Nonlinear Response Surface Research Articles

Open-loop swept frequency response of nonlinear structures subjected to weak coupling

AbstractThe present study demonstrates a common behaviour of a forced nonlinear structure with smooth nonlinearity, while coupled dynamics are apparent, originating from the attached electrodynamic shaker. This appears as a variation in the transmitted forcing amplitude and is often subjected to a hysteretic (multi-state) behaviour for up and down open-loop sweeping. This situation differs from the ideal constant amplitude harmonic excitation, on which parameter extraction and engineering comprehension are based on. Untreated or ignored, this can lead to the misinterpretation of the underlying dynamics through the measured nonlinear frequency response curves and their force-normalised version, often called quasi-frequency response function. In this paper, a post-processing solution is introduced for the correct interpretation of frequency response curves at constant forcing amplitudes through the open-loop construction and resectioning of the so-called frequency response surface. The phenomenon and the proposed methodology are demonstrated using a two-degrees-of-freedom model on a shaker-nonlinear beam structure. First, open-loop frequency sweeps are executed on the mechanical system to create the nonlinear frequency response surface, where their actual amplitudes and hysteresis widths are significantly different from the ideal constant forcing amplitude case. The response surface is then sectioned at the assumed constant forcing values by using an appropriate interpolation law. These resectioned curves represent the forced nonlinear standalone structure under ideal constant harmonic excitation. The frequency response surfaces are characterised and resectioned on a nonlinear structure with stiffening and softening cases. Furthermore, an improvement in the operational resonance decay (ORD) method in its filtering and automation is shown to extract the backbone curves (BBCs). The BBC and the resectioned surface provide a complete picture and cross-validation of the underlying dynamics. Finally, the BBC and its distortion are also shown in the response surfaces in relation with the excitation normalization.

Non-linear Contact Analysis and Response Surface Optimization of Railway Wheel Using ANSYS

Non-linear Contact Analysis and Response Surface Optimization of Railway Wheel Using ANSYS

A metaheuristic particle swarm optimization for enhancing energetic and exergetic performances of hydrogen energy production from plastic waste gasification

In recent decades, there has been a surge in demand for the development of renewable energies, leading to extensive research efforts focused on the gasification process. Consequently, a wide range of studies has been conducted to explore different feedstocks for gasification, with particular emphasis on plastic waste. Although a wide range of studies conducted various optimization methods for the gasification process, there was no specific study to employ metaheuristic methods in the field of plastic waste gasification. This study aimed to perform a multi-objective particle swarm optimization (MOPSO) method to solve a multi-objective plastic waste gasification optimization problem for enhancing energetic and exergetic viewpoints. Moreover, exact methods including non-linear optimization and response surface methodology (RSM) were conducted to be compared with the results derived from MOPSO. Pareto-front solutions obtained from MOPSO were ranked using grey relational analysis (GRA) and the optimum responses were 517 kJ/kg, 84 %, and 57 % for lower-heating value, cold gas efficiency, and exergy efficiency, respectively, which were compared to optimum options obtained from multi-objective non-linear optimization and RSM techniques. While the MOPSO model may not have performed as well as other methods in this particular problem, it is important to acknowledge its capabilities. Future research can concentrate on improving the behavior and performance of the MOPSO method when dealing with a larger number of points or when applied to different problem domains.

Photodynamic Inactivation of Bovine Coronavirus with the Photosensitizer Toluidine Blue O.

Coronaviruses (CoVs) belong to the group of enveloped positive-sense single-strand RNA viruses and are causative agents of respiratory, gastro-intestinal, and central nervous systems diseases in many host species, i.e., birds, mammals, and humans. Beta-CoVs revealed a great potential to cross the barrier between species by causing three epidemics/pandemics among humans in the 21st century. Considering the urgent need for powerful antiviral agents for decontamination, prevention, and treatment of BCoV infections, we turned our attention to the possibility of photodynamic inactivation with photosensitizers in combination with light irradiation. In the present study, we evaluated, for the first time, the antiviral activity of toluidine blue O (TBO) against Beta-coronavirus 1 (BCoV) in comparison to methylene blue (MB). First, we determined the in vitro cytotoxicity of MB and TBO on the Madin-Darby bovine kidney (MDBK) cell line with ISO10993-5/Annex C. Thereafter, BCoV was propagated in MDBK cells, and the virus titer was measured with digital droplet PCR, TCID50 assay and plaque assay. The antiviral activity of non-toxic concentrations of TBO was estimated using the direct inactivation approach. All effects were calculated in MAPLE 15® mathematical software by developing programs for non-linear modeling and response surface analysis. The median inhibitory concentration (IC50) of TBO after 72 h of incubation in MDBK cells was 0.85 µM. The antiviral activity of TBO after the direct inactivation of BCoV (MOI = 1) was significantly stronger than that of MB. The median effective concentration (EC50) of TBO was 0.005 µM. The cytopathic effect decreased in a concentration-dependent manner, from 0.0025 to 0.01 µM, and disappeared fully at concentrations between 0.02 and 0.3 µM of TBO. The number of virus particles also decreased, depending on the concentration applied, as proven by ddPCR analysis. In conclusion, TBO exhibits significant potential for direct inactivation of BCoV in vitro, with a very high selectivity index, and should be subjected to further investigation, aiming at its application in veterinary and/or human medical practice.

Predicting the shear capacity of composite steel plate shear wall with the application of RSM

This research aims to predict the maximum shear capacity of Composite Steel Plate Shear Walls (CSPSWs) through nonlinear Finite Element (NLFE) analyses and Response Surface Method (RSM). The variables are concrete thickness and compressive strength, steel infill plate thickness, and yield stress. A parametric study was performed on CSPSW comprising a concrete layer on one side of the infill plate and the corresponding models having the concrete layer between the two plates. The results show that RSM is a reliable practice for precisely predicting the maximum shear capacity of the studied models. Furthermore, comparing the RSM results with those acquired by Linear Regression (LR) indicated that RSM is more accurate than LR. Moreover, in the models with the internal concrete layer, the concrete contributed more to the shear capacity of the specimens, and this difference expands with an increase in the thickness of the concrete layer.

Modeling stream baseflow nitrate concentration in an agricultural watershed using neural network and bootstrap method

The evaluation of water resource vulnerability to nonpoint source pollution in the presence of uncertainty remains a crucial concern. To enhance the accuracy of the assessment and pinpoint the key factors that affect watershed water quality, the integration of an artificial neural network (ANN) into the evaluation process is imperative. The research involved the collection of streams baseflow samples from thirty-eight sites between 1994 and 1999 in the Tomorrow-Waupaca River Watershed in central Wisconsin, USA, with a focus on examining the relationship between nitrate concentrations and a range of environmental and land use variables extracted from the watershed GIS database. This study utilized ANN methodology, combined with a bootstrap technique that employed a random resampling approach from a single input dataset, to simulate monthly stream baseflow nitrate concentrations. The effectiveness and predictive ability of the ANN model were assessed by comparing it to conventional multivariate regression methods. Through the use of ANN, more precise outcomes can be achieved while taking into account the uncertainty associated with the analysis. The findings demonstrated that the ANN outperformed both the multivariate linear regression and nonlinear quadratic response surface models in explaining the variance of stream nitrate and in external prediction consistency. This study also highlighted several key variables, such as the areal percentage of agricultural land and grassland, stream order, and the average slope of the groundwater flow path, that significantly impacted the stream baseflow nitrate concentrations in this watershed that was dominated by dairy farming and groundwater. Of these variables, the percentage of agricultural land emerged as the most significant factor.

Microparameters Calibration for Discrete Element Method Based on Gaussian Processes Response Surface Methodology

Microparameter calibration is an important problem that must be solved in the discrete element method. The Gaussian process (GP) response surface methodology was proposed to calibrate the microparameters based on the Bayesian principle in machine-learning methods, which addresses the problems of uncertainty, blindness, and repeatability in microparameter calibration methods. Using the particle flow code (PFC) as an example, the effects of the microparameters on the macroparameters were evaluated using the control-variable method, and the range of the microparameters was determined based on the macroparameters. The uniform design (UD) method and numerical calculation were used to obtain training samples, and a GP response surface methodology suitable for multifactor, multilevel, and nonlinear processes was used to establish the response surface relationships for macro–micro parameters of rock-like materials in discrete element method. According to the macroparameters obtained from the uniaxial experiments conducted on rock specimens, the microparameters were calibrated using the GP response surfaces. Numerical calculations of uniaxial compression and Brazilian splitting were performed using microparameters, and the results were compared with laboratory experiments for verification. The results showed that the relative errors of the GP response surface and laboratory test values were 5.3% for the modulus of elasticity, −7.8% for compressive strength, and −2.6% for tensile strength. The nonlinear GP response surface considered the characteristics of multiple interacting factors, and the established nonlinear response surface relationship between the microparameters and macroparameters can be used for the calibration of microparameters. The accuracy of the microparameters was verified according to the stress–strain curve and failure morphology of the rock specimens. The method of using the GP response surface to establish the macro–micro parameter relationship in the discrete element method can also be extended to other numerical simulation methods and can provide a basis for accurately analysing the microdamage mechanism of rock materials under complex loading conditions.

Probabilistic Analysis of Shallow Foundations on c-φ Soils Using 2nd Order Response Surface Methods

The HL-Reliability Index is utilized to investigate the applicability of several linear and nonlinear response surface models based on design experiments techniques to evaluate the safety under random loading, against bearing capacity failure of shallow foundations resting on c-φ soils with multivariate correlated variables. The reliability results obtained using FORM/SORM coupled with these models, are checked by Monte Carlo simulation method. It is demonstrated that the application of these models significantly reduces the execution time and memory requirements, with the central composite design scheme being the most accurate. It is also concluded, that consideration of correlation, significantly affects the reliability index for large values of soil friction angle uncertainty. The reliability index is found to be highly sensitive to uncertainties of soil friction angle more than the cohesion and the loading which have approximately the same influence, especially for the case of lognormally distributed variables. In addition, the probabilistic results show that reliability index decreases substantially with the increase of the applied pressure, and that there is significant difference between the reliability indices values computed, based on the assumption of normal distribution as compared to lognormal distribution, especially for the lower ranges of applied loading.

Reliable emulation of complex functionals by active learning with error control.

A statistical emulator can be used as a surrogate of complex physics-based calculations to drastically reduce the computational cost. Its successful implementation hinges on an accurate representation of the nonlinear response surface with a high-dimensional input space. Conventional "space-filling" designs, including random sampling and Latin hypercube sampling, become inefficient as the dimensionality of the input variables increases, and the predictive accuracy of the emulator can degrade substantially for a test input distant from the training input set. To address this fundamental challenge, we develop a reliable emulator for predicting complex functionals by active learning with error control (ALEC). The algorithm is applicable to infinite-dimensional mapping with high-fidelity predictions and a controlled predictive error. The computational efficiency has been demonstrated by emulating the classical density functional theory (cDFT) calculations, a statistical-mechanical method widely used in modeling the equilibrium properties of complex molecular systems. We show that ALEC is much more accurate than conventional emulators based on the Gaussian processes with "space-filling" designs and alternative active learning methods. In addition, it is computationally more efficient than direct cDFT calculations. ALEC can be a reliable building block for emulating expensive functionals owing to its minimal computational cost, controllable predictive error, and fully automatic features.

SGD-Based Cascade Scheme for Higher Degrees Wiener Polynomial Approximation of Large Biomedical Datasets

The modern development of the biomedical engineering area is accompanied by the availability of large volumes of data with a non-linear response surface. The effective analysis of such data requires the development of new, more productive machine learning methods. This paper proposes a cascade ensemble that combines the advantages of using a high-order Wiener polynomial and Stochastic Gradient Descent algorithm while eliminating their disadvantages to ensure a high accuracy of the approximation of such data with a satisfactory training time. The work presents flow charts of the learning algorithms and the application of the developed ensemble scheme, and all the steps are described in detail. The simulation was carried out based on a real-world dataset. Procedures for the proposed model tuning have been performed. The high accuracy of the approximation based on the developed ensemble scheme was established experimentally. The possibility of an implicit approximation by high orders of the Wiener polynomial with a slight increase in the number of its members is shown. It ensures a low training time for the proposed method during the analysis of large datasets, which provides the possibility of its practical use in the biomedical engineering area.

Design and Employing of a Non-Linear Response Surface Model to Predict the Microbial Loads in Anaerobic Digestion of Cow Manure: Batch Balloon Digester

Biogas is among the sources of renewable energy with a great potential to mitigate global energy challenges by virtue of the ease of implementation of the technology. The study focused on monitoring the total viable bacteria counts with the number of days, daily average ambient temperature and pH from a balloon type biodigester fed with 2500 L of cow manure (500 L of slurry each day for five successive days) with six months retention time using data acquisition system, standard methods and mathematical model. A non-linear response surface model was developed to predict the total viable bacteria counts with the predictors. The predictors were ranked by weights of importance to the desired targets by reliefF test. At the end of the anaerobic digestion cycle the cumulative volume of biogas was 6.75 m3 with 65.8% methane and 31.2% carbon dioxide. The ranking by weights of the predictors revealed that all the input parameters were primary factors and number of days contributed the most. Based on the testing data set, the response surface model was capable of predicting the total viable bacteria counts with high accuracy as the determination coefficient, root mean square error and p-value were 0.959, 0.197 and 0.602.

Method for Predicting Barge Impact Force Based on Nonlinear Spring Stiffness

Accurate prediction of barge impact force contributes greatly to the research of the soundness of the bridge under barge impact. Toward this end, the calculation method of barge impact force caused by ship-bridge collision is investigated in this study. Firstly, a comparative analysis for different energy conversion relationships is conducted via the high-precision finite element method (HPFEM) and the coupled vessel impact analysis (CVIA). A construction method of nonlinear spring stiffness (NSS) is proposed therefrom. Secondly, a high-precision finite element model is developed to simulate the barge-bridge collision under different barge masses and impact velocities. NSS under each condition is obtained, and the influences of barge mass and impact velocity on NSS are further discussed. An NSS model considering the effects of impact mass and impact velocity is proposed. Lastly, based on the NSS model, a prediction method of barge impact force is introduced. The results show that the impact mass has little influence on the peak value of NSS; however, the impact mass and impact velocity have a great influence on the tail of the NSS curve. According to the characteristics of NSS, four key control points can be extracted and NSS is simplified into a polyline model. The NSS model of the barge is obtained by nonlinear response surface fitting. The impact force can be predicted by combining the simplified NSS model and the proposed method in this study. The proposed method in this paper does not consider the pier stiffness; hence, it can be combined with NSS to quickly estimate the impact force, which can provide a design basis for the impact force in ship-bridge collision design. The rigid wall and a continuous rigid frame bridge impacted by the barge are studied; the results show that the proposed method can reasonably estimate the impact force.

Sensitivity analysis of factors affecting motion reliability of manipulator and fault diagnosis based on kernel principal component analysis

AbstractAs an important index to quantitatively measure the motion performance of a manipulator, motion reliability is affected by many factors, such as joint clearance. The present research utilized a UR10 manipulator as the research object. A factor mapping model for influencing the motion reliability was established. The link flexibility factor, joint flexibility factor, joint clearance factor, and Denavit–Hartenberg (DH) parameters were comprehensively considered in this model. The coupling relationship among the various factors was concisely expressed. Subsequently, the nonlinear response surface method was used to calculate the reliability and sensitivity of the manipulator, which provided an applicable reference for its trajectory planning and motion control. In addition, a data-driven fault diagnosis method based on the kernel principal component analysis (KPCA) was used to verify the motion accuracy and sensitivity of the manipulator, and joint rotation failure was considered as an example to verify the accuracy of the KPCA method. This study on the motion reliability of the manipulator is of great significance for the current motion performance, adjusting the control strategy and optimizing the completion effect of the motion task of a manipulator.

Process intensification of hydrogen production by catalytic steam methane reforming: Performance analysis of multilayer perceptron-artificial neural networks and nonlinear response surface techniques

Uncertainty about how process factors affect output might lead to waste of resources in laboratory experiments. To address this constraint, a data-driven method might be used to describe the non-linear connection between process parameters and desired output. A Multi-Layer Perceptron-Artificial Neural Network (MLP-ANN) and non-linear response surface method are used to predict hydrogen generation by catalytic steam methane reforming. The impact of training methods (scaled conjugate and gradient descent), hidden layer variation, artificial neuron variation, and activation functions were studied in 80 MLP-ANN combinations (hyperbolic tangent function and sigmoid function). The performance of MLP-ANN models was affected by the training techniques, activation functions, layer count, and number of artificial neurons. The model with the sigmoid function and 3 input layers, 17 artificial neurons in the first layer, 15 artificial neurons in the second layer, and 2 output nodes had the greatest performance among the 40 configurations of scaled conjugate trained ANNs. It projected an 89.55% maximal hydrogen yield with a coefficient of determination (R2) of 0.997 and reduced errors with Mean absolute percentage error (MAPE) and mean squared error (MSE) of 0.199 and 0.121, respectively. Similarly, the gradient descent ANN model with hyperbolic tangent activation function had the greatest performance among the 40 gradient descent trained-ANN configurations. The 3–15–7–2 gradient descent trained ANN model projected a maximum hydrogen output of 89.73% compared to the experimental results of 89.51%. The MLP-ANN models outperformed nonlinear response surface methods, with R2, MAPE, and MSE of 0.231, 0.191, and 0.988, respectively. The updated Garson algorithm indicated that the input parameters impacted the hydrogen production in the sequence reaction temperature>methane partial pressure>steam partial pressure. The sensitivity analysis might assist identify how resources should be spent.

Modeling photocatalytic hydrogen production from ethanol over copper oxide nanoparticles: a comparative analysis of various machine learning techniques

The production of hydrogen is one way to meet the ever-increasing demand for cleaner and renewable energy sources. In this study, various machine learning techniques such as Levenberg–Marquardt neural networks (LMNN), scaled conjugate gradient descent neural networks (SCDNN), and support vector machine (SVM) in comparison with nonlinear regression model (NLM) and response surface model (RSM) were employed for modeling photocatalytic hydrogen production from ethanol using copper oxide (CuO) nanoparticles as photocatalyst. The effects of input parameters such as the irradiation time, the CuO content, the catalyst dosage, and the ethanol concentration on hydrogen production were considered in the modeling process. Optimized network configurations of 4-12-1 and 4-5-1 representing the input nodes, hidden neurons, and output node were used for the LMNN and SCDNN, respectively. Both the LMNN and SCDNN show superior prediction of hydrogen production compared with the SCDNN, SVM, NLM, and RSM as indicated by the high R values of 0.998 and 0.997 for LMNN and SCDNN, respectively. The LMNN displayed the best prediction of hydrogen production with R value of 0.998. The sensitivity analysis shows that all the input parameters influenced the LMNN model output. However, the predicted hydrogen from the LMNN model was best influenced by the irradiation time.

Nonlinear regression analysis and response surface modeling of Cr (VI) removal from synthetic wastewater by an agro-waste Cocos Nucifera: Box-Behnken Design (BBD)

In this study mixture of coconut shell and coir was used for Cr (VI) removal from synthetic wastewater and statistical tool Response Surface Modeling (RSM) was applied to optimize process parameters. The solution pH (2–6), reaction time (20–100 minutes) and adsorbent quantity (0.03–0.2 g) was optimized to find the maximum response of Cr (VI) removal using statistical Box-Behnken design (BBD) software. The equilibrium data obtained by the batch experiment were analyzed by ANOVA and found fitted in a second-order polynomial equation through multiple regression analysis. The optimum value of pH, adsorbent quantity and reaction time for 99% of Cr(VI) was found as 2, 0.1 g and 100 minutes, respectively. By using non-linear regression method it was found that Freundlich isotherm and Pseudo-second-order kinetic with high correlation coefficient (R 2), low Chi-square (χ 2) and root mean squares errors (RMSE), best describe the adsorption of Cr (VI) on mixture of coconut shell and coir (MCSC) surface. Positive enthalpy (ΔH°) and negative Gibbs free energy (ΔGo) values confirm the endothermic and spontaneous nature of adsorption process. Pre and post adsorption phenomenon was confirmed by characterization of adsorbent using AFM, FTIR, SEM, and EDX analysis. The adsorbent MCSC has regenerative property and can be reused 3–4 times after treating with alkaline medium (0.2 N NaOH) and offered more than 60% removal of Cr (VI) at the fourth cycle. It can be inferred based on this study that MCSC is an effective adsorbent for Cr (VI) removal and can be used on an industrial scale for social and environmental benefit. Novelty statement An agriculture waste mixture of coconut shell and coir (MCSC) without the addition of any chemical reagent, was used for Cr(VI) removal. As per literature survey and best of our knowledge, the adsorbent MCSC has not been reported for Cr (VI) removal. In the previous study, authors reported either coconut coir pith or coconut shell or coconut charcoal as adsorbent for Cr (VI) removal. The adsorbent MCSC is efficient even at very low doses (0.1 g) as compared to the reported adsorbent.

Source and sectoral contribution analysis of PM2.5 based on efficient response surface modeling technique over Pearl River Delta Region of China

Identifying and quantifying source contributions of pollutant emissions are crucial for an effective control strategy to break through the bottleneck in reducing ambient PM2.5 levels over the Pearl River Delta (PRD) region of China. In this study, an innovative response surface modeling technique with differential method (RSM-DM) has been developed and applied to investigate the PM2.5 contributions from multiple regions, sectors, and pollutants over the PRD region in 2015. The new differential method, with the ability to reproduce the nonlinear response surface of PM2.5 to precursor emissions by dissecting the emission changes into a series of small intervals, has shown to overcome the issue of the traditional brute force method in overestimating the accumulative contribution of precursor emissions to PM2.5. The results of this case study showed that PM2.5 in the PRD region was generally dominated by local emission sources (39–64%). Among the contributions of PM2.5 from various sectors and pollutants, the primary PM2.5 emissions from fugitive dust source contributed most (25–42%) to PM2.5 levels. The contributions of agriculture NH3 emissions (6–13%) could also play a significant role compared to other sectoral precursor emissions. Among the NOX sectors, the emissions control of stationary combustion source could be most effective in reducing PM2.5 levels over the PRD region.

Recycling of discharged soil from EPB shield tunnels as a sustainable raw material for synchronous grouting

EPB shield tunnel construction will discharge a large amount of soil. Directly transporting this discharged soil to dumping grounds not only increases the machinery and labor costs but also raises environmental concerns. In this paper, we presented and explored a guiding framework for recycling the discharged soil from EPB shield tunnel construction as the raw materials for synchronous grouting. The proposed method was proved to be feasible by a detailed experimental study based on samples taking from the Zhengzhou metro line 3 project. The preparation and formulation process of those raw materials was designed to meet the requirements not only for engineering application but also for green environmental protection and sustainable development. The properties and performance of the synchronous grouting material, including its specific gravity, fluidity, gel time, bleeding rate, bulk shrinkage rate and unconfined compression strength, were investigated by the U15∗ (154) uniform design experimentation. The effects of ratios of water/binder (cement + fly flash), the binder/coarse-grains (the discharged soil from the west bound tunnel + river sand), fine-grains (the discharged soil from the east bound tunnel)/water and the fly flash/cement on the response value of the synchronous grouting material performances have been investigated with stepwise nonlinear regression analysis model and 3D response surface diagrams. Moreover, the optimal mass ratio for the synchronous grout is also proposed with a new Goal Programming model to obtain an optimum performance. The results indicate that the discharged soil from the east bound tunnel in this project can be directly reused as bentonite, while the discharged soil from the west bound tunnel should be mixed with river sand at a mass ratio of 1:1 before reusing it as the raw material of synchronous grout. Furthermore, the performance of the synchronous grouting was demonstrated highly depending on the proper selection and optimization of mass ratios for water/binder, binder/coarse-grains, fine-grains/water and fly-ash/cement. The presented experimental investigation and the proposed strategy for determining the optimal formulation for synchronous grouting materials demonstrated a feasible way of recycling discharged soil from EPB shield tunnel construction.

Simulation and optimization of gamma-ray linear attenuation coefficients of barite concrete shields

The remarkable increment in radioactivity risks of today’s industrial world is required to the efficient design of shielding structures. In the present study, the optimal design parameters of barite concrete shields for providing the highest gamma radiation shielding capability were researched by using a hybrid technique of the Box-Behnken Design based response surface method and Particle Swarm Optimization. Barite aggregate fraction, water-to-cement ratio and cement content of the shields were limited as 0:100 (by weight), 0.30:0.70 (by weight) and 200:600 (kg/m3) in the optimization problem, respectively. The regression equation derived from the regression learning process presented an excellent correlation to define the XCOM linear attenuation coefficients. A nonlinear response surface fitted to the regression equation was used as the validation of the PSO results obtained from MATLAB. The results of this study have shown that the proposed method provides satisfactory predictions for the barite concrete radiation-shielding capability depending on the design parameters. In addition, it was found that the linear attenuation coefficient could be increased by 102% by the design of the best shield according to the poorest mixture.

Optimization of methanol production via CO2 hydrogenation: comparison of sampling techniques for process modeling

This paper compares performances of three different sampling techniques in representing nonlinear response surface for optimization problem, with five decision variables. Three studied sampling techniques are Central Composite Design (CCD), Box – Behnken Design (BBD) and Latin Hypercube Sampling ( LHS). Simulation – based optimization of methanol production via CO2 hydrogenation process was used as a case study. The objective of this optimization problem is to minimize the methanol production cost. The nonlinear model ( the objective function) represents the relationship between operating conditions and methanol production cost. The results show that the response surface of this case study is trend to be the third order model ( with R – squared value greater than 0.97) for all sampling techniques. BBD is the most suitable sampling technique in this study, resulting in the percent error less than 1.2. The LHS shows comparable performance with BBD if it has suitable number of sample points.