Optimizing injection molding simulations: comparative performance of Kriging and RSM surrogate models for process efficiency

Patch‐repaired plain woven composite structures were exposed to internal damage caused by impact during service, which reduced mechanical properties. A multi‐scale modeling strategy was proposed to study the impact resistance characteristics of patch‐repaired plain woven carbon‐fiber‐reinforced‐polymer (CFRP) laminates. The micro representative volume element (RVE) was extracted from the yarn; a local homogenization method was used to obtain the equivalent cross‐ply laminate (ECPL) cells corresponding to the mesoscale RVE. The finite element model (FEM) of patch‐repaired plain woven laminate was established by extending the ECPL cells. The FEM was checked by the low‐velocity impact (LVI) tests, and the impact parameter errors were within 10%. Furthermore, impact resistance of repaired specimens under different impact conditions (e.g., the impact energy was 3 ~ 20 J) was studied. Finally, patch parameters (patch thickness, patch size, off‐axis angle) of the repaired specimen were optimized by multi‐objective optimization based on the surrogate model and response surface method (RSM). After multi‐objective function optimization, the optimal patch parameter configuration (the thickness of the patch was 0.87 mm, the diameter was 66 mm, and the off‐axis angle was 44.2°) reduced the absorbed energy value of the repaired specimen from 4.9089 to 4.1640 J, and the delamination area of the repaired specimen from 605 to 280 mm2. All the results provide a reference for patch repair of plain woven composites.

The first and foremost aim with this book is to serve as a guide and reference for engineers that want to use surrogate modeling techniques when they design or develop products, systems and components. Additionally, the book constitutes part of the literature for the courses in Design Optimization and Multidisciplinary Design Optimization at Linköping University. It is the intention of the author that the content should serve as an easily understood introduction to surrogate modeling. The more advanced details are briefy mentioned but can be found in the scientifc papers referenced in this book. There exist numerous books and review articles regarding surrogate modeling, e.g. Forrester, Sóbester, and Keane, 2008 and Krawczyk and Arabas, 2025, which means that all methods presented here can be found elsewhere. The two main advantages of this book are Many methods are exemplifed using numerical examples Some practical guidelines recommended by the author are presented

Recent progress on machine learning techniques for flow field optimization toward performance and commercial scale proton exchange membrane fuel cell: A systematic review

Creep rupture life prediction for the A231 T91 alloy steel has been optimized using the Kriging surrogate model. Creep rupture data published by NIMS data sheet was used in this optimization, and isothermal creep rupture life-stress and TTP(Time-Temperature Parameter)-stress curves were optimized with Kriging model. The creep rupture data having the rupture life of less than 10,000 hours was interpolated with the K海ing surrogate model and theKriging extrapolation to the creep life of 100,000 hours was verified by comparing with experimental data. It was found that the Kriging model could fit to the data within 3% of relative error. Furthermore, the Kriging surrogate model was compared to Wilshire, Manson-Brown, Manson-Haferd, and MCX models. It can be found that the creep rupture stress extrapolated to 100,000 hours by Kriging surrogate showed a relatively good accuracy and uncertainty of 4% - 16%.

This study presents an optimization flow for structural parameters of orthotropic steel bridge decks (OSDs) based on the fatigue performance and the structural weight. The effects of structural parameters, namely, the thicknesses of the deck plate, the U-rib, the diaphragm, and the longitudinal diaphragm, on equivalent fatigue stress ranges were investigated using surrogate modelling based on the response surface methodology (RSM). Finally, the Pareto optimum front was obtained via the nondominated sorting genetic algorithm II (NSGA-II). The results show that the established surrogate response surface model can predict the local equivalent stress amplitudes well. The deck thickness is the most significant factor for the fatigue performance of the deck to U-rib weld and the U-rib to diaphragm weld. The objectives of minimizing the equivalent stress range and the total structural weight are truly conflicting, and the optimum solutions for structural parameters can be obtained from the Pareto optimum front.

The objective of this paper is to minimize the weight of the forearm of the bucket-wheel stacker reclaimer on the premise of guaranteeing strength, stiffness, and non-resonance. Because the stacking and reclaiming are inseparable from the motion of the forearm, the consumed energy is positively proportional to the self-weight and the forearm supports a lot of loads during the working process; it is necessary to minimize the weight under the requirements of strength, stiffness, and non-resonance. However, it is a high-dimensional problem, and it is of low efficiency when the finite element model is used for optimization. Morris method is used to perform the sensitivity analysis on all the variables. Those with great influence, named main factors, are screened out in order to decrease the number of variables taken into account. Surrogate models are introduced to improve the efficiency of optimization. Herein, Kriging models of the weight, the maximum stress, the maximum displacement, the first-order nature frequency under no-load situation, and the second nature frequency under full-load situation are constructed. In order to improve the model with poor precision, the sequential multi-point infill criterion is introduced. Finally, the weight reduction optimization is performed based on the constructed Kriging models. Compared with the initial design, the weight is reduced greatly. Besides, the Kriging models are of excellent accuracy, which proves that Kriging models or surrogate models are effective substitutes for expensive finite element models to deal with optimization problems.

Surrogate models have been used to replace computationally expensive analysis models in engineering design problems. However, time-dependent variables and historical data are usually ignored in the surrogate modeling process. For instance, in a dam network design, using hydraulic simulations to estimate the water flow is computationally expensive, and the data is in the form of time series. So, we need time-dependent surrogate models to replace these simulations and manage this computational complexity. In this paper, we describe surrogate models to predict the amount of water flow into a reservoir. The challenge is that the flow is a time-dependent variable, and we need to incorporate time series into surrogate models. Thus, there are three contributions: (1) using surrogate modeling to predict flow for dam network design, (2) incorporating time series analysis in surrogate models for water network design, (3) using an ensemble of surrogates to increase the accuracy of prediction. We also demonstrate how to integrate surrogate models and machine learning with time series analysis for more accurate and faster prediction. Due to the availability of data, we use the Buffalo Reservoir in the Red River Basin as an example. Based on the time series data for flow, evaporation, precipitation, and maximum and minimum temperature, three surrogate models are used to examine the impact of integrating time series into surrogate models. These are multivariate autoregressive integrated moving average (MARIMA), a classic time series analysis method; artificial neural network (ANN), and random forest (RF) methods, two machine learning surrogate models. We use seven different time lags as features within an RF model, as an ensemble of surrogate models, and predict the flow for seven-time steps ahead. We successfully incorporate the time series data and particularly the concept of the time lag within surrogate models. We show that RF as the ensemble of surrogates provides more accurate predictions than the other two surrogate models. Although this method has been demonstrated for the Red River Basin, it could also be applied to designing anything in which time-dependent flow is an issue, for example, in biomedical applications, the management of manufacturing processes and product sales as well as any products in which fluid flow is an issue.

Developments in rapid manufacturing techniques such as electron beam freeform fabrication have made it easier to manufacture objects with complex shapes (like panel with curvilinear stiffeners). In this paper, design optimization of stiffened panels is carried out using different types of response surfaces. Placement and sizing variables are optimized using integrated high-performance, commercially available software. The proposed approach has two optimization loops. The sizing optimization is carried out in the first loop through finite element analysis using gradient-based optimization method for different placement variables. In the second loop, optimal placement of stiffeners is carried out using response surfaces. Because of response surface construction using whole design space, the proposed approach does not suffer from getting trapped in a local minima. The proposed approach is applied to square panels subjected to in-plane biaxial and uniform surface pressure loadings. Panel weight is minimized with buckling, displacements, and stress constraints. An approach to perform both placement and sizing optimization of panels with curvilinear stiffeners is also discussed and a surrogate model is developed for placement and shape optimization of stiffeners.

Lithium-ion batteries (LIBs) have found widespread application in energy storage due to their high energy density, low self-discharge and low maintenance characteristics. However, the stability and longevity of the batteries under extreme operating conditions is yet to be fully understood. Numerous experimental and simulation studies have been performed to elucidate the effect of temperature, current, depth of discharge, and the number of cycles [1,2,3] on the performance of LIBs. These studies show that the solid-electrolyte interface (SEI) layer and gas formation accelerate at high C-rates due to increased electrolyte decomposition [4,5]. Consequently, the cell's internal resistance increases, resulting in ever-increasing irreversible heat generation inside the cell [6]. This heat generation leads to high internal temperature and a corresponding reduction in cell capacity. The data of cell temperature for a wide range of ambient temperatures and cycling rates is limited because cell performance is typically reported at room temperature. The design of battery packs for electric vehicles(EVs) is also based on test data taken at room conditions. Given that the cell's capacity, specific energy, maximum power output is bound to depend on C-rate and ambient temperature, it is necessary to test and design battery packs based on these parameters.The thermal characteristics of a lithium-ion cell can be predicted using a physics-based thermal model or data-driven methods (DDM) relying on empirical data. Experimental determination of internal cell parameters required in physics-based thermal models is challenging and time-consuming for commercial cells. On the other hand, DDM requires only cell cycling data at specific operating conditions, thereby eliminating the need for internal parameter estimation. This model predicts the experimental input and output data pattern and fits the response surface to estimate the unknown output. In this study, surrogate modelling has been employed to estimate the surface temperature, capacity, energy, and average power of commercial lithium-ion cells for different discharge currents and ambient temperatures. Surrogate modelling, a popular data analysis and reduced-order modelling technique, aims to find a global minimum of a particular objective function using a few objective function evaluations [7]. The surrogate-based model divides experimental data into training and test data sets. The training data set is employed to train the algorithm. After that, the testing data set is used to validate the model's accuracy. Experiments were performed to develop a surrogate model, with the number of experiments decided using the design of experiments[8] for a current range of 0.5C to 3C-rate and ambient temperature range of 0°C to 45°C . The cycling of cells was performed using a high current battery cycler (Arbin), and the ambient temperature was maintained using a thermal chamber (Cincinnati). The surface temperature of commercial 18650 (NMC811) lithium-ion cells was recorded using T-type thermocouples and a National Instruments DAQ module. A polynomial response surface was fitted using surrogate modelling on experimentally obtained data. The response surface shown in figure 1. contains nine data points for the preliminary study, sub-divided into a set of seven training and two testing data. The prediction error sum of squares (PRESS) is currently bounded within 10% due to the limited training data set availability and is expected to be within a band of 1% after adding data from ongoing experiments. The estimation of temperature, capacity, and specific energy can be used to optimize and develop an improved thermal management system for electric vehicles that works under various operating conditions. References Waldmann, T., Wilka, M., Kasper, M., Fleischhammer, M., & Wohlfahrt-Mehrens, M. (2014). Journal of Power Sources, 262, 129-135.Guan, T., Sun, S., Yu, F., Gao, Y., Fan, P., Zuo, P., Du,C., & Yin, G. (2018). Electrochimica Acta, 279, 204-212.Simolka, M., Heger, J. F., Traub, N., Kaess, H., & Friedrich, K. A. (2020). Journal of The Electrochemical Society, 167(11), 110502.Xu, B., Diao, W., Wen, G., Choe, S. Y., Kim, J., & Pecht, M. (2021). Journal of Power Sources, 510, 230390.Rashid, M., & Gupta, A. (2017). Electrochimica Acta, 231, 171-184.Leng, F., Tan, C. M., & Pecht, M. (2015). Scientific reports, 5(1), 1-12.Queipo, N. V., Haftka, R. T., Shyy, W., Goel, T., Vaidyanathan, R., & Tucker, P. K. (2005). Progress in aerospace sciences, 41(1), 1-28.Li, W., Xiao, M., Peng, X., Garg, A., & Gao, L. (2019). Applied Thermal Engineering, 147, 90-100. Figure 1

Enhanced weathering (EW) of minerals could potentially absorb atmospheric CO2 at gigaton scale per year and store it as bicarbonate and carbonate in the ocean. However, this process must be accelerated by engineered reactors, in which optimal reaction conditions maximise the CO2 capture rate and minimise the energy and water consumption. In this work, trickle beds (TBs) and packed bubble columns (PBCs), operated with fresh water and CO2 -rich flue gas, are chosen as typical chemical reactors to perform the EW-based CO2 capture. We firstly develop experimentally validated physics-based mechanistic models then generate data to train data-driven surrogate models to achieve rapid prediction of performance and multi-variable optimization. Two surrogate models, namely, response surface methodology (RSM) and extended adaptive hybrid functions (E-AHF), are developed and compared, in which the effect of five design variables on three objective functions are investigated. Results show that the R2 for the prediction of CO2 capture rate (CR) and water consumption (WC) through RSM and E-AHF is higher than 0.84. For TB reactors, in particular, the calculated R2 is higher than 0.96. The prediction accuracy of energy consumption (EC) through the RSM approach is, however, relatively poor (R2 ∼ 0.79), but is improved by using the E-AHF surrogate model, increasing to R2 ∼ 0.89. The developed data-driven surrogate model can rapidly predict the performance indicators of TB and PBC reactors without solving complex mechanistic models consisting of many partial differential equations. After optimization using the surrogate models, improvements were achieved in the objectives for TB and PBC reactors as follows: CR increased by 37.8 % and 13.1 %, EC reduced by 37.4 % and 23.8 %, and WC reduced by 12.5 % and 40.7 %, respectively.

Response surface methods have been used for a variety of applications in aerospace engineering, particularly in multidisciplinary design optimization. We investigate the use of kriging models as alternatives to traditional second-order polynomial response surfaces for constructing global approximations for use in a real aerospace engineering application, namely, the design of an aerospike nozzle. Our objective is to examine the difeculties in building and using kriging models to create accurate global approximations to facilitate multidisciplinary design optimization. Error analysis of the response surface and kriging models is performed, along with a graphical comparison of the approximations. Four optimization problems are also formulated and solved using both sets of approximation models to gain insight into their use for multidisciplinary design optimization. We end that the kriging models, which use only a constant “global” model and a Gaussian correlation function, yield global approximations that are slightly more accurate than the response surface models.

Process optimization of a Non-circular drawing (NCD) sequence of a pearlitic steel wire was performed to improve the mechanical properties of a drawn wire based on surrogate assisted meta-heuristic algorithms. The objective function was introduced to minimize inhomogeneity of effective strain distribution at the cross-section of the drawn wire, which could deteriorate delamination characteristics of the drawn wires. The design variables introduced were die geometry and reduction of area of the NCD sequence. Several surrogate models and their combinations with the weighted sum technique were utilized. In the process optimization of the NCD sequence, the surrogate models were used to predict effective strain distributions at the cross-section of the drawn wire. Optimization using Differential evolution (DE) algorithm was performed, while the objective function was calculated from the predicted effective strains. The accuracy of all surrogate models was investigated, while optimum results were compared with the previous study available in the literature. It was found that hybrid surrogate models can improve prediction accuracy compared to a single surrogate model. The best result was obtained from the combination of Kriging (KG) and Support vector regression (SVR) models, while the second best was obtained from the combination of four surrogate models: Polynomial response surface (PRS), Radial basic function (RBF), KG, and SVR. The optimum results found in this study showed better effective strain homogeneity at the cross-section of the drawn wire with the same total reduction of area of the previous work available in the literature for fewer number of passes. The multi-surrogate models with the weighted sum technique were found to be powerful in improving the delamination characteristics of the drawn wire and reducing the production cost.

In electronic circuit design, preliminary analyses of the circuit performances are generally carried out using time-consuming simulations. These analyses should be performed as fast as possible because of the strict temporal constraints on the industrial sector time to market. On the other hand, there is the need of precision and reliability of the analyses. For these reasons, there is more and more interest toward surrogate models able to approximate the behavior of a device with a high precision making use of a limited set of samples. Using suitable surrogate models instead of simulations, it is possible to perform a reliable analysis in less time. In this work, we are going to analyze how the surrogate models given by the support vector machine (SVM) perform when they are used to approximate the behavior of industrial circuits that will be employed in consumer electronics. The SVM is also compared to the surrogate models given by the response surface methodology using a commercial software currently adopted for this kind of applications.

High-speed forming processes, such as electrohydraulic forming, have recently attracted attention with the development of forming technology. However, because the high-speed operation (above 100 m/s) raises safety concerns, most experiments are conducted in a closed die, which hides the forming process. Therefore, the experimental process can only be observed in a numerical simulation with accurate material properties. The conventional quasistatic material properties are improper for high-speed forming simulations with high strain rates (>102 s−1). In this study, the material properties of Al 6061-T6, which reflect the deformation behavior in the high-strain-rate region, were investigated in a numerical approach based on a reduced order model and a surrogate model in which the numerical results resemble the experimental results. The strain rate effect on the material was determined by the Cowper–Symonds constitutive equation, and two strain rate parameters were predicted. The surrogate model takes two material parameters as inputs and outputs a weighting coefficient calculated by the reduced order model. The surrogate model is based on the Kriging method to reduce the simulation cost. Next, the optimal material parameters that minimize the error between the surrogate model and the experiments are estimated by nonlinear least-squares optimization using a genetic algorithm and the constructed surrogate model. The predicted optimal parameters were verified by comparing the results of the experiment, numerical simulation, and surrogate model.

In this paper, a novel nano antenna with two radiation modes is introduced. The structure of this nano antenna consists of a ring coupler and two patch antennas placed on a SiO2 substrate. The direction of the main lobe of the radiation pattern of this nano antenna can be adjusted to be either in the broadside or the endfire direction. The proposed nano antenna is optimized to minimize the losses and to maximize the radiation efficiency in addition to achieve maximum discrimination between the two desired directions of the main beam. In optimizing the proposed structure, the computationally expensive full-wave electromagnetic simulation is replaced by cheaper surrogate models, which are kriging models. Two optimization techniques, namely multi-objective particle swarm with preference ranking organization METHod for enrichment evaluations method and design centering using the normed distances, are used to obtain the optimal values of the design parameters. A convergence test is performed to ensure the validity of the obtained simulation results. A sensitivity analysis is performed to show how the manufacturing tolerance in each design parameter is affecting the performance of the proposed nano antenna.