Traditional Response Surface Methodology Research Articles

Enhanced predictive optimization of methane dry reforming via ResponseSurface methodology and artificial neural network approaches: Insights using a novel nickel-strontium-zirconium-aluminum catalyst

This study investigates the molecular dynamics of methane dry reforming catalyzed by a novel nickel-strontium-zirconium-aluminum (5Ni+3Sr/10Zr+Al) catalyst, leveraging both Response Surface Methodology (RSM) and Radial Basis Function Neural Network (RBFNN) for predictive optimization. Focusing on the impact of operational parameters—hourly space velocity, reaction temperature, and CO2:CH4 mole ratio—on the conversion rates and formation of reaction components, we aim to predict optimal conditions and corresponding process variables. Through a comparison of a three-layer Feed Forward Neural Network, optimized at a 3:10:1 topology, with traditional RSM approaches, our findings highlight the superior predictive capabilities of ANN models. Notably, ANN demonstrated exceptional performance with Radj2and F_Ratio values significantly surpass those of RSM, alongside lower statistical error terms. This superiority is attributed to ANN's robust handling of nonlinear relationships between inputs and outputs, asserting its potential for enhancing predictive accuracy in chemical process optimization. At optimum predicted conditions like 1 CH4/CO2,750 °C reaction temperature, 12000 cm3g−1h−1 space velocity, NiSrZrAl outperformed with > 85 % CH4 and CO2 conversion with H2/CO ∼1 up to 20 h time on stream. Our research underscores the importance of integrating advanced modeling techniques for the efficient and accurate prediction of catalytic reactions, offering valuable insights for future applications in chemical engineering and catalysis.

Cyclodextrin-assisted extraction as a green alternative for the recovery of phenolic compounds from Helichrysum plicatum DC. flowers

Helichrysum plicatum DC. is an important source of bioactive secondary metabolites with a variety of pharmacological activities. To obtain highly potent extracts with the maximum level of phenolic glycosides and total phenolic compounds, this study aimed to establish an eco-friendly cyclodextrin-assisted extraction procedure from H. plicatum flowers. Response surface methodology (RSM) and artificial neural networks (ANN) were used to optimize the ultrasound-assisted extraction (UAE) by evaluating sonication temperature, time, concentrations of ethanol and two types of cyclodextrins (β-CD and HP-β-CD). Comprehensive statistical validation revealed better predicting capacity of the created ANN models compared to the traditional RSM. The highest positive effects were observed for the ethanol concentration and the extraction temperature. Both types of CDs showed not only positive impact on the extraction efficiency of bioactives, but also on their stability after exposure to stress conditions. Molecular docking was used to additionally reveal interactions within the studied inclusion complexes. Conclusively, the HP-β-CD-assisted extraction conducted at 80 °C for 40 min, utilizing 62% ethanol and 1.60% HP-β-CD, was the most optimal due to its ability to minimize ethanol consumption while achieving maximal recovery of bioactives, in comparison to β-CD (80%). Under these optimized conditions, experimentally obtained results for isoquercitrin (0.50 mg/g DW), kaempferol-3-O-glucoside (5.83 mg/g DW), apigenin-7-O-glucoside (1.34 mg/g DW), and total polyphenolic (28.51 mg GAE/g DW) content were in agreement with the values predicted by ANN.

Optimization of β-cyclodextrin based ultrasonic-assisted extraction of apigenin and luteolin from celery seed using support vector regression and different nature-inspired optimization algorithms

This study aimed to extract apigenin and luteolin from celery seeds using 2-hydroxypropyl-β-cyclodextrin (HP-β-CD) based ultrasonic-assisted technique. Optimal extraction conditions were determined through the integration of support vector regression combined with various optimization algorithms, including Genetic Algorithm, Particle Swarm Optimization, Gray Wolf Optimizer, Bat Algorithm, Firefly Algorithm, and Cuckoo Search Algorithm. The identified optimal conditions included an extraction time of 52 min, an HP-β-CD concentration of 24 mg/mL, and a solvent-to-solid ratio of 24 mL/g. Under these conditions, the predicted apigenin and luteolin content in the extract were 0.156 and 0.814 mg/g, respectively, closely aligning with the actual values of 0.158 ± 0.005 mg/g and 0.807 ± 0.008 mg/g. Notably, the HP-β-CD/water extract exhibited significantly higher concentrations of active ingredients and antioxidant activity compared to the water extract, with the content of apigenin and luteolin in the water extract being only 25 and 45%, respectively, compared to the HP-β-CD/water extract. Regarding the antioxidant effect, the water extract displayed a 50% scavenging capacity (SC50) of 331.29 ± 20.5 g/mL, whereas the SC50 for the HP-β-CD/water extract was 89.04 ± 4.70 g/mL. Molecular modeling and IR spectra analysis also suggested the formation of inclusion complexes between HP-β-CD and apigenin/luteolin. These findings suggested that HP-β-CD could be a preferable alternative to conventional solvents due to its advantages, such as easier control, safety, and cost-effectiveness. In addition, the use of support vector regression and nature-inspired optimization algorithms could be promising alternatives to traditional response surface methodology.

Calibration of Small-Grain Seed Parameters Based on a BP Neural Network: A Case Study with Red Clover Seeds

In order to enhance the accuracy of discrete element numerical simulations in the processing of small-seed particles, it is essential to calibrate the parameters of seeds within the discrete element software. This study employs a series of physical tests to obtain the physical and contact parameters of red clover seeds. A discrete element model of red clover seeds is established. Plackett–Burman Design, steepest ascent, and Central Composite Design experiments are sequentially conducted. The simulation deviation of the resting angle of red clover seeds is employed as the evaluation criterion for parameter optimization. The results indicate that the coefficients of static friction between red clover seeds, the coefficients of rolling friction between red clover seeds, and the coefficients of static friction between red clover seeds and the steel plates significantly influence the resting angle. Modeling was performed using a backpropagation neural network, a genetic algorithm–optimized BP network, particle swarm optimization, and simulated annealing. It was found that GA-BP ensured both accuracy and stability. Compared to the traditional response surface methodology, GA-BP showed better fitting performance. For the optimized red clover seed simulation, the error between the angle of repose and the physical experiment was 0.98%. This research provides new insights into the calibration of small-grain seed parameters, demonstrating the value of GA-BP for precision modeling.

Influence of hydroxypropyl-β-cyclodextrin complexation on the extraction efficiency of rutin, quercetin and total polyphenols from Fagopyrum esculentum Moench

With the aim to provide valuable insight into the experimental conditions which significantly influence extraction efficiency of the specific bioactive components from the common buckwheat aerial parts, Box–Behnken method was employed to design experiments that were performed using maceration at a room temperature. The effects of three process variables, ethanol (EtOH) concentration, extraction time and hydroxypropyl-β-cyclodextrin (HP-β-CD) concentration, were evaluated using response surface methodology (RSM) and artificial neural network (ANN). Obtained results revealed superior accuracy of the created ANN model over the traditional RSM, with the suggested optimal conditions: 40% EtOH concentration, 4% HP-β-CD concentration and 72 h extraction time. HP-β-CD encapsulation significantly enhanced the stability of rutin and quercetin in the optimal extract after exposure to stress conditions during the 30-day period. Additionally, Fourier-transform infrared spectroscopy (FT-IR) and molecular dynamics simulations were used for the structural characterization of the cyclodextrin inclusion complexes at the molecular level.

Genetic-neural optimization approach for gas metal arc welding of dissimilar aluminium alloys of AA5083-O/AA6061-T6

Distinct alloys have different chemical and thermal characteristics, making it difficult to weld together. For the purpose of maximizing tensile strength and weld hardness of the joint, the gas metal arc (GMA) welding process for the dissimilar aluminium alloys AA5083-O and AA6061-T6 was modelled and optimized in the current study. A genetic-neural approach was attempted, in which optimal artificial neural network (ANN) was applied to model the process and genetic algorithm (GA) approach was extended to optimize the parameters. The proposed genetic-neural (GA-ANN) approach was also compared to the traditional response surface methodology (RSM). In predicting the reactions of a GMA welded joint made of two different alloys, AA5083-O and AA6061-T6, the suggested optimum ANN model was shown to be more accurate (error 6%). The genetic-neural optimization technique has less inaccuracy (approximately 5% error) than the RSM optimization approach, however the more computational time was required to select GA-ANN parameters.

K-nearest neighbor based computational intelligence and RSM predictive models for extraction of Cadmium from contaminated soil

• CI predictive models’ application on soil washing are scare in literature. • Predictive models faced dwindling accuracy when few sample data are available. • Performance of Cd ions soil extraction prediction using KNN were investigated. • KNN performance was better over traditional RSM for Cd soil extraction. • KNN are suitable for soil washing predictions under RSM few samples data. Computational intelligence (CI) predictive models based on k -Nearest Neighbor (KNN) algorithms were developed for Cd ions removal from contaminated soil using environmentally friendly chelating-agent polyaspartate. Based on extracted Cd ions into the chelating-agent, residual Cd ions in treated soil and Cd removal efficiency, the performances of the KNN models were compared with response surface methodology (RSM) models using whole data set (KNN1) and split data (KNN2) scenarios using correlation coefficient (R 2 ) and root mean square error (RMSE). Optimal performances of the developed KNN based models were found to be significantly influenced by the nearest neighbor’s k -parameter attributed to the disparity in the two approaches. The KNN1 demonstrated better performances characterized by higher R 2 = 0.984–0.999 and lower RSME of 0.399–6 against the RSM models’ R 2 = 0.7882–0.990 and RSME 2.08–20.36, respectively. For the KNN2 models, even though lower performances were obtained, yet the soil remediation efficiency models, demonstrated enhanced performance over the RSM models.

Assessing the competency of a semi-parametric expert system in the realms of response characterization uncertainty in premixed methanol dual fuel diesel combustion strategies: In critique to RSM

Engine response characterization endeavours of the day are faced with the contradictory obligations of developing an accurate engine response map in face of an ever-expanding parametric space and decreasing test-bench based prototype development time cycles. Under such imperatives of sparse experimental regimens, the present study focuses on the pivotal notions of reliability in a data-driven multi-variate response modelling endeavour in the complex realms of a premixed methanol dual fuel diesel operation. In the study, the Gene Expression Programming (GEP) technique with its distinguishing features of adaptivity in model evolution has been critically examined for its credibility as an expert system in such emerging combustion strategies. The relevance and competency of the GEP method has been rationalized to this end by comparing its performance with the traditional Response Surface Methodology which has been the mainstay in such engine response characterization objectives. Model integrity has been analysed and compared through a multitude of conventional and improvised statistical goodness-of-fit measures encompassing absolute and relative error metrics. Model reliability was adjudged through an exhaustive uncertainty analysis. Information theoretic measures of Kullback-Leibler divergence and improvised Thiel uncertainty coefficients were employed to compare the quality of system knowledge gained by the competing techniques. Generalization capability was reckoned through all the respective metrics applied across a test data set held blind to the meta-model training sequence. Comparable regression scores across conventional and standardized correlation measures notwithstanding, all GEP evolved meta-models registered substantially lower footprints in all statistical error metrics together with lower uncertainty bandwidths of estimation and information loss across both training and test data simultaneously for all responses explored. The outcome of the study arguably evokes considerable reconsideration on the choice of conventional RSM based characterization strategies in the paradigms of system response uncertainty prevalent in the emergent engine combustion strategies involving significant yet unknown degrees of non-linearity in its parametric operational space.

Multi-objective optimization of a multi-cellular aluminum extruded crush rail subjected to dynamic axial and oblique impact loading conditions

This work presents a multi-objective shape optimization study of a multi-cellular aluminum extrusion subjected to dynamic axial and oblique (20° angled) impact loading conditions. Finite element models are developed, validated with experimental data, parameterized, and used to exhaust the design space using a full factorial design of experiments. An analysis of different energy absorption characteristics, such as axial and oblique mean crush force, crush efficiency, and oblique impact coefficient, are presented. A multi-objective optimization problem is defined to generate new solutions that dominate a baseline profile in all aspects of performance, which produced a geometry with up to 16% improvements in energy absorption. The parametric study is used to define the “true” Pareto front, which is the set of non-dominated designs and the solution to the optimization problem. The response surface methodology (RSM) is used to perform the multi-objective optimization analysis. The traditional RSM approach is compared to an adaptive surrogate-assisted response surface method (ASA-RSM) in their speed and ability to identify the true Pareto front correctly. Using the traditional metamodel constraint, the traditional RSM approach could only identify 18% of the true Pareto front using up to 8% of the design domain. After relaxing the constraint, the traditional RSM approach still required approximately 63% of the entire domain to identify 67% of the true Pareto front accurately. In comparison, the ASA-RSM approach was able to identify 84.5% of the true Pareto front using 42% of the entire domain. In some instances, the ASA-RSM approach correctly identified 100% of the true Pareto front by using as little as 18% of the domain. However, the ASA-RSM approach’s peak performance is dependent on the initial sampling and resulting metamodel. This study provides a comprehensive understanding of the performance gains of multi-objective optimization in the application of structural crashworthiness considering various loading conditions.

Data-driven machine learning approach for exploring and assessing mechanical properties of carbon nanotube-reinforced cement composites

Traditional experimental investigation on the mechanical properties of cement composites is deprecated due to the intensive time and labor involved. Existing predictive models can hardly map the complicated relationships among mechanical attributes and behavior. This study first adopts machine learning to predict the mechanical properties of carbon nanotube (CNT)-reinforced cement composites. For this purpose, predictive models are trained on the previously published experimental data and results demonstrate that machine learning models present better generalization ability and predictive performance than the traditional response surface methodology. A sensitivity analysis indicates that the factor having the maximum influence on compressive strength is the length of CNTs, whereas that having the maximum influence on flexural strength is the curing temperature. Thus, it can be concluded that compared with the traditional experimental investigation and regression methods, machine learning can efficiently and accurately predict the mechanical properties of CNT-reinforced cement composites.

Optimizacija višestrukog odgovora kod EDM postupka korišćenjem meta-modela simboličke regresije

Electrical Discharge Machining (EDM) is a popular non-traditional machining process that is widely used due to its ability to machine hard and brittle materials. It does not require a cutting tool and can machine complex geometries easily. However, it suffers from drawbacks like a poor rate of machining and excessive tool wear. In this research, an attempt is made to address these issues by using a metamodel coupled with global optimization approach to predict suitable combinations of input parameters (current, pulse on-time and pulse off-time) that would effectively increase the material removal rate and minimize the tool wear. The metamodels are built by using a novel symbolic regression approach carried out using Genetic Programming (GP). On comparative evaluation against traditional response surface methodology (RSM) metamodels, the GP metamodels show much better and accurate estimation. GP metamodels are then coupled with a genetic algorithm to carry out multiobjective optimization of the EDM process.

Efficient optimized design of solar power tower plants based on successive response surface methodology

AbstractRecently the optimal design of the solar power tower (SPT) plants have attracted increasing attention. In this paper, an improved algorithm combing the successive response surface methodology (SRSM) and simulated annealing (SA) global algorithm was proposed to achieve the efficient optimization design of the molten salt SPT plant with 2650 heliostats in Sevilla, Spain. Based on the traditional response surface methodology (RSM) and the adaptive domain reduction method, the SRSM was established to surrogate the complex thermo-economic model of the SPT plant to the updated approximation function, which was a high-order polynomial form to define the relationship between the objective parameter of the levelized cost of energy (LCOE) and 12 design variables related to the 4 subsystems of the SPT plant. After that, the SPT plant optimization design was performed by the SA global algorithm on the basis of SRSM. According to a comparison between the results obtained by the proposed method and the actual model-based global algorithm, the high accuracy and low computation time of the proposed strategy was proved.

A sequential weighted Laplacian‐regularized optimal design for response surface modeling of expensive functions with outliers: An application in linear elastic fracture mechanics

AbstractThere are several sequential and adaptive strategies designed to reduce the number of experiments in response surface methodology (RSM). However, most of the existing sequential and adaptive methods are sensitive to the existence of possible outliers. In this paper, we propose an active learning methodology based on the fundamental idea of adding a Laplacian penalty to the D‐optimal design and integrate that with robust regression to look for the most informative settings to be measured, while reducing the influence of possible outliers. To leverage the intrinsic geometry of the factor settings in highly nonlinear spaces, we extend the proposed methodology to reproducing Kernel Hilbert space (RKHS). Through an extensive simulation study accompanied by a thorough sensitivity analysis, we show that the proposed framework outperforms traditional RSM designs in the presence of outliers. We also conduct a study utilizing a hierarchical function used in linear elastic fracture mechanics to illustrate practicality of the proposed methodology.

Modelling and Optimization of Biogenic Synthesis of Gold Nanoparticles from Leaf Extract of Swertia chirata Using Artificial Neural Network

Swertia chirata is a medicinal plant studied for its ability to synthesize polyshaped gold nanoparticles (AuNP). The process of AuNP biosynthesis was studied using artificial neural networks (ANN) with different activation function on output node (logistic or linear) and different training algorithm (back propagation or Levenberg–Marquardt). The maximum biosynthesis was checked under the optimized condition of 17.24% leaf extract, pH 4.61, gold chloride concentration 4 mM and temperature 53.61 °C. A significant improvement in the model efficiency for predicting AuNP biosynthesis around 37.60%, in terms of root mean square error was obtained with the developed ANN-linear2 model, compared to the traditional response surface methodology.

Improved 1,3-propanediol production with maintained physical conditions and optimized media composition: Validation with statistical and neural approach

This work is aimed at assessing the use of response surface methodology (RSM) and artificial neural networks (ANNs) for modelling, and predicting, the optimum parameters for 1,3-Propanediol production by Lactobacillus brevis N1E9.3.3 from glycerol and glucose co-fermentation. A preliminary study of physical parameters was conducted using Plackett-Burman design to reduce the number of input variables up to seven; i) beef extract, ii) yeast extract, iii) MgSO4·7H2O, iv) MnSO4·H2O, v) vitamin B12, vi) glycerol and vii) glucose. The traditional RSM models were improved by ANN models between a 54.08% and 12.19% in terms of root mean square error (RMSE). This study suggested that RSM and ANN can be considered as effective tools to model and predict optimum parameters for 1,3-Propanediol production by L. brevis N1E9.3.3.

Improving the Efficiency and Efficacy of Stochastic Trust-Region Response-Surface Method for Simulation Optimization

Stochastic Trust-Region Response-Surface method (STRONG) is a new response-surface-based framework for simulation optimization. The appeal of STRONG lies in that it preserves the advantages, yet eliminates the disadvantages, of traditional response surface methodology (RSM) that has been used for more than 50 years. Specifically, STRONG does not require human involvement in the search process and can guarantee to converge to the true optimum with probability one (w.p.1). In this paper, we propose an improved framework, called STRONG-X, that enhances the efficiency and efficacy of STRONG to widen its applicability to more practical problems. For efficiency improvement, STRONG-X includes a newly-developed experimental scheme that consists of construction of optimal simulation designs and an assignment strategy for random number streams to obtain computational gains. For efficacy improvement, a new variant, called STRONG-XG, is developed to achieve convergence under generally-distributed responses, as opposed to STRONG and STRONG-X where convergence is guaranteed only when the response is normal. An extensive numerical study is conducted to evaluate the efficiency and efficacy of STRONG-X and STRONG-XG. Moreover, two illustrative examples are provided to show the viability of STRONG-X and STRONG-XG in practical settings.

Application of Grey Taguchi-based response surface methodology (GT-RSM) for optimizing the plasma arc cutting parameters of 304L stainless steel

Plasma arc cutting (PAC) is a highly promising thermal cutting process because of its wide industrial applications involving cutting of different materials at high speeds. The competing abilities of PAC with laser cutting combined with its less polluting nature have shifted the research attention towards the process. The cutting parameters like arc current, torch stand-off, cutting speed and gas pressure play an important role in determining the quality of a cut surface. In the present work, the quality characteristics of the cut surface were assessed by measuring the surface roughness and kerf width while cutting the 304 L stainless steel. The experimental trials were designed by Taguchi’s L18 orthogonal array unlike the central composite design used with traditional response surface methodology (RSM), and an integrated approach of Grey Taguchi-based response surface methodology (GT-RSM) was disclosed for predicting the optimal combination of cutting parameters. The GT-RSM approach was found to improve the quality characteristics studied in the work significantly. The results will offer a good cutting database for the textile, chemical and pharmaceutical processing industries.

Optimización multirespuesta para mejora de la calidad. Comparación de enfoque clásico con el enfoque bayesiano y el de redes neuronales

El trabajo tiene por objetivo revisar las metodologías existentes sobre optimización multirespuesta, integrarlas en una sola y desarrollar un nuevo algoritmo que permita superar las limitaciones existentes.Para tal efecto se revisaron las metodologías de optimización estadística mediante metodología de superficie de respuesta tradicional,con diseño robusto; seguidamente se revisó la aplicación del enfoque bayesiano a lo obtenido con la estadística tradicional; y finalmente se revisaron aplicaciones de redes neuronales artificiales a casos de optimización. Luego de realizar el análisis y discusión sobre el tema se integrólas tres metodologías en una sola, habiendo desarrollado un nuevo algoritmo que permite superar las limitaciones y deficiencias de los métodos anteriores. Asimismo, se compararon los resultados obtenidos con otros métodos con los que se obtendrían con el nuevo método, siendo resultado favorable.Por tanto se ha desarrollado una metodología de optimización multirespuesta que considera relaciones lineales y no lineales, que tiene las cualidades de lasmetodologías de la estadistica tradicional,la estadística bayesiana, y las redes neuronales artificiales.

Combining STRONG with screening designs for large-scale simulation optimization

Simulation optimization has received a great deal of attention over the decades due to its generality and solvability in many practical problems. On the other hand, simulation optimization is well recognized as a difficult problem, especially when the problem dimensionality grows. Stochastic Trust-Region Response Surface Method (STRONG) is a newly developed method built upon the traditional Response Surface Methodology (RSM). Like the traditional RSM, STRONG employs efficient design of experiments and regression analysis; hence, it can enjoy computational advantages for higher-dimensional problems. However, STRONG is superior to the traditional RSM in that it is an automated algorithm and has provable convergence guarantee. This article exploits the structure of STRONG and proposes a new framework that combines STRONG with efficient screening designs to enable the solving of large-scale problems; e.g., hundreds of factors. It is shown that the new framework is convergent with probability one. Numerical experiments show that the new framework is capable of handling problems with hundreds of factors and its computational performance is far more satisfactory than other existing approaches. Two illustrative examples are provided to show the viability of the new framework in practical settings.

Stochastic Trust-Region Response-Surface Method (STRONG)—A New Response-Surface Framework for Simulation Optimization

Response surface methodology (RSM) is a widely used method for simulation optimization. Its strategy is to explore small subregions of the decision space in succession instead of attempting to explore the entire decision space in a single attempt. This method is especially suitable for complex stochastic systems where little knowledge is available. Although RSM is popular in practice, its current applications in simulation optimization treat simulation experiments the same as real experiments. However, the unique properties of simulation experiments make traditional RSM inappropriate in two important aspects: (1) It is not automated; human involvement is required at each step of the search process; (2) RSM is a heuristic procedure without convergence guarantee; the quality of the final solution cannot be quantified. We propose the stochastic trust-region response-surface method (STRONG) for simulation optimization in attempts to solve these problems. STRONG combines RSM with the classic trust-region method developed for deterministic optimization to eliminate the need for human intervention and to achieve the desired convergence properties. The numerical study shows that STRONG can outperform the existing methodologies, especially for problems that have grossly noisy response surfaces, and its computational advantage becomes more obvious when the dimension of the problem increases.