Polynomial Response Surface Methodology Research Articles

Hydrogen storage systems performance and design parameters using response surface methods and sensitivity analysis

DesignDesign of metal hydride-based hydrogen storage reactors is often performed using numerical/experimental modelling which is computationally/economically difficult. This paper investigates the applicability of Response Surface Methodology (RSM) coupled Local/Global Sensitivity Analysis (L/GSA) to investigate – i) the applicability of advanced RSMs in predicting the responses for storage systems efficiently, ii) the applicability of advanced RSMs to perform L/GSA to identify the sensitive input design parameters based on their effect on the Outputs of Interests (OIs), i.e., reaction fraction (i.e., C) and bed temperature (i.e., T), and iii) the dependence of importance ranking of design parameters on the employed L/GSA methodology. The study is conducted in two stages. In the first stage, the most accurate RSM was identified among fourteen traditional and advanced RSMs, i.e., radial basis, kriging, quadratic, moving least square, support vector machine etc., employing a measure of precision, i.e., Nash–Sutcliffe Efficiency (NSE). RSMs were constructed based on the values of OIs estimated using finite element simulation using COMSOL software for random realizations of inputs generated via Latin Hypercube Sampling (LHS). In the second stage, the importance ranking of design parameters was estimated for both OIs using six different L/GSAs based on the input-output relationships estimated in stage one. All the codes of RSMs and L/GSAs were written and validated in MATLAB. Finite element simulations of the random realizations were performed using COMSOL software. For the present study, NSEs of the considered RSMs were ranging between 0.6262-0.8544 and 0.4652–0.8081 for C and T respectively, indicating the importance of selection of appropriate RSM. RBF-augmented Compact-I and kriging were the most accurate RSMs with NSEs approximately 10%–20 % higher to those of frequently used polynomial RSM. Time (t) and mass of hydrogen to be stored (MH) were the most; and external temperature (Text) and porosity (E) were the least sensitive inputs corresponding to C and T, with differences of 80–90 % in the sensitivity indices respectively. The ranking prediction was highly dependent upon the employed L/GSA methodology, with Morris's screening observed to be the least accurate. The RSM methods described in this study help to design and investigate the metal hydride reactors for various applications (space heating, hydrogen storage, storage for vehicular application, metal hydride compressor) without undergoing detailed mathematical modelling of the system. The proposed methodology may significantly assist the designers to focus (or vary) on the sensitive inputs only during the physical modelling of systems to improve their performance. This sensitivity analysis is helpful to find out the most advance sensitivity analysis method which can be used to find out the most sensitivity parameter which can be varied according to their rankings to achieve the required performance of metal hydride reactor for the particular application. The advanced RSMs assist to identify these sensitive inputs quickly by reducing the mathematical efforts in the L/GSA by providing the accurate input-OIs relationships based on the limited numerical simulations. This will significantly save the resources and time of industries required in physical modelling/numerical simulations significantly, which otherwise would have been invested on investigating the non-sensitive inputs.

Optimization of fermentation medium components by response surface methodology (RSM) and artificial neural network hybrid with genetic algorithm (ANN-GA) for lipase production by Burkholderia cenocepacia ST8 using used automotive engine oil as substrate

Bioconversion of used automotive engine oil (UEO) into lipase was conducted via submerged fermentation by Burkholderia cenocepacia ST8, as a strategy for value-added product generation and waste management. Response surface methodology (RSM) and artificial neural network hybrid with genetic algorithm (ANN-GA) were employed to optimize the fermentation medium for enhancing extracellular lipase production by B. cenocepacia ST8. Employing a four-factor-five-level central composite rotatable experimental design (CCRD), a reduced quartic polynomial RSM model and ANN model (4-4-1) trained using Bayesian Regularization were developed to attain the optimized fermentation medium for maximum level of lipase production. The RSM model predicted the following as the optimum media constituents: 2.28% v/v of Tween 80, 2.26% v/v of UEO, 0.79% w/v of nutrient broth, and 1.33% w/v of gum arabic, with an actual lipase yield of 216 U/mL. While, ANN-GA predicted the optimum media constituents to be 3% v/v of Tween 80, 3% v/v of UEO, 0.72% w/v of nutrient broth, and 3.38% w/v of gum arabic, with actual lipase yield of 225 U/mL. In comparison to the unoptimized medium, optimized RSM and ANN-GA systems both demonstrated a 1.6-fold increment in lipase production. Tween 80 and nutrient broth concentrations were the most important variables influencing the lipase production. The findings of this study indicated that the ANN-GA and RSM could be useful for effective optimization of the fermentation medium for enzyme production.

Neural network approach to response surface development for reaction model optimization and uncertainty minimization

We examine the state-of-the-art neural network (NN) approach and its flexible implementations in combustion reaction model uncertainty quantification (UQ), optimization, and uncertainty minimization (UM). The work is motivated by addressing the problem of limited scalability of the traditional polynomial response surface methodology in handling large size of rate parameters and target data sets. Features of the NN training, accuracy, and trade-offs in several key aspects of the NN application are discussed. We show that for high-dimensional reaction model optimization and UM, a shallow NN with only one hidden layer is more robust and accurate than the polynomial response methodology. Further, we demonstrate that NN allows for adaptive training. New neural networks that augment new input parameters or updates in a trial reaction model can be adapted from the existing networks with much smaller training efforts. In addition, deep neural networks are capable of covering functional dependencies of initial thermodynamic conditions and boundary conditions, thus yielding generalized response surfaces with rate parameters and thermodynamic/mixture conditions as the input for a given combustion property. The NN approach can be readily integrated into the framework of the Method of Uncertainty Minimization using Polynomial Chaos Expansions (MUM-PCE) developed earlier. We present a test case that uses the trial Foundational Fuel Chemistry Model Version 2.0 (FFCM-2, a model consisting of 96 species and 1054 reactions for combustion of relevant C0–4 species), optimizing it against FFCM-1 targets, to illustrate the efficiency and accuracy of the NN method.

Reliability and Reliability-based Sensitivity Analyses of Steel Moment-Resisting Frame Structure subjected to Extreme Actions

The ground external columns of buildings are vulnerable to the extreme actions such as a vehicle collision. This event is a common scenario of buildings' damages. In this study, a nonlinear model of 2-story steel moment-resisting frame (SMRF) is made in OpenSees software. This paper aims investigating the reliability analysis of aforementioned structure under heavy vehicle impact loadings by Monte Carlo Simulation (MCS) in MATLAB software. To reduce computational costs, meta-model techniques such as Kriging, Polynomial Response Surface Methodology (PRSM) and Artificial Neural Network (ANN) are applied and their efficiency is assessed. At first, the random variables are defined. Then, the sensitivity analyses are performed using MCS and Sobol's methods. Finally, the failure probabilities and reliability indices of studied frame are presented under impact loadings with various collision velocities at different performance levels and thus, the behavior of selected SMRF is compared by using fragility curves. The results showed that the random variables such as mass and velocity of vehicle and yield strength of used materials were the most effective parameters in the failure probability computation. Among the meta-models, Kriging can estimate the failure probability with the least error, sample number with minimum computer processing time, in comparison with MCS.

Design optimization of S-shaped compressor transition duct using particle swarm optimization algorithm

A high-bypass turbofan engine transfers air from low- to the high-pressure compressor through an S-shaped transition duct. Minimization of the total pressure loss and maximization of uniform flow are key factors to ensure the maximum performance of the S-shaped transition duct. The conventional design approach is time-consuming and does not guarantee an optimal solution. Hence, the present article is based on the application of optimization for the S-shaped compressor transition duct. The optimization is carried out on the basis of shape parameters to minimize objectives namely pressure loss coefficient and non-uniformity with the reduction of length of the S-shaped transition duct. The 2-D axisymmetric approach of computational fluid dynamics is used as a design tool for performance evaluation with optimization techniques. The simulation model is validated with the available experimental results of the literature. The correlation between the response and independent variables is established with the help of the second-order polynomial response surface methodology. Further, individual optimization is carried out for single-objective consideration using particle swarm optimization and gray wolf optimization algorithms. As the results of single-objective optimization depict the conflicts between both objectives, later optimization using multi-objective particle swarm optimization and multi-objective gray wolf optimization algorithms is carried out. The performance metrics are obtained and compared. The ‘TOPSIS’ method is applied to get best solution out of multiple solutions. The optimized duct reduced pressure loss coefficient and non-uniformity index by 28.14% and 43.33% with a reduction of 6.37% of length compared to baseline S-shaped duct.

Modified and generalized full cubic polynomial response surface methodology in engineering mixture design

This paper presents the modified and generalized full cubic polynomial Response Surface Methodology (RSM) in engineering mixture design. It provided comprehensive parameters definitions that enable development of adequate regression of dependent – independent variables in mixture design with ease. Necessary equations and useful insights were identified and their application outlined. Step-by-step and parameters description necessary in statistical model validation and adequacy using the student’s t -test and the fisher test were provided. NULL and ALTERNATE hypotheses based on standard statistical values techniques were also elaborated. These comprehensive principles and applications in mixture design were based on an extensive review of literature. Hence, difficulties usually experienced by numerous researchers in mixture models development to third degree would be overcome, while model validations and adequacy techniques are made handy. It is believed that this study would motivate vigorous research on the applications of non-conventional materials such as vegetable fibers, soil, wastes from industry, mining and agriculture, alongside the traditional materials, such as: cement, lime, earth, stone, sand and water for engineering applications. Keywords: Mixture Design, Simplex Lattice, Cubic Polynomials, Scheffe’s Model, Adequacy Tests

The Effect of FEM Mesh Density on the Failure Probability Analysis of Structures

In the analysis of finite elements, mesh density can highly influence the accuracy of the results. Hence, researchers consider the determination and refinement of mesh an attractive issue. However, the subject has not been suitably investigated for the reliability evaluation of structures. This paper investigates the effects of mesh density on the reliability evaluation and the reliability-based sensitivity of structures. For this purpose, two common engineering problems modeled by Finite Element Method (FEM), with different mesh densities and their reliability results determined by Monte Carlo simulation and polynomial Response Surface Methodology (RSM). The analytical solutions to the proposed problems were present in the literature. Hence, the effects of the FEM mesh densities on the reliability results could be compared with the theoretical results. The outcomes based on the FEM results showed that RSM can very accurately evaluate the performance of these structures. However, the main achievement of the study was the finding that though a determined mesh density can be considered acceptable from the deterministic analysis viewpoint, its employment in reliability analysis could produce 100% error in estimating the failure probability of a structure.

Investigation of the train driver injuries and the optimization design of driver workspace during a collision

The purpose of this study was to analyze train driver injuries under secondary impact and to optimize the driver workspace to reduce the driver impact injury risk. The console–seat–dummy collision analysis model of train cab is established using MADYMO. The driver dynamic impact response and the driver injury results were obtained from the collision model. The optimization of driver workspace parameters was conducted to reduce the driver injury risk. Fifteen samples were chosen for numerical simulation based on the optimal Latin hypercube design; the polynomial response surface methodology was adopted to fit the relationship between the driver injury criteria and the workspace parameters. The driver injury results show that the driver injury is considerably severe. The optimization results indicate that the driver injury is minimal when factors A, B, C, and D are 356.6 mm, 404.6 mm, 145 mm, and 200 mm, respectively. Compared with the initial collision model, all six driver injury criteria after optimization decrease obviously and are well within the tolerance limits, respectively. The analysis of the optimization results and the results of computer simulation refined after the optimization confirm that the optimization results show good correlation with the injury results of the collision numerical model and the effectiveness of the optimization design in reducing the severity of the driver injury during a secondary impact.

Optimisation of temperature-programmed gas chromatographic separation of organochloride pesticides by response surface methodology

A response surface methodology (RSM) approach is applied to optimise the temperature-programme gas-chromatographic separation of 16 organochloride pesticides, including 12 compounds identified as highly toxic chemicals by the Stockholm Convention on Persistent Organic Pollutants. A three-parameter relationship describing both linear and curve temperature programmes is derived adapting a model previously used in literature to describe concentration gradients in liquid chromatography with binary eluents. To investigate the influence of the three temperature profile descriptors (the starting temperature, the gradient duration and a shape parameter), a three-level full-factorial design of experiments is used to identify suitable combinations of the above variables spanning over a useful domain. Resolutions of adjacent peaks are the responses modelled by RSM using two alternative methods: a multi-layer artificial network (ANN) and usual polynomial regression. The proposed ANN-based approach permits to model simultaneously the resolutions of all the consecutive analyte pairs as a function of the temperature profile descriptors. Four critical pairs giving partially overlapped peaks are identified and multiresponse optimisation is carried out by analysing the surface plot of a global resolution defined as the average of the resolutions of the critical pairs. Descriptive/predictive performance and applicability of the ANN and polynomial RSM methods are compared and discussed.

Sensitivity Analysis of Industrial Multicrystalline PERC Silicon Solar Cells by Means of 3-D Device Simulation and Metamodeling

How successfully an improved solar cell concept is transferred to mass production depends not only on the realized cell efficiency, but crucially on the stability of the fabrication process, i.e., on the distribution of the current-voltage (I-V) parameters. To model such distributions, we use three-dimensional (3-D) full-size device simulations of passivated emitter and rear cells (PERCs). The number of these time-consuming simulations is drastically reduced by changing all input parameters concurrently in a design of experiment approach. A simple polynomial response surface methodology (RSM) model is obtained from these simulations by regression analysis. The RSM contains all the mutual nonlinear interactions between the device parameters, and is therefore called a metamodel. The metamodel is applied: 1) to find maximum efficiency; 2) to compute how sensitively each device parameter influences the I-V parameters; 3) to explain, predict, and manipulate the distribution of the I-V parameters in mass production; and 4) to find an optimum starting point for experiments. For example, we demonstrate how the choice of the distance between the rear local point contacts leads to either maximal median efficiency but with a broad distribution, or to a slightly reduced median cell efficiency but with a narrow distribution and a reduced number of bad cells.

Artificial neural network modeling and response surface methodology of desalination by reverse osmosis

Response surface methodology (RSM) and artificial neural network (ANN) have been used to develop predictive models for simulation and optimization of reverse osmosis (RO) desalination process. Sodium chloride aqueous solutions were employed as model solutions for a RO pilot plant applying polyamide thin film composite membrane, in spiral wound configuration. The input variables were sodium chloride concentration in feed solution, C, feed temperature, T, feed flow-rate, Q, and operating hydrostatic pressure, P. The RO performance index, which is defined as the salt rejection factor times the permeate flux, has been considered as response. Both RSM and ANN models have been developed based on experimental designs. Two empirical polynomial RSM models valid for different ranges of feed salt concentrations were performed. In contrast, the developed ANN model was valid over the whole range of feed salt concentration demonstrating its ability to overcome the limitation of the quadratic polynomial model obtained by RSM and to solve non-linear problems. Analysis of variance (ANOVA) has been employed to test the significance of response surface polynomials and ANN model. To test the significance of ANN model, the estimation of the degree of freedom due to residuals has been detailed. Finally, both modeling methodologies RSM and ANN were compared in terms of predictive abilities by plotting the generalization graphs. The optimum operating conditions were determined by Monte Carlo simulations considering: (i) the four input variables, (ii) for typical brackish water with a fixed concentration of 6g/L and (iii) for typical seawater with a fixed concentration of 30g/L. Under the obtained optimal conditions maximum RO performance indexes have been achieved experimentally.

A comparative study on quality design of fixture planning for sheet metal assembly

Fixture plays an important role in enhancing the weld quality of the sheet metal assembly process. However, the traditional experience-based fixturing scheme and the purely optimal fixturing scheme are often sensitive to location fluctuation of the designed locators. In this paper, the three quality design models of a non-linear programming model, a polynomial response surface methodology (RSM) and a neural network (NN)-enhanced RSM are presented for fixture planning of a sheet metal assembly with resistance spot weld. In the non-linear programming model, both performance and variance are considered in the formulation of objective function. The polynomial RSM is used to fit a feasible response surface by 3 k fractional factorial design and analysis of the variance; by inspecting the influence of each design variable, one can gain insight into the existence of multiple design choices and select the optimum design based on more factors. NN can be used to confidently generate additional design points added to the original data set to form the enhanced data set; the NN-enhanced RSM can help to improve the accuracy. An industrial case study of a car door assembly is used to illustrate the feasibility of the presented quality design models. This work provides a basis for improving the quality of the body-in-white assembly process in the design phase.

Evaluation of the aerobic biodegradation of trichloroethylene via response surface methodology

Response surface methodology (RSM) was used to evaluate the effect of additives for enhancing the aerobic biodegradation of trichloroethylene (TCE). The parameters investigated include the initial TCE concentration, addition of extra bacteria, use of toluene as an inducer and hydrogen peroxide as terminal electron acceptor (TEA). Without additive, degradation efficiencies of ≥ 80% were obtained for TCE concentrations < 700 mg/L. According to the second-order polynomial RSM and biodegradation results, the use of toluene to induce enzyme production inhibited degradation at TCE concentrations < 300 mg/L. The addition of hydrogen peroxide did improve the overall degradation efficiency but decreased the degradation rate. The RSM model for toluene, extra bacteria and TEA predicted that the best approach to optimize degradation of high TCE concentrations is to ensure adequate population in conjunction with supplemental TEA.