Dual Response Surface Research Articles

A Mathematical Model for Control and Optimization of Industrial Rotary Alumina Kiln Process

Temperature is a crucial factor for clinker quality in the Industrial Rotary Alumina Kiln Process(IRAKP). However, the characteristic of the high temperature, complex kinetics, multivariable, non-linearreaction kinetics, long-time delayed reaction and various raw materials make it difficult to accurately controlthe temperature in IRAKP through an existing control technology. This paper proposes a dual-responsesurface-based process control (DRSPC) system for the IRAKP in a novel manner. In the DRSPC, instead ofthe more precise and complicated nonlinear equations, the dual response surface models are fitted to describethe reaction kinetics in the IRAKP and track their standard deviations for stable operation purpose. Because asimultaneous consideration of multiple control targets could address the problem of unstable operation inkilns; the objectives of the DRSPC study are designed as optimizing product quality, minimizing energyconsumption and temperature fluctuations. Therefore, the proposed DRSPC goals are to achieve a uniformquality clinker, a high fuel efficiency, and a long refractory life. A weight optimization approach is used tohandle these multiple objective functions. The proposed DRSPC can estimate the working conditions of a kilnand predict some optimal manipulated variables to the control system in each control time interval forimproving the efficiency of IRAKP. The DRSPC is applied to a real IRAKP for demonstrating itsapplicability and advantages.

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.

Wind fragility analysis of RC chimney with temperature effects by dual response surface method

Wind fragility analysis (WFA) of concrete chimney is often executed disregarding temperature effects. But combined wind and temperature effect is the most critical limit state to define the safety of a chimney. Hence, in this study, WFA of a 70 m tall RC chimney for combined wind and temperature effects is explored. The wind force time-history is generated by spectral representation method. The safety of chimney is assessed considering limit states of stress failure in concrete and steel. A moving-least-squares method based dual response surface method (DRSM) procedure is proposed in WFA to alleviate huge computational time requirement by the conventional direct Monte Carlo simulation (MCS) approach. The DRSM captures the record-to-record variation of wind force time-histories and uncertainty in system parameters. The proposed DRSM approach yields fragility curves which are in close conformity with the most accurate direct MCS approach within substantially less computational time. In this regard, the error by the single-level RSM and least-squares method based DRSM can be easily noted. The WFA results indicate that over temperature difference of 150°C, the temperature stress is so pronounced that the probability of failure is very high even at 30 m/s wind speed. However, below 100°C, wind governs the design.

Robust design of offshore jacket platform structure under random wave in dual response surface framework

This paper presents robust design optimisation (RDO) of offshore jacket platforms under random wave force. It is well-established that the direct Monte Carlo Simulation (MCS) is the most accurate way to deal with RDO under uncertainty. However, such approach requires extensive computational time for real complex structures. In the present study, a new cumulative distribution function (CDF)-based RDO formulation is proposed in the framework of dual response surface method (RSM) with due consideration to record-to-record variation of random wave force. The proposed approach avoids direct MCS in RDO, thereby evading several repetitive nonlinear dynamic analyses inside the optimisation loop. As the conventional least-squares method-based RSM may be erroneous in response approximation, the adaptive moving least-squares method is adopted in the present study to construct the response surfaces. The RDO is posed as a two-criterion equivalent optimisation problem, where the expected value of objective function and its standard deviation are optimised, satisfying constraint feasibility criteria under uncertainty. Two illustrative examples are presented to demonstrate the effectiveness of the proposed RDO approach. The results show that the proposed approach yields more accurate and robust solutions than the conventional least-squares method-based RDO approach when compared with the most accurate direct MCS-based RDO results.

Fast Dual-Stimuli-Responsive Dynamic Surface Wrinkles with High Bistability for Smart Windows and Rewritable Optical Displays

The dynamic dual-stimuli-responsive surface wrinkles on a bilayer film with high bistability are unattainable and attractive for the applications of smart windows and optical displays. Here, we report a new strategy in developing moisture and temperature dual-responsive surface wrinkles on the polyvinyl alcohol/polydimethylsiloxane (PVA/PDMS) bilayer film by rationally designing the modulus changes of the PVA skin layer upon moisture and temperature. By optimizing the thickness of the PVA layer to 4.5 μm, the as-prepared surface wrinkles show long-awaited properties, such as fast response time, excellent reversibility without degradation of optical contrast, and high light transmittance modulation, which greatly outperforms the reported surface wrinkles. Moreover, the surface wrinkles on the bilayer film remain highly bistable without additional energy consumption for more than five months in ambient room conditions both in the opaque and transparent states. These promising dual-stimuli-responsive surface wrinkles on bilayer films hold great promises for various applications triggered by moisture and temperature, such as smart windows and rewritable optical displays.

High Breakdown Estimator for Dual Response Optimization in the Presence of Outliers

Nowadays, dual response surface approach is used extensively, and it is known as one of the powerful tools for robust design. General assumptions are the data is normally distributed, and there is no outlier in the data set. The traditional procedures for robust design is to establish the process location and process scale models of the response variable based on sample mean and sample variance, respectively. Meanwhile, the ordinary least squares (OLS) method is often used to estimate the parameters of the regression response location and scale models. Nevertheless, many statistics practitioners are unaware that these existing procedures are easily influenced by outliers, and hence resulted in less accurate estimated mean response obtained through non-resistant method. As an alternative, the use of MM-location, MM-scale estimator, and MM regression estimator is proposed, in order to overcome the shortcomings of the existing procedures. This study employs a new penalty function optimization scheme to determine the optimum factor settings for robust design variables. The effectiveness of our proposed methods is confirmed by well-known example and Monte Carlo simulations.

Comparative Study of Metamodeling and Sampling Design for Expensive and Semi-Expensive Simulation Models Under Uncertainty

In spite of the wide improvements in computer simulation packages, many complex simulation models, particularly under uncertainty, may be inefficient to run in terms of time, computation, and resources. To address such a challenge, integrating metamodels and robust design optimization has been applied. In the current paper, a systematic comparative study is implemented to evaluate the performance of three common metamodels, namely polynomial regression, kriging, and radial basis function. The required experiments are designed by different space-filling methods including the orthogonal array design and three forms of Latin hypercube sampling such as randomized, maximin, and correlation approaches. Although, the impact of sample size on the performance of metamodels in robust optimization results are investigated. All methods are analyzed using five two-dimensional test problems and one engineering problem while all of them are considered in two forms that are expensive (with a small sample size) and semi-expensive (with a large sample size). Uncertainty is assumed in all problems as a source of variability, so all test problems are conducted in the format of robust optimization in the class of dual response surface in order to estimate robust Pareto frontier. The performances of methods are studied in two terms of accuracy and robustness. Finally, the results of comparison, an applicable guideline is provided to aid the practitioners in selecting the appropriate combination of metamodels and sampling design methods for investigating set of robust optimal points (estimated Pareto frontier) in simulation–optimization problems under uncertainty.

Comparative study of metamodeling and sampling design for expensive and semi-expensive simulation models under uncertainty

In spite of the wide improvements in computer simulation packages, many complex simulation models, particularly under uncertainty, may be inefficient to run in terms of time, computation, and resources. To address such a challenge, integrating metamodels and robust design optimization has been applied. In the current paper, a systematic comparative study is implemented to evaluate the performance of three common metamodels, namely polynomial regression, kriging, and radial basis function. The required experiments are designed by different space-filling methods including the orthogonal array design and three forms of Latin hypercube sampling such as randomized, maximin, and correlation approaches. Although, the impact of sample size on the performance of metamodels in robust optimization results are investigated. All methods are analyzed using five two-dimensional test problems and one engineering problem while all of them are considered in two forms that are expensive (with a small sample size) and semi-expensive (with a large sample size). Uncertainty is assumed in all problems as a source of variability, so all test problems are conducted in the format of robust optimization in the class of dual response surface in order to estimate robust Pareto frontier. The performances of methods are studied in two terms of accuracy and robustness. Finally, the results of comparison, an applicable guideline is provided to aid the practitioners in selecting the appropriate combination of metamodels and sampling design methods for investigating set of robust optimal points (estimated Pareto frontier) in simulation–optimization problems under uncertainty.

Robust Die Compensation in Sheet Metal Design through the Integration of Dual Response Surface and Shape Function Optimization

In sheet metal forming, springback represents a major drawback increasing die set-up problems, especially for ultra-high strength steels. Finite Element Analysis is a well-established method to simulate the process during design, and multicriteria optimizations, for example, via surrogate models, are investigated in order to develop integrated design. Since to take into account also springback compensation die design may involve a large number of geometric variables, this paper presents a robust design formulation, based on the adoption of the shape function optimization, to describe springback in terms of weights directly associated to global shape variations of the die shape. Doing so, multicriteria optimization, which involves also die compensation, can be set up in a more intuitive approach, as requested in the preliminary steps of die design. After the introduction of the industrial problem, the mathematical formulation of the shape function optimization is presented together with its novel extension to Robust Design, which is based on the Dual Response Surface. Through a test case derived from the head part of a B-pillar, stamped from a Dual Phase sheet 1.5 mm thick, this novel extension investigates the effect of 6% variation from nominal values of initial yield stress and thickness. Results demonstrate the feasibility of the procedure, underlying that an optimal compensation may not be optimal in terms of process robustness.

Collision performance and multi-objective robust optimization of a combined multi-cell thin-walled structure for high speed train

Based on the Simplified Super Folding Element (SSFE) theory, the theoretical prediction of average crushing force (Favg) for multi-cell thin-walled structures is inferred and a combined five-cell thin-walled structure used in high speed train is proposed and investigated in this paper. The finite element model of the proposed structure and the theoretical prediction are validated by a full scaled impact experiment. Then, parametric studies are performed to evaluate the effects of design variables, including the thickness (t) and the side length (a) of the orthohexagonal cell, on collision responses based on the validated FE model and theoretical prediction. It is found that both specific energy absorption (SEA) and the maximum initial force (Fmax) are obviously affected by the design parameters. Particularly, the effect of parameter t on crushing performance is greater than that of parameter a. In further, to minimize the Fmax and maximum SEA under the constraint of Favg, a multi-objective robust optimization methodology is adopted. The Optimal Latin Hypercube Design (OLHD) and orthogonal design are combined to perform Design of Experiment (DoE) and dual response surface models (DRSM) are constructed for the optimization. The optimal results of deterministic optimization indicate that the Fmax decreases by 11.07% compared with the original design while the robust optimization optimal result of Fmax decreases by 10.01%. However, the robust optimization optimal design is more acceptable considering the robustness, which means the robust optimization is more attractive than deterministic optimization in practical engineering application.

Voltammetric method for simultaneous determination of ascorbic acid, paracetamol and guaifenesin using a sequential experimentation strategy

Cold is a leading cause of school and work absenteeism. Most cold over-the-counter medicines (OTC) contain paracetamol (PA), guaifenesin (GU) and other active ingredients. Ascorbic acid (AS) in pharmaceutical preparations is designed for preventing and treating respiratory viral infections. Thus, we report a robust voltammetric method for simultaneous determination of AS, PA and GU in their effervescent dosage form. The advantages of nanotechnology and chemometrics were combined to enhance the performance of electroanalysis. Fractional factorial design (FrFD) and dual response surface method (DRSM) were sequentially conducted. The method was validated in agreement with ICH guidelines; it showed accuracy over the concentration range of 11.3–108.9, 14.6–140.3, 4.6–43.9 μg ml−1 for AS, PA and GU, respectively. Based on findings, a robust and not time-consuming procedure was applied.

Support vector regression based metamodeling for seismic reliability analysis of structures

• Improved seismic reliability analysis by support vector regression based metamodel. • A simple effective algorithm to minimize the mean square error to obtain the model parameters. • Generating a suite of metamodels to implicitly takes into account the record to record variation. • Simulation by random metamodel selection with no additional computational burden and distribution assumption. • Numerical elucidation of the effectiveness of the proposed approach for seismic reliability analysis. The present study deals with support vector regression-based metamodeling approach for efficient seismic reliability analysis of structure. Various metamodeling approaches e.g. response surface method, Kriging interpolation, artificial neural network, etc. are usually adopted to overcome computational challenge of simulation based seismic reliability analysis. However, the approximation capability of such empirical risk minimization principal-based metamodeling approach is largely affected by number of training samples. The support vector regression based on the principle of structural risk minimization has revealed improved response approximation ability using small sample learning. The approach is explored here for improved estimate of seismic reliability of structure in the framework of Monte Carlo Simulation technique. The parameters necessary to construct the metamodel are obtained by a simple effective search algorithm by solving an optimization sub-problem to minimize the mean square error obtained by cross-validation method. The simulation technique is readily applied by random selection of metamodel to implicitly consider record to record variations of earthquake. Without additional computational burden, the approach avoids a prior distribution assumption about approximated structural response unlike commonly used dual response surface method. The effectiveness of the proposed approach compared to the usual polynomial response surface and neural network based metamodels is numerically demonstrated.

Developing a Statistical Model to Improve Drinking Water Quality for Water Distribution System by Minimizing Heavy Metal Releases

This paper proposes a novel statistical approach for blending source waters in a public water distribution system to improve water quality (WQ) by minimizing the release of heavy metals (HMR). Normally, introducing a new source changes the original balanced environment and causes adverse effects on the WQ in a water distribution system. One harmful consequence of blending source water is the release of heavy metals, including lead, copper and iron. Most HMR studies focus on the forecasting of unfavorable effects using precise and complicated nonlinear equations. This paper uses a statistical multiple objectives optimization, namely Multiple Source Waters Blending Optimization (MSWBO), to find optimal blending ratios of source waters for minimizing three HMRs in a water supply system. In this paper, three response surface equations are applied to describe the reaction kinetics of HMR, and three dual response surface equations are used to track the standard deviations of the three response surface equations. A weighted sum method is performed for the multi-objective optimization problem to minimize three HMRs simultaneously. Finally, the experimental data of a pilot distribution system is used in the proposed statistical approach to demonstrate the model’s applicability, computational efficiency, and robustness.

Kriging-Assisted Robust Black-Box Simulation Optimization in Direct Speed Control of DC Motor Under Uncertainty

In spite of the wide improvement in computer simulation packages, analyzing, and optimizing the simulation model, particularly under uncertainty can still be computationally expensive and time-consuming. This paper aims to tackle these features by proposing a comprehensive methodology applied to black-box stochastic simulation models under uncertainty. For this purpose, the common surrogate model as Kriging metamodel is served to fit the simulation input-output data produced by Latin hypercube sampling experimental design. Taguchi terminology of robust design enables the optimization methods to control uncertainty and uncontrollable environmental factors. So as to formulate robust counterpart optimization, three different models in the class of dual-response surface are integrated with metamodel and robust design. Leave-one-out cross-validation is applied to validate the Kriging metamodel. Finally, a numerical case study as a direct speed control of dc motor under uncertainty is served to demonstrate the applicability of the proposed method in real engineering problems. This simplified and practical mechatronics case illustrates how the proposed procedure can be expanded for analyzing and optimizing the real complex systems.

Ensemble modeling based on 0–1 programming in micro-manufacturing process

Abstract As to micro-manufacturing processes, constructing accurate models plays an important role in the continuous quality improvement. This paper proposes an ensemble modeling technique based on 0–1 programming, in which the redundant models will be eliminated from a set of candidates and then the selected models are combined to construct the final ensemble model. As an alternative way of using a single modeling technique in dual response surface methodology, it would be beneficial to adopt multiple techniques to construct an ensemble model. A laser beam micro-drilling process and a numerical example are used to demonstrate the effectiveness of the proposed modeling technique. The comparison results illustrate that the technique can not only improve the robustness of the model predictions, but also provide a reliable scheme for optimizing the machining parameters.

Uncertainty analysis and multi-objective billet robust optimization for transitional region of multi-rib component under isothermal local loading forming

Isothermal local loading forming is promising to manufacture the large-scale Ti-alloy multi-rib component, but the folding, die underfilling, and strain concentration (SC) are undesired characteristics existing in transitional region due to the reciprocating material transfer between loading region and unloading region. The current research showed that the optimized billet could eliminate or improve these defects. However, it may also lead to unacceptable results due to the variation of the uncertainty factors, such as the manufacturing tolerance of the billet, the fluctuation of the stroke length, friction factor, and forming temperature. Aiming at this issue, an uncertainty analysis and the multi-objective robust optimization of the billet are performed based on 3D finite element simulation and dual-response surface model. Firstly, a valid FE model of the eigenstructure is established to represent the transitional region. Then, the significance analysis of the uncertainty factors is carried out and the significant uncertainty factors are obtained. Subsequently, a multi-objective robust optimization model concerning the mean and standard deviation of the die underfilling rate and average strain of SC zone under the condition of avoiding folding is established. Finally, the Pareto-optimal solutions are obtained by NSGA-II and the minimum distance selection method is employed to acquire the satisfied solution. The comparison results between the robust optimization and deterministic optimization showed that not only the folding is effectively avoided under the uncertainty factors, but also more robust die filling and deformation homogeneity can be achieved.

A Stochastic Dual Response Surface Method for Reliability Analysis Considering the Spatial Variability

To solve spectral stochastic finite element problems, the collocation-based spectral stochastic finite element method (SSFEM) was developed, and the Stochastic Response Surface Method (SRSM) was used to represent uncertainty propagation. Therefore, the accuracy of SRSM is important for obtaining more accurate probabilistic results. The weighted SRSM was developed to improve the global accuracy of SRSM, but it is not suitable for random field problems because weights might distort the response surface. In this study, a new Stochastic Dual-response Surface Method (SDRSM) was developed to improve the accuracy of SRSM. The SDRSM combines the conventional SRSM and target-weighted SRSM (TWSRSM), which is assigned a weight for the numerical result corresponding to the collocation point. Then, the proposed method was extended to deal with problems involving random fields. For comparison with the conventional methods (SRSM and WSRSM), two numerical examples involving random fields were carried out. Compared with Monte Carlo simulation results, SDRSM shows the smallest error without the addition of the collocation points. In addition, the mean absolute errors for equally spaced probability intervals were compared, and their mean and standard deviation of SDRSM were relatively smaller than that of other methods.

Robust optimization of the billet for isothermal local loading transitional region of a Ti-alloy rib-web component based on dual-response surface method

Billet optimization can greatly improve the forming quality of the transitional region in the isothermal local loading forming (ILLF) of large-scale Ti-alloy rib-web components. However, the final quality of the transitional region may be deteriorated by uncontrollable factors, such as the manufacturing tolerance of the preforming billet, fluctuation of the stroke length, and friction factor. Thus, a dual-response surface method (RSM)-based robust optimization of the billet was proposed to address the uncontrollable factors in transitional region of the ILLF. Given that the die underfilling and folding defect are two key factors that influence the forming quality of the transitional region, minimizing the mean and standard deviation of the die underfilling rate and avoiding folding defect were defined as the objective function and constraint condition in robust optimization. Then, the cross array design was constructed, a dual-RSM model was established for the mean and standard deviation of the die underfilling rate by considering the size parameters of the billet and uncontrollable factors. Subsequently, an optimum solution was derived to achieve the robust optimization of the billet. A case study on robust optimization was conducted. Good results were attained for improving the die filling and avoiding folding defect, suggesting that the robust optimization of the billet in the transitional region of the ILLF was efficient and reliable.

Dual-response optimization using a patient rule induction method

ABSTRACTA dual-response surface optimization approach assumes that response surface models of the mean and standard deviation of a response are fitted well to experimental data. However, it is often difficult to satisfy this assumption when dealing with a large volume of operational data from a manufacturing line. The proposed method attempts to optimize the mean and standard deviation of the response without building response surface models. Instead, it searches for an optimal setting of input variables directly from operational data by using a patient rule induction method. The proposed approach is illustrated with a step-by-step procedure for an example case.

Bacterial adaptability of enzyme and pH dual-responsive surface for infection resistance.

A major challenge in antibacterial surface preparation is the elaborated implementation of controlled antibacterial agent delivery on demand, typically at appropriate concentrations and sites, which can be an efficient way to lower bacteria resistance and improve therapy effectiveness. Herein, we present a bacterial hyaluronidase (HAase) and pH dual-responsive antimicrobial surface, which is constructed by sequential layer-by-layer (LbL) assembly of NHS-PEG-NHS (PEG-bis(succinimidyl succinate)) and PEI (polyethylenimine), immobilization of antibiotic vancomycin (Van) by an acid-labile β-carboxylic linker and electrostatic adsorption of HA. The HA upper layer can endow the multilayer surface with excellent biocompatibility under normal physiological conditions. Once bacteria invade, the secreted HAase specifically enzymolyzes the HA layer, and then the bound Van will be released in response to the bacteria-triggered local acidification to eliminate bacteria. Our work provides a versatile strategy in the design of a smart antibacterial surface with controlled antibacterial agent delivery, implying great potential for application in infection-resistant medical devices.