Polynomial Response Surface Method Research Articles

Surrogate-based shape optimization and sensitivity analysis on the aerodynamic performance of HCW configuration

With an additional wing upon the fuselage, the novel high-pressure capturing wing (HCW) configuration exhibits remarkable aerodynamic characteristics at hypersonic speeds under beneficial aerodynamic interference. This bi-wing structure can also enhance the lift at subsonic speeds, positioning HCW configuration as an excellent aerodynamic layout under wide-speed range conditions. In this paper, a single-wing principle HCW configuration is carried out to analyze the influence of the variations in the geometric parameters of the HCW on the aerodynamic performance. Drawing on extant research, four key geometric parameters of the HCW are chosen as design variables, and the hypersonic as well as supersonic conditions are selected for surrogate-based shape optimization. Utilizing polynomial response surface method and method of moving asymptotes, the single-objective optimization studies are carried out with the objectives of maximum lift-to-drag ratio at Ma = 6 and minimum drag coefficient at Ma = 3. Subsequently, the sensitivity analysis is performed for each design parameter. The above methods exhibit notable precision and favorable results. The results show that except for the leading-edge sweep angle, the other three optimization results exhibit divergent trends in their variations. The setting angle has the most significant influence on the aerodynamic forces, owing to the influences of its variation on the shock wave intensity and reflection angle. Based on the stronger intensity of shock wave, this sensitivity indices are higher at Ma = 6. The other three parameters (half-span, leading-edge sweep angle, and trailing-edge sweep angle) modify the aerodynamic forces by adjusting the area of high-pressure region on HCW. Due to the different flow field structures, optimum parameters exhibit diverse effects on lift coefficient and lift-to-drag ratio.

Optimization of a high through-flow design turbine using response surface method

Enhancing the through-flow capability of the turbine facilitates the potential to decrease the external dimension of the engine, leading to a reduction in weight and an increase in the thrust-to-weight ratio. The optimization of blade profile in terms of aerodynamic design is an essential strategy to improve the overall performance of the high through-flow design turbine. This study aims to develop an automated optimization technique, utilizing the response surface method (RSM), to enable reliable prediction and rapid optimization of aerodynamic performance. A parametric modeling method is devised to generate blade profiles with continuous curvature throughout the automated optimization process. The Box–Behnken experimental design, in combination with Reynolds-averaged Navier–Stokes numerical calculation, is employed to construct a second-order polynomial RSM approximation model. The optimization process comprises two levels: improving the through-flow capability and reducing blade profile loss. The optimized profile, Opt1, achieves a substantial 13.19% improvement in through-flow capability at the cost of a 12.27% increase in blade profile loss. Thus, further optimization is performed to minimize blade profile loss based on the Opt1 scheme. Geometric constraints are applied to the most influential parameters affecting through-flow capability to mitigate their impacts. Compared to the Opt1, the final optimized profile, Opt2, achieves a substantial 31.83% decrease in blade profile loss with a negligible sacrifice of 0.23% in through-flow capability.

Surrogate indirect adaptive controller tuning based on polynomial response surface method and bioinspired optimization: Application to the brushless direct current motor controller

The increment of autonomous systems has stimulated the research of new controller tuning techniques to face the unpredictable disturbances and parametric uncertainties inherent in any autonomous system that affect its performance. The indirect adaptive controller tuning approach based on the general dynamic model (IACTA-GDM) and bioinspired optimization is one of the most successful elections facing parametric uncertainties and disturbances, which are intricate to handle by other controller tuning techniques. However, this controller tuning approach is limited by the complexity of the dynamic model due to the computational burden, restricting its application to relatively small systems or systems with slow responses where the tuning is updated at large time intervals. The present work proposes a novel surrogate indirect adaptive controller tuning approach based on the response surface method (SIACTA-RSM) to address computational burden limitations. The proposal is tested on the speed regulation controller of a brushless direct current motor, with the aim of reducing the speed regulation error and the control system’s power consumption. The closed-loop system performance and the required computational time obtained by the proposed SIACTA-RSM are compared to the ones of a well-established IACTA-GDM. The descriptive and inferential statistics, as well as graphical comparisons, show that the system performance obtained by the SIACTA-RSM proposal is as competitive as the IACTA-GDM approach, keeping a mean difference among the results by up to 3.18% while reducing the computational burden of IACTA-GDM by up to 90%. These outcomes show that the SIACTA-RSM proposal is a reliable alternative to overcome the computational burden limitations that affect the IACTA-GDM approach while maintaining competitive performance.

A comparative study of various metamodeling approaches in tunnel reliability analysis

Various metamodeling approaches are applied in conjunction with Monte Carlo simulation and or the second moment-based method for reliability analyses of underground tunnels. However, there is no study regarding the suitability of such metamodels for reliability analyses of tunnels. An attempt is made here to make a comparative assessment of different metamodeling approaches for tunnel reliability analysis to comprehend the performances of various metamodels from the subset of machine learning methods. In doing so, the least square method based polynomial response surface method (RSM), mostly used in tunnel reliability analyses, and its improved version i.e., moving least square method-based RSM, are taken up for comparison. Further, the most successful empirical risk minimization-based Kriging model and the structural risk minimization principle-based support vector regression model are considered for comparison. Also, the sparse Bayesian regression found to be useful in solving various structural reliability analysis problems, is taken up for the present comparative study. Two numerical examples demonstrate the effectiveness of the selected metamodels in tunnel reliability analysis. It has been generally noted that the Kriging and SVR-based metamodels outperform in reliability estimates of underground tunnels.

Modeling (in)congruence in groups: A how-to guide for applying polynomial regression and response surface method to multilevel data.

Modeling (in)congruence in groups: A how-to guide for applying polynomial regression and response surface method to multilevel data.

Multi-Objective Optimization of Square Corrugation Multilayer Nested Structures

Thin-walled structures, when used for high-speed railways, can effectively mitigate the irreversible destruction when a malfunction occurs. Nested thin-walled tubes, as energy-absorbing structures, possess excellent specific energy absorption (SEA) and crushing force efficiency (CFE). This paper conducts multi-objective optimization by focusing on a square corrugation nested structure with a double octagon inner wall, namely SCOD, to ameliorate the crashworthiness of the nested structure. The finite element model of the SCOD is constructed and validated by test data. A set of experimental design points with good spatial distribution are obtained using the optimal Latin hypercube (LHC) method. The polynomial response surface (PRS) method was applied to establish the fitting relationship between design variables and optimization objectives, and validation is accomplished. The DCNSGA-III algorithm is employed for optimization, resulting in a Pareto alternative solution set with good population diversity and convergence. In addition, to observe the optimized performance, a set of optimal solutions considering a single objective value is derived, and a comprehensive optimal solution is obtained by applying the minimum distance selection method (TMDSM). Finally, the proposed optimized system is analyzed and validated. According to the alternative reference solutions, the initial peak force (IPCF) reduces by 53.75% and CFE increases by 8.7%. This paper provides some reference for the optimization design in practical engineering.

Understanding digital information production in virtual communities from the perspective of Actor-Network Theory

Organizational management has been extended to tourism virtual entities. This study is to explore the organizational practice in the virtual scenario, through which investigates the process of knowledge creation. The online questionnaire survey is applied to collect the multisource and time-lagged data from boards of Internet forums. The polynomial regression and response surface method are used to examine the (in)congruence effect. The hypothesized relations are simultaneously estimated using structural equation modeling. Results show that when the forum moderator's (i.e., formal leader) and the opinion leader's bricolage capacity are in congruence and at the high level (high-high congruence), collaborative knowledge creation in an Internet forum is found to be the highest. Moreover, asymmetrical incongruence effects are found wherein the higher bricolage capacity of opinion leaders can weaken the adverse effect of the lower bricolage capacity of formal leaders on collaborative knowledge creation in an Internet forum. This study reveals the group dynamics in the information coproduction process on virtual communities, which expands the integration of Actor-Network Theory (ANT) and media networks and displays the fine-grained micro-picture of information production.

Reliability analysis of composite laminate patch repaired structures based on response surface proxy model

In this paper, the reliability analysis of composite laminate patch repaired structures under unidirectional static load was studied by means of a probability model. First, a proxy model for the maximum static load carrying capacity of the repaired structure was established using quadratic polynomial response surface method (RSM) considering the repair material properties, repair patch design and adhesive layer thickness. Second, the probability distribution input of various basic random parameters including geometric characteristics and material properties were considered based on actual repair data. Finally, both the reliability and sensitivity analysis of the repaired structure were investigated by means of Monte Carlo simulation method. The results show that the reliability analysis model is of great significance for the subsequent design and properties evaluation of composite repaired structures.

Supplemental Material for Modeling (In)Congruence in Groups: A How-To Guide for Applying Polynomial Regression and Response Surface Method to Multilevel Data

Supplemental Material for Modeling (In)Congruence in Groups: A How-To Guide for Applying Polynomial Regression and Response Surface Method to Multilevel Data

Nataf transformation based univariate decomposable polynomial RSM for engineering reliability analysis

For engineering problems, the correlation exists among the common random variables. For those with highly correlated variables accompanying the high nonlinearity, large error would be induced if ignoring the influence of their correlation matrix. Considering correlated variables, an executing mode of polynomial response surface method based on Nataf transformation and univariate decomposition is introduced in this paper, called as N-UDPRSM. The correlated variables can be converted into the independent standard normal space and all of the univariate component polynomials can be determined separately. Besides, high order terms can be adopted into N-UDPRSM to balance the accuracy and efficiency for high nonlinear engineering problems. The corresponding practical implementation for engineering reliability analysis is designed in detail. A typical engineering structure is studied. The results indicate that it performs well in balancing accuracy and efficiency, and it also preserve some superiority contrast with other state-of-art methods.

Full-Scale Train-to-Train Impact Test and Multi-Body Dynamic Simulation Analysis

When a train crashes with another train at a high speed, it will lead to significant financial losses and societal costs. Carrying out a train-to-train crash test is of great significance to reproducing the collision response and assessing the safety performance of trains. To ensure the testability and safety of the train collision test, it is necessary to analyze and predict the dynamic behavior of the train in the whole test process before the test. This paper presents a study of the dynamic response of the train in each test stage during the train-to-train crash test under different conditions. In this study, a 1D/3D co-simulation dynamics model of the train under various load conditions of driving, collision and braking has been established based on the MotionView dynamic simulation software. The accuracy of the numerical model is verified by comparing with a five-vehicle formations train-to-train crash test data. Sensitivities of several key influencing parameters, such as the train formation, impact velocity and the vehicle mass, are reported in detail as well. The results show that the increase in the impact velocity has an increasing effect on the movement displacement of the vehicle in each process. However, increasing the vehicle mass and train formation has almost no effect on the running displacement of the braking process of the traction train. By sorting the variables in descending order of sensitivity, it can be obtained that impact speed > train formation > vehicle mass. The polynomial response surface method (PRSM) is used to construct the fitting relationship between the parameters and the responses.

Multi-objective optimization of adhesively bonded single-lap joints of carbon fiber reinforced polymer laminates based on genetic algorithm

To improve its structural performance, the multi-objective optimization of adhesively bonded single-lap joints of carbon fiber reinforced polymer (CFRP) laminates was carried out based on genetic algorithm. Firstly, finite element (FE) models were constructed using 3D Hashin damage criteria and triangle cohesive zone model (CZM), those well capture the intra-laminar, inter-laminar and adhesive damages during the tensile loads, respectively. And its effectiveness was verified through experiments. Secondly, using the Latin hypercube sampling (LHS) method and polynomial response surface method (RSM), a multi-objective optimization agent model with tensile strength and shear strength as the objective function was established based on lap the length, the adhesive thickness and the width of the bonded parts. Finally, the tensile strength and shear strength agent model was optimized to obtain Pareto solution set based on genetic algorithm (GA), and the Pareto solution set was sequenced by technique for order preference by similarity to ideal solution (TOPSIS) method to obtain the optimized single-bonded joint structure design scheme. The result shows that the experimental measurements of tensile load tests concur with the numerical predictions and validate the FE models. The tensile strength and shear strength of the adhesively bonded single-lap joints of CFRP laminates have a significant correlation with the lap length, the thickness of the adhesive layer and the width of the bonded parts. Compared with the numerical simulation results, the error of the quadratic response surface proxy model results is less than 2.3%. Compared with the conventional single lap bonding structure, the tensile strength and shear strength are increased by 2.65% and 17.24%, respectively.

A new response surface method based on the adaptive bivariate cut-HDMR

PurposeThe purpose of this study is to improve the efficiency and accuracy of response surface method (RSM), as well as its robustness.Design/methodology/approachBy introducing cut-high-dimensional representation model (HDMR), the delineation of cross terms and the constitution analysis of component function, a new adaptive RSM is presented for reliability calculation, where a sampling scheme is also proposed to help constructing response surface close to limit-state.FindingsThe proposed method has a more feasible process of evaluating undetermined coefficients of each component function than traditional RSM, and performs well in terms of balancing the efficiency and accuracy when compared to the traditional second-order polynomial RSM. Moreover, the proposed method is robust on the parameter in a wide range, indicating that it is able to obtain convergent result in a wide feasible domain of sample points.Originality/valueThis study constructed an adaptive bivariate cut-HDMR by introducing delineation of cross-terms and constitution of univariate component function; and a new sampling technique is proposed.

An experimental and numerical study on the crush responses and energy absorption characteristics of single- and bi-layer cups under low-velocity impact

Observations on the crush responses and the energy absorption characteristics of single- and bi-layer deep-drawn cups subjected to experimental axial impact loading are presented in this manuscript. Bi-layer plates composed of aluminum and stainless steel alloys were fabricated by joining with adhesive and formed by a deep drawing process to produce the final cup shape. Impact testing was performed using a custom-built drop-tower system with a mass of 45.45 kg and impact velocities ranging from 2.8 m/s to 4.5 m/s. Various material and geometric parameters for the bi- and single-layer cups were considered in the study. Numerical simulations were conducted to investigate the deformation mechanisms and crushing behavior of the combined shells. Furthermore, based on the polynomial response surface method and using non-domain sorting genetic algorithm II, some multi-objective optimizations were performed on specific energy absorption, stroke efficiency, specific total efficiency, and initial peak load. Experimental and numerical results illustrated that the deformation of the bi-layer cups was different from the single-layer cups, especially in the head zone. Moreover, the specific total efficiency for specimens having a diameter of 55 mm and 65 mm were approximately 35% and 55% less than cups with a diameter of 45mm, respectively. It was found that the layer order of the bi-layer cup influences the energy absorption capacities of the specimen. Specifically, cups with steel as the outer layer experienced crush force efficiency and total efficiency of 6% and 5% higher than those with an aluminum outer layer, respectively.

Experimental, numerical, and multi-objective optimization investigations on the energy absorption features of single- and bi-layer deep-drawn cups

In this article, the energy absorption features of single- and bi-layer deep-drawn cups (S- and B-cups, respectively) under a quasi-static axial loading are investigated experimentally and numerically. The S-cups were made of 304L stainless steel and explosively welded B-cups were composed of aluminum and 304L stainless steel layers. A multi-objective optimization was performed on specific energy absorption and initial peak force based on the polynomial response surface method. Furthermore, to compare the energy absorption features of deep-drawn cups, two groups of 304L stainless steel tubes (with the same mass or the same height as the S-cups) were axially compressed. The experimental results indicated that the S-cups experienced total energy absorption and mean crush force approximately 24% and 51% greater than those of tubes with the same mass and thickness, respectively. Furthermore, the total efficiency and specific total efficiency of the S-cups were approximately 0.23 and 1.82 times greater than those of tubes with the same height and thickness. Moreover, the energy absorbing effectiveness factor of B-cups was approximately twice of the S-cup.

A generalized moving least square–based response surface method for efficient reliability analysis of structure

To improve the efficiency and accuracy of traditional least squares method–based polynomial response surface method (RSM) for reliability analysis of structure, the application of various adaptive metamodeling approaches is notable. The moving least squares method (MLSM)–based RSM is the simplest one and found to be effective in this regard. But, its performance in reliability analysis of structure largely depends on the proper choice of the parameter of weight function involved. In the present study, a generalized scheme to appropriately obtain the hyper-parameter of the MLSM-based RSM to approximate implicit responses of structure for reliability analysis is proposed. The algorithm is hinged on the fact that for reliability analysis, one is interested in the sign of the approximated limit state function (LSF) rather than its magnitude. Thereby, it is sufficient to obtain the hyper-parameter for which the first derivative of the probability of failure as obtained from the approximated LSF with respect to the hyper-parameter is zero. The effectiveness of the proposed algorithm is elucidated through three numerical examples. The improvement achieved by the proposed MLSM-based RSM has been compared with the reliability results obtained by the MLSM-based RSM considering the commonly recommended value of the hyper-parameter and also by the approach where the parameters are obtained by leave one out cross-validation procedure.

Run-out distance exceedance probability evaluation and hazard zoning of an individual landslide

Due to large uncertainties embedded in their geotechnical parameters, dynamic numerical models of landslide run-out distance can only be reliably applied to conduct post-failure back analyses, rather than accurate physical-based forward predictions. Therefore, it is important to quantify these uncertainties, and their effects, to improve the reliability of predictions. This paper proposes a run-out distance prediction methodology within a probabilistic framework to assess the exceedance probability of run-out distance for an individual landslide using a depth-integrated continuum method (Massflow) and a polynomial response surface method coupled with the first-order reliability method (RSM-FORM). The input parameters (i.e., friction angle and pore pressure ratio) are considered as random variables with reasonable probability density functions. The limit state function (LSF) is established based on a given threshold value of the run-out distance. The RSM is then adopted to establish a mathematical function that approximates the real LSF; and then, based on the fitted response surface, the FORM is employed to calculate the probability of the run-out distance exceeding the given threshold value. The 2015 Shenzhen landslide is considered as an example to illustrate the proposed methodology. The results show that our proposed methodology can successfully assess the exceedance probability of the run-out distance at different locations with acceptable computational errors. In addition, the computational efficiency is significantly improved compared to conventional Monte Carlo simulations. Moreover, according to the run-out distance-exceedance probability curve, the area potentially affected by the Shenzhen landslide can be classified into five categories (i.e., extremely high, high, medium, low, and extremely low) based on the different threshold values of exceedance probability (i.e., 50%, 10%, 1%, and 0.1%). The observed deposition area of the Shenzhen landslide lies within the extremely high and high hazard zones, demonstrating the feasibility of conducting landslide hazard zoning using the exceedance probability of the run-out distance. This study thus presents a practical procedure for enhancing the probabilistic run-out distance prediction of individual landslides and provides new ideas for conducting hazard zoning.

Adaptive anisotropic response surface method based on univariate dimension-reduction model and its high-order revision

PurposeBased on univariate dimension-reduction model, this study aims to propose an adaptive anisotropic response surface method (ARSM) and its high-order revision (HARSM) to balance the accuracy and efficiency for response surface method (RSM).Design/methodology/approachFirst, judgment criteria for the constitution of a univariate function are derived mathematically, together with the practical implementation. Second, by combining separate polynomial approximation of each component function of univariate dimension-reduction model with its constitution analysis, the anisotropic ARSM is proposed. Third, the high-order revision for component functions is introduced to improve the accuracy of ARSM, namely, HARSM, in which the revision is also anisotropic. Finally, several examples are investigated to verify the accuracy, efficiency and convergence of the proposed methods, and the influence of parameters on the proposed methods is also performed.FindingsThe criteria for constitution analysis are appropriate and practical. Obtaining the undetermined coefficients for every component functions is easier than the existing RSMs. The existence of special component functions is useful to improve the efficiency of the ARSM. HARSM is helpful for improving accuracy significantly and it is more robust than ARSM and the existing quadratic polynomial RSMs and linear RSM. ARSM and HARSM can achieve appropriate balance between precision and efficiency.Originality/valueThe constitution of univariate function can be determined adaptively and the nonlinearity of different variables in the response surface can be treated in an anisotropic way.

Application of the response surface method (RSM) to optimize of the conditioning of primitive rye grain krzyca (Secale cereale var. multicaule) before milling

The aim of the current study is to optimize the conditioning process of a primitive rye called (in Polish) krzyca which has recently been reintroduced to farming. The experiment was conducted according to the Box-Behnken model with three independent variables: the temperature of water used for grain conditioning (10, 15, 20 oC), the duration of the conditioning process (4, 10, 16 h) and the final grain moisture (13, 14, 15 %). In the obtained flours, four dependent variables were determined (time of grain milling, yield of extraction flour, ash content of flour and falling number value). The obtained polynomial equations and response surface method showed on significance of the used ranges of independent values, with the highest impact noted for flour ash and falling number values.

Non-probabilistic Integrated Reliability Analysis of Structures with Fuzzy Interval Uncertainties using the Adaptive GPR-RS Method

Due to its weak dependence on the quantity of variable samples, the non-probabilistic reliability analysis method based on the convex set model is applicable to practical problems in structural engineering with inherent uncertainties. However, when dealing with the black-box limit-state function issues in practical complex structural engineering, the traditional quadratic polynomial response surface (QP-RS) method has the problem of insufficient precision in approximating a highly nonlinear function. Meanwhile, fixing the limits of interval variables is trickier in case of scant samples and meager statistical information. To remedy the above deficiencies, this paper introduces a reasonable integrated reliability analysis approach. First, an adaptive Gaussian process regression response surface (GPR-RS) method that dynamically improves the fitted accuracy near the design point of the black-box limit-state function is formulated. Furthermore, the integrated reliability index with consideration of fuzzy interval uncertainties is presented. Three validation and two application examples are employed, which have justified the approach as a more reasonable assessor of practical complex structural reliability with safer results.