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2 pages, 157 KiB

Open AccessEditorial

Overview on the Special Issue on “Simulation-Based Optimization: Methods and Applications in Engineering Design”

by Riccardo Pellegrini and Andrea Serani

Algorithms 2023, 16(4), 191; https://doi.org/10.3390/a16040191 - 30 Mar 2023

Viewed by 1127

Abstract

The simulation-based design optimization (SBDO) paradigm is a well-known approach that has assisted, assists, and will continue to assist designers to develop ever-improving systems [...] Full article

(This article belongs to the Special Issue Simulation-Based Optimization: Methods and Applications in Engineering Design)

Research

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18 pages, 6796 KiB

Open AccessArticle

Research of Flexible Assembly of Miniature Circuit Breakers Based on Robot Trajectory Optimization

by Yan Han, Liang Shu, Ziran Wu, Xuan Chen, Gaoyan Zhang and Zili Cai

Algorithms 2022, 15(8), 269; https://doi.org/10.3390/a15080269 - 31 Jul 2022

Cited by 5 | Viewed by 2230

Abstract

This paper is dedicated to achieving flexible automatic assembly of miniature circuit breakers (MCBs) to resolve the high rigidity issue of existing MCB assembly by proposing a flexible automatic assembly process and method with industrial robots. To optimize the working performance of the [...] Read more.

This paper is dedicated to achieving flexible automatic assembly of miniature circuit breakers (MCBs) to resolve the high rigidity issue of existing MCB assembly by proposing a flexible automatic assembly process and method with industrial robots. To optimize the working performance of the robot, a time-optimal trajectory planning method of the improved Particle Swarm Optimization (PSO) with a multi-optimization mechanism is proposed. The solution uses a fitness switch function for particle sifting to improve the stability of the acceleration and jerk of the robot motion as well as to increase the computational efficiency. The experimental results show that the proposed method achieves flexible assembly for multi-type MCB parts of varying postures. Compared with other optimization algorithms, the proposed improved PSO is significantly superior in both computational efficiency and optimization accuracy. Compared with the standard PSO, the proposed trajectory planning method shortens the assembly time by 6.9 s and raises the assembly efficiency by 16.7%. The improved PSO is implemented on the experimental assembly platform and achieves smooth and stable operations, which proves the high significance and practicality for MCB fabrication. Full article

(This article belongs to the Special Issue Simulation-Based Optimization: Methods and Applications in Engineering Design)

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26 pages, 2207 KiB

Open AccessArticle

Multi-Fidelity Low-Rank Approximations for Uncertainty Quantification of a Supersonic Aircraft Design

by Sihmehmet Yildiz, Hayriye Pehlivan Solak and Melike Nikbay

Algorithms 2022, 15(7), 250; https://doi.org/10.3390/a15070250 - 19 Jul 2022

Cited by 2 | Viewed by 2572

Abstract

Uncertainty quantification has proven to be an indispensable study for enhancing reliability and robustness of engineering systems in the early design phase. Single and multi-fidelity surrogate modelling methods have been used to replace the expensive high fidelity analyses which must be repeated many [...] Read more.

Uncertainty quantification has proven to be an indispensable study for enhancing reliability and robustness of engineering systems in the early design phase. Single and multi-fidelity surrogate modelling methods have been used to replace the expensive high fidelity analyses which must be repeated many times for uncertainty quantification. However, since the number of analyses required to build an accurate surrogate model increases exponentially with the number of random input variables, most surrogate modelling methods suffer from the curse of dimensionality. As an alternative approach, the Low-Rank Approximation method can be applied to high-dimensional uncertainty quantification studies with a low computational cost, where the number of coefficients for building the surrogate model increases only linearly with the number of random input variables. In this study, the Low-Rank Approximation method is implemented for multi-fidelity applications with additive and multiplicative correction approaches to make the high-dimensional uncertainty quantification analysis more efficient and accurate. The developed uncertainty quantification methodology is tested on supersonic aircraft design problems and its predictions are compared with the results of single- and multi-fidelity Polynomial Chaos Expansion and Monte Carlo methods. For the same computational cost, the Low-Rank Approximation method outperformed both in surrogate modeling and uncertainty quantification cases for all the benchmarks and real-world engineering problems addressed in the present study. Full article

(This article belongs to the Special Issue Simulation-Based Optimization: Methods and Applications in Engineering Design)

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35 pages, 6328 KiB

Open AccessArticle

Multi-Fidelity Gradient-Based Optimization for High-Dimensional Aeroelastic Configurations

by Andrew S. Thelen, Dean E. Bryson, Bret K. Stanford and Philip S. Beran

Algorithms 2022, 15(4), 131; https://doi.org/10.3390/a15040131 - 16 Apr 2022

Cited by 10 | Viewed by 3487

Abstract

The simultaneous optimization of aircraft shape and internal structural size for transonic flight is excessively costly. The analysis of the governing physics is expensive, in particular for highly flexible aircraft, and the search for optima using analysis samples can scale poorly with design [...] Read more.

The simultaneous optimization of aircraft shape and internal structural size for transonic flight is excessively costly. The analysis of the governing physics is expensive, in particular for highly flexible aircraft, and the search for optima using analysis samples can scale poorly with design space size. This paper has a two-fold purpose targeting the scalable reduction of analysis sampling. First, a new algorithm is explored for computing design derivatives by analytically linking objective definition, geometry differentiation, mesh construction, and analysis. The analytic computation of design derivatives enables the accurate use of more efficient gradient-based optimization methods. Second, the scalability of a multi-fidelity algorithm is assessed for optimization in high dimensions. This method leverages a multi-fidelity model during the optimization line search for further reduction of sampling costs. The multi-fidelity optimization is demonstrated for cases of aerodynamic and aeroelastic design considering both shape and structural sizing separately and in combination with design spaces ranging from 17 to 321 variables, which would be infeasible using typical, surrogate-based methods. The multi-fidelity optimization consistently led to a reduction in high-fidelity evaluations compared to single-fidelity optimization for the aerodynamic shape problems, but frequently resulted in a cost penalty for cases involving structural sizing. While the multi-fidelity optimizer was successfully applied to problems with hundreds of variables, the results underscore the importance of accurately computing gradients and motivate the extension of the approach to constrained optimization methods. Full article

(This article belongs to the Special Issue Simulation-Based Optimization: Methods and Applications in Engineering Design)

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26 pages, 622 KiB

Open AccessArticle

Combinatorial Integral Approximation Decompositions for Mixed-Integer Optimal Control

by Clemens Zeile, Tobias Weber and Sebastian Sager

Algorithms 2022, 15(4), 121; https://doi.org/10.3390/a15040121 - 31 Mar 2022

Cited by 3 | Viewed by 2473

Abstract

Solving mixed-integer nonlinear programs (MINLPs) is hard from both a theoretical and practical perspective. Decomposing the nonlinear and the integer part is promising from a computational point of view. In general, however, no bounds on the objective value gap can be established and [...] Read more.

Solving mixed-integer nonlinear programs (MINLPs) is hard from both a theoretical and practical perspective. Decomposing the nonlinear and the integer part is promising from a computational point of view. In general, however, no bounds on the objective value gap can be established and iterative procedures with potentially many subproblems are necessary. The situation is different for mixed-integer optimal control problems with binary variables that switch over time. Here, a priori bounds were derived for a decomposition into one continuous nonlinear control problem and one mixed-integer linear program, the combinatorial integral approximation (CIA) problem. In this article, we generalize and extend the decomposition idea. First, we derive different decompositions and analyze the implied a priori bounds. Second, we propose several strategies to recombine promising candidate solutions for the binary control functions in the original problem. We present the extensions for ordinary differential equations-constrained problems. These extensions are transferable in a straightforward way, though, to recently suggested variants for certain partial differential equations, for algebraic equations, for additional combinatorial constraints, and for discrete time problems. We implemented all algorithms and subproblems in AMPL for a proof-of-concept study. Numerical results show the improvement compared to the standard CIA decomposition with respect to objective function value and compared to general-purpose MINLP solvers with respect to runtime. Full article

(This article belongs to the Special Issue Simulation-Based Optimization: Methods and Applications in Engineering Design)

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Figure 1
Example visualization of the GreedyTime algorithm. We use two candidate control solutions, here from CIA and SCIA, to construct new candidates. We perform an enumeration between 0 and 1 at all times <math display="inline"><semantics> <msub> <mi>t</mi> <mi>j</mi> </msub> </semantics></math> when the input vectors differ. Then, the two candidate solutions <math display="inline"><semantics> <mi mathvariant="bold">w</mi> </semantics></math> are fixed and we evaluate (MIOCP) for both vectors. We compare the resulting objective function values with their previous values. Moreover, the binary <math display="inline"><semantics> <msub> <mi mathvariant="bold">w</mi> <mi>j</mi> </msub> </semantics></math> values with the lower objective values are fixed in the candidate solutions. This procedure is repeated on the next grid point with unequal candidate solutions. Full article ">Figure 2
Visualization of the singular arc block recombination heuristic for two MILP control vectors (which we name CIA and SCIA) with three singular arcs. Every possible variation from the singular arcs and candidate controls is generated and we evaluate (MIOCP) for each of the constructed variation. The minimal objective value of all variations represents the heuristic’s result. Full article ">Figure 3
Performance profile comparing the deviation of differential states based on SCIA and CIA solutions. Relaxed solutions are shown in maximum norm and log-scale. The results are based on the instances “Double tank (Multimode)” and “Lotka–Volterra (absolute fishing variant)” from the mintoc.de benchmark library. Using (SCIA1) or (SCIAmax) can improve the performance of the CIA decomposition significantly. Full article ">Figure 4
Performance profile comparing objective deviation from the relaxed solution in percentage and log-scale of <math display="inline"><semantics> <mi>λ</mi> </semantics></math>-CIA and CIA solutions. The results are based on the instance “Quadrotor (binary variant)” from the mintoc.de benchmark library. (<math display="inline"><semantics> <mi>λ</mi> </semantics></math>CIA) appeared to provide no clear improvement compared with the (CIA) solutions. Full article ">Figure 5
Performance profile comparing objective deviation from the relaxed solution in percentage and log-scale of (CIA) and its backward variant solutions. The results are based on the instance “Lotka–Volterra (terminal constraint violation)” from the mintoc.de benchmark library. Using (CIA1B) or (CIAmaxB) can improve the performance of the CIA decomposition significantly. Full article ">Figure 6
Box plot comparing objective deviation from the relaxed solution in percentage and log-scale of several MILP (marked in blue) and recombination heuristic (marked in red) solutions. The results are based on instances from the mintoc.de benchmark library. The box borders are 1/4 and 3/4-quantiles, whereas the whiskers represent 1/20 and 19/20-quantiles. We visualize the median values by black lines in the box and additionally display them numerically above the box. We represent the average values of the respective algorithms by red asterisks and the outliers by black crosses. The boxes of recombination strategies are shifted towards lower objective values compared with (CIA) algorithms and, thus, can improve the CIA decomposition performance significantly. Full article ">Figure 7
Log plot of run time and objective value deviation from the relaxed solution of the constructed solutions for different approaches and for the Lotka–Volterra multimode problem, with differential state discretization N = 12,000. The numbers in the plot indicate the applied corresponding number of control grid points M. We illustrate the outcomes of the solutions constructed by (CIAmax), <math display="inline"><semantics> <mrow> <mi>Opt</mi> <mo>(</mo> <msup> <mi>S</mi> <mi>CIA</mi> </msup> <mo>)</mo> </mrow> </semantics></math>, the GreedyTime recombination heuristic, and the MINLP solver Bonmin. By <math display="inline"><semantics> <mrow> <mi>Opt</mi> <mo>(</mo> <msup> <mi>S</mi> <mi>CIA</mi> </msup> <mo>)</mo> </mrow> </semantics></math>, we denote the best objective value outcome of over all MILP solutions. For each control discretization, we connect the outcomes of the four approaches with lines in order to compare the behavior for different discretizations. One observes the convergence of all approaches towards the lower bound provided by the relaxed solution and the closure of the gap between (CIAmax) and Bonmin solutions for a fixed discretization. GreedyTime is roughly two orders of magnitude slower than (CIAmax), but is faster than Bonmin. Full article ">

13 pages, 3712 KiB

Open AccessArticle

Dynamic Line Scan Thermography Parameter Design via Gaussian Process Emulation

by Simon Verspeek, Ivan De Boi, Xavier Maldague, Rudi Penne and Gunther Steenackers

Algorithms 2022, 15(4), 102; https://doi.org/10.3390/a15040102 - 22 Mar 2022

Cited by 1 | Viewed by 2296

Abstract

We address the challenge of determining a valid set of parameters for a dynamic line scan thermography setup. Traditionally, this optimization process is labor- and time-intensive work, even for an expert skilled in the art. Nowadays, simulations in software can reduce some of [...] Read more.

We address the challenge of determining a valid set of parameters for a dynamic line scan thermography setup. Traditionally, this optimization process is labor- and time-intensive work, even for an expert skilled in the art. Nowadays, simulations in software can reduce some of that burden. However, when faced with many parameters to optimize, all of which cover a large range of values, this is still a time-consuming endeavor. A large number of simulations are needed to adequately capture the underlying physical reality. We propose to emulate the simulator by means of a Gaussian process. This statistical model serves as a surrogate for the simulations. To some extent, this can be thought of as a “model of the model”. Once trained on a relative low amount of data points, this surrogate model can be queried to answer various engineering design questions. Moreover, the underlying model, a Gaussian process, is stochastic in nature. This allows for uncertainty quantification in the outcomes of the queried model, which plays an important role in decision making or risk assessment. We provide several real-world examples that demonstrate the usefulness of this method. Full article

(This article belongs to the Special Issue Simulation-Based Optimization: Methods and Applications in Engineering Design)

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Figure 1
Visualization of the finite element simulation consisting of a flat bottom hole plate (blue) and a line heater (yellow). The line heater moves above the sample in a linear motion. For a more detailed figure and explanation, we refer the reader to [<a href="#B2-algorithms-15-00102" class="html-bibr">2</a>]. Full article ">Figure 2
Response surface as generated in [<a href="#B2-algorithms-15-00102" class="html-bibr">2</a>]. The surface is generated from 1000 finite element simulations, using eight input parameters. The simplified response surface has all input parameters fixed, except for the heat load and the source velocity. The fixed parameters are: <math display="inline"><semantics> <msub> <mi>d</mi> <mrow> <mi>h</mi> <mi>e</mi> <mi>a</mi> <mi>t</mi> <mo>−</mo> <mi>c</mi> <mi>a</mi> <mi>m</mi> </mrow> </msub> </semantics></math> = 425 mm, <math display="inline"><semantics> <msub> <mi>d</mi> <mrow> <mi>s</mi> <mi>t</mi> <mi>a</mi> <mi>r</mi> <mi>t</mi> </mrow> </msub> </semantics></math> = 5.8 mm, <math display="inline"><semantics> <msub> <mi>D</mi> <mrow> <mi>h</mi> <mi>o</mi> <mi>l</mi> <mi>e</mi> </mrow> </msub> </semantics></math> = 9 mm, <math display="inline"><semantics> <msub> <mi>d</mi> <mrow> <mi>h</mi> <mi>e</mi> <mi>i</mi> <mi>g</mi> <mi>h</mi> <mi>t</mi> </mrow> </msub> </semantics></math> = 430 mm, <math display="inline"><semantics> <msub> <mi>T</mi> <mrow> <mi>a</mi> <mi>m</mi> <mi>b</mi> <mi>i</mi> <mi>e</mi> <mi>n</mi> <mi>t</mi> </mrow> </msub> </semantics></math> = 48 <math display="inline"><semantics> <msup> <mrow/> <mo>°</mo> </msup> </semantics></math>C. Using this response surface, one can find the best temperature difference as a valley or top. Full article ">Figure 3
Graphical visualization of the learning process of the Gaussian process for 5 runs of 500 iterations. (a) represents the root mean square error (RMSE) of the learned surrogate compared to the response surface created in [<a href="#B2-algorithms-15-00102" class="html-bibr">2</a>]. (b) shows the average standard deviation of the Gaussian process posterior prediction. Full article ">Figure 4
Visualization of the temperature difference for six different defect diameters. (a) 12 mm, (b) 14 mm, (c) 16 mm, (d) 18 mm, (e) 20 mm and (f) 22 mm. Red indicates temperature differences that might result in damaging the sample under inspection. These plots serve as a warning when designing a setup. Full article ">Figure 4 Cont.
Visualization of the temperature difference for six different defect diameters. (a) 12 mm, (b) 14 mm, (c) 16 mm, (d) 18 mm, (e) 20 mm and (f) 22 mm. Red indicates temperature differences that might result in damaging the sample under inspection. These plots serve as a warning when designing a setup. Full article ">Figure 5
Visualization of the temperature difference for six different defect diameters. (a) 12 mm, (b) 14 mm, (c) 16 mm, (d) 18 mm, (e) 20 mm and (f) 22 mm. Red are temperature differences below 5 °C, yellow above 25 °C and green in between. Only the green regions are of practical value in real-world applications. Full article ">

19 pages, 1080 KiB

Open AccessArticle

Multi-Fidelity Sparse Polynomial Chaos and Kriging Surrogate Models Applied to Analytical Benchmark Problems

by Markus P. Rumpfkeil, Dean Bryson and Phil Beran

Algorithms 2022, 15(3), 101; https://doi.org/10.3390/a15030101 - 21 Mar 2022

Cited by 4 | Viewed by 2762

Abstract

In this article, multi-fidelity kriging and sparse polynomial chaos expansion (SPCE) surrogate models are constructed. In addition, a novel combination of the two surrogate approaches into a multi-fidelity SPCE-Kriging model will be presented. Accurate surrogate models, once obtained, can be employed for evaluating [...] Read more.

In this article, multi-fidelity kriging and sparse polynomial chaos expansion (SPCE) surrogate models are constructed. In addition, a novel combination of the two surrogate approaches into a multi-fidelity SPCE-Kriging model will be presented. Accurate surrogate models, once obtained, can be employed for evaluating a large number of designs for uncertainty quantification, optimization, or design space exploration. Analytical benchmark problems are used to show that accurate multi-fidelity surrogate models can be obtained at lower computational cost than high-fidelity models. The benchmarks include non-polynomial and polynomial functions of various input dimensions, lower dimensional heterogeneous non-polynomial functions, as well as a coupled spring-mass-system. Overall, multi-fidelity models are more accurate than high-fidelity ones for the same cost, especially when only a few high-fidelity training points are employed. Full-order PCEs tend to be a factor of two or so worse than SPCES in terms of overall accuracy. The combination of the two approaches into the SPCE-Kriging model leads to a more accurate and flexible method overall. Full article

(This article belongs to the Special Issue Simulation-Based Optimization: Methods and Applications in Engineering Design)

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16 pages, 4336 KiB

Open AccessArticle

Design of Selective Laser Melting (SLM) Structures: Consideration of Different Material Properties in Multiple Surface Layers Resulting from the Manufacturing in a Topology Optimization

by Jan Holoch, Sven Lenhardt, Sven Revfi and Albert Albers

Algorithms 2022, 15(3), 99; https://doi.org/10.3390/a15030099 - 19 Mar 2022

Cited by 4 | Viewed by 3106

Abstract

Topology optimization offers a possibility to derive load-compliant structures. These structures tend to be complex, and conventional manufacturing offers only limited possibilities for their production. Additive manufacturing provides a remedy due to its high design freedom. However, this type of manufacturing can cause [...] Read more.

Topology optimization offers a possibility to derive load-compliant structures. These structures tend to be complex, and conventional manufacturing offers only limited possibilities for their production. Additive manufacturing provides a remedy due to its high design freedom. However, this type of manufacturing can cause areas of different material properties in the final part. For example, in selective laser melting, three areas of different porosity can occur depending on the process parameters, the geometry of the part and the print direction, resulting in a direct interrelation between manufacturing and design. In order to address this interrelation in design finding, this contribution presents an optimization method in which the three porous areas are identified and the associated material properties are considered iteratively in a topology optimization. For this purpose, the topology optimization is interrupted in each iteration. Afterwards, the three areas as well as the material properties are determined and transferred back to the topology optimization, whereby those properties are used for the calculation of the next iteration. By using the optimization method, a design with increased volume-specific stiffness compared to a design of a standard topology optimization can be created and will be used in the future as a basis for the extension by a global strength constraint to maintain the maximum permissible stress and the minimum wall thickness. Full article

(This article belongs to the Special Issue Simulation-Based Optimization: Methods and Applications in Engineering Design)

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