Second-order Response Surface Research Articles

Comparison of the Three Types of Central Composite Designs Over Subsets of Reduced Models by Design Optimality Criteria

The purpose of this article is to compare the 3 important types of central composite designs (CCDs) consisting of central composite circumscribed design (CCCD), central composite inscribed design (CCID), and central composite face-centroid design (CCFD) in response surface methodology (RSM). The difference among these designs is the distance from the center design to the axial points. The comparison was performed across the full second-order response surface model and across a set of reduced models for 3, 4, and 5 design factors ( 3, 4, and 5) including 1, 3, and 5 center runs ( 1, 3, and 5). This study used D-, A-, and G- optimality criteria to evaluate the performance of CCDs by presenting the design optimality criteria comparison ranking throughout the reduced-model subsets of 43, 224, and 839 models for 3, 4, and 5 design variables, respectively. The results showed that CCCD was superior to CCID and CCFD according to A- and D- optimality criteria, while CCCD and CCID performed better than CCFD based on G- optimality criterion over a set of reduced models for 3, 4, and 5 design factors. It was observed that D-, A-, and G- optimality efficiencies were robust to changes in the linear and cross-product terms and sensitive to deviation in the square terms. The study will provide recommendations to assist the experimenters in the choice of the best design among the candidate designs for practice applications when some model effects may be insignificant. HIGHLIGHTS Comparison of 3 classifications of CCD. Assessment by using D-, A-, and G- optimality criteria over the reduced-model subsets for the full second-order response surface model. Generated the reduced models by using weak heredity. CCCD was superior to CCID and CCFD according to A- and D- optimality criteria, while CCCD and CCID performed better than CCFD based on G- optimality criterion over a set of reduced models for 3, 4, and 5 design factors. GRAPHICAL ABSTRACT

Real-Time Implementable Reduced-Order Energy Model for an Electric Vehicle

<div>Accurate estimation of vehicle energy consumption plays an important role in developing advanced energy-saving connected automated vehicle technologies such as Eco Approach and Departure, PHEV mode blending, and Eco-route planning. The present study developed a reduced-order energy model with second-order response surfaces and torque estimation to estimate the energy consumption while just relying on the drive cycle information. The model is developed for fully electric Chevrolet Bolt using chassis dynamometer data. The dyno test data encompasses the various EPA test cycles, real-world, and aggressive maneuvers to capture most powertrain operating conditions. The developed model predicts energy consumption using vehicle speed and road-grade inputs for a drive cycle. The accuracy of the model is validated by comparing the prediction results against track and road test data. The developed model was able to accurately predict the energy consumption for track drive cycles within the error of ±4.0% of that measured from the experimental data. Finally, the model has been tested and verified for real-time implementation using the dSPACE MicroAutoBox II HIL test bench.</div>

Modular gas-cooled reactor core optimal design and additive manufacturing performance based on SiC matrix dispersed with TRi-structural ISOtropic fuel

High-temperature gas-cooled reactors present significant technical competitiveness in various fields, such as low-carbon electricity, thermal energy, and hydrogen supply. Silicon Carbide (SiC) matrix dispersed with TRi-structural ISOtropic (TRISO) particle fuel is characterized by high-temperature tolerance, radiation resistance, and good neutron economy, which has emerged as a pivotal technological pathway for reactor core design. With the rapid advancement of SiC Additive Manufacturing (AM) technology, there is a substantial increase in core design flexibility, and an innovative gas-cooled reactor design was proposed by Monte Carlo (MC) method in this paper. The Non-uniform Rational B-spline (NURBS), Latin Hypercube Sampling (LHS), second-order polynomial response surface, as well as Genetic Algorithm (GA) were coupled to realize the optimization design for the coolant channel. Besides, a modular fuel design was proposed, and the AM SiC shell was fabricated using Binder Jetting (BJ) technology. Furthermore, the densification of the AM SiC shell and the matrix with SiC powder and SiC microspheres (TRISO simulator) was investigated by Chemical Vapor Infiltration (CVI). Finally, the microscopic morphology analysis and thermal-mechanical performance characterization of the samples were conducted, which demonstrated the technical feasibility and advanced capabilities of the SiC matrix dispersed with TRISO fuel based on AM technology.

Research on the Characterization of Bonding Parameters for Ore Particles Based on Response Surface Methodology

Ore is a crucial component in the process of industrialization, and its crushing is a practice that is inextricably linked to our society. This study aims to simulate the crushing process of minerals in a comminution device using the Discrete Element Method (DEM) by characterizing the bonding parameters of mineral particles. Utilizing the EDEM software (2018) for discrete element simulations, the study investigated the influence of bonding parameters on the compressive strength and other performance indicators of the particle bonding model. The study was executed through the application of a Box–Behnken Design (BBD) and Response Surface Methodology (RSM), which facilitated the construction of a second-order response surface regression model. The optimal values for normal stiffness per unit area, shear stiffness per unit area, critical normal stress, and critical shear stress were meticulously determined. The subsequent simulation experiments strongly verify the feasibility of the proposed characterization method for key parameters.

Laser-induced oxidation of Cf/SiC composites: Oxidation behavior analysis and parameter optimization

Cf/SiC composite is widely utilized in aerospace and defense sectors owing to their outstanding high-temperature and mechanical performance. However, this material is a typical hard-to-machining material. Building upon prior research on the novel laser-induced oxidation-assisted milling technology, this paper conducted an in-depth study of the oxidation of Cf/SiC composite under laser induction. The study combined thermodynamic analysis with the detection of oxidation products to ascertain the oxidation reaction types of Cf/SiC composite. The oxidation process under the induction of lasers with different energy densities was investigated by combining the oxide layer morphology, element distribution, and high-speed photography results. And the oxidation mechanism was elucidated. A second-order response surface model for the oxide layer thickness with respect to the laser energy density, scanning speed, and scanning path spacing was established, and parameter optimization was performed based on this model. Experimental validation demonstrated the reliability of the model predictions.

Effect of Fermentation Time, pH, and Their Interaction on the Production of Volatile Fatty Acids from Cassava Wastewater

Acidogenic fermentation is a technology that involves halting methanogenesis in the conventional anaerobic digestion process to produce mainly volatile fatty acids (VFAs). VFAs serve as direct precursors to energy-rich or higher value-added products upon undergoing additional processing. In this study, batch reactors were utilized to assess the individual and interaction effects of fermentation time and pH variables on VFA production from acidogenic fermentation of cassava wastewater through the establishment of a completely randomized design and a second-order response surface (rotatable central composite design), respectively. The maximum VFA production observed was 3444.04 mg of acetic acid (HAc)/L (0.58 gCODVFA/gCOD) in a fermentation time of 6 days, with acetic (48.5%), propionic (28.3%), and butyric (13.6%) acids identified as the main metabolites. Additionally, in the assessment of the effect of pH, the maximum VFA production reached 2547.72 mgHAc/L (0.34 gCODVFA/gCOD) at pH 5.9, and acetic acid was identified as the predominant organic acid. Statistically, the fermentation time and pH variables individually affect VFA production from cassava wastewater; however, the interaction between them generated a non-significant effect.

Reliability analysis and optimization design of magnetic fluid dynamic seal shell structure under thermal/mechanical load

In order to study the reliability of Magnetic fluid dynamic seal shell structure under thermal/mechanical load, the improving cooling structure, calculating fuzzy fatigue reliability, and collaborative optimization design of fatigue reliability and lightweight are studied in this paper. The temperature model of the shell structure under four temperature conditions is established to analyze the influence of the thermal deformation caused by excessive local temperature. The cooling structure is improved, and the maximum temperature under the maximum temperature condition is reduced by 40.154 °C. For the sake of calculating the reliability of the new shell structure, a strength analysis model under thermal/mechanical load is built, and the fuzzy fatigue reliability function is obtained based on Latin hypercube sampling and the second-order response surface method. Four kinds of reliability are acquired by coding the functional functions and four kinds of membership functions with MATLAB, but all of them are lower than 90 % of the industrial requirements. To improve the reliability of the new shell structure and carry out the anti-fatigue lightweight design at the same time, an approximate model was constructed based on the interval analysis method and second-order response surface method for analysis. The accuracy of the approximate model was verified by re-sampling and finite element analysis. Based on the non-dominated sorting genetic algorithm, the optimal solution is determined. The optimization results show that the stress target value is reduced by 19.3 %, the weight target value is reduced by 3 %, and the fuzzy fatigue reliability reaches 94.65 %, 94.58 %, 93.89 %, and 96.31 % respectively. A new cooling structure of the Magnetic fluid dynamic seal is obtained and the maximum temperature is reduced. Moreover, the reliability of the new shell structure under thermal/mechanical load coupling is improved.

Multi-axis CNC finishing and surface roughness prediction of TC11 titanium alloy open integral micro impeller

The titanium alloy open integral micro impeller has a strong material strength and high removal rate in the field of multi-axis CNC machining. The flow channel is tiny and the blades are thin and highly twisted. It is difficult to control the surface accuracy and prone to overcutting and undercutting. The NX2212 software post-processing module plans two distinct blade finishing process routes and verifies them using virtual machine tool simulation, taking into account the technical challenges of micro impeller machining. Following verification, the tool path machining code is imported into MATLAB for data fitting. The workpiece surface working condition is determined based on the simulation findings, the blade surface roughness value is calculated, and a physical simulation model of blade finishing is created in the finite element analysis software. The outcomes demonstrate how well the “segmented and sub-regional cutting” processing method may raise blade accuracy. The leading and trailing edges of the blade both had surface roughness increases of 4.86% and 4.19%. The surface morphology of the micro impeller is measured using a white light interferometer, and it is CNC machined using two distinct process methods. The findings demonstrate that there is a significant difference between the value calculated by the finite element analysis software and the surface roughness value measured experimentally which together make up less than 5%. An investigation of the impact of cutting parameters on the surface roughness of micro-structure components is carried out using a three factor, three-level BBD experiment that is founded on the second-order response surface method. The findings indicate that the feed per tooth influences surface roughness more significantly than cutting depth and cutting speed for a reasonable range of cutting parameters; Surface roughness will rise with lower or higher cutting speeds; Raising the feed per tooth and the cutting speed simultaneously may reduce surface roughness; Surface roughness can be accurately predicted and controlled using the second-order response surface method.

Variable stiffness design for the soft landing of a 2016HO3 asteroid probe

China plans to launch a probe to detect and sampling on the near-Earth asteroid 2016HO3 around 2025. In view of this, this paper discusses an alternative landing strategy with passive variable stiffness landing gears, which help to land the probe stably on the asteroid for sufficient sampling time. First, a three-legged lander is introduced, following which, a four-bar-linkage-based variable stiffness leg is designed considering the design constraint of landing clearance. Then, a numerical model of the probe for landing simulation is established. Moreover, a surrogate model is obtained using the second-order response surface method (RSM) to improve computational efficiency. Based on the surrogate, the variable stiffness leg and the pressing force are optimized to reduce the impact forces at touchdown and the landing time. Finally, the optimal solution is validated using the dynamics analysis model.

A Study on the Shrinkage and Compressive Strength of GGBFS and Metakaolin Base Geopolymer under Different NaOH Concentrations.

Geopolymers (GPs) are gaining prominence due to their low carbon emissions and sustainable attributes. However, one challenge with GPs, particularly those made with ground granulated blast furnace slag (GGBFS), is their significant shrinkage during the geopolymerization process, limiting its practical applicability. This study focuses on how the substitution ratio of metakaolin (MK) and the concentration of sodium hydroxide (NaOH) in the activator can influence the shrinkage and strength of a GGBFS-based GP. The experimental approach employed a 3 × 3 parameter matrix, which varied MK substitution ratios (0%, 50%, and 100%) and adjusted the NaOH concentration (6 M, 10 M, and 14 M). The results revealed that increasing MK substitution, particularly with 6 M NaOH activation, reduced the GP shrinkage but also diminished compressive strength, requiring higher NaOH concentrations for strength improvement. Statistical tools, including analysis of variance (ANOVA) and second-order response surface methodology (RSM), were employed for analysis. ANOVA results indicated the significant impacts of both the MK content and NaOH concentration on compressive strength, with no observable interaction. However, the shrinkage exhibited a clear interaction between MK content and NaOH concentration. The RSM model accurately predicted compressive strength and shrinkage, demonstrating a high predictive accuracy, for which the coefficients of determination (R2) were 0.99 and 0.98, respectively. The model provides a reliable method for determining the necessary compressive strength and shrinkage for GGBFS-based GP based on MK substitution and NaOH concentration. Within the optimization range, the RSM model compared with experimental results showed a 6.04% error in compressive strength and 0.77% error in shrinkage for one interpolated parameter set. This study establishes an optimized parameter range ensuring a GP performance that is comparable to or surpassing OPC, with a parameter set achieving a compressive strength of 34.9 MPa and shrinkage of 0.287% at 28 days.

Optimization and experiment research of the cylinder block of the roller piston pump

The roller piston pump is a new type of axial piston pump. The pump has the advantages of high limiting speed, low noise, and vibration compared to the traditional axial piston pump. However, the structure and flow channel of the cylinder block of the roller piston pump are more complicated. When the cylinder block is subjected to high hydraulic pressure, its radial compressive deformation is large, which will lead to wear of the cylinder block and distribution shaft. For this problem, the paper will optimize the structural parameters of the cylinder block. Eight key parameters of the cylinder block are selected as the design variables, and the maximum radial deformation and mass of the cylinder block are taken as the optimization objectives. The central composite design method is used to generate 81 sets of sample data, and the second-order response surface model is obtained by regression analysis. The optimal structural parameters of the cylinder block are obtained through multi-objective optimization, and the material of the cylinder block is optimized. Finally, an experiment bench was built for experimental validation, and the efficiency of the pump was further investigated. The optimization results show that the maximum compression deformation of the inner diameter surface of the cylinder block decreases from 15.865 to 4.903 µm, and the mass of the cylinder block increases from 434.951 to 489.892 g. The experimental results show that the load-bearing pressure of the optimized roller piston pump increases from less than 15 to 35 MPa, and compared with the traditional axial piston pump, there is an increase in both mechanical efficiency and volumetric efficiency.

Effect of nanosized titanium dioxide and zinc oxide as antimicrobial agents on early compressive strength of high-performance concrete

Incorporation of antimicrobial agents in concrete can enhance the resistance of the concrete to biodeterioration. However, there is lack of adequate knowledge on the effect of antimicrobial agents on performance measures of high-performance concrete (HPC), particularly during early strength development, when the hydration reaction is ongoing, is not well understood. Therefore, the effect of antimicrobial agents on early compressive strength (CS) of HPC was investigated. The cement in HPC samples was partially replaced with nanosized titanium dioxide (TiO2) and zinc oxide (ZnO) by up to 2% by weight of the cement. Using response surface methodology, 21 combinations of TiO2 and ZnO contents were generated. The combinations were adopted for preparation of the samples. Individual and combined effects of TiO2 and ZnO on 7-day CS of the samples were evaluated. The standard form of the second-order response surface model is adopted to develop a model to fit the strength data. Statistics of the data verify that the model can be employed to predict the 7-day CS of HPC that employs nanosized TiO2 and ZnO as antimicrobial agents.

48 Evaluation of Branched-Chain Amino Acid Interactions in 13 to 23 kg Nursery Pigs Using a Central Composite Design

Abstract Two groups of 240 pigs (PIC 337 X 1050, PIC Genus, Hendersonville, TN) with initial body weight (BW) 13.20 ± 3.05 kg were used to investigate interactions between the branched-chain amino acids (BCAA). At weaning, pigs were placed into 40 pens with three barrows and three gilts per pen and fed a common diet for 3 weeks. On day 21 post-weaning, pens were randomly assigned to 1 of 15 dietary treatments arranged in a rotatable central composite design. Experimental diets were formulated to various levels of standardized ileal digestible (SID) leucine, isoleucine, and valine by replacing corn starch and glycine with L-leucine, L-isoleucine, and L-valine in the base diet. Levels of BCAA were expressed as ratios to SID lysine and ranged from 98 to 180 for Leu, 46 to 64 for Ile, and 51 to 78 for Val. Diets were formulated to be sub-limiting in lysine at 1.19% SID Lys and exceed all other essential amino acid requirements. Additionally, diets were formulated to be isocaloric and isonitrogenous and met or exceeded NRC (2012) vitamin and mineral requirements. Pen weights and feed intake were measured for the 21-day experiment to calculate daily gain (ADG), average daily feed intake (ADFI), and feed efficiency (G:F). Data were fit as a second-order response surface model according to the central composite design in R version 4.2.1 (R Core Team, 2022). The model included linear and quadratic effects of Leu, Ile, and Val, and their cross-products. Pen was the experimental unit, and variables were considered significant at P ≤ 0.10. Valine linearly and quadratically impacted ADG and G:F, regardless of Leu and Ile levels. There was an interaction between Leu and Ile for ADG (P = 0.079) and G:F (P = 0.031), where, at increasing levels of Leu, decreasing Ile improved ADG and G:F. Conversely, ADG and G:F decreased as both Leu and Ile increased. Isoleucine did not impact ADFI (P ≥ 0.458); however, there was an interaction between Leu and Val (P = 0.088), where Leu negatively impacted ADFI at low levels of Val, but did not influence ADFI at greater levels of Val. In conclusion, the response of nursery pig ADG and G:F to Val is independent of Leu and Ile levels, while ADG and G:F are reduced at greater levels of Leu and Ile, which is resolved as either Leu or Ile are reduced. Furthermore, at deficient levels of Val, ADFI is negatively impacted by increased Leu; however, the negative impacts of increasing Leu on ADFI are negated when Val is adequate or above requirement. This experiment emphasizes the complexity of amino acid metabolism in nursery pigs and the importance of understanding potential interactions among amino acids when conducting research.

Box–Behnken design to determine optimal fermentation conditions for apple-fortified mulberry wine using Saccharomyces bayanus

Wine is a fermented product of fruit juice. Mulberry and apple juice can also be used to produce wine. Several factors influence the alcoholic fermentation of the must; therefore, the optimization of the mulberry wine fermentation conditions with the dry yeast strain Saccharomyces bayanus (concentration varied from 0.15 to 0.25 g/L), fermentation conditions as pH value (from 3.5 to 4.5), and total soluble solid (TSS) content (24–28°Brix) were performed in this study. To evaluate the influence of these factors, a Box–Behnken design was used to minimize the number of factor combinations required, which allows the determination of optimal fermentation conditions (pH, TSS content, and dry yeast concentration) to produce wines with high alcohol and bioactive compounds (total anthocyanin (TAC) and polyphenol content (TPC)). Based on the analysis of experimental data, the second-order response surface models were developed to describe the relationship between initial pH value, TSS, and dry yeast concentration on wine quality acquisition (ethanol content and bioactive compounds). The results of the analysis of variance (ANOVA) showed that the model setup by response surface quadratic regression was suitable for predicting the wine quality. It was observed that the quality of the apple-fortified mulberry wine was significantly affected by all variables. The optimal contents of ethanol, total anthocyanin, and total polyphenol were achieved at 12.97% (v/v), 171.85 mg/L, and 87.17 mgGAE/L, respectively, when fermented in juice medium with optimal values of pH, TSS, and yeast concentration of 3.9, 26°Brix, and 0.22 g/L, respectively.

Multi-Objective Parameter Optimized Design of Self-Oscillating Cavitation Jet Nozzles

Self-oscillating cavitation jet technology has become a research hotspot of scholars in various fields. However, existing research lacks a summary of the rules of the influence of various factors on the cavitation performance, such that efficient and stable extensive engineering applications are impossible to achieve. This paper aims at optimizing the design of the self-oscillating cavitation jet nozzle (SOCJN) as the objective; this is carried out by the experimental design, optimal Latin hypercube method, and response surface method in (design of experiment) DOE methods on the basis of the ISIGHT optimization method. In addition, taking the vapor volume fraction and cavitation number as a research objective, the obtained optimal structural parameters of the nozzles are applied under the condition of clear water to establish the function mapping relationship between the external geometric characteristics and the vapor volume fraction and cavitation number; then, this is compared with the experiment. The results indicate that the second-order response surface approximate model is suitable for the SOCJN and there is an error smaller than 8% between the approximate model results and the calculated results of the nozzle response. When the diameter of the upper nozzle is D1 = 4.7 mm, the ratio of the upper nozzle’s diameter to the lower’s diameter (D1/D2) is 2.6 and the ratio of the chamber length to the chamber diameter (L/D) is 0.63; pulse jets from the SOCJN have the best pitting effect on the sample at the monitoring point when the convergence angle of collision wall α is 120°. When the structural parameters of the nozzle are optimal structural parameters, the cavitation performance is the best at the initial pressure of 4.8 MPa. This research provides a reference for the optimized design of the SOCJN for industrial applications.

A calibration method for contact parameters of agricultural particle mixtures inspired by the Brazil nut effect (BNE): The case of tiger nut tuber-stem-soil mixture

The lack of calibration methods for the contact parameters of agricultural particle mixtures limits the numerical simulation optimization of agricultural equipment. In this study, a novel method for calibrating contact parameters in agricultural particle mixtures inspired by the Brazil nut effect was proposed. The effectiveness of the proposed method was evaluated using a case study of a tiger nut tuber-stem-soil mixture. The intrinsic and contact parameters of monomaterials were first determined by conventional tests to provide data for vibration simulation tests. Vibration segregation tests were then performed on binary mixtures. The determination coefficient R2 between the physical and simulation data of the target particle volume concentration in the mixture was used as a response indicator. The second-order response surface regression model between the contact parameters and R2 was fitted by response surface methodology (RSM). The significance of the effect of the contact parameters on the indicator was quantified, and the optimal values of each parameter were determined. Finally, the applicability and accuracy of the calibrated parameters were verified using the self-flow sieving test. The results showed that the distribution of the mixture on the sieving surface and in the receiving box obtained from the calibrated test best matched the physical test results; at this time, the maximum relative errors of the physical and simulated values of the mass percentages of the tuber, stem and soil in the bin were 8.2%, 7.6%, and 6.5%, respectively, indicating that the calibrated parameters have good applicability and accuracy. The calibration test method can guide the calibration of contact parameters for other agricultural particle mixtures.

A Progressive Trigonometric Mixed Response Surface Method for Double-Loop Interval Optimization

For some highly nonlinear problems, the general second-order response surface method (RSM) cannot satisfy the accuracy requirement. To improve accuracy, the highest order number has to be determined in advance. Thus, a progressive trigonometric mixed response surface method (PTMRSM) was proposed to enhance the approximation accuracy and define the highest order number, rather than determining it in advance. After that, a double-loop interval optimization process could be constructed using this PTMRSM to save time while maintaining accuracy when compared to other experimental or computational methods. Unfortunately, the traditional double-loop interval optimization method had issues with the probability of reliable constraints. Then, for the construction of this double-loop interval optimization process, the modified reliable constraints were introduced. A more reliable and effective double-loop interval optimization was introduced for addressing practical engineering problems using the effective approximate method of the PTMRSM and the amended reliable constraints. Two numerical test functions and a composite submersible hull were performed to verify the accuracy and effectiveness of the PTMRSM and the double-loop interval optimization.

Heat Transfer Analysis and Structural Optimization for Spiral Channel Regenerative Cooling Thrust Chamber

There is currently a lack of efficient heat transfer analysis methodologies for spiral channel regenerative cooling that has been increasingly applied in liquid rocket engines. To figure out the heat transfer characteristics of the spiral channel regenerative cooling thrust chamber, a simple 1D method based on the traditional semi-empirical formula after correcting the flow velocity is proposed. The accuracy of this approach is verified by the 3D numerical simulation. The verified method is further used to analyze the distribution of inner wall temperature in the test case and optimize the channel’s parameters. The research shows that the maximum inner wall temperature cooled by the spiral channel is 8.5% lower than that of the straight channel under the same channel size and boundary condition, indicating that the application of the spiral channel significantly improves the cooling effect. In addition, the 1D model combined with the second-order response surface model is employed to optimize the channel width, channel height, pitch, and inner wall thickness aiming for the best cooling effect. The calculated maximum temperature of the inner wall after the structure optimization is 586.6 K, which is 29.8% lower than the initial structure before optimization.

Optimization Method Based on Hybrid Surrogate Model for Pulse-Jet Cleaning Performance of Bag Filter

The pulse-jet cleaning process is a critical part of the bag filter workflow. The dust-cleaning effect has a significant impact on the operating stability of bag filters. Aiming at the multi-parameter optimization problem involved in the pulse-jet cleaning process of bag filters, the construction method of hybrid surrogate models based on second-order polynomial response surface models (PRSMs), radial basis functions (RBFs), and Kriging sub-surrogate models is investigated. With four sub-surrogate model hybrid modes, the corresponding hybrid surrogate models, namely PR-HSM, PK-HSM, RK-HSM, and PRK-HSM, are constructed for the multi-parameter optimization involved in the pulse-jet cleaning process of bag filters, and their objective function is the average pressure on the inner side wall of the filter bag at 1 m from the bag bottom. The genetic algorithm is applied to search for the optimal parameter combination of the pulse-jet cleaning process. The results of simulation experiments and optimization calculations show that compared with the sub-surrogate model PRSM, the evaluation indices RMSE, R2, and RAAE of the hybrid surrogate model RK-HSM are 9.91%, 4.41%, and 15.60% better, respectively, which greatly enhances the reliability and practicability of the hybrid surrogate model. After using the RK-HSM, the optimized average pressure F on the inner side wall of the filter bag at 1 m from the bag bottom is −1205.1605 Pa, which is 1321.4543 Pa higher than the average pressure value under the initial parameter condition set by experience, and 58.4012 Pa to 515.2836 Pa higher than using the three sub-surrogate models, verifying its usefulness.

Normative database of response surface method for human trunk extension in isometric mode.

Recent studies show that asymmetric movements are important Low Back Disorders risk factors. Measuring the trunk strength and identifying the coupling effects in different postures can provide an objective tool to assess one's task capacity. This paper estimates the maximum performance capacity for isometric trunk extension and accompanying torques. Thirty males performed maximum voluntary isometric extension in 33 trunk postures on Sharif Lumbar Isometric Strength Tester device. Corresponding moments and angular positions were collected. Second-order full response surface models (RSM) were exploited to formulate the relationship between strengths and three trunk angles. The results of correlation coefficient, percent of standard estimation error and lack of fit reflected the adequacy of models. In conclusion, the main torque was the extension, but at the same time lateral bending and rotation torques were observed. For predicting these three torques in a specific posture and injury prevention, the second order RSM is a useful tool. The presented models can be used in the fields of ergonomics, occupational biomechanics and sport.