Response Surface Function Research Articles

Optimized design of energy absorption of aluminum foam filled CFRP thin-walled square tube based on agent model

PurposeAluminum foam-filled thin-walled unit structures have received much attention for their excellent energy absorption properties. To improve the energy absorption effect of car energy absorption box under axial compression, this paper optimizes the fiber lay-up sequence, fiber angle and aluminum foam density of aluminum foam filled carbon fiber reinforced plastic (CFRP) thin-walled square tubes.Design/methodology/approachDesign of sample points required to construct the proxy model using design of experiments (DOE) method, and the data sample points of different models are obtained through Abaqus simulation and test. A double high-precision proxy model with the maximum specific energy absorption (SEA) and the minimum initial peak crash force (PCF) as the evaluation index is constructed based on the response surface function method. The NSGA-II multi-objective genetic algorithm was used to optimize the design parameters and obtain the optimal solution for the Pareto front, and the results were verified by using the multi-objective optimization toolbox in design-expert.FindingsThe results show that the optimal solution to the multi-objective optimization problem with the inclusion of the lay-up sequence is ρ = 0.5g/cm3 for a fiber lay-up angle varying in the range ±15–90° and an aluminum foam density varying in the range 0.2g/cm3-0.5g/cm3, with a lay-up method of [±87°/±16°/±15°/±89°]. The two optimization methods correspond to SEA and PCF errors of 2.109% and 4.1828%, respectively. The optimized SEA value is 18.2 J/g and the PCF value is 18,230 N. The optimized design reduces the peak impact force and increases the specific energy absorption, which improves the energy absorption effect of thin-walled energy-absorbing boxes for automobiles.Originality/valueIn this paper, the impact resistance of CFRP thin-walled square tubes filled with aluminum foam is optimized. Based on numerical simulations and experiments to obtain the sample point data for constructing the dual-agent model, we investigate the effect of filling with different densities of aluminum foam under the simultaneous change of fiber lay-up angle and order on its mechanical properties in this process, and carry out the multi-objective optimization design with NSGA-II algorithm.

Optimization of a novel lateral energy dissipation system for cable-stayed bridge with short piers based on seismic vulnerability analysis

Cable-stayed bridges with short piers are susceptible to becoming the structural weak link in seismic resistance during strong earthquakes. Traditional lateral restraint systems, such as fixed and sliding bearing systems, may impose substantial lateral forces and displacement demands, affecting the entire bridge's seismic safety. A butterfly-shaped steel plate damper has been developed and integrated into a lateral energy dissipation system along with elastoplastic cables to address this. Given the significant computational challenges and the complexity of identifying the optimal parameters for the energy dissipation system, this paper combines the probabilistic seismic demand model (PSDM) with the response surface method (RSM) to propose the seismic vulnerability fitting optimization method (SVFOM). Based on SVFOM, utilizing a central composite design (CCD), 17 analysis scenarios that account for the parameter variations of the lateral energy dissipation system are established. By developing response surface functions for bearing damage (ys) and pier damage (yp) through the seismic response fitting of the structure across all scenarios, we determined the optimal parameters for the lateral energy dissipation system to minimize damage to both bearings and piers. The finite element model validation analysis, which demonstrated significant reductions in pier displacement and the probability of bearing damage, confirms the effectiveness of the SVFOM. Optimized parameters showed that the new lateral energy dissipation system can significantly enhance the lateral seismic performance of cable-stayed bridges with short piers. Compared to scenarios without energy dissipation and with lateral sliding bearings, they demonstrated that this optimized system reduces the relative displacement of the piers and girders by 56 % and the probability of complete bearing failure by 87 % while maintaining pier damage within acceptable limits. This optimized system offers a valuable reference for the seismic design of similar bridge structures.

Analysis and optimization of the dynamic response characteristics of aircraft cargo rack

In order to effectively achieve the optimization design of the aircraft cargo rack, based on finite element modal simulation, the structure was redesigned and analyzed using two schemes of surrogate model size optimization and topology optimization, ensuring the strength requirements while improving the natural frequency and reducing the weight. According to the modal shape of vibration, additional bridge structures were added at the weak points to improve the dynamic stiffness of the structure. According to the optimization design requirements, the response surface function was constructed, and the particle swarm optimization algorithm was applied in the size optimization and surrogate model solution. A multi-objective optimization model was established for flexibility and low-order natural frequencies, and topology optimization was carried out in HyperWorks. The structural dynamic modification of the topology optimization model was performed using the modal strain energy analysis method. The research results show that both optimization methods can achieve good lightweight design. The static performance of the optimized structure is stable, and the overall modal frequency is improved.

Optimization of reduction gear in anchor winch based on modal analysis

In order to achieve more scientific design of the reduction gear and reduce material waste, pre-stressed modal analysis method was combined with multi-objective optimization algorithm to optimize the structure of the reduction gear basic body. The model was simplified and parameterized and the maximum stress and equivalent stiffness under different parameter size combinations were obtained through finite element analysis. Separately, genetic clustering method, neural network method, and Kriging method were used to construct the response surface function. Through error verification and comparison, it was found that the Kriging method was more suitable for the gear model. In the design of variable extremum search, multi-objective genetic algorithm and sequential quadratic programming were compared and analyzed. The results show that the mass of the gear can be reduced by 39.9 %, while the maximum stress remains unchanged, the equivalent stiffness is not reduced, and a good optimization design effect is achieved.

Dynamics analysis and collaborative optimization of vehicle steering mechanism

In order to improve the dynamic response characteristics of the steering mechanism, a research scheme for increasing the natural frequency based on lightweight design was proposed. Based on the finite element method and the collaborative optimization method, the modal characteristics and harmonic response characteristics of the model were studied and analyzed to verify the strength and stiffness performance of the optimized structure. The modal shapes between the free mode and the constrained mode were compared and analyzed. With the second-order natural frequency as the optimization objective, the response surface function of the equivalent stiffness was constructed. Through optimization calculation, the design variables that satisfy the constraint conditions can be obtained. The results show that the optimized structure can increase the second-order natural frequency by 14.4 % on the premise of reducing the mass by 5.2 %, effectively avoiding the excitation frequency of the engine.

Structure optimal design of 500 kV dry-type air-core shunt reactor based on response surface method

The hotspot temperature of the reactor is one of the important indices in reactor design, and the appropriate hotspot value can ensure that the reactor will not overheat failure and threaten the safety of the power system. In this paper, the temperature field simulation model of a 500 kV dry-type air-core shunt reactor is established, and the hotspot temperature of the reactor is obtained by COMSOL software. Then, the radial basis function response surface function is used to construct the response surface function of the hotspot temperature and its related variables, and the applicability of the response surface function is tested to analyze the rationality and accuracy of the response surface function. Finally, the optimal solution of the response surface function under the coordination of variables and related constraints is obtained by using the constrained simulated annealing algorithm. The results show that the hotspot temperature of the reactor envelope winding decreases obviously after optimization.

Reduction of Heating Energy Demand by Combining Infrared Heaters and Infrared Reflective Walls

We study the potential of infrared (IR) heaters in combination with IR reflective walls to reduce heating energy demand in buildings. Using IR heaters increases radiant temperature. Combined with IR reflective walls, less radiant heat is absorbed by the surrounding walls, and more is reflected to and absorbed by the occupants. This allows for lower air temperatures while maintaining constant thermal comfort. Lower air temperatures result in heating energy savings. In simulations, we examine the impact of four parameters on the thermal comfort indicator Predicted Mean Vote (PMV): wall temperature, inlet air temperature, IR heater power, and IR emissivity of the walls. To reduce the number of data points needed, we use a Central Composite Design for the layout of the simulation plan. The results show that the PMV can be changed from 0.15 to 1.16 only by lowering the emissivity of the surrounding walls from 0.9 to 0.1. At high IR heater power and at low wall temperature the impact of the emissivity on the PMV becomes larger. From the simulation data, we derive a response surface function to determine the required IR heating power for any given room conditions, which could be used for automated IR heater control.

Seismic reliability analysis of slope in spatially variable soils using multiple response surfaces

PurposeThis paper aims to develop an efficient algorithm combining straightforward response surface functions with Monte Carlo simulation to conduct seismic reliability analysis in a systematical way.Design/methodology/approachThe representative slip surfaces are identified and based on to calibrate multiple response surface functions with acceptable accuracy. The calibrated response surfaces are used to determine the yield acceleration in Newmark sliding displacement analysis. Then, the displacement-based limit state function is adopted to conduct seismic reliability analysis.FindingsThe calibrated response surface functions have fairly good accuracy in predicting the yield acceleration in Newmark sliding displacement analysis. The seismic reliability is influenced by such factors as PGA, spatial variability and threshold value. The proposed methodology serves as an effective tool for geotechnical practitioners.Originality/valueThe multiple sources of a seismic slope response can be effectively determined using the multiple response surface functions, which are easily implemented within geotechnical engineering.

Physics-Constrained Bayesian Optimization for Optimal Actuators Placement in Composite Structures Assembly

Complex constrained global optimization problems such as optimal actuators placement are extremely challenging. Such challenges, including nonlinearity and nonstationarity of engineering response surfaces, hinder the use of ordinary constrained Bayesian optimization (CBO) techniques with standard Gaussian processes as surrogate models. To overcome those challenges, we propose a physics-constrained Bayesian optimization with multi-layer deep structured Gaussian processes, <i>MGP-CBO</i>. Specifically, we introduce a surrogate model with a multi-layer deep Gaussian process (MGP) mean function. The hierarchical structure of our model enables the applicability of constrained Bayesian optimization to complex nonlinear and nonstationary processes. The deep Gaussian process regression model, <i>MGP</i>, can efficiently and effectively represent the response surface function between actuators and dimensional deformations, thus yielding a better estimated global optimum in a shorter computational time. The proposed <i>MGP-CBO</i> model can realize faster convergence to the global optimum with lower constraint violations. Through extensive evaluations carried out on synthetic problems and a real-world engineering design problem, we show that <i>MGP-CBO</i> outperforms existing benchmarks. Although we use the optimal actuators placement as a demonstration example, the proposed <i>MGP-CBO</i> model can be applied to other complex nonstationary engineering optimization problems. <i>Note to Practitioners</i>&#x2014;Bayesian optimization is a widely used sequential design strategy for engineering optimization because it does not rely on functional forms of response surfaces. This paper helps address two questions in practice: (i) how to incorporate physics constraints into Bayesian optimization. (ii) How to do Bayesian optimization when the systems have hierarchical structures. In practice, the hierarchical system structure is ubiquitous, and the engineering optimization is constrained by physical laws or special requirements. Therefore, the proposed physics-constrained Bayesian optimization with a multi-layer Gaussian process could provide a new tool for engineering design optimization problems. The computational convergence and complexity have been investigated. The proposed method is applicable to broad complex and nonstationary engineering optimization problems.

Experimental study on optimization of continuous steel box girder bridge deck

ABSTRACT In order to accurately optimize the structural parameters of steel bridge deck(OSD), an optimal design method of continuous steel box girder bridge deck based on response surface method is proposed. Optimization design process includes full scale model test, finite element analysis, response surface function fitting and design parameter optimization. The orthotropic steel bridge deck’s deck thickness, stiffener thickness, diaphragm thickness, stiffener height, and diaphragm opening form are chosen as independent variables, and the internal forces of important structural components discovered are used as dependent variables. Design-Expert software created a five-factor, three-level response surface test. A multivariate quadratic response surface regression model between structural parameters and target response values was developed after the objective function and constraint criteria were identified. Numerical theory’s variance analysis was used to find the best combination, and Design Expert software was used to confirm it to make sure the design value was accurate. The findings indicate that optimized structural parameters are trustworthy because the difference between the predicted value and the theoretical value is less than 5%. An orthotropic steel bridge deck’s structural parameters can be optimized using the response surface approach. It serves as a reference for subsequent steel bridge deck design and construction.

Influence of coupling factors on structural reliability based on polynomial response surface optimization model

The sensitivity analysis model is frequently used to express the influence of conditional elements on structural reliability. However, the traditional sensitivity analysis model is limited to a few influencing factors, and has a small scope of application. In this paper, a modified sensitivity model is proposed by combining the optimal polynomial response surface function with the Sobol sensitivity algorithm. And the sensitivity calculation approach was combined with coupling factor test design, range verification, multi-body dynamics analysis and structural statics analysis, which enables to achieve the quantitative sensitivity value of the influence of conditional factors on structural reliability. Finally, a typical harvester structure is selected as a case, to verify the evaluation accuracy and effectiveness of the revised model. The results show that the sensitivity of threshing drum speed has the greatest influence, while the sensitivity of granary load has the least influence. The average quantitative prediction accuracy of revised approach is up to 97.36%. The revised model can accurately evaluate the sensitivity value of coupled influencing factors for industrial equipment.

An Application of Mixture Design: A Case Study on Blending of Olive Oils by Design-Expert

or quality control, raw material, semi-finished, and finished product analysis in chemistry, biochemistry, food, and environmental sciences, well-designed experimental strategies are needed to perform all experimental studies at minimum cost and under optimum conditions. The steps in the experimental strategies essentially constitute the experimental procedure followed, and here the aim is to select a model for the experimental procedure, to determine the number of experiments and experimental factor limitations for each run, to identify the correlation between experimental results and factors, and to optimise the experimental factors. The response surface methodology as an experimental design method also reduces the number of experiments required for multi-factor trials for optimisation. Mixture design, a special type of response surface function, is a very effective method for determining the proportions of components or variables in a mixture. A three-component mixture is represented by a triangle, which is a two-dimensional cross-section of a three-dimensional space represented by a cube representing the region where the proportions of the three components are added up to 100%. The points within this triangle or blend area represent possible blends, where: three corners correspond to single components, points along the edges to binary mixtures, the dots in the triangle to triad mixtures, and the centre of the triangle to an equal mix of all three components. Several common designs can be considered as ways to determine the logical number and arrangement of points in a simplex, the most well-known being the Simplex Centroid and Simplex Lattice patterns. This study focused on an experimental design application for fourteen blends of olive oils from four cultivars A–D mixed in the design presented together with a taste panel score for each blend and statistical evaluation of the results for mixture design applications. The higher the score is the better the taste of the olive oil. Here, the mixture design chosen for optimising blending ratios was Simplex-Lattice, and DesignExpert 7.3 software was used for statistical analysis. Comparing of calculated correlation coefficients of the response surface function and its parameters, and function constants, it could be understood that as the correlation coefficient would be 0.21 for used linear terms only, adding quadratic terms into the function increases it to 0.92 drastically.

Prediction of concrete strength using response surface function modified depth neural network.

In order to overcome the discreteness of input data and training data in deep neural network (DNN), the multivariable response surface function was used to revise input data and training data in this paper. The loss function based on the data on the response surface was derived, DNN based on multivariable response surface function (MRSF-DNN) was established. MRSF-DNN model of recycled brick aggregate concrete compressive strength was established, in which coarse aggregate volume content, fine aggregate volume content and water cement ratio are influencing factors. Furthermore, the predictive analysis and extended analysis of MRSF-DNN model were carried out. The results show that: MRSF-DNN model had high prediction accuracy, the correlation coefficient between the real values and the forecast values was 0.9882, the relative error was between -0.5% and 1%. Furthermore, MRSF-DNN had more stable prediction ability and stronger generalization ability than DNN.

Multi-Response Optimization of Thermochemical Pretreatment of Soybean Hulls for 2G-Bioethanol Production

Soybean is a major crop used in the production of human food. The soybean hull (SH) is also known as the seed coat and it constitutes about 5–8% of the total seed on a dry weight basis, depending on the variety and the seed size. Dilute sulfuric acid was employed for the thermochemical pretreatment of SH prior to enzymatic saccharification and alcoholic fermentation. Empirical modeling of response surface, severity factor and multi-response desirability function methodology, were used to perform the process optimization. Temperature, acid concentration and reaction time were defined as operational variables, while furfural, 5-hydroxymethylfurfural and solubilized hemicellulose and cellulose were defined as response variables. Mathematical models satisfactorily described the process and optimal conditions were found at 121 °C; 2.5% w/v H2SO4 and 60 min. More than 80% and 90% of hemicelluloses and celluloses, respectively, were able to solubilize at this point. The fermentation performance of an industrial Saccharomyces cerevisiae strain was also evaluated. The glucose available in the hydrolysates was completely consumed in less than 12 h, with an average ethanol yield of 0.45 gethanol/gglucose. Thus, the thermochemical conditioning of SH with dilute sulfuric acid is a suitable operation for 2G-bioethanol production.

Numerical Analysis on Water-Exit Process of Submersible Aerial Vehicle under Different Launch Conditions

To study the influence of launch conditions and wave interference on the stability of submersible aerial vehicles at the water–air interface, a coupling model for water-exit motion of submersible aerial vehicles was established by using the RNG k-ε turbulence model and VOF method. The water-exit processes of submersible aerial vehicles under different initial inclination angles and velocities were numerically simulated and the effects of initial inclination angle and velocity on the water-exit motion of submersible aerial vehicles were obtained. Based on the response surface function theory, a mathematical model for the motion stability of submersible aerial vehicles at the water–air interface was established, so that the submersible aerial vehicle’s pitch angle and velocity at the end of vehicle’s water-exit process, corresponding to any initial inclination angle and velocity, can be solved. The deviation between the simulated calculation result and the established fitting function model result was 2.7%. The minimum water-exit velocity of submarine aerial vehicles should be greater than 10.8 m/s. The research provides technical support for the trans-media motion stability analysis and hydrodynamic performance design of the submersible aerial vehicle.

Application of Virtual Sample Generation and Screening in Process Parameter Optimization of Botanical Medicinal Materials.

The small sample problem widely exists in the fields of the chemical industry, chemistry, biology, medicine, and food industry. It has been a problem in process modeling and system optimization. The aim of this study is to focus on the problems of small sample size in modeling, the process parameters in the ultrasonic extraction of botanical medicinal materials can be obtained by optimizing the extraction rate model. However, difficulty in data acquisition results in problem of small sample size in modeling, which eventually reduces the accuracy of modeling prediction. A virtual sample generation method based on full factorial design (FFD) is proposed to solve the problem ofa small sample size. The experiments are first conducted according to the Box- Behnken Design (BBD) to obtain small-size samples, and the response surface function is established accordingly. Then, virtual sample inputs are obtained by the FFD, and the corresponding virtual sample outputs are calculated by the response surface function. Furthermore, a screening method of virtual samples is proposed based on an extreme learning machine (ELM). The connection weights of ELM are used for further optimization and screening of the generated virtual samples. The results show that virtual sample data can effectively expand the sample size. The precision of the model trained on semi-synthetic samples (small-size experimental simples and virtual samples) is higher than the model trained merely on small-size experimental samples. The virtual sample generation and screening methods proposed in this paper can effectively solve the modeling problem of small samples. The reliable process parameters can be obtained by optimizing the model trained by the semi-synthetic samples.

Optimization of freeze drying parameters for moringa (Moringa oleifera) flower powder by using response surface methodology and principal component analysis

Moringa oleifera Lam. is an incredible plant because of vital nutrients such as minerals, vitamins and phytochemicals. The present work is focused on studying the optimization and quality attributes retention in moringa flowers in a freeze dryer (FD). Because the conventional drying process takes more time and energy which will affect the product quality and safety. Response surface methodology (RSM) was employed to optimize the effect of drying temperature (- 65 to - 45°C), vacuum pressure (0.5 to 2.5 mmHg) and drying time (18 to 24 h.) on the vitamin C, total antioxidant activity(TAA) and hygroscopicity (HS) of moringa flower. The developed model response R2 values of vitamin C 0.96, total antioxidant activity 0.97 and hygroscopicity0.95. Based on response surface and desirability (0.74) functions, moringa flower was freeze sdried at - 63.75°C for18 hr under 0.55 vacuum pressure had an optimum level of vitamin C 285.84 mg/100g, TAA 453.20 mg/100g and HS 1.57 percent. Freeze dried moringa flower powder at -55°C had maximum drying characteristics with special reference to high powder recovery (98.75%) and excellent flowability.The first principal component, accounting for 52.15 per cent and two 23.02 per cent of the total variance resolved the different drying temperatures.

Optimization of Assay Conditions for t-RNA by Experimental Design

A design of an experiment is generally to fictionalize an execution of an experimental process and the term of experimental design strategy usually refers to a two-stage modeling. The first of all named as working strategy is the determination of the experimental execution model and the last one is that a mathematical model for response surface function to define the relationship between the experimental factors. In this work, it was selected optimization of assay conditions for t-RNA using Central Composite Design, the influence of three factors, namely pH, enzyme concentration and amino acid concentration as an experimental design application, and improved an experiment strategy in order to optimize the effective operation factors on this chemical reaction and mathematical solution techniques of the response surface function. As examining of the coefficients of the response surface equation and its graphics, we can say that the most effective parameter on the esterification process is enzyme concentration alone and together with pH.

A Robust Asymmetric Kernel Function for Bayesian Optimization, With Application to Image Defect Detection in Manufacturing Systems

Some response surface functions in complex engineering systems are usually highly nonlinear, unformed, and expensive to evaluate. To tackle this challenge, Bayesian optimization (BO), which conducts sequential design via a posterior distribution over the objective function, is a critical method used to find the global optimum of black-box functions. Kernel functions play an important role in shaping the posterior distribution of the estimated function. The widely used kernel function, e.g., radial basis function (RBF), is very vulnerable and susceptible to outliers; the existence of outliers is causing its Gaussian process (GP) surrogate model to be sporadic. In this article, we propose a robust kernel function, asymmetric elastic net radial basis function (AEN-RBF). Its validity as a kernel function and computational complexity are evaluated. When compared with the baseline RBF kernel, we prove theoretically that AEN-RBF can realize smaller mean squared prediction error under mild conditions. The proposed AEN-RBF kernel function can also realize faster convergence to the global optimum. We also show that the AEN-RBF kernel function is less sensitive to outliers, and hence improves the robustness of the corresponding BO with GPs. Through extensive evaluations carried out on synthetic and real-world optimization problems, we show that AEN-RBF outperforms the existing benchmark kernel functions. Note to Practitioners—Some industrial systems cannot be accurately represented by physical models. In this situation, data-driven black-box optimization is necessary for advancing the system automation and intelligence. BO is one of the widely used strategies for learning the global optimum of black-box functions. BO has been applied to robotics, anomaly detection, automatic learning algorithm configuration, reinforcement learning, and deep learning. This article proposes one new kernel function, named after AEN-RBF. The new kernel function will make BO with GPs more robust to outliers and lower the data quality barrier of model training. This article was motivated by the hyperparameter tuning problem of deep learning models for image defect detection in advanced manufacturing, but the method can be easily extended to other applications where kernel functions are needed. Our proposed method is verified by synthetic and real-world optimization problems.

Application of optimal experiment design method to detect the ideal sensor positions: A case study of Milan metro line 5

This paper proposes a concept of optimal experimental design (OED) to enable an efficient parameter identification through an inverse analysis and to design an optimized monitoring set up. This method intends to provide a systematic and reproducible approach for parameter determination in mechanized tunnel modelling from field measurements during excavation. In this concept, identification of most relevant parameters is followed by a secondary spatial and temporal global sensitivity analyses in various time scales to find the most relevant positions in the existing monitoring set-up for parameter identification. To afford the computational costs, metamodeling approach was employed to substitute the FE model with a response surface function. To validate the numerical model and to justify the applicability of this concept for a real case, the measured tunnel-induced settlements in a shallow founded nine-storey building, undercrossed by the new double tube Milan metro line 5, are adopted. Results indicated that the OED-assisted design of sensor arrangements enables adequate identification of the model parameters with least uncertainty and less monitoring effort (e.g. fewer sensors), while no expert decision is required in the process. Finally, comparison of results from standard and OED-designed monitoring setups indicates a significant enhancement in the reliability of numerical results considering the measurement tolerances.