combustor performance based on combustion efficiency, pattern factor, total pressure drop, Carbon monoxide (CO) and Nitrogen oxides (NOx) with variations in three design variables: swirl number, secondary hole diameter and dilution hole diameter. We use central composite design for design of experiments (DOE) and genetic aggregation for response surface generation. Design space refinement is carried out to identify the blow-off region and limit the search space for optimal designs to swirl number greater than 0.9. Exclusion of blow-off design points while generating the response surface resulted not only in 57.2% average reduction of root mean square error in the response surface predictions but also smoother trends away from the blow-off region. A candidate optimal design point with swirl number = 1.0, secondary hole diameter = 12.24 mm and dilution hole diameter = 15.26 mm is chosen using multi objective genetic algorithm on the response surface. Finally, uncertainty quantification with six sigma DOE analysis quantifies the confidence intervals for performance parameters based on the variations in geometric design variables. This preliminary design methodology can be used to improve existing combustors and guide the design of novel combustor concepts.

Concurrent topology and fiber orientation optimization method for fiber-reinforced composites based on composite additive manufacturing

Additive manufacturing of fiber-reinforced composite (FRC) parts provides a new rapid prototyping technique for designs. However, restricted by the layer-by-layer style of additive manufacturing techniques, the designed fiber orientations should be parallel to the print plane, and that will result in a reduced design space for the orientation optimization. To enlarge the orientation design space under this constraint, this paper proposes a new optimization method for FRC parts. The optimized structure is composed of several groups of components, and the fiber orientation of each group of components is constrained to a specific plane. Based on the composite additive manufacturing technology, these components can be fabricated separately and joined together to form the whole structure. The number of the component groups (also the fiber print planes) is predefined. In this method, the structure is optimized by concurrently designing the topology, the components partitioning and the fiber orientations. The structural topology and components partitioning are described by the SIMP interpolation scheme and discrete material optimization (DMO) interpolation scheme, respectively. The discrete-continuous parameterization (DCP) method with two sub-intervals is applied in the orientation optimization to avoid the local optimum of the angle variables, and a unified formulation is given for the concurrent optimization design. Furthermore, a density projection strategy with self-adaptive threshold parameters for multi-material optimization problems is proposed to get the distinct component interfaces. A stable convergence can be obtained without manually adjusting the projection parameters during the optimization iterations. The corresponding angle filtering method is developed to smooth the optimized fiber orientations. Numerical examples and manufacturing experiments are presented to demonstrate the effectiveness of the proposed method.

A marine propeller design method based on two-fidelity data levels

A Simulation Based Design Optimization method for marine propellers design using a two-fidelity levels metamodel for global design space exploration and optimization is presented. Response surfaces are built using the co-Kriging approximation, i.e. a multi-output Gaussian process that combines large low-fidelity dataset with few, costly, high-fidelity data. The method is applied for the hydrodynamic shape optimization of the E779A propeller using, as fidelity levels, two different physical models for the propeller performances prediction, namely an inviscid, potential based Boundary Element Method (low-fidelity) and a viscous, finite volume RANS solver (high-fidelity). Results demonstrate the feasibility of multi-objective, constrained, design procedures, like those involving marine propellers, using these multi-fidelity response surfaces. At the same time, the need of good correlations between low- and high-fidelity data feeding the response surfaces is highlighted as a requisite for robust and reliable predictions using these approximated methods.

Optimization of Design Space for Vertically Stacked Junctionless Nanosheet FET for Analog/RF Applications

Optimization of Design Space for Vertically Stacked Junctionless Nanosheet FET for Analog/RF Applications

A Bi-stage Multi-objective Reliability-based Design Optimization Using Surrogate Model for Reusable Thrust Chambers

To reduce the computational burden of Multi-Objective Reliability-Based Design Optimization (MORBDO) and promote its application in complex practical systems, a bi-stage MORBDO procedure using surrogate models is proposed in this paper. The novel process consists of two stages: in the first stage, a narrowed solution space named as MORBDO design space is obtained by a pre-multi-objective deterministic design optimization in the whole original design space; In the second stage, the MORBDO design space is extended to form an augmented space by considering uncertainties, and then the MORBDO is executed with the double-loop strategy over the augmented space. Besides, the multiple response surface (MRS) is adopted in the bi-stage MORBDO procedure to replace the time-consuming finite element analysis. The proposed method is validated by conducting MORBDO on a lab-scale reusable LOX/H2 thrust chamber aiming at maximum residual strength and cyclic life. Compared with the traditional MORBDO implemented in the whole original design space, the bi-stage MORBDO can significantly reduce the computational burden of the surrogate model by 49.33% and only one-quarter of the optimization population is required in NSGA II to search for the optimal solution. Finally, a sensitivity analysis is performed to quantify the importance ranking of design variables of thrust chambers. The results indicate that the geometry of cooling channels near the throat plays the most important role in the thrust chamber's residual strength and cyclic life. The proposed method is easy to be conducted and holds great potentials in the MORBDO of other complex practical systems.

CAD-integrated topology optimization method with dynamic extrusion feature evolution for multi-axis machining

This paper proposes a subtractive geometry projection topology optimization approach to simulate the multi-axis machining process and remove material from the initial design domain. Each geometric primitive is described by a plane extrusion operation based on a 2D closed cubic spline curve controlled by boundary points. The reference plane for the 3D extrusion operation can freely rotate and translate in the design space for optimization. The primitive is then projected onto the mesh based on the Heaviside function to modify the density distribution. The cutting primitives are combined using the p-norm aggregation function to produce the final subtractive design. The method of moving asymptotes method is implemented to optimize each geometry primitive based on analytical gradients. One of the major advantages of the proposed method is its ability to readily integrate the modeling history into the optimization process, paving the way to construct commercial CAD compatible designs.

A Systematic Design Optimization Approach for Multiphysics MEMS Devices Based on Combined Computer Experiments and Gaussian Process Modelling.

This paper presents a systematic and efficient design approach for the two degree-of-freedom (2-DoF) capacitive microelectromechanical systems (MEMS) accelerometer by using combined design and analysis of computer experiments (DACE) and Gaussian process (GP) modelling. Multiple output responses of the MEMS accelerometer including natural frequency, proof mass displacement, pull-in voltage, capacitance change, and Brownian noise equivalent acceleration (BNEA) are optimized simultaneously with respect to the geometric design parameters, environmental conditions, and microfabrication process constraints. The sampling design space is created using DACE based Latin hypercube sampling (LHS) technique and corresponding output responses are obtained using multiphysics coupled field electro–thermal–structural interaction based finite element method (FEM) simulations. The metamodels for the individual output responses are obtained using statistical GP analysis. The developed metamodels not only allowed to analyze the effect of individual design parameters on an output response, but to also study the interaction of the design parameters. An objective function, considering the performance requirements of the MEMS accelerometer, is defined and simultaneous multi-objective optimization of the output responses, with respect to the design parameters, is carried out by using a combined gradient descent algorithm and desirability function approach. The accuracy of the optimization prediction is validated using FEM simulations. The behavioral model of the final optimized MEMS accelerometer design is integrated with the readout electronics in the simulation environment and voltage sensitivity is obtained. The results show that the combined DACE and GP based design methodology can be an efficient technique for the design space exploration and optimization of multiphysics MEMS devices at the design phase of their development cycle.

Device design and optimization of CNTFETs for high-frequency applications

Carbon nanotube (CNT) field-effect transistors (FETs) have recently reached high-frequency (HF) performance similar to that of silicon RF-CMOS at the same gate length despite a tube density and current per tube that are far from the physical limits and suboptimal device architecture. This work reports on an investigation of the optimal device design for practical HF applications in terms of cut-off frequencies, power gain, and linearity. Different fundamental designs in the gate contact arrangement are considered based on a 3D device simulation of both CNTs and contacts. First, unit cells with a single CNT and minimal contact sizes are compared. The resulting simulation data are then extended toward a structure with two gate fingers and realistic contact sizes. Corresponding parasitic capacitances, as well as series and contact resistances, have been included for obtaining realistic characteristics and figures of merit that can be used for comparison with corresponding silicon RF MOSFETs. Finally, a sensitivity analysis of the device architecture with the highest performance is performed in order to find the optimal device design space.

Gradient-free aerodynamic shape optimization using Large Eddy Simulation

In this paper we demonstrate the ability to perform gradient-free aerodynamic shape optimization using Large Eddy Simulation (LES) with the Mesh Adaptive Direct Search (MADS) optimization algorithm. We first outline the challenges associated with performing gradient-based optimization using LES, specifically chaotic divergence of the adjoint. We then introduce a Dynamic Polynomial Approximation (DPA) procedure, which allows the high-order solution polynomial representation used by the flow solver to be increased, or decreased, depending on the poll size being used by MADS. This allows rapid convergence towards the optimal design space using lower-fidelity simulations, followed by automatic transition to higher-fidelity simulations when close to the optimal design point. We demonstrate the utility of MADS for optimization of simple chaotic problems, specifically the Lorenz system. We then demonstrate the utility of DPA for aerodynamic optimization of a low Reynolds SD7003 airfoil, highlighting the benefits of the binary DPA approach. Finally, we perform aerodynamic optimization of a turbulent SD7003 airfoil with a final design that increases the mean lift to drag ratio by 32% relative to experimental data, demonstrating that shape optimization using LES and MADS is feasible for aerodynamic design.

Artificial intelligence assisted MOPSO strategy for discerning the exergy efficiency potential of a methanol induced RCCI endeavour through GA coupled multi-attribute decision making approach

The present study undertakes a comprehensive effort to explore the exergy efficiency-emissions-stability-combustion quality characteristics of premixed methanol with diesel reactivity controlled operation. The combustion phasing of the dual fuel operation primarily depends on the methanol participation rate, wherein the peak in-cylinder pressure and heat release rate decreases with increased methanol injection duration. Though simultaneous reductions of NOx and soot were observed in this study, the stability of the operations deteriorates along with unburned hydrocarbon (UHC) and carbon monoxide (CO) with increasing methanol participations resulting in a trade-off situation. Besides, the severe instability of the operation at 50% load causes misfire due to excessive dilution of the charge at higher methanol participation. The study further explores the potential of Gene Expression Programming assisted meta-model coupled Multi-objective Particle Swarm optimization (MOPSO) algorithm based multi-objective optimization endeavour to explore the optimal operational design space considering the multiple responses of exergy efficiency, NOx, PM, UHC, CO, Coefficient of Variance of indicated mean effective pressure (COVIMEP), lowest normalized value (LNV) of indicated mean effective pressure. In this present case of study, the optimization endeavor has yielded 350 numbers of Pareto solutions, while only 26 numbers of Pareto solutions were observed in the experimental counterpart. Moreover, the experimental domain of the present study has produced only single set of experiment which can satisfy the respective emission limits of NHC and PM altogether, whereas 13 sets were evident in the optimization study to maintain the NHC and PM footprint under the emission constraints simultaneously. The overall analysis of the Pareto solutions evolved in the optimization study has revealed that to attain the minimum NHC and PM footprints, the penalty of exergy efficiency and CO emissions must be incurred. The overall minimum of NHC footprint in the optimization study was recorded as 4.19 g/kWhr, compared to 6.58 g/kWhr as observed in the experimental endeavor. Similarly, the footprint of minimum PM was discovered as 0.13 g/kWhr in the optimization regime, which was 27% lower than the experimental counterpart. However, an imperceptible penalty of 1% was incurred in exergy efficiency, despite of significant lowering of overall minimum CO emissions by 84% in the optimization endeavor compared to the experimental counterpart.

Design optimization of a marine current turbine having winglet on blade

Winglets on a turbine blade can modify flow features and improve a marine current turbine (MCT). In this work, to maximize the power coefficient (CP) and torque (T), cant angle (α), and height (h) of a winglet of an MCT were modified. The problem was solved using a high-fidelity solver code Fluent 2019R2 containing Reynolds-Averaged Navier–Stokes (RANS) equations. The flow domain meshed with tetrahedral elements. Nine different designs were produced to fill the design space for optimization. A set of low fidelity models such as second-order regression, kriging, and neural network models were used to approximate the high-fidelity results. The optimal designs further validated with the high-fidelity simulated results. The optimal design, increased CP by 7% for α = 33.2o and h = 2.04% of the turbine radius, reduced the recirculation zone at the trailing edge, increased the pressure gradient, and reduced the tip vortex.