Response Surface Construction Research Articles

Online robust parameter design using sequential support vector regression based Bayesian optimization

Traditional robust parameter design (RPD) is an effective offline quality improvement method, but it cannot update the optimal settings in a timely manner. To resolve the drawback of traditional one-time modeling methods, online RPD comes into being. In online RPD, when the setting for controllable factor is unreasonable, it can be regarded as a new sample to update the optimal setting, which improves the efficiency of constructing response surface. Now, one of the mainstream approaches is to use support vector regression (SVR) as a response surface for online RPD. However, in the process of adding samples and updating the response surface, the parameters of the model are not updated. If the parameters do not change after adding samples, the accuracy of the model may decrease, which is obviously not desirable. To address this problem, this paper proposes Bayesian optimization sequential SVR based on online RPD (BOSSVR-RPD) strategy, which can simultaneously update the parameters and response surface in real time. In the proposed strategy, we can use the optimal setting of previously controllable factors, the currently observed noise factor and the corresponding response as new samples to add to the response surface to improve the accuracy of the response surface, and at the same time use the Bayesian optimization method to optimize the parameters of the model. By repeating this process, we can find the desirable optimal setting for controllable factor. This paper verifies the method through four cases, proving that the proposed BOSSVR-RPD strategy can find the optimal setting for controllable factors. Compared with the existing method without parameter optimization, the model proposed in this paper is more accurate, so the optimal setting for controllable factors can be found faster and the controllable factors obtained are more reliable.

Research and experimental verification of lightweight loader rims

The safety performance and structural stiffness of a rim, which is the main load-bearing structure of the loader during operation, influence the overall performance, stability, and braking capabilities of the machine. In the industry, researchers are currently pursuing lightweight and high-strength rims as a primary objective. A low weight not only enhances machinery fuel efficiency but also aligns with societal demands for sustainable development, energy conservation, and emission reduction. In this article, multiobjective optimization analysis on rims composed of three different materials is performed, and the relationships between various optimization parameters and target parameters are established using the results of response surface construction. Multiobjective genetic algorithms are utilized to derive various optimization plans, which are subsequently evaluated through static analysis, fatigue analysis, and weight loss analysis. The final optimization plan is determined based on the calculation results while considering production costs. Field tests are conducted on the optimized rims under various working conditions to verify the test results, evaluate the reliability of the finite element analysis results, and confirm the safety of the optimized rim.

Optimized spouted bed production of antioxidant dried powder from green tea

This study evaluated the feasibility and optimization of the spouted bed drying to produce standardized dried Camellia sinensis extract. We explored processing variables such as inert particle type (Teflon® or glass beads), drying aid concentration (colloidal SiO2—Aerosil 200®), and drying inlet temperatures (80, 110, or 140 °C). Regression analysis of the results allowed for constructing response surface graphs, highlighting variable impacts on product properties and spouted bed performance. The optimal conditions involved Teflon® beads and a drying temperature of 110 °C, resulting in a product with excellent moisture content, water activity, and active constituent retention. The product demonstrated significant antioxidant activity in DPPH assays, with an IC50 between 4.4 to 6.7 µg/mL, surpassing the synthetic antioxidant butylated hydroxytoluene (BHT), which had an IC50 of 12.5 µg/mL. Rancimat assays showed that the dried extract effectively protected crude sunflower oil from oxidation, increasing its shelf life from 8.2 to 13.1 months.

Stochastic analysis of thin beams and plates incorporating von-Kármán nonlinear strains using meshless method

The current paper proposes methods for stochastic meshless analysis of thin beams and plates, by considering von-Kármán nonlinear strains. Here, Young’s modulus is assumed to have a spatial variation over the domain and is modeled as a homogeneous random field. Further, it is discretized utilizing moving least square based shape functions. Gaussian and lognormal properties are presumed to model the randomness related to Young’s modulus. Element-free Galerkin method is used as the meshless tool. The present study suggests employing perturbation method if the quantities of interest are limited to the first or second probabilistic moments of the responses. The nonlinear equations in the proposed perturbation formulations are solved using Newton-Raphson iterative scheme for finding out the deterministic part of the response, as well as its initial two derivatives with respect to random variables. Additionally, if there is an interest in higher probabilistic moments, probability density functions, cumulative distribution functions, and so forth, the study proposes a method using high-dimensional model representation (HDMR) in the meshless framework. In HDMR, the nonlinear connection between input variables and the output response is represented in terms of hierarchical correlated function expansions. These hierarchical functions are approximated over the response values evaluated using deterministic analysis on selected number and combinations of control points of random variables involved. Lagrange interpolation method is employed for the construction of response surfaces. Unlike Monte Carlo simulation (MCS) which needs numerous deterministic nonlinear analyses to be performed during each simulation, HDMR requires only a few deterministic nonlinear analyses to construct the component functions. Hence, simulations performed on the reduced order models of high-dimensional response can be used to estimate the probabilistic moments as well as density functions and cumulative distributions of response, with high computational efficiency compared to MCS. The probabilistic moments and distributions produced for a range of coefficient of variation of input random field up to 30%, for both the normal and lognormal input random fields are compared with those provided by crude MCS on the system of equations and are observed to be matching well.

Combined FEM and phase field method for reliability design of forward degradation in SiC bipolar device

The reliability of 4H-SiC bipolar devices is compromised by the expansion of single Shockley stacking faults (SSFs) during forward-current operation. Because SSF expansion is governed by multiphysical aspects, including electrical, thermal, and stress states, analysis of the mounted structure is important for improving power module design. We propose a practical design method that analyzes the critical condition due to SSF expansion using a combined method with a multiphysical finite element method (FEM) and phase field model based on the time-dependent Ginzburg–Landau equation. In preliminary studies, the thermal deformation of the demonstration module and the variation of threshold current of a bar-shaped SSF were verified from experimental and reference data. Estimating the SSF expansion rate on the constructed response surface under the mutiphysical inputs from FEM, the proposed design method can be used effectively in the design process by changing the various design variables.

Лабораторное исследование дозирующего устройства для кормовых добавок

The experimental study presented in the article forms the basis for designing a dispenser servicing a robotic feed table on livestock farms. In the introduction, the author analyzes trends in the development of machines for on-farm production of compound feeds using dosing and weighing equipment, and describes the role and key performance indicators of the use of compound feeds of on-farm production for livestock breeding complexes. The articles presents a method for optimizing the design parameters of screw-type feed additive dispensers, a schematic diagram and a photo of an experimental installation. To control the electric motor of the experimental installation, a mathematical model was developed that takes into account the electric motor speed. A second-order mathematical model was used as a mathematical framework for processing experimental data, constructing response surfaces and regression equations. The experiment assumed a fi ve-fold weight measurement of the dosing error of feed additives for each type of the screw design.

СИНТЕЗ НЕЧІТКОГО РЕГУЛЯТОРА ТЕМПЕРАТУРИ ПАСТЕРИЗАЦІЇ МОЛОКА

The article solves the actual scientific and technical task of reducing the energy intensity of pasteurization of milk in the POU5 apparatus by means of research and development of an automated system for controlling the pasteurization temperature regime. A study of the features of the device's functioning, setting the parameters of the control process was carried out; the improvement of the mathematical model and the algorithm for regulating milk pasteurization parameters was carried out; an automated system for controlling the temperature of milk pasteurization in the POU5 installation was created. The synthesis of a fuzzy regulator of milk pasteurization temperature was carried out. Constructed response surface of milk temperature changes depending on the consumption of milk for pasteurization and the temperature of the hot water of the heat exchange r. The application of the fuzzy logic apparatus for building an adaptive system makes it possible to create adaptive systems with optimal control for the purpose of approximating the output variable of the fuzzy controller.A structural scheme of the milk pasteurizer was created, as well as effective methods of temperature control and para-metric schemes of sections (recovery, pasteurization and cooling of the plate milk pasteurizer) were developed, which allow improving the accuracy of technological process control.As a result of conducting theoretical research, a dynamic characteristic of the pasteurization section was obtained ac-cording to the channel «hot water consumption - temperature of pasteurized milk». The specified model will allow to develop temperature control algorithms to increase pasteurizer productivity

Effect of Paste Fluidity and Paste-to-Aggregate Ratio on the Strength and Permeability of Porous Mortar from Manufactured Sand.

Many places in the world suffer from a shortage of river sand because of population growth and environmental protection, and people have to replace river sand with manufactured sand (M-sand). In this study, M-sand was adopted as aggregate and the effect of the mix design (paste fluidity (PF) and paste-to-aggregate ratio (P/A)) on the properties of porous mortar was investigated through a combined experimental, statistical and response surface method (RSM). By including variations in both P/A (0.16-0.26) and PF (160-200 mm), the method was utilized to develop ANOVA models and construct response surface and contour lines. The experimental results revealed that the compressive strength of the porous mortar increased by 62.3% to a value of 34.1 MPa while the PF increased to 190 mm from 160 mm at a P/A of 0.20, and the water permeability coefficient was 7.2 mm/s under the same conditions. In addition, the ANOVA analysis of the measured properties revealed a strong interactive effect of the paste-to-aggregate ratio and paste fluidity on the porous mortar properties, and the developed relationship models between the variables and responses were accurate. A porous mortar with a compressive strength over 30 MPa and a permeability coefficient over 7 mm/s could be conveniently designed by RSM. Additionally, the compressive strength of the porous concrete reached more than 40 MPa at a P/A of 0.26.

Multi-objective shape optimization of siphon outlet in pumping station considering two-phase flow

The siphon outlet is widely used in pumping stations due to its reliable and convenient cut-off performance. Long siphoning time or high hydraulic loss caused by the inappropriate design of the siphon outlet can significantly affect the safety of stations. The air compressibility volume-of-fluid (VOF) method is conducted to simulate the two-phase flow in the siphoning formation process at the design points selected by the optimal Latin hypercube design (OLHD), the results of which show good agreement with the experimental data. In this work, the siphoning time and hydraulic loss coefficient are selected as the objective functions, and a multi-objective shape optimization strategy is proposed for the siphon outlet in conjunction with the response surface method (RSM). This optimization strategy can not only reconcile conflicting objective functions but also obtain the effect and interaction of design variables. Sensitivity analysis on the constructed response surface models indicates that among three design variables, the aspect ratio has the greatest effect on the objective functions, the descending angle has the second greatest effect, and the ascending angle has almost no effect. Compared with the original design, the hydraulic loss coefficient and siphoning time of the optimized design are reduced by 2.95% and 26.76%, respectively. A higher vorticity magnitude and more uniform outflow are created in the optimized design, which results in the improvement of hydraulic performance.

Degradation of Dyes in Real Textile Industry Wastewater Samples by Fenton Process

This research proposes a solution to the problem of industrial safety and the improvement of environmental processes in the textile industry through the degradation of dyes from its processes using the Fenton reaction. This advanced oxidation technology makes it possible to reduce the possible environmental impacts caused by the organic matter generated in industrial activity. Sampling was conducted under real operating conditions in the homogenization tank of the Industrias Printex SAS wastewater treatment plant. Advanced oxidation was carried out applying the Fenton process using iron from ferrous sulfate heptahydrate as a catalyst and hydrogen peroxide at different concentrations in a 6-post flocculator. Among the results obtained, an optimal dose of 571 ppm of iron and 38 ppm of hydrogen peroxide was found through statistical analysis with the STATGRAPHICS program using the 2k factorial design and constructing response surfaces. A comparative study between the Fenton treatments, treatment with hydrogen peroxide, and treatment with ferrous sulfate heptahydrate showed the Fenton reaction at neutral pH, attributed to the presence of some organic acids such as citric acid, used as a chelating agent (Fenton modified). The proposed treatment was compared with the one that uses chlorine, applying it in three (3) different tanks through a multifactorial ANOVA with the data collected when scaling the treatment, finding that the proposed Fenton treatment is more efficient. This research was innovative because it demonstrated the feasibility of scaling up the Fenton process to neutral pH in a textile wastewater treatment plant, reducing operating costs and minimizing environmental impact.

Design and Development of Oral Mucoadhesive Drug Delivery System Based onNatural Polymer

This research paper explains the isolation of gum from the seeds of Samanea saman. Mucoadhesive tablets of Valsartan were formulated using novel gum of Samanea saman as a mucoadhesive polymer and Instamodel 41 as a release retardant. The formulation parameters like the concentration of Samanea saman gum and Instamodel 41 were optimized by using design expert software by constructing response surface graph, contour, and desirability graph. A relationship between variables was developed by constructing a polynomial equation using a quadratic and linear model. The optimized tablet formulation shows mucoadhesive strength 4635.65 Dynes/cm2 and Ex vivo Residence Time 382 min and complete drug release within 12 hours. In the ANOVA model F value, 292.58 for Mucoadhesive strength of tablet and 19.59 for t100% implies that the model is significant. Korsmeyer-Peppas model, suggests anomalous transport of drug release. Stability study suggests that optimized formulation is stable at the accelerated condition of temperature and humidity.

Efficient approach for calibration of load and resistance factors in the limit state design of a breakwater foundation

This study proposes a facile procedure to overcome extensive computational burdens in Monte Carlo simulation (MCS)-based load and resistance factors (LRFs) calibration. Accordingly, a reliability analysis (RA) was conducted on a surrogate set of the constructed response surface functions (RSFs) rather than direct application to the actual implicit problems. Owing to the simplicity of the RA approach, the LRFs were then calibrated using an optimization framework. An adaptive boundaries algorithm was proposed to effectively reduce the number of iterations in the optimization. To elucidate the proposed procedure, four examples: two on slopes and two on foundation stability of breakwaters under earthquake loading were investigated. The results revealed that the surrogate RSFs set that was constructed for numerous failure surfaces not only accurately evaluated the system RA of the actual problems but also allowed for a relatively easier calibration of the LRFs within the optimization framework. In addition, it was found that in the calibration of the LRFs, the RSFs need to be reconstructed to properly account for the variation in the sampling points. The successful convergence of the proposed optimization model took only tens of minutes instead of dozens of days required using the basic. This validates the efficiency and accuracy of the proposed procedure.

A novel response surface method for structural reliability

The response surface method is a common method to solve structural reliability problems. The core principle of this method is the approximation of the actual limit state function using the response surface function for subsequent analytical calculations. The existing response surface method for structural reliability has poor approximation ability and waste of the actual limit state function of the experimental points. These problems lead to low computational efficiency and inability to satisfy high-precision engineering requirements. This paper proposes a novel response surface method for structural reliability. The efficiency and accuracy are improved by the new experimental point selection strategy of the proposed method. This method has the following obvious advantages: the experimental point is close to the actual limit state function, the actual number of calculations is reduced, and the effect of the constructed response surface function approximation is improved. In addition, the single response surface function form is not used in the proposed method to improve the iterative efficiency. Compared with other response surface methods for structural reliability, three calculation examples prove the accuracy and efficiency of the proposed method.

Формирование адсорбционных свойств углеродных наноструктурированных материалов термохимической активации шлам-лигнина

Pyrolysis is an effective way to process waste of the pulp and paper industry, in particular, sludge-lignin, which makes it possible to obtain a commercial product – a carbon adsorbent. The method of thermochemical activation using sodium and potassium hydroxides is now widely used in pyrolysis of wood waste processing. This method enables the production of carbon nanostructured materials with high adsorption properties, especially when adsorbed from the liquid phase. The paper studies the influence of conditions for the synthesis of carbon adsorbents of sludge-lignin on their adsorption properties using sodium hydroxide as an activating agent. Sludge-lignin was obtained under laboratory conditions by treating lignin-containing wastewater with aluminum oxychloride coagulant. We applied the method of the planned experiment: a rotatable central composite design of the second order for three factors. We studied the influence of the main factors determining the adsorption properties of coals, namely, temperature, pyrolysis duration and sodium hydroxide dosage, on the values of output parameters characterizing the adsorption efficiency from the liquid phase, i.e. the iodine number and the adsorption capacity of methylene blue removal. We obtained experimental data, which were used to construct response surfaces illustrating the influence of the experimental factors on the output parameters. The positive effect of pyrolysis temperature and alkali dosage on the adsorption properties of the synthesized coals was found. The following results were obtained: the adsorption activity for iodine – 300 %, for methylene blue – 1000 mg/g; indicating a developed micro- and mesoporous surface and the possibility of using these compounds for adsorption of both gases and vapors, and organic substances from solutions. Therefore, samples of activated carbons synthesized from sludge-lignin were tested as lignin adsorbents of lignin-containing wastewater. The obtained dependences correlate well with the data describing the influence of pyrolysis parameters on the coal adsorption capacity of methylene blue removal. The high efficiency of adsorbents of sludge-lignin in the removal of lignin from solutions was shown. The value of the specific adsorption was about 1500 mg/g.

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.

Evaluation of 3-D Computational Model of Oscillating Water Column Converter with Constructal Design with Three Degrees of Freedom and Limited Chimney Height

Theoretically, ocean waves contain enough mechanical energy to supply the entire world’s demand and, as of late, are seen as a promising source of renewable energy. To this end, several different technologies of Wave Energy Converters (WEC) have been developed such as Oscillating Water Column (OWC) devices. OWCs are characterized by a chamber in which water oscillates inside and out in a movement similar to that of a piston. This movement directs air to a chimney where a turbine is attached to convert mechanical energy. The analysis conducted was based on the Constructive Design Method, in which a numerical study was carried out to obtain the geometric configuration that maximized the conversion of wave energy into mechanical energy. Three degrees of freedom were used: the ratio of height to length of the hydropneumatic chamber (H1/L), the ratio of the height of the chimney to its diameter (H2/d) and the ratio of the width of the hydropneumatic chamber to the width of the wave tank (W/Z). A Design of Experiments (DoE) technique coupled with Central Composite Design (CCD) allowed the simulation of different combinations of degrees of freedom. This allowed the construction of Response Surfaces and correlations for the efficiency of the system depending on the degrees of freedom (width and height of the chamber), as well as the optimization of the system based on the Response Surfaces.

Uncertainty analysis in mechanism reduction via active subspace and transition state analyses

A systematic approach is formulated for the uncertainty analysis of kinetic parameters on combustion characteristics during skeletal reduction. The active subspace method together with sensitivity analysis is first employed to identify extreme low-dimensional active subspace of input parameter space and to facilitate the construction of response surfaces with small size of samples. An intermediate transition state during reduction is then defined such that the uncertainty change arising from uncertainty parameter truncation and reaction coupling during reduction can be decoupled and quantified. The approach is demonstrated in the reduction of a 55-species, 290-reaction dimethyl ether (DME) mechanism, with the rate constants characterized by independent lognormal distribution. Three representative skeletal mechanisms are identified for the uncertainty analysis, with each of the subsequent reduction yielding significant errors in the single-stage and/or two-stage DME-air auto-ignition process. Results show that sensitivity analysis can reduce the number of kinetic parameters from 290 down to 32, and the active subspace method can further identify a dominant active direction within this 32-dimensional subspace, which greatly facilitates the polynomial fitting for constructing the response surface of the ignition delay times. The uncertainty analysis with the polynomial chaos expansion method shows that the reduction from DME42 with 42 species to DME40 with 40 species has influential effect on the high-temperature reaction pathway; while the reduction from DME55 to DME42 and from DME40 to DME30 mainly affects the low-temperature pathway. In addition, the uncertainty change associated with parameter truncation is shown to be proportional to the change in the most active direction, which could further accelerate uncertainty analysis.

Utilization of response surfaces in the optimization of roll-pass design in hot-rolling

The hot-rolling process is a very intense energy-consuming process, and deformation energy is one of the major cost items. The deformation energy consumed in the hot-rolling process is highly related to the design of the roll-pass sequence. In this study, the response surface methodology has been utilized to optimize minor geometric parameters – namely, radii and angle – in a box-pass design. Set values of the independent variables of the constructed response surface have been determined by central composite design. Simulation experiments based on the finite-element method have been carried out to estimate deformation energies. The methodology used in the simulations has been verified by modeling an industrial production process and comparing the simulation results with the industrial data. Optimization has been verified by applying the optimized radius and angle values to a roll-pass sequence with five stages. A decrease in deformation energy by 7.44% has been established by optimization with respect to conventional roll-pass design.

Efficient reliability-based robust design optimization of structures under extreme wind in dual response surface framework

This paper deals with an efficient reliability-based robust design optimization (RBRDO) of structures under extreme wind excitation. To solve such problems in the direct Monte Carlo simulation (MCS) framework, extensive computational time is required. To circumvent this, a new CDF-based RBRDO approach is proposed using the dual response surface method (RSM) framework. In the proposed approach, once the response surfaces are obtained by the dual RSM, the direct MCS can be fully avoided during optimization. Thereby, the approach evades several repetitive executions of finite element analyses code inside the optimization loop. Generally, RSM uses least squares method (LSM) which is reported to be a major source of error in few recent studies. Thus, the proposed approach utilizes the adaptive nature of moving least squares method (MLSM) for construction of response surfaces. The RBRDO is performed by using a two-criterion equivalent optimization problem, where the mean value of the cost of a structure and its standard deviation are optimized—ensuring constraint feasibility under parameter uncertainty. The dynamic response of structures necessary to define constraint functions is obtained using a random wind field model, which considers the effect of coherence and wind directionality. Two illustrative examples are presented to demonstrate the efficiency of the proposed RBRDO approach. When benchmarked through direct MCS results, the proposed MLSM-based RBRDO approach yields more accurate and robust solutions compared with that of the conventional LSM-based approach.

Constructing response surface designs with orthogonal quadratic effects using cyclic generators

The central composite designs (CCDs [1]) and small composite designs (SCDs [2,3]) are designs for sequential experimentation for response surface optimization. The CCDs for fitting the second-order response surface require a 2-level factorial or a resolution V fraction at the first stage (screening stage). The SCDs developed for fitting the same model require many fewer runs at the first stage as they only require a resolution III* fraction. This paper introduces an algorithm which can augment a 2-level first-order design with additional 3-level runs to form a second-order design. This algorithm does not require the 2-level first-order design in stage I to be a resolution V or resolution III* fraction. These augmented runs are made up of circulant matrices. Since CCDs and SCDs are special cases of the designs constructed this way, we call the new designs generalized composite designs or GCDs. Like CCDs and SCDs, GCDs have orthogonal quadratic effects. GCDs can often be found with numbers of runs between those of SCDs and CCDs. This is useful because SCDs often have poorly estimated parameters and CCDs often require substantially more runs than required to fit a full quadratic model.