Polynomial Response Surface Model Research Articles

Dynamic optimization of die-less spinning process through autonomous modeling of time-varying forming law

Die-less spinning is a typical incremental forming technology with flexible processing parameters, including the roller path and loading parameters, whose forming law changes dynamically and easy-to-produce defects of excessive thinning and flange wrinkling. This brings a great challenge to the process design of die-less spinning. In this study, we proposed a novel dynamic optimization approach and system considering the time-varying forming law for the processing parameters in die-less spinning. The idea of proposed approach is that simulating the spinning process step by step through autonomous finite element modeling, real-time extracting and modeling the simulated spinning status at each forming step to capture the time-varying forming law, then gradually optimizing the processing parameters through efficient multi-objective optimization algorithm. By conducting the proposed dynamic optimization approach to the first spinning pass of die-less spinning, series of polynomial response surface models (PRSM) of wall thickness and flange wrinkling at various forming steps were developed to describe the time-varying forming law. On this basis, the roller path and matching loading parameters in each step were gradually optimized through a differential evolution algorithm with the multi-objective of minimizing wall thickness reduction, reducing flange wrinkling and maximizing forming efficiency. The optimized process produced better spun part than the traditional spinning process, presenting the wall thickness reduction ≤5 % and the flange wrinkling ≤2.5 mm. Furthermore, the time-varying influence of processing parameters on the wall thickness and flange wrinkling were elucidated based on the PRSM of spinning status at various forming steps.

Buckling Defect Optimization of Constrained Ring Rolling of Thin-Walled Conical Rings with Inner High Ribs Combining Response Surface Method with FEM

A buckling defect will appear on the outer surface of the deformed ring during the constrained ring rolling (CRR) of an aluminum alloy thin-wall conical ring with inner high ribs (AATWCRIHR) if the geometrical dimension of the ribs does not match the wall thickness. To avoid the buckling defect, a quantitative method for characterizing the degree of the buckling defect is proposed using the area of the buckling profile. Then, an orthogonal experimental scheme was designed, taking the width of the middle rib, thickness of wall, and height of the middle rib as the design variables and defining the area of the buckling profile as the optimization objective. Subsequently, a quadratic polynomial response surface model was established by combining the optimization algorithm with the finite element method (FEM), and the geometrical dimension of the middle ribs of the deformed AATWCRIHR is optimized. Moreover, the optimal parameter combination to minimize the area of the buckling profile is obtained and verified using FE simulation. The results show that the AATWCRIHR after optimization does not generate the buckling defect during constrained ring rolling, and it is proven that the quantitative buckling defect representation method and the optimization design method based on the response surface model and the finite element simulation results are feasible for the constrained ring-rolling process of the AATWCRIHR.

Macro–micro investigation on stabilization sludge as subgrade filler by the ternary blending of steel slag and fly ash and calcium carbide residue

This study investigates the efficacious utilization of sludge as a subgrade filler through in-situ shallow stabilization, employing cementitious industrial waste materials including steel slag (SS), fly ash (FA), and calcium carbide residue (CCR) as binding agents. The primary emphasis lies in the evaluation of the macro unconfined compression strength of stabilized sludge over a seven-day curing period, facilitated by a quadratic polynomial response surface model to determine the optimal composite stabilizer (WZ01) proportions. Furthermore, an array of meticulous microstructural analyses encompassing X-ray diffraction, X-ray fluorescence, scanning electron microscopy, and energy-dispersive spectroscopy were undertaken to elucidate the development of internal cementitious products and the intrinsic mechanisms underpinning sludge stabilization in tandem with WZ01. The findings ascertain that the optimum WZ01 composition stands at SS: FA: CCR = 32:28:40. Prominent mineralogical constituents within the stabilized sludge encompass amorphous calcium silicate hydrate, calcium aluminate hydrate, and crystalline ettringite. The amelioration in stabilized sludge properties stems from intricate processes involving ion exchange, hydration reactions, and pozzolanic activities. Significantly, the WZ01 curing agent demonstrates heightened cost-effectiveness and environmental merits compared to conventional Portland cement.

A predicting method for the mechanical property response of the marine riser based on the simulation and data-driven models

The accurate and real-time prediction of the mechanical property response for the safety assessment of the marine riser is necessary during offshore oil and gas production. However, a finite element simulation is time-consuming, which obstructs the real-time monitoring and evaluation of the marine riser. Therefore, to obtain the real-time mechanical response of the marine riser, a predicting method based on the simulation and data-driven models is proposed. To obtain the prediction data, the finite element simulation model under the typical working conditions is established by the Abaqus software, and then the sensitivity analysis of influence factors is conducted due to the varied working conditions. The orthogonal experimental method is used to select the typical working conditions of the marine riser, and the selection of the sensitive influence factors is ensured based on the typical working conditions, the range analysis, and the grey relational method. To obtain enough training data, the Latin hypercube sampling method is used to enlarge the data for the analysis process. To find a more reliable prediction algorithm, four typical single surrogate models, which are the polynomial response surface model, the radial basis model, the kriging model, and the support vector machine regression model, are selected to establish a predicting model library. Meanwhile, a combining surrogate model, including the average weight surrogate model and the adaptive weight surrogate model, is established based on the combining weight to further improve the predicting accuracy. As a result, an optimal surrogate model is selected from the above four single and two combining surrogate models based on four evaluation criteria including the mean absolute percentage error, the mean absolute error, the root mean square error, and the goodness of fit. The cases show that the optimal surrogate model has a highly rapid response, with average relative errors are 8.17%, 3.42%, and 11.40% for the maximum bending moment, the maximum equivalent stress, and the maximum lateral deformation, respectively. In the above study, the accurate and reliable prediction method of the mechanical property responses will provide a theoretical basis for ensuring the safety of the marine riser.

Mechanical properties evaluation of waste gangue-based cemented backfill materials based on an improved response surface model.

Traditional mining methods damage the cultivated land and produce gangue waste that often contaminates the environment. Yet, these problems can be mitigated by transforming the waste into gangue-based cemented backfill material (GCBM), whose mechanical properties are crucial for surface protection. Therefore, in this study, an intelligent model based on laboratory tests was developed to evaluate the GCBM's mechanical properties. The strength tests and polynomial response surface model (PRSM) were used to analyze the non-linear correlation between the influencing factors and the uniaxial compressive strength (UCS). Meanwhile, the importance of multidimensional factors was analyzed by the mean impact value, revealing that concentration and gangue proportion are the most sensitive factors. In addition, an intelligent response surface model (IRSM) based on support vector regression model was constructed by enhancing an optimization algorithm with chaotic mapping and adaptive methods. The performance of the traditional PRSM and the novel IRSM was compared, and the IRSM was validated. The IRSM can predict UCS more efficiently and effectively than the traditional PRSM under high-dimensional factors, with R2 of 0.96 and MBE of 0.05. This indicated that the IRSM has the potential to promote coal mine waste reduction and environmental protection.

Structural parameters of venturi injector for periodic air recovery based on response surface methodology

This work is devoted to the study of the structural parameters of a venturi injector for periodic air recovery. Using a push chain concrete spraying machine as a case, a numerical simulation study was conducted on the venturi injector under different structural parameter combinations. The venturi injector structure parameters diameter ratio of the throat to pipe a, convergent angle α, throat length to diameter ratio b, and diffusional angle β are designed and combined by the response surface method. The numerical simulation results and the prediction model obtained by the response surface method were verified by experiments, and the simulation results and prediction model were in good agreement with the experimental results. The results show that the residual air recovery of the push chain concrete spraying machine is best when a, α, b, and β are 0.8, 25°, 2.5, and 10°, respectively. In addition, the quadratic polynomial response surface model of the venturi injector pressure variation coefficient Cv and pressure drop Pd concerning the structural parameters was established, and the influence rules of each structural parameter on the Cv and Pd were obtained. The variation patterns of turbulent kinetic energy in the venturi at different times and stable sections at the back end are revealed. This paper can provide help for the design of venturi structures used for periodic air recovery in other chemical fields.

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.

Simulation-driven Wind Load Analysis and Prediction for Large Steerable Radio Telescopes

Large steerable radio telescopes can rotate in azimuth and elevation, with various upwind postures and complex wind load characteristics. In order to 5 Corresponding authors obtain the wind load distribution on the reflector and the wind force coefficients in different upwind postures, this work took the reflector of the QiTai Telescope in Xinjiang as the object. The wind pressure distribution, drag coefficient, side force coefficient, lift coefficient, and total force coefficient of 361 groups of reflectors with different upwind postures were calculated and analyzed by a numerical simulation method. The results show that the force on the reflector when the concave surface faces the wind is significantly greater than when the convex surface faces the wind. The surrogate models for calculating wind force coefficients were established based on the polynomial response surface model (PRSM) and regularized minimum-energy tensor-product spline (RMTS). The adjusted R-squared of RMTS is 0.98, and the root mean square error is below 0.1, which proves RMTS is significantly better than PRSM. Compared with the numerical simulation values, the absolute errors of the drag coefficient, side force coefficient, lift coefficient, and total force coefficient of the reflector with azimuth and elevation of 45° predicted by RMTS are 0.02, 0.027, 0.032, and 0.046, respectively. The relative errors are 2.42%, 2.76%, 2.23%, and 2.43% , respectively. It is proved that the RMTS surrogate model is reliable and that the predicted data can fast provide sufficient information for the wind-resistant design of the large steerable radio telescopes.

A novel dynamic model updating method for composite laminate structures considering non-probabilistic uncertainties and correlations

This paper presents a novel dynamic model updating procedure to efficiently update the intervals and non-probabilistic correlation coefficients matrix (NPCCM) of modal parameters, and establish its accurate and reliable uncertainty boundary. To accomplish these features, an ellipsoidal convex model is adopted to quantify the non-probabilistic uncertainties and correlations of the measured multi-responses, and the dynamic model updating problem for composite laminate structures is divided into an interval updating problem and a correlation updating problem. Then, a performance measure approach (PMA) and the non-probabilistic covariance propagation equations are developed to achieve the intervals and NPCCM of the calculated responses respectively. By using optimization algorithms to reduce the errors of the intervals and the NPCCM between the measured modal responses and calculated modal responses, the intervals and the NPCCM of modal parameters can be updated effectively, and their multidimensional ellipsoidal model can be established eventually. To improve the stability and efficiency of the updating processes, the Sobol sensitivity analysis method is applied to determine the important modal parameters, and an optimal polynomial response surface model is developed to replace the original complex structures. An experimental example for composite laminate structure is investigated to verify the effectiveness and accuracy of the proposed method.

Research on the Operational Modal Prediction of Dry Gas Seal System Based on Response Surface Method

The cross power spectrum function is used to realize the operational modal analysis and identification of the dry gas seal device system through the multi-reference point least squares complex frequency domain method. The steady state diagram and mathematical indicators MAC, MPD, MPC, MOV and MIF are used to verify the modal results. At the same time, based on the response surface method, with two different operating conditions of medium pressure and rotating speed, modal direction and modal order as the response surface variables, a time-varying modal recognition model is established. Through the Full Factorial experiment design, Box-Behnken experiment design and Central Composite experiment design, the suitable variable sample points are formed. A complete quadratic polynomial response surface model of the system operational modal parameters is established. The complex correlation coefficient, the modified complex correlation coefficient and the root mean square error are used to verify the effectiveness of the response surface model. It provides new method and technical support for realizing time-varying modal identification in this paper.

Multiobjective optimization of the cooling system of a marine diesel engine

AbstractAn intelligent cooling system directly influences the thermal load of high‐temperature components, heat distribution, and fuel economy of a diesel engine. An optimal coolant pump rotational speed map is a key factor in intelligent cooling control strategies. In this study, we designed an experimental variable coolant flow system for a maritime diesel engine. Experiment design and D‐optimal designs were used to optimize the parameters of the diesel engine cooling system. The diesel engine speed, load, and freshwater rotational pump speed were selected as variables. The temperature of the high‐thermal‐load zone of the combustion chamber components, fuel consumption rate, effective power, and peak cylinder pressure were selected as response variables, and the D‐optimal method was used to sample the experimental points. Polynomial response surface models were obtained using a stepwise algorithm. A multiobjective optimization problem was converted into a simple‐objective optimization problem using the ideal point method. A genetic algorithm was used to optimize the single‐objective function globally to obtain the optimal freshwater pump speed map for a diesel engine under all conditions. On average, the optimized cooling system decreased the fuel consumption by 1.901%. Six typical propulsive conditions were selected to confirm the validity of the optimization results. The experimental results indicate that the fuel consumption decreased by 2.35%, the effective power increased by 2.26%, and the power consumption of the water pump decreased by 17.83%. The combination of experiment design and D‐optimal designs offers the advantages of low cost, high efficiency, and high precision in solving multiobjective optimization problems involving strong coupling and nonlinear systems. The results of this research provide data support and a theoretical basis for intelligent cooling control strategies.

Multi-objective optimization and experiment of nylon cord rubber in expandable packer

Nylon cord rubber has the advantages of small residual deformation and is easy to lift and lower the tubing string in low-permeability oil and gas reservoirs. However, it is associated with low-pressure resistance and poor sealing performance. To enhance the performance of nylon cord rubber, a three-dimensional numerical model of the nylon cord rubber was established and its accuracy experimentally determined. The Plackett–Burman test, the Steepest climbing test and the Response surface method were used to acquire the polynomial response surface model connecting structural parameters with bearing and sealing pressure. Using genetic algorithms, optimal structural parameters of nylon cord rubber were determined depending on field operation. The reliability of the optimized results was verified by laboratory tests. It was shown that after optimization, the bearing capacity of the expandable packer increased by 25% while the sealing performance increased by 66%. In addition, the bearing pressure was 70 MPa while the sealing pressure was 50 MPa. These measurements effectively met the on-site requirements of high-pressure and fine fracturing in low-permeability oil and gas reservoirs.

Stress-constrained optimization using graded lattice microstructures

In this work, we propose a novel method for predicting stress within a multiscale lattice optimization framework. On the microscale, a scalable stress is captured for each microstructure within a large, full factorial design of experiments. A multivariate polynomial response surface model is used to represent the microstructure material properties. Unlike the traditional solid isotropic material with a penalization-based stress approach or using the homogenized stress, we propose the use of real microscale stress components with macroscale strains through linear superposition. To examine the accuracy of the multiscale stress method, full-scale finite element simulations with non-periodic boundary conditions were performed. Using a range of microstructure gradings, it was determined that 6 layers of microstructures were required to achieve periodicity within the full-scale model. The effectiveness of the multiscale stress model was then examined. Using various graded structures and two load cases, our methodology was shown to replicate the von Mises stress in the center of the unit lattice cells to within 10% in the majority of the test cases. Finally, three stress-constrained optimization problems were solved to demonstrate the effectiveness of the method. Two stress-constrained weight minimization problems were demonstrated, alongside a stress-constrained target deformation problem. In all cases, the optimizer was able to sufficiently reduce the objective while respecting the imposed stress constraint.

Aerodynamic optimisation of a high-speed train head shape using an advanced hybrid surrogate-based nonlinear model representation method

A global optimisation strategy based on the hybrid surrogate model method and the competitive mechanism-based multi-objective particle swarm optimisation (CMOPSO) algorithm was developed to improve the accuracy of the aerodynamic performance optimisation of a high-speed train running in open air without a crosswind. Free-form deformation was used to improve the optimisation efficiency without remodelling or remeshing. The sample points and their responses were obtained via optimal Latin hypercube sampling and computational fluid dynamics (CFD) simulations. The hybrid surrogate model (HSM) was constructed by using the theory of optimal weighted surrogate to combine a polynomial response surface (PRS) model with a radial basis function (RBF) model. Comprehensive error evaluation results indicated that the prediction accuracy achieved with the HSM was higher than that achieved with either the PRS model or the RBF model; thus, the HSM was selected for use in each iteration to approximate the CFD simulation model of the high-speed train in subsequent optimisation. Then, the CMOPSO algorithm was selected as the optimisation algorithm. After optimisation, a series of Pareto-optimal solutions was obtained, and the optimal and original head shapes were compared. The use of the hybrid surrogate model and the CMOPSO algorithm greatly improved the optimisation efficiency.

Finite Element Model Modification of an Arch Bridge Based on Response Surface Method

Usually the structure of the initial finite element model can not reflect the actual situation of structure, the finite element model updating is for the initial finite element model of the structure, according to the static and dynamic response of the structure of the measured optimize the model parameters are adjusted, the revised model response is more close to the actual structural response, so as to get a more accurate finite element model. In this paper, the finite element model of the bridge is updated by using the second order incomplete polynomial response surface model. Then determine the sample data, use the least squares method to fit the undetermined coefficients of the second-order incomplete polynomial, and perform the accuracy test. Then the objective function based on frequency is constructed, and the updated optimal design parameters are obtained by quadratic sequence programming. Finally, using the optimal design parameters for modal analysis, it is found that the frequency error has decreased. It is proved that the correction by the response surface method (RSM) can improve the accuracy of the finite element model.

Estimation of opening discharge coefficient of naturally ventilated dairy buildings by response surface methodology

The discharge coefficient (Cd) is a characteristic parameter of an opening, which represents the effect of flow contraction and frictional losses when the flow goes across the opening. It is an important parameter for the ventilation rate determination when using the orifice equation method. The objectives of this study were to investigate the relationship between Cd and its potential influencing factors, i.e. opening ratio (r), building length to width ratio (α), wind speed (U), and wind direction (θ), and to evaluate the sensitivity of each factor on the Cd for naturally ventilated dairy buildings (NVDBs). The investigations were performed using the response surface methodology together with Box-Behnken Design and Computational Fluid Dynamics simulation methods. A second-order polynomial response surface model for the estimation of the discharge coefficient was developed and verified. The results showed that the Cd was significantly affected by the individual factors of r and θ, with more sensitivity to r when r > 42.5%. By contrast, the effects from the individual factors of α and U on Cd were insignificant. In addition, the interaction effects between r and θ, and between α and θ on Cd were also identified. It was concluded that the effects from both individual factors and interactions are required to be considered in the estimation of the opening discharge coefficient for NVDBs.

Response surface optimization of prodigiosin production by mutagen-treated Serratia marcescens in different growth media

Background: Prodigiosin is a bioactive bacterial pigment produced by Serratia marcescens and possesses anticancer, antibiotic, antifungal, antibacterial, and immunosuppressive activities without any toxic effects on human cells. Objectives: The study was planned to optimize the effect of ultravoilet (UV) light and acridine orange (AO), as mutagens and incubation time on prodigiosin production by S. marcescens in nutrient agar broth and peptone glycerol broth. Materials and Methods: The optimization was done by constructuing a quadratic polynomial response surface model using a bifactorial central composite design. The S. marcescens starian was treated with UV light (0, 30, 60, 90, and 120 s) and various concentrations of AO (0, 50, 100, 150, and 200 μg/mL) and incubated in the selected growth media for different times (0, 15, 30, 45, and 60 h). The prodigiosin production was measured in terms of change in pH and optical density (OD) of the ethanolic extracts of culture media. Results: The prodigiosin production was found to be a significant linear and quadratic function of incubation time in both of the culture media. However, a statistically non-significant increased prodigiosin production, in terms of pH and OD of the extracts, was observed under the influence of both mutagens. The optimum values of incubation time to achieve optimal production of prodigiosin from UV light-exposed and AO-treated cultures were found to be in the range of 37–60 h, respectively. Conclusion: The pigment production was increased significantly with an increase in the incubation time. The study provides the optimum conditions for the production of prodigiosin in research and commercial field.

Damage detection of long-span bridge structures based on response surface model

In order to solve the problem of high risk and low precision of existing damage detection methods for long-span Bridges, a new method based on fourth-order polynomial response surface model is proposed. Response surface model is constructed by using fourth order polynomial function. The parameters of the finite element model of the bridge are modified according to the response surface model. Based on the finite element model, the modal strain energy before and after the damage of the element was calculated, and the damage index of the element was obtained, so as to realize the damage detection of the long-span bridge structure. Experimental results show that the proposed method can accurately detect the damage location of long-span Bridges under different damage conditions, and the detection error of damage degree is less than 1%, which has a broad application prospect.

WIND LOAD ANALYSIS OF RADAR ANTENNA BASED ON RESPONSE SURFACE MODEL

Based on the theory of polynomial response surface model, a method for accurately constructing wind load response surface model of radar antennas is proposed. Firstly, the sample points design matrix is constructed by Optimal Latin Hypercubes Design of Experiment (DOE) procedure. Secondly, the customization and automation of data flow and work flow are realized by means of secondary development of commercial software, and each process is integrated in iSIGHT platform. Finally, the fitting accuracy of response surface models were checked by Leave-one-out Cross Validation method. The results show that the wind load analysis method based on response surface model is fast in calculation and good in convergence. It can meet the engineering accuracy requirements, and is convenient for multi-person collaborative work. In all, this method has high engineering application value.

Research on Antenna Cabin Structure Optimization Based on Response Surface and Multi-island Genetic Algorithm

This paper focuses on the characteristics of high efficiency and high accuracy in the optimization design of the antenna bay structure. The polynomial response surface model is used to replace the computationally intensive target characteristic analysis model in the original genetic algorithm and a multi-island genetic algorithm is combined with the sequential quadratic programming. In this method, the square steel structure of the antenna module is optimized, which not only ensures the search for the global optimal solution, but also improves the calculation efficiency. The optimized results meet the rigid strength requirements of the antenna module under working wind load, and the weight of the antenna module is reduced by 33.5%, which greatly saves costs.