Surrogate Model-based Optimization Research Articles

Management strategy of granular sludge settleability in saline denitrification: Insights from machine learning

The settleability of granular sludge is a crucial factor in maintaining an adequate amount of granules in the wastewater treatment process (WWTP). However, Accurate measurement of settleability is challenging due to the complex interactions in WWTP. To address this issue, an intelligent strategy for controlling the settleability of granular sludge is required. This study developed a machine learning (ML)-based model to predict the sludge volume index (SVI30). Three ML models, namely artificial neural networks (ANNs), random forest (RF), and support vector machine (SVM) models, were employed with an ANNs-based mixed liquor suspended solids (MLSS) soft sensor, which served as input data for predicting SVI30 using ML. The combination of the soft sensor’s output and ANNs yielded the highest performance with R2 and mean absolute error (MAE) of 0.8946 and 5.5 mL/g, respectively. The Shapely Additive Explanations (SHAP) analysis revealed that MLSS, salinity, glucose loading rate, and pH were significant factors influencing SVI30. The surrogate model-based optimization strategy of SVI30 was conducted using core control parameters (CCPs), namely glucose loading rate, effluent pH, and salinity. It was suggested that a glucose loading rate over 3.0 kg-N/m3-d and an effluent pH exceeding 9.0 can deteriorate the SVI30. To the best of our knowledge, this is the first study on the surrogate model-based suggestion of the management strategy in the granular sludge process under saline denitrification conditions.

Multi-objective optimization and energy efficiency improvement for rotor duct in integrated energy recovery-pressure boost device

To reduce the volumetric mixing rate of the integrated energy recovery-pressure boost device, a novel symmetrical duct structure with diversion surface was proposed. The surrogate model-based multi-objective optimization framework was established, and obtained the optimal ducts V1 and V2 combined with computational fluid dynamics simulation. Numerical results indicate that optimized duct structure could promote the formation of plug flow and effectively improve the collision efficiency between high-pressure brine and low-pressure seawater, and the volumetric mixing rate corresponding to the ducts V1 and V2 was reduced by 31.52% and 22.18%, and the duct volume efficiency was increased by 16.04% and 19.56%, respectively. Finally, the performance of optimized device was verified through seawater reverse osmosis desalination system under actual working conditions. Experimental results showed that the mixing rate of optimized ducts had a significant decrease of 30.86% and 20.53% in the applicable range, and the energy recovery efficiency improved at most 5.41% and 7.55%, respectively. The optimized ducts could significantly reduce the specific energy consumption of the desalination system by 26.01% and 18.22%, respectively, and the specific energy consumption reached the lowest level of 3.02 kWh/m3, demonstrating the superiority of the structure and the accuracy and effectiveness of the optimization strategy.

Surrogate Model-Based Filter Optimization by a Field-Circuit Model Mapping

Surrogate Model-Based Filter Optimization by a Field-Circuit Model Mapping

Variable-Fidelity Surrogate Model-Based Airfoil Optimization at a Moderate Reynolds Number

Airfoil shape optimization for enhanced aerodynamic performance at a moderate Reynolds number is carried out using a novel technique for constrained optimization of expensive engineering functions. The proposed method is a co-kriging surrogate model using two levels of fidelity in conjunction with a gradient-free trust-region method to drive the model towards the global optimum. The methodology is first applied on a generic test function to demonstrate its efficiency. Later, the proposed optimization framework is applied on constrained airfoil shape optimization problems involving maximizing the lift-to-drag ratio, maximizing the endurance factor, and minimizing the drag coefficient of an Eppler E214 airfoil. The optimal lift-to-drag ratio and the endurance factor are found to be 13.25% and 16.05%, respectively, higher than the baseline airfoil. The optimal drag coefficient is 6.86% lower than the baseline airfoil. The flow transition is also delayed for the some of the optimal airfoils. The present results show that the proposed optimization methodology is successful in improving the aerodynamic characteristics in the sensitive low/moderate Reynolds number regime.

Accelerating sampling-based tolerance–cost optimization by adaptive surrogate models

ABSTRACT High numbers of function evaluations are inevitable to guarantee the reliability and optimality of sampling-based tolerance–cost optimization. Despite using different countermeasures to increase its efficiency, unreasonably long computation times and unreliable results currently hinder its profitable application. Motivated to overcome this shortcoming, this article presents a novel strategy harmonizing metaheuristic optimization and surrogate modelling. It is based on the idea of adaptive surrogate model-based optimization substituting the tolerance analysis subroutine with a surrogate model, which is iteratively re-modelled with intermediate optimization results to improve its accuracy continuously in potential optima regions. On the one hand, a directed intensification of promising solutions and, on the other hand, an accelerated exploration of the search space is achieved. Optimization studies prove its positive effect on overall efficiency, where a case study with multiple nonlinear assembly response functions and geometrical tolerances serves as a use case.

Performance improvement for the CMOS rail-to-rail amplifier via APSO-based design and SNN’s training

This paper proposes an adaptive Particle Swarm Optimization(APSO) global search algorithm and Spiking Neural Network(SNN) surrogate model-based optimization design method for analog integrated circuits performance enhancement. The initial design parameters are calculated by numerical computation. The global design space is extended and explored using APSO in the main loop, with constraint testing ensuring the transistor works in the right conditions. A Spiking Neural Network (SNN) model aids in predicting circuit performance during local searches, in which training data for the local design space is generated through parallel SPICE simulations. The optimization framework is applied to rail-to-rail amplifiers of two topologies. The results show that the proposed method accelerates the optimization process, achieving up to a 35.4x speed enhancement compared to Particle Swarm Optimization(PSO) based on the SPICE simulation. Moreover, Compared with traditional approaches based on multiobjective optimization, the proposed method provides an advantage in performance improvement and is valid for different CMOS processes.

Surrogate model-based multi-objective optimization algorithm for train-ballast turnout system: Balancing safety and vibration damping in parameter design

In rail transportation structural parameter design, multi-objective optimal algorithms (MOOAs) have advanced significantly in safety, comfort, and aerodynamics domain. However, the vital factor of environment vibration remains neglected, impeding depot cover technology advancements. To address this challenge, with a focus on both safety and vibration damping. Firstly, the mechanistic models are constructed to establish a surrogate modeling database. Subsequently, a surrogate model is proposed, integrating stacked denoising autoencoders (SdAEs), self-attention (SA), and the gated recurrent unit (GRU). In addition, A novel MOOA, Dynamic Population-Multi-Objective Harris Hawks Optimization-Crowding Distance-Elitist Learning Strategy (D-MOHHO-CD-ELS), is proposed and its efficacy is validated against five existing MOOAs using the CTP1∼CTP7 test functions. Moreover, the train-ballast No.12 turnout system is considered as an engineering case. Importantly, the accuracy of both the mechanistic model and surrogate model is thoroughly validated. Among them, the performance of the data preprocessing and prediction algorithms is substantiated through a comparison of the proposed SdAEs-SA-GRU model against simulation results and eight other algorithms. Furthermore, the surrogate-based D-MOHHO-CD-ELS method, applied to tackle a multi-objective optimization problem with nine optimization parameters and four optimization objectives, demonstrates an efficiency improvement of 1 to 2 orders of magnitude compared to traditional methods. Consequently, following optimization, the wheel load reduction rate, derailment coefficient, capsizing coefficient and vibration damping effect are improved by 15.5%, 11.1%, 5.5% and 24.8% respectively, which reveals the effectiveness of enhancements in both the safety and damping efffect. the study offers a novel perspective for parameter design of TBT.

Surrogate model-based optimization of methanol synthesis process for multiple objectives: A pathway towards achieving sustainable development goals

This work combines a generalized regression neural network (GRNN) with a non-dominated sorting genetic algorithm (NSGA-II) to optimize a methanol synthesis plant for multiple objectives. The proposed method begins by developing and validating the model for the methanol synthesis involving the recycling of unreacted gas stream into the methanol reactor feed. The data generated using this model is used to develop a GRNN-based surrogate model to expedite the evaluation of fitness values for the optimization algorithm. The objective functions considered for simultaneous optimization are minimizing the total energy cost per unit of energy input (TEC), maximizing overall resource utilization (R), and minimizing CO2-gram equivalent emissions per unit of energy input (EPEI). Pareto optimal solutions are obtained for three bi-and one tri-objective optimization case studies using the GRNN-assisted multi-objective optimization (GRNNAMOO) method. The developed GRNNAMOO approach reduces the computational time from multiple days to a few seconds for all case study scenarios. For the tri-objective optimization case, the operating point selected using multi-criteria decision-making achieves 84.37% of R, 10.45 $/GJ of TEC, and an EPEI value of 81.34 gCO2eq/MJ. These results represent 7.05% higher R, 0.34 $/GJ lower TEC, and 0.82 gCO2eq/MJ lower EPEI than the Aspen plus simulation results. Further, the carbon footprint values obtained are significantly lower than 110 gCO2eq/MJ reported for modern methanol plants for nearly the same R and TEC values. The proposed approach aligns with the United Nations' sustainability development goals by lowering energy costs and promoting sustainable energy through improved environmental sustainability in methanol production plants.

Optimization Assisted by Neural Network-Based Machine Learning in Electromagnetic Applications

We introduce an optimization assisted by a neural network (ONN) predictor to the electromagnetic community. ONN belongs to the class of the surrogate model-based optimization approaches, and approximates the objective function using a non-linear approximator – neural network. We provide a comprehensive description of the ONN algorithm and the details of its mathematical formulations. We apply ONN to optimize three popular benchmark functions and compare its performance with some commonly used optimization algorithms, namely particle swarm optimization, genetic algorithm, and Bayesian optimization. For the first time, we demonstrate ONN’s applicability and effectiveness in antenna design problems by optimizing a six-element Yagi-Uda antenna and by solving a challenging ten-dimensional dual-band slotted patch antenna constrained optimization problem. To achieve this, ONN is linked with a full-wave electromagnetic simulation solver through an application user interface. The optimized slotted patch is fabricated and measured to demonstrate how ONN can be part of the full antenna design process. Our empirical results indicate that ONN requires less objective function evaluations to reach the same qualitative point and reaches better optimal points for the same number of iterations for the studied benchmark functions and antenna optimization problems compared to the aforementioned baseline optimization algorithms.

Thermal Modeling With Surrogate Model-Based Optimization of Direct Oil Cooling Heat Transfer Coefficient for HEV Motor

Thermal Modeling With Surrogate Model-Based Optimization of Direct Oil Cooling Heat Transfer Coefficient for HEV Motor

Data driven surrogate model-based optimization of the process parameters in electric discharge machining of D2 steel using Cu-SiC composite tool for the machined surface roughness and the tool wear

Electrical discharge machining (EDM) is mainly utilized for the die manufacturing and also used to machine the hard materials. Pure Copper, Copper based alloys, brass, graphite, steel are the conventional electrode materials for EDM process. While machining with the conventional electrode materials, tool wear becomes the main bottleneck which led to increased machining cost. In the present work, the composite tool tip comprises 80% Copper and 20% silicon carbide was used for the machining of hardened D2 steel. The powder metallurgy route was used to fabricate the composite tool tip. Electrode wear rate and surface roughness were assessed with respect to the different process parameters like input current, gap voltage, pulse on time, pulse off time and dielectric flushing pressure. During the analysis it was found that Input current (I p ), Pulse on time (T on ) and Pulse off time (T off ) were the significant parameters which were affecting the tool wear rate (TWR) while the I p , T on and flushing pressure affected more the surface roughness (SR). SEM micrograph reveals that increase in I p leads to increase in the wear rate of the tool. The data obtained from experiments were used to develop machine learning based surrogate models. Three machine learning (ML) models are random forest, polynomial regression and gradient boosted tree. The predictive capability of ML based surrogate models was assessed by contrasting the R 2 and mean square error (MSE) of prediction of responses. The best surrogate model was used to develop a complex objective function for use in firefly algorithm-based optimization of input machining parameters for minimization of the output responses.

Analytical temperature estimation process of the air supply system of the proton exchange membrane fuel cell stack in fuel cell electric vehicles

The air supply system of the proton exchange membrane fuel cell stack in fuel cell electric vehicles should be included as one of the components of the balance of plant. However, the air supply system consists of a centrifugal air compressor, driven by an ultra-high-speed motor. Therefore, there occurs a large amount of thermal energy from losses and the temperature of the air supply system should be considered. Accordingly, this study suggests the temperature estimation process for an air supply system based on a lumped parameter thermal network (LPTN). First, performance modeling is introduced using not only the empirical approach but also electromagnetic finite element analysis (FEA). Subsequently, thermal modeling based on the LPTN is presented. For this procedure, optimization techniques, screening, and surrogate model-based optimization are used. Finally, the results of LPTN construction are investigated. Furthermore, an additional experiment is conducted, and the result of this study is verified.

Hybrid Surrogate Model-Based Multi-Objective Lightweight Optimization of Spherical Fuel Element Canister

A number of canisters need to be lightweight designed to store the spherical fuel elements (SFE) used in high-temperature gas-cooled reactors (HTGR). The main challenge for engineering is pursuing high-accuracy and high-efficiency optimization simultaneously. Accordingly, a hybrid surrogate model-based multi-objective optimization method with the numerical method for the lightweight and safe design of the SFE canister is proposed. To be specific, the drop analysis model of the SFE canister is firstly established where the finite element method—discrete element method (FEM–DEM) coupled method is integrated to simulate the interaction force between the SFE and canister. Through simulation, the design variables, optimization objectives, and constraints are identified. Then the hybrid radial basis function—response surface method (RBF–RSM) surrogate method is carried out to approximate and simplify the accurate numerical model. A non-dominated sorting genetic algorithm (NSGA-II) is used for resolving this multi-objective model. Optimal design is validated using comprehensive comparison, and the reduction of weight and maximum strain can be up to 2.46% and 44.65%, respectively. High-accuracy simulation with high-efficiency optimization is successfully demonstrated to perform the lightweight design on nuclear facilities.

Radial Basis Function Surrogate Model-Based Optimization of Small Light-Weight Lead-Bismuth Reactor Core

Owing to their high miniaturization potential and strong natural circulation capability, lead-bismuth reactors have been widely employed for nuclear energy utilization as well as military and civilian applications. However, there is a need to optimize the design of these reactors. To solve the complex high-dimensional nonlinear single-/multiobjective optimization problem of lead-bismuth reactors, we proposed a single-/multiobjective optimization method (termed as RBF-OLHS-NGA/NSGA II method) for optimizing the reactor core, which is based on the radial basis function (RBF) surrogate model (for prediction), orthogonal Latin hypercube sampling, niche genetic algorithm (for single-objective optimization), and nondominated sorting genetic algorithm (for multiobjective optimization). In view of this approach, the design optimization procedure of the lead-bismuth reactor based on RBF (DOPPLER-R) was developed, which combined the reactor Monte Carlo (RMC) code and the steady-state thermo-hydraulic analysis calculation (STAC) code to sample, predict, and optimize reactor core parameters. Furthermore, the single-/multiobjective optimization approach was verified by considering the core fuel loading and active zone volume of SPALLER-4 as the optimization objectives. The results show that the RBF surrogate model can accurately and rapidly predict the core characteristic parameters of lead-bismuth reactors. When compared to the value calculated using the RMC code, the relative error associated with the predicted effective multiplication factor ( <math xmlns="http://www.w3.org/1998/Math/MathML" id="M1"> <msub> <mrow> <mi>k</mi> </mrow> <mrow> <mi>e</mi> <mi>f</mi> <mi>f</mi> </mrow> </msub> </math> ) is within ±0.1%. Compared to the unoptimized values, the single-objective optimized fuel loading reduced by 400 kg, multiobjective optimized fuel loading decreased by 455–493 kg (optimization ratio of 78%–84%), and active zone volume reduced by 166362–182888 cm3 (optimization ratio of 72%–79%). These results prove that the proposed optimization method is feasible, exhibits high efficacy, and can provide new technical ideas for single-/multiobjective optimization of multiphysics, multivariable, and multiconstraint lead-bismuth reactors.

Strategies for flexible operation of power-to-X processes coupled with renewables

Power-to-X (PtX) is a large-scale, long-term energy storage approach for converting renewable electrical energy into various chemical fuels. Unlike conventional fossil fuel production processes that operate continuously, PtX processes encounter operational challenges due to fluctuations in renewable power supply. To improve the operational flexibility of PtX processes for industrial applications, it is crucial to develop systematic strategies that can adapt to these fluctuations, which will increase PtX's energy and cost efficiencies. This study comprehensively explores various strategies for flexible operation of renewable-powered PtX processes, which include the use of additional energy buffers and grid connections. Power and material allocation models are developed for PtX processes based on islanded; grid-assisted; and grid-assisted, bidirectional connections by using three possible energy buffers (i.e., hydrogen intermediate storage, Li-ion batteries, and Carnot batteries). Surrogate model-based optimization is performed to establish an economically optimal design for each case. A power-to-methanol process implemented in Kramer Junction, California is studied to investigate the effects of flexible operation strategies on process performance in terms of production cost, renewable penetration, and energy efficiency. The findings of this study offer new insights into the operational flexibility of PtX processes and provide general recommendations for improving the flexibility and performance of PtX, particularly with respect to the establishment of a grid connection and the selection of an appropriate energy buffer.

Surrogate Model-Based Multiobjective Optimization of High-Speed PM Synchronous Machine: Construction and Comparison

This article employs surrogate models for large-scale high-speed (HS) electrical machine optimization to reduce heavy computational burden caused by the finite-element method (FEM) based on nondominated sorting genetic algorithm II. Three artificial neural networks, namely, multilayer perceptron (MLP), support vector regression (SVR), and generalized regression neural network (GRNN), and the classical Kriging model are developed based on the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${K}$ </tex-math></inline-formula> -fold crossing validation method. To find out the most suitable surrogate model, a HS permanent magnet synchronous machine (PMSM) applied in electrically assisted turbocharger (EATC) considering its multiphysics characteristics is optimized by different models. A detailed comparison is provided in terms of prediction accuracy and modeling time consumption. The optimal design is verified to guarantee the accuracy of optimization results. The key contributions of this article include an automatic HSPMSM optimization process is proposed, where complete modeling and tuning method as well as a reasonable comprehensive evaluation metric of different surrogate models are conducted. It is found that invalid samples from the initial dataset contain useful information to improve prediction accuracy. Hence, an entire surrogate process should benefit from a pretrained classifier. Also, it reveals that MLP, SVR, and Kriging model can greatly improve the design optimization effectiveness with high accuracy, whereas GRNN is not suitable for this specific optimization scenario.

Sealing design optimization of nuclear pressure relief valves based on the polynomial chaos expansion surrogate model

Pressure relief valve (PRV) is one of the important control valves used in nuclear power plants, and its sealing performance is crucial to ensure the safety and function of the entire pressure system. For the sealing performance improving purpose, an explicit function that accounts for all design parameters and can accurately describe the relationship between the multi-design parameters and the seal performance is essential, which is also the challenge of the valve seal design and/or optimization work. On this basis, a surrogate model-based design optimization is carried out in this paper. To obtain the basic data required by the surrogate model, both the Finite Element Model (FEM) and the Computational Fluid Dynamics (CFD) based numerical models were successively established, and thereby both the contact stresses of valve static sealing and dynamic impact (between valve disk and nozzle) could be predicted. With these basic data, the polynomial chaos expansion (PCE) surrogate model which can not only be used for inputs-outputs relationship construction, but also produce the sensitivity of different design parameters were developed. Based on the PCE surrogate model, a new design scheme was obtained after optimization, in which the valve sealing stress is increased by 24.42% while keeping the maximum impact stress lower than 90% of the material allowable stress. The result confirms the ability and feasibility of the method proposed in this paper, and should also be suitable for performance design optimizations of control valves with similar structures.

Adaptive approximation-based multi-objective hybrid optimization method for dual-gradient top-hat structures

In this article, an adaptive approximation-based multi-objective hybrid optimization method, integrating a multi-objective decision-making method, adaptive approximation method and hybrid optimization method, is developed. In particular, a multi-objective decision-making method developed by combining a weight strategy inspired by grey relational analysis and entropy analysis is applied to normalize multiple objectives; the trust region is introduced into the support vector regression model to solve the problem of the sequential sampling for the approximation model; a hybrid optimization algorithm combining the genetic algorithm pattern search algorithm is developed to further assist the surrogate model-based optimization. Finally, a novel dual-gradient structure with graded thickness and graded material property along the axial direction is applied to the crashworthiness optimization design. The results demonstrate that the developed hybrid method has faster optimization efficiency than the Pointer algorithm built into Isight commercial software, and the final optimized structure is superior to the original one.

Surrogate Model-based Multi-Objective Optimization in Early Stages of Ship Design

The abstract is the early stages of ship design, the decision of the ship's main dimensions significantly impacts the ship's performance and the total cost of ownership. This paper focuses on an optimization approach based on surrogate models at the early stages of ship design. The objectives are to minimize power requirements and building costs while still satisfying the constraints. We compare three approaches of surrogate models: Kriging, BPNN-PSO (Backpropagation Neural Network-Particle Swarm Optimizer), and MLP (Multi-Layer Perceptron) in two multi-objective optimization algorithms: MOEA/D (Multi-Objective Evolutionary Algorithm Decomposition) and NSGA-II (Non-Dominated Sorting Genetic Algorithm II). The experimental results show that MLP surrogate models get the best performance with MAE 6.03, and BPNN-PSO gets the second position with MAE 7.2. BPNN-PSO and MLP with MOEA/D and NSGA-II improve the design with around 58% smaller adequate power and 6% less steel weight than the original design. However, BPNN-PSO and MLP have lower hypervolume than Kriging for both optimization algorithms MOEA/D and NSGA-II. On the other hand, Kriging has the most inadequate model accuracy performance, with an MAE of 22.2, but produces the highest hypervolume, lowest computational time, and far lower objective values than BPNN-PSO and MLP for both optimization algorithms, MOEA/D and NSGA-II. Nevertheless, the three surrogate model approaches can significantly improve ship design solutions and reduce work time in the early stages of design.

A Surrogate Model Based Multi-Objective Optimization Method for Optical Imaging System

An optimization model for the optical imaging system was established in this paper. It combined the modern design of experiments (DOE) method known as Latin hypercube sampling (LHS), Kriging surrogate model training, and the multi-objective optimization algorithm NSGA-III into the optimization of a triplet optical system. Compared with the methods that rely mainly on optical system simulation, this surrogate model-based multi-objective optimization method can achieve a high-accuracy result with significantly improved optimization efficiency. Using this model, case studies were carried out for two-objective optimizations of a Cooke triplet optical system. The results showed that the weighted geometric spot diagram and the maximum field curvature were reduced 5.32% and 11.59%, respectively, in the first case. In the second case, where the initial parameters were already optimized by Code-V, this model further reduced the weighted geometric spot diagram and the maximum field curvature by another 3.53% and 4.33%, respectively. The imaging quality in both cases was considerably improved compared with the initial design, indicating that the model is suitable for the optimal design of an optical system.