Sequential Approximate Optimization Research Articles

Surrogate Based Optimization of Functionally Graded Plates

Functionally Graded Materials (FGM) are composites, usually made of ceramic and metal, in which the volume fraction of their constituents varies smoothly along an interest direction. These materials were initially proposed as a solution for the development of thermal barriers, but are currently used in different applications. The variation in composition results in a gradual change in their properties, improving the performance of structures subjected to thermal and mechanical loads, but making structural analysis more complex. Plates, on the other hand, are three-dimensional flat structures in which the thickness is much smaller than their other two dimensions. For projects involving functionally graded plates, both the choice of their constituents and the definition of the distribution of volume fractions are necessary. Computational methods, which simulate the behavior of these structures, and optimization techniques, which explore the design space, are used to obtain a more efficient solution. However, the computational cost of structural analyses can be a limiting factor in the optimization process, since bioinspired algorithms require the analysis of a large number of trial solutions to find the optimal design. Thus, this work addresses the use of surrogate models capable of efficiently approximating the results of numerical simulations. These models are an alternative to reduce the computational cost of the design optimization of complex structures. Surrogates have been incorporated into an optimization methodology known as Sequential Approximate Optimization (SAO), where the approximate response surface is continuously updated and improved by the insertion of new points, enhancing the model approximation. The proposed methodology will be used in the design optimization functionally graded plates considering buckling and free vibration. The results will be evaluated in terms of accuracy and efficiency based on a set of benchmarks.

Inaccurate search based sequential approximate constrained optimization method for Solid Rocket Motor design

Surrogate based constrained optimization methods are widely utilized in practical solid rocket motor (SRM) design problems. To improve the design performance, this paper proposes an inaccurate search based sequential approximate constrained optimization (ISSACO) method consisting of an efficient recursive evolution Latin hypercube design (RELHD) method and a three-stage constrained sampling method. The RELHD method divides large-sample experiment design problem into several small-sample design problems to ensure the computational efficiency and the design uniformity at the same time. The three-stage constrained sampling method employs the elite archives mechanism to balance the feasibility and the optimality in optimization. Results of the numerical cases indicate that the proposed ISSACO algorithm is competitive with other state-of-art constrained optimization method in efficiency and effectiveness. The finocyl grain design and the impulse mass ratio optimization are also conducted to make further verifications, and the ISSACO method can efficiently obtain feasible optimum and proves to be a potential method for computationally intensive solid rocket motor design problems.

Optimal energy distribution in hydraulic hammer forging for minimizing total energy and forging load

Hammer forging is an important manufacturing technology in heavy industry to produce high stiffness product. Forging using mechanical press produces the product by controlling the distance between dies whereas the hydraulic hammer forging utilizes the energy given by the sum of hydraulic energy and potential energy of die, and the product is then produced through several blows. The energy at each blow is conventionally determined through the trial-and-error method. The process to produce the product is simple and the response of hammer foundations and anvil is mainly discussed in the literature, but the optimal energy distribution to successfully produce the product is rarely discussed. In this paper, the optimal energy distribution in hydraulic hammer forging is determined using numerical simulation coupled with design optimization technique. To determine the optimal energy distribution through the process, multi-objective design optimization for minimizing both the total energy and the maximum forging load is performed. High dimensional accuracy is generally required in the forged product, and the underfill is handled as the design constraint. The numerical simulation in hydraulic hammer forging is computationally so expensive that sequential approximate optimization that response surface is repeatedly constructed and optimized is adopted to identify the pareto-frontier between the total energy and the maximum forging load. It is clarified through the numerical result that the total energy is drastically reduced without the underfill in comparison with the conventional one. The experiment is also conducted to examine the proposed approach.

Artificial neural network-based sequential approximate optimization of metal sheet architecture and forming process

Abstract This paper introduces a sequential approximate optimization method that combines the finite element method (FEM), dynamic differential evolution (DDE), and artificial neural network (ANN) surrogate models. The developed method is applied to address two optimization problems. The first involves metamaterial design optimization for metal sheet architecture with binary design variables. The second pertains to optimizing process parameters in multi-stage metal forming, where the discrete nature arises owing to changing tool geometries across stages. This process is highly nonlinear, accumulating contact, geometric, and material nonlinear effects discretely through forming stages. The efficacy of the proposed optimization method, utilizing ANN surrogate models, is compared with traditionally used polynomial response surface (PRS) surrogate models, primarily based on low-order polynomials. Efficient learning of ANN surrogate models is facilitated through the FEM and Python integration framework. Initial data for surrogate model training is collected via Latin hypercube sampling and FEM simulations. DDE is employed for sequential approximate optimization, optimizing ANN or PRS surrogate models to determine optimal design variables. PRS surrogate models encounter challenges in dealing with nonlinear changes in sequential approximate optimization concerning discrete characteristics such as binary design variables and discrete nonlinear behavior found in multi-stage metal forming processes. Owing to the discrete nature, PRS surrogate models require more data and iterations for optimal design variables. In contrast, ANN surrogate models adeptly predict nonlinear behavior through the activation function's characteristics. In the optimization problem of Metal Sheet Architecture for design target C, the ANN surrogate model required an average of 4.6 times fewer iterations to satisfy stopping criteria compared to the PRS surrogate model. Furthermore, in the optimization of multi-stage deep drawing processes, the ANN surrogate model required an average of 6.1 times fewer iterations to satisfy stopping criteria compared to the PRS surrogate model. As a result, the sequential global optimization method utilizing ANN surrogate models achieves optimal design variables with fewer iterations than PRS surrogate models. Further confirmation of the method's efficiency is provided by comparing Pearson correlation coefficients and locus plots.

A Collaboratively Iterative Sequential Approximate Optimization Method for Aerodynamic Optimization

A Collaboratively Iterative Sequential Approximate Optimization Method for Aerodynamic Optimization

Investigating the machinability behaviour of Al7075/SiC5CS5 hybrid composite with the variation of tool geometry

This research investigates the machinability behavior of an Al7075 hybrid composite fabricated with micro-sized cenosphere (CS) and silicon carbide (SiC) particles. The composite was fabricated using stir-casting with ultrasonic assistance. The experimental study investigated the effect of variation of machining regimes (i.e., feed rate, cutting speed, and depth of cut) and tool geometry (tool nose radii) on main cutting force and tool tip temperature. For the study, the Cermet tool was considered as tool material for the dry turning of aluminum alloy and composite. In addition, a regression model was created using the response surface method (RSM) technique. The results indicate that the developed model can accurately predict output regimes with an accuracy ranging from 80.44 to 99.98%. Further, by using sequential approximation optimization, the optimal combination of input regimes for maximal metal removal rate was identified.

Collapse-resistance optimization of fabricated single-layer grid shell based on sequential approximate optimization

In this work, the surrogate model of the collapse load in terms of the structural morphology is established based on the radial basis function (RBF) network, and the form-finding optimization of the fabricated single-layer grid shell aiming at the improvement of collapse-resistance capacity is realized. To improve the accuracy of the optimal solution, the density function is used to determine the sparse region in the design domain and add new sample points in the sparse region. Avoiding that the optimization is trapped in a poor local optimum, the starting point is updated to approach the global optimum. Three types of fabricated single-layer grid shells, including cylindrical surface, free-form surface with symmetric supports, and free-form surface with asymmetric supports, are selected for form-finding optimization. The results prove the efficiency of the optimization algorithm. The proposed optimization method considers the mechanical properties of assemble joints and reflects the mechanical characteristics of the actual structure. It can be used for form-finding optimization and shape selection in structural design and thus has engineering significance.

Hybrid adaptive deep learning classifier for early detection of diabetic retinopathy using optimal feature extraction and classification.

Diabetic retinopathy (DR) is one of the leading causes of blindness. It is important to use a comprehensive learning method to identify the DR. However, comprehensive learning methods often rely heavily on encrypted data, which can be costly and time consuming. Also, the DR function is not displayed and is scattered in the high-definition image below. Therefore, learning how to distribute such DR functions is a big challenge. In this work, we proposed a hybrid adaptive deep learning classifier for early detection of diabetic retinopathy (HADL-DR). First, we provide an improved multichannel-based generative adversarial network (MGAN) with semi-maintenance to detect blood vessels segmentation. By reducing the reliance on the encoded data, the following high-resolution images can be used to detect the indivisible features of some semi-observed MGAN references. Scale invariant feature transform (SIFT) function is then extracted and the best function is selected using the improved sequential approximation optimization (SAO) algorithm. After that, a hybrid recurrent neural network with long short-term memory (RNN-LSTM) is utilized for DR classification. The proposed RNN-LSTM classifier evaluated through standard benchmark Kaggle and Messidor datasets. Finally, the simulation results are compared with the existing state-of-art classifiers in terms of accuracy, precision, recall, f-measure and area under cover (AUC), it is seen that more successful results are obtained.

Lightweight design of a clamp band joint via a constrained sequential approximate optimization method in the irregular design domain

The clamp band joint (CBJ) is a multi-component and complex device for connecting and separating satellites from launch vehicles. In this article, the pre-tightening and connection process are analysed sequentially through an implicit–explicit calculation method. Because of the time-consuming nonlinear analysis, a constrained sequential approximate optimization (CSAO) method in the irregular design domain is proposed for the lightweight optimization design of CBJs. A novel constrained space-filling and non-collapsing sequential sampling method is adopted to address the sampling inefficiency of conventional experimental designs in the irregular domain, while the sequential sampling of exploration and exploitation strategies is balanced for the global and local approximation accuracy. Finally, comparison with the traditional sequential approximate optimization method shows that the proposed method can search the optimum in the feasible region more efficiently. Besides, compared to the initial design, the optimized structure improved the connection stiffness by 56.7% and reduced the weight by 8.3%.

Geometry Optimization of the Runner Insert for Improving the Appearance Quality of the Injection Molded Auto Part.

Appearance quality is one of the most important indexes for many injection-molded products, like optical parts, automotive parts etc., especially at the area near the injection gate. Different from the work that focused on designing the dimensions of the runner, this work proposed a method which is based on the insert technology to improve the appearance quality of a standard automotive part. An insert was introduced into the runner system which located before the gate. Three different shapes of this insert (circular, rectangular and diamond) were used to study the effect of geometrical factors on the appearance quality in this paper. All inserts were parameterized to describe their location and dimensions. Based on the geometrical design parameters, expected improvement optimization problem about the appearance quality were solved by using sequential approximate optimization method. The appearance qualities of three cases are improved by 13.77%, 21.56%, 14.37% respectively. Results showed that the best geometrical design scheme of the insert is rectangular with the optimal geometrical location and dimensions. The reasons were discussed by investigating the flow and thermal history in detail. Compared with the design case without any insert, the heat was absorbed and the velocity field was changed by the insert before the polymer melts ran into the cavity. It changed the complicated thermo-mechanical history inside the material during the entire processing history, which improved the final appearance quality of this auto part.

A novel decoupled time-variant reliability-based design optimization approach by improved extreme value moment method

Time-variant reliability-based design optimization (t-RBDO) is an effective tool to guarantee a high reliability of the product during the full life cycle. This paper proposes a new decoupled method for t-RBDO via an improved extreme value moment method (EVMM). In the proposed method, a weight approach based on sparse grid numerical integration (WA-SGNI) is employed to establish the local approximation of the extreme value moment. Since evaluating the failure probability functions (FPFs) using fourth-moment transformation method has certain limitations, a local approximation method for quantile functions (QFs) is proposed to consider the time-variant reliability constraints in t-RBDO. After the local approximations of QFs are established, t-RBDO problem is decoupled into a deterministic one in the design sub-region. Combining sequential approximation optimization, a unified t-RBDO framework is presented. Four numerical examples are investigated to validate the accuracy and efficiency of the proposed method.

Sequential approximate optimization with adaptive parallel infill strategy assisted by inaccurate Pareto front

Sequential Approximate Optimization (SAO) has been widely used in engineering optimization design problems to improve efficiency. The infilling strategy is one of the critical techniques of the SAO, which is of paramount importance to the surrogate model accuracy and optimization efficiency. In this paper, an adaptive parallel infill strategy for surrogate-based single-objective optimization is proposed within a multi-objective optimization framework to balance exploration and exploitation during the optimization process. Within this method, an inaccurate Pareto Front is adopted to assist the infilling of the sampling points. The proposed SAO method with its adaptive parallel sampling strategy is tested on several numerical test cases and an engineering test case with the optimization results compared to state-of-the-art optimization algorithms. The results show that the proposed SAO with the adaptive parallel sampling strategy possesses excellent performance and better stability.

Surrogate-Based Optimization Design for Air-Launched Vehicle Using Iterative Terminal Guidance

In recent years, the penetration of low-cost air-launched vehicles for nano/micro satellites has significantly increased worldwide. Conceptual design and overall parameters optimization of the air-launched vehicle has become an exigent task. In the present research, a modified surrogate-based sequential approximate optimization (SAO) framework with multidisciplinary simulation is proposed for overall design and parameters optimization of a solid air-launched vehicle system. In order to reduce the large computation costs of time-consuming simulation, a local density-based radial basis function is applied to build the surrogate model. In addition, an improved particle swarm algorithm with adaptive control parameters is proposed to ensure the efficiency and reliability of the optimization method. According to the LauncherOne air-launched vehicle, the overall optimization design problem aims to improve payload capacity with the same lift-off mass. Reasonable constraints are imposed to ensure the orbit injection accuracy and stability of the launch vehicle. The influences of the vehicle configuration, optimization method, and terminal guidance are considered and compared for eight different cases. Finally, the effect on the speed of optimization convergence of employing a terminal guidance module is investigated. The payload capability of the optimized configurations increased by 27.52% and 23.35%, respectively. The final estimated results and analysis show the significant efficiency of the proposed method. These results emphasize the ability of SAO to optimize the parameters of an air-launched vehicle at a lower computation cost.

Optimization of a Permanent Magnet Synchronous Motor for e-Mobility Using Metamodels

Permanent magnet synchronous motors (PMSMs) with rectangular coils in hairpin windings exhibit improved fill factor and reduced end turn of the coils, which in turn improve the efficiency and power density of PMSMs, making them ideal for e-mobility applications. Herein, the shape of a PMSM was optimized for torque ripple reduction using metamodels to improve the noise and vibrational performance of the motor. The objective function of the optimal design aimed to minimize the torque ripple, and the average torque and efficiency were set as constraints. The notch width and depth and barrier length were selected as the design variables to satisfy the objective function and constraints. Using the optimal Latin hypercube design technique, 27 experimental points were selected, and a finite element analysis (FEA) was performed for each point. Furthermore, a function approximation was performed using six metamodels, and the best metamodel was selected using the root mean square error test. Moreover, the optimization was performed by combining the best metamodels for each variable with a sequential two-point diagonal quadratic approximation optimization algorithm. The torque ripple was improved by approximately 1.63% compared with the initial model, whereas the constraint values remained constant. Finally, an FEA was performed on the optimal point, and the FEA results matched with those of the optimal method.

Multi-objective optimization of billet shape and process parameters in multi-stage hot forging

Multi-stage hot forging is a typical manufacturing technology to produce mechanical components with complex shape. In the multi-stage hot forging, flash should always be minimized for material saving, and the uniform deformation is also preferable for high strength of a product. Billet shape directly affects the flash, and it is important to determine the billet shape minimizing the flash. In addition, the process parameters in multi-stage hot forging such as die stroke have an influence on the flash and the uniform deformation. In this paper, the billet shape and the process parameters in multi-stage hot forging is optimized so as to minimize the flash and the equivalent strain. Therefore, multi-objective optimization is performed. The three-dimensional numerical simulation is so intensive that sequential approximate optimization using radial basis function network is adopted for the design optimization. It is found from the numerical result that the trade-off between the flash and the equivalent strain is clarified, and the flash is drastically reduced compared to the conventional billet shape.

逐次近似最適化を用いた熱間多段鍛造におけるプロセスパラメータの多目的最適設計

In the multi-stage hot forging, flash should always be minimized for material saving, and the uniform deformation is also preferable for high strength of a product. In this paper, the billet shape and the process parameters in multi-stage hot forging is optimized so as to minimize the flash and the equivalent strain using sequential approximate optimization. It is found from the numerical result that the trade-off between the flash and the equivalent strain is clarified, and the flash is drastically reduced compared to the conventional billet shape.

Optimization of process parameters in rapid heat cycle molding using heater system

Plastic injection molding (PIM) is a manufacturing technology to plastic products. In PIM, weldline that affects the strength and surface quality of products, and it is then important to determine the optimal process parameters for the weldline reduction. Rapid heat cycle molding (RHCM) is an attracted PIM technology for weldline reduction that by heating up the mold temperature, the melt plastic is smoothly flowed into the die cavity and consequently the weldline is well reduced. In RHCM, since various heating systems are adopted but which have problem that long cycle time. In this paper, to quickly heat up the mold temperature, a heater system is newly introduced and the process parameters in the RHCM using heater system are optimized. A multi-objective optimization for minimizing both weldline and cycle time is considered, and the ratio of mold temperature to injection time is maximized for the weldline reduction, whereas the cycle time is minimized for high productivity. Sequential approximate optimization that the response surface is repeatedly constructed and optimized is adopted for the design optimization, and the pareto-frontier is identified. Based on the numerical result, the experiment is also conducted to examine the validity of the proposed RHCM.

Decoupled reliability-based optimization using Markov chain Monte Carlo in augmented space

An efficient framework is proposed for reliability-based design optimization (RBDO) of structural systems. The RBDO problem is expressed in terms of the minimization of the failure probability with respect to design variables which correspond to distribution parameters of random variables, e.g. mean or standard deviation. Generally, this problem is quite demanding from a computational viewpoint, as repeated reliability analyses are involved. Hence, in this contribution, an efficient framework for solving a class of RBDO problems without even a single reliability analysis is proposed. It makes full use of an established functional relationship between the probability of failure and the distribution design parameters, which is termed as the failure probability function (FPF). By introducing an instrumental variability associated with the distribution design parameters, the target FPF is found to be proportional to a posterior distribution of the design parameters conditional on the occurrence of failure in an augmented space. This posterior distribution is derived and expressed as an integral, which can be estimated through simulation. An advanced Markov chain algorithm is adopted to efficiently generate samples that follow the aforementioned posterior distribution. Also, an algorithm that re-uses information is proposed in combination with sequential approximate optimization to improve the efficiency. Numeric examples illustrate the performance of the proposed framework.

Optimization design of rockoons based on improved sequential approximation optimization

In this study, a multidisciplinary design optimization framework and detailed procedure based on improved sequential approximation optimization (SAO) and 3-degree-of-freedom trajectory simulation are proposed for conceptual design and parameters optimization of a rockoon (from rocket and balloon) system. A reliable and efficient strategy, which considers the approximation accuracy of the response surfaces in the sampling process, is proposed to reduce the evaluation times of the original model for finding the global optimal solution. Besides, a modified SAO algorithm based on the multistage adaptive sampling strategy is presented, and the obtained tested results verify the fine robustness, high efficiency, reliability, and validity of the proposed SAO algorithm. The objective is to minimize the liftoff gross mass of the launch vehicle which reflects the cost for satellite launching. Constraints are imposed to ensure the orbit injection accuracy and stability of the launch vehicle. Finally, based on the multidisciplinary design framework with modified SAO, the optimal design results in 12 design cases from various payload mass, objective orbit, and ignition altitude are discussed and compared with the generic launch vehicle.

A Multidisciplinary Approach for Optimization Design of CNC Machine Tools

The main objective of this research is to propose a multidisciplinary approach for the development and design of Computer Numerical Control (CNC) machine tools using numerical optimization methods combined Multi-Body Dynamic (MBD) analysis and to control design co-simulation. Metamodels based Sequential Approximate Optimization (SAO) for the co-simulation optimization problems are developed. The metamodels are constructed as approximate models for exact dynamic analysis responses by using simultaneous Kriging metamodeling method. SAO problems for single objective and multi-objective optimization designs are carried out based on the augmented Lagrange multiplier (ALM) method. An application of the proposed method on optimizing Proportional-Integral-Derivative (P-I-D) coefficients of PID controllers of a CNC machine tool model is performed to demonstrate the usefulness of integrating different research methods in numerical simulation. Therefore, this work overcomes a difficult task in tuning the PID controller which requires extensive experience and understandings of research and development (R&D) engineers. Moreover, the optimal PID controllers obtained by the multidisciplinary approach can help to increase the contouring accuracy of the CNC machine tools.