Relevant bibliographies by topics / Multivariate Response Surface

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Multivariate Response Surface'

Author: Grafiati
Published: 8 September 2023

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Journal articles on the topic "Multivariate Response Surface"

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Moslemi, Amir, and Mirmehdi Seyyed-Esfahani. "A novel robust multivariate regression approach to optimize multiple surfaces." RAIRO - Operations Research 52, no. 4-5 (October 2018): 1233–43. http://dx.doi.org/10.1051/ro/2018016.

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Response surface methodology involves relationships between different variables, specifically experimental inputs as controllable factors, and a response or responses by incorporating uncontrollable factors named nuisance. In order to optimize these response surfaces, we should have accurate response models. A common approach to estimate a response surface is the ordinary least squares (OLS) method. Since OLS is very sensitive to outliers, some robust approaches have been discussed in the literature. Most problems face with more than one response which are mostly correlated, that are called multi-response problem. This paper presents a new approach which takes the benefits of robust multivariate regression to cope with the mentioned difficulties. After estimating accurate response surfaces, optimization phase should be applied in order to have proper combination of variables and optimum solutions. Global criterion method of multi-objective optimization has also been used to reach a compromise solution which improves all response variables simultaneously. Finally, the proposed approach is described analytically by a numerical example.
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Bratchell, N. "Multivariate response surface modelling by principal components analysis." Journal of Chemometrics 3, no. 4 (September 1989): 579–88. http://dx.doi.org/10.1002/cem.1180030406.

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Moslemi, Amir, and Mirmehdi Seyyed-Esfahani. "Robust optimization of multistage process: response surface and multi-response optimization approaches." International Journal of Nonlinear Sciences and Numerical Simulation 23, no. 2 (November 26, 2021): 163–75. http://dx.doi.org/10.1515/ijnsns-2017-0003.

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Abstract A multistage system refers to a system contains multiple components or stages which are necessary to finish the final product or service. To analyze these problems, the first step is model building and the other is optimization. Response surfaces are used to model multistage problem as an efficient procedure. One regular approach to estimate a response surface using experimental results is the ordinary least squares (OLS) method. OLS method is very sensitive to outliers, so some multivariate robust estimation methods have been discussed in the literature in order to estimate the response surfaces accurately such as multivariate M-estimators. In optimization phase, multi-response optimization methods such as global criterion (GC) method and ε-constraints approaches are different methods to optimize the multi-objective-multistage problems. An example of the multistage problem had been estimated considering multivariate robust approaches, besides applying multi-response optimization approaches. The results show the efficiency of the proposed approaches.
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Kumar, Rupak, and Meega Reji. "Response surface methodology (RSM): An overview to analyze multivariate data." Indian Journal of Microbiology Research 9, no. 4 (January 15, 2023): 241–48. http://dx.doi.org/10.18231/j.ijmr.2022.042.

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In recent years, the fascinating range of Response surface methodology (RSM) applications has captured the interest of many researchers and engineers worldwide. RSM is entirely based on well-known regression principles and variance analysis principles that enable the user to improve, develop and optimize the process or product under study. An overview of the theoretical principles of RSM, the experimental strategy and its tools and components, along with the applications and pros and cons, are described in this paper. Some of the widely used experimental designs of RSM compared in terms of its characteristics and efficiency are included, which helps to point out the importance of design of experiments (DOE) in optimization using RSM. The live demonstrations of a few optimization examples using response surface methodology in different research manuscripts included in this paper also provide a better understanding of the characteristics of RSM in different scenarios.
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Patel, Trina, Donatello Telesca, Saji George, and André E. Nel. "Toxicity profiling of engineered nanomaterials via multivariate dose-response surface modeling." Annals of Applied Statistics 6, no. 4 (December 2012): 1707–29. http://dx.doi.org/10.1214/12-aoas563.

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Flandrois, C., C. Lahet, D. Feldmann, J. M. Gabastou, A. Gonnon, and I. Maire. "Urinary alanine aminopeptidase assay improved as result of multivariate response-surface analysis." Clinical Chemistry 34, no. 5 (May 1, 1988): 954–57. http://dx.doi.org/10.1093/clinchem/34.5.954.

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Abstract Optimization of determination of alanine aminopeptidase in urine by univariate study led to a method involving pretreatment of urine with Sephadex G50. Re-examination of the optimization by multivariate study led us to recommend higher optimal concentrations: 5.8 mmol/L for the substrate and 300 mmol/L for the Tris buffer. Under these new conditions, pretreatment of urine was no longer necessary and the assay could be completely automated.
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Gatley-Montross, Caitlyn M., John A. Finlay, Nick Aldred, Harrison Cassady, Joel F. Destino, Beatriz Orihuela, Michael A. Hickner, et al. "Multivariate analysis of attachment of biofouling organisms in response to material surface characteristics." Biointerphases 12, no. 5 (December 2017): 051003. http://dx.doi.org/10.1116/1.5008988.

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Li, Yingjie, Xiangliang Liu, Biaojun Zhang, Qun Zhao, Ping Ning, and Senlin Tian. "Aquatic photochemistry of sulfamethazine: multivariate effects of main water constituents and mechanisms." Environmental Science: Processes & Impacts 20, no. 3 (2018): 513–22. http://dx.doi.org/10.1039/c7em00548b.

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Ghattas, Badih, and Diane Manzon. "Machine Learning Alternatives to Response Surface Models." Mathematics 11, no. 15 (August 4, 2023): 3406. http://dx.doi.org/10.3390/math11153406.

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In the Design of Experiments, we seek to relate response variables to explanatory factors. Response Surface methodology (RSM) approximates the relation between output variables and a polynomial transform of the explanatory variables using a linear model. Some researchers have tried to adjust other types of models, mainly nonlinear and nonparametric. We present a large panel of Machine Learning approaches that may be good alternatives to the classical RSM approximation. The state of the art of such approaches is given, including classification and regression trees, ensemble methods, support vector machines, neural networks and also direct multi-output approaches. We survey the subject and illustrate the use of ten such approaches using simulations and a real use case. In our simulations, the underlying model is linear in the explanatory factors for one response and nonlinear for the others. We focus on the advantages and disadvantages of the different approaches and show how their hyperparameters may be tuned. Our simulations show that even when the underlying relation between the response and the explanatory variables is linear, the RSM approach is outperformed by the direct neural network multivariate model, for any sample size (<50) and much more for very small samples (15 or 20). When the underlying relation is nonlinear, the RSM approach is outperformed by most of the machine learning approaches for small samples (n ≤ 30).
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Murakami, Kenya, Tatsuya Iizaka, Tomoji Kanno, Tetsuro Matsui, Makoto Shimosawa, and Akihiro Takano. "Improvement of Solar Cells Efficiency by Response Surface Method based on Multivariate Analysis Models." IEEJ Transactions on Electronics, Information and Systems 131, no. 8 (2011): 1424–30. http://dx.doi.org/10.1541/ieejeiss.131.1424.

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Dissertations / Theses on the topic "Multivariate Response Surface"

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Hässig, Fonseca Santiago. "Applications and optimization of response surface methodologies in high-pressure, high-temperature gauges." Thesis, Georgia Institute of Technology, 2012. http://hdl.handle.net/1853/44902.

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High-Pressure, High-Temperature (HPHT) pressure gauges are commonly used in oil wells for pressure transient analysis. Mathematical models are used to relate input perturbation (e.g., flow rate transients) with output responses (e.g., pressure transients), and subsequently, solve an inverse problem that infers reservoir parameters. The indispensable use of pressure data in well testing motivates continued improvement in the accuracy (quality), sampling rate (quantity), and autonomy (lifetime) of pressure gauges. This body of work presents improvements in three areas of high-pressure, high-temperature quartz memory gauge technology: calibration accuracy, multi-tool signal alignment, and tool autonomy estimation. The discussion introduces the response surface methodology used to calibrate gauges, develops accuracy and autonomy estimates based on controlled tests, and where applicable, relies on field gauge drill stem test data to validate accuracy predictions. Specific contributions of this work include: - Application of the unpaired sample t-test, a first in quartz sensor calibration, which resulted in reduction of uncertainty in gauge metrology by a factor of 2.25, and an improvement in absolute and relative tool accuracies of 33% and 56%, accordingly. Greater accuracy yields more reliable data and a more sensitive characterization of well parameters. - Post-processing of measurements from 2+ tools using a dynamic time warp algorithm that mitigates gauge clock drifts. Where manual alignment methods account only for linear shifts, the dynamic algorithm elastically corrects nonlinear misalignments accumulated throughout a job with an accuracy that is limited only by the clock's time resolution. - Empirical modeling of tool autonomy based on gauge selection, battery pack, sampling mode, and average well temperature. A first of its kind, the model distills autonomy into two independent parameters, each a function of the same two orthogonal factors: battery power capacity and gauge current consumption as functions of sampling mode and well temperature -- a premise that, for 3+ gauge and battery models, reduces the design of future autonomy experiments by at least a factor of 1.5.
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Liggett, Rachel Esther. "Multivariate Approaches for Relating Consumer Preference to Sensory Characteristics." The Ohio State University, 2010. http://rave.ohiolink.edu/etdc/view?acc_num=osu1282868174.

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King, Adam C. "The Cressbrook Creek alluvial aquifer system, Southeast Queensland : hydrochemistry and isotopes to determine hydrological processes and response to floods." Thesis, Queensland University of Technology, 2014. https://eprints.qut.edu.au/78443/1/Adam_King_Thesis.pdf.

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This study developed an understanding of hydrological processes within the Cressbrook Creek catchment of the upper Brisbane River, in particular for the alluvial aquifers. Those aquifers within the lower catchment are used for intensive irrigation, and have been impacted by long-term drought followed by flooding. The study utilised water chemistry, isotopic characters and hydraulic measurements to determine factors such as recharge, links between creeks and groundwater, and variations in water quality. The catchment-wide study will enable improved management of the local water resources.
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Moberg, My. "Liquid Chromatography Coupled to Mass Spectrometry : Implementation of Chemometric Optimization and Selected Applications." Doctoral thesis, Uppsala : Acta Universitatis Upsaliensis, 2006. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-7071.

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Rodrigues, Marlon Casagrande. "Estudo da influência dos parâmetros de injeção de combustível no ruído emitido por motores diesel, fazendo uso do planejamento multivariado de experimentos." [s.n.], 2011. http://repositorio.unicamp.br/jspui/handle/REPOSIP/265284.

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Orientador: Roy Edward Bruns
Dissertação (mestrado profissional) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecânica
Made available in DSpace on 2018-08-18T11:44:59Z (GMT). No. of bitstreams: 1 Rodrigues_MarlonCasagrande_M.pdf: 2084739 bytes, checksum: 4206c434cf21dfc145d73ca304a9981b (MD5) Previous issue date: 2011
Resumo: Nos últimos anos a emissão de ruído tem sido decisiva para aceitação de veículos no mercado, não somente devido a legislação, mas também no que diz respeito a satisfação do cliente. Por este motivo as empresas fabricantes de veículos e ou motores de combustão interna tem sido obrigadas a dar uma atenção especial as emissões de ruído para poderem competir com suas concorrentes. Neste trabalho realizou-se estudo da influencia dos parâmetros de injeção de combustível do motor MWM 6.12 TCE no nível de ruído emitido pelo motor Diesel na condição de marcha lenta, por meio da técnica de planejamento multivariado de experimentos. Foram escolhidas duas técnicas de medição indireta de ruído (ruído de combustão e aceleração na saia do bloco) para serem utilizadas como variável resposta do planejamento de experimentos. Para verificação da eficácia dos planejamentos realizou-se ensaios qualitativos e quantitativos de ruído propriamente dito. Foi feito um planejamento fatorial fracionário 28-4 para fazer uma triagem de oito fatores de acordo com seus efeitos nas respostas aceleração na saia do bloco e ruído de combustão. Os fatores com efeitos mais significativos, pressão do rail, ponto de injeção principal, ponto de pré-injeção 2 e debito da pré-injeção 2, foram investigados usando um planejamento composto central e superfícies de respostas foram determinadas para cada uma das respostas. Os resultados mostraram que apenas a variável resposta vibração na saia do bloco apresentou resultados satisfatórios para esta condição especifica do motor tanto nos testes quantitativos como qualitativos (redução de 2 dB e melhora na qualidade sonora respectivamente). Apos verificação da influencia dos parâmetros de injeção no ruído emitido verificou-se também a influencia destas alterações no consumo de combustível e emissões dos gases de escape e foi observado que existem influencias significativas nas emissões dos gases de escape
Abstract: In recent years the noise level has been decisive for acceptance of vehicles on the market, not only because of legislation but also with regard to customer satisfaction. For this reason the manufacturers of vehicles and internal combustion engines have been forced to give special attention to the emission of noise to compete with their competitors. In this work, the influences of fuel injection parameters on the noise level of the MWM 6.12 TCE diesel engine emitted under low idle condition were determined using multivariate statistical design of experiments. Two techniques for the indirect measurement of noise, combustion noise and engine crankcase vibration, were chosen as the response variables for the experimental design. To check design effectiveness both qualitative and quantitative noise measurements were carried out. A 28-4 fractional factorial design was performed to screen eight factors according to their effects on engine crankcase vibration, and combustion noise. The factors with the most significant effects, rail pressure, pre-injection point, main injection point and the pre-injection delivery, were investigated using a central composite design and response surfaces were determined for each response. The results showed that only the engine crankcase vibration showed satisfactory results for this particular engine condition in both the quantitative and qualitative analyses (reduction of 2 dB and an improvement in sound quality, respectively). After verification of the influences of the injection parameters on the noise the influences of these changes on fuel consumption and exhaust emissions were also analyzed. Significant influences were observed on the exhaust gas emissions
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Williamson, Martin Rodney. "Multivariate Optimization of Neutron Detectors Through Modeling." 2010. http://trace.tennessee.edu/utk_graddiss/924.

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Due to the eminent shortage of 3He, there exists a significant need to develop a new (or optimize an existing) neutron detection system which would reduce the dependency on the current 3He-based detectors for Domestic Nuclear Detection Office (DNDO) applications. The purpose of this research is to develop a novel methodology for optimizing candidate neutron detector designs using multivariate statistical analysis of Monte Carlo radiation transport code (MCNPX) models. The developed methodology allows the simultaneous optimization of multiple detector parameters with respect to multiple response parameters which measure the overall performance of a candidate neutron detector. This is achieved by applying three statistical strategies in a sequential manner (namely factorial design experiments, response surface methodology, and constrained multivariate optimization) to results generated from MCNPX calculations. Additionally, for organic scintillators, a methodology incorporating the light yield non-proportionality is developed for inclusion into the simulated pulse height spectra (PHS). A Matlab® program was developed to post-process the MCNPX standard and PTRAC output files to automate the process of generating the PHS thus allowing the inclusion of nonlinear light yield equations (Birks equations) into the simulation of the PHS for organic scintillators. The functionality of the developed methodology is demonstrated on the successful multivariate optimization of three neutron detection systems which utilize varied approaches to satisfying the DNDO criteria for an acceptable alternative neutron detector. The first neutron detection system optimized is a 3He-based radiation portal monitor (RPM) based on a generalized version of a currently deployed system. The second system optimized is a 6Li-loaded polymer composite scintillator in the form of a thin film. The final system optimized is a 10B-based plastic scintillator sandwiched between two standard plastic scintillators. Results from the multivariate optimization analysis include not only the identification of which factors significantly affect detector performance, but also the determination of optimum levels for those factors with simultaneous consideration of multiple detector performance responses. Based on the demonstrated functionality of the developed multivariate optimization methodology, application of the methodology in the development process of new candidate neutron detector designs is warranted.
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Books on the topic "Multivariate Response Surface"

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1951-, Christensen Ronald, ed. Advanced linear modeling: Multivariate, time series, and spatial data; nonparametric regression and response surface maximization. 2nd ed. New York: Springer, 2001.

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Christensen, Ronald. Advanced Linear Modeling: Multivariate, Time Series, and Spatial Data; Nonparametric Regression and Response Surface Maximization. Springer London, Limited, 2013.

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Christensen, Ronald. Advanced Linear Modeling: Multivariate, Time Series, and Spatial Data; Nonparametric Regression and Response Surface Maximization. Springer New York, 2010.

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Lee, Li-Chu. Empirical Bayes estimation of the response function and multivariate regression model. 1989.

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Surrogates: Gaussian Process Modeling, Design, and Optimization for the Applied Sciences. Taylor & Francis Group, 2020.

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Gramacy, Robert B. Surrogates: Gaussian Process Modeling, Design, and Optimization for the Applied Sciences. Taylor & Francis Group, 2020.

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Gramacy, Robert B. Surrogates: Gaussian Process Modeling, Design, and Optimization for the Applied Sciences. Taylor & Francis Group, 2020.

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Gramacy, Robert B. Surrogates. Taylor & Francis Group, 2020.

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Gramacy, Robert B. Surrogates: Gaussian Process Modeling, Design, and Optimization for the Applied Sciences. Taylor & Francis Group, 2020.

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Book chapters on the topic "Multivariate Response Surface"

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Carter, C. W. "Experimental Design, Quantitative Analysis, and the Cartography of Crystal Growth." In Crystallization of Nucleic Acids and Proteins. Oxford University Press, 1999. http://dx.doi.org/10.1093/oso/9780199636792.003.0008.

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This chapter is about practical uses of mathematical models to simplify the task of finding the best conditions under which to crystallize a macromolecule. The models describe a system’s response to changes in the independent variables under experimental control. Such a mathematical description is a surface, whose two-dimensional projections can be plotted, so it is usually called a ‘response surface’. Various methods have been described for navigating an unknown surface. They share important characteristics: experiments performed at different levels of the independent variables are scored quantitatively, and fitted implicitly or explicitly, to some model for system behaviour. Initially, one examines behaviour on a coarse grid, seeking approximate indications for multiple crystal forms and identifying important experimental variables. Later, individual locations on the surface are mapped in greater detail to optimize conditions. Finding ‘winning combinations’ for crystal growth can be approached successively with increasingly well-defined protocols and with greater confidence. Whether it is used explicitly or more intuitively, the idea of a response surface underlies the experimental investigation of all multivariate processes, like crystal growth, where one hopes to find a ‘best’ set of conditions. The optimization process is illustrated schematically in Figure 1. In general, there are three stages to this quantitative approach: (a) Design. One must first induce variation in some desired experimental result by changing the experimental conditions. Experiments are performed according to a plan or design. Decisions must be made concerning the experimental variables and how to sample them. (b) Experiments and scores. Each experiment provides an estimate for how the system behaves at the corresponding point in the experimental space. When these estimates are examined together as a group, patterns often appear. For example, a crystal polymorphism may occur only in restricted regions of the variable space explored by the experiment. (c) Fitting and testing models. Imposing a mathematical model onto such patterns provides a way to predict how the system will behave at points where there were no experiments. The better the predictions, the better the model. Adequate models provide accurate interpolation within the range of experimental variables originally sampled; occasionally a very good model will correctly predict behaviour outside it (1).
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Arnold, Stevan J. "The Selection Surface and Adaptive Landscape for Multiple Traits." In Evolutionary Quantitative Genetics, 58–82. Oxford University PressOxford, 2023. http://dx.doi.org/10.1093/oso/9780192859389.003.0005.

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Abstract Selection is often viewed and analyzed as a single-trait phenomenon or multiple traits are treated as isolated, single traits. This univariate focus is unfortunate because it misses crucial aspects of selection that are only revealed in a multivariate treatment of the problem. Crucial new aspects uncovered in multivariate selection analysis allow us to: (1) distinguish between direct and indirect targets of selection, (2) diagnose the correct shape of the selection surface and hence the shape of the adaptive landscape, (3) estimate the force of directional selection in units that can be used to assess evolutionary responses of trait means to selection, and (4) estimate the force of nonlinear selection in units that can be used to assess immediate effects on genetic variance and covariance, as well as long-term contributions to evolutionary patterns, such as stasis. However, all of these selling points are subject to provisos and limitations. Nevertheless, the case for pursuing multivariate rather than univariate selection analysis is compelling.
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Sharma, Pankaj. "Applications of Statistical Tools for Optimization and Development of Smart Drug Delivery System." In Smart Drug Delivery [Working Title]. IntechOpen, 2021. http://dx.doi.org/10.5772/intechopen.99632.

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In the novel dosage form development, quality is the key criterion in pharmaceutical industry. The quality by design tools used for development of the quality products with tight specification and rigid process. The specifications of statistical tools are essentially based upon critical process parameters (CPPs), critical material attributes (CMAs), and critical quality attributes (CQAs) for the development of quality products. The application of quality by design in pharmaceutical dosage form development is systematic, requiring multivariate experiments employing process analytical technology (PAT) and other experiments to recognize critical quality attributes depend upon risk assessments (RAs). The quality by design is a modern technique to stabilize the quality of pharmaceutical dosage form. The elements of quality by design such as process analytical techniques, risk assessment, and design of experiment support for assurance of the strategy control for every dosage form with a choice of regular monitoring and enhancement for a quality dosage form. This chapter represents the concepts and applications of the most common screening of designs/experiments, comparative experiments, response surface methodology, and regression analysis. The data collected from the dosage form designing during laboratory experiments, provide the substructure for pivotal or pilot scale development. Statistical tools help not only in understanding and identifying CMAs and CPPs in product designing, but also in comprehension of the role and relationship between these in attaining a target quality. Although, the implementation of statistical approaches in the development of dosage form is strongly recommended.
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Conference papers on the topic "Multivariate Response Surface"

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Morelli, Eugene, and Richard DeLoach. "Response surface modeling using multivariate orthogonal functions." In 39th Aerospace Sciences Meeting and Exhibit. Reston, Virigina: American Institute of Aeronautics and Astronautics, 2001. http://dx.doi.org/10.2514/6.2001-168.

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Luchino, Federico, Martin Ordonez, German G. Oggier, and John E. Quaicoe. "MOSFET power loss characterization: Evolving into multivariate response surface." In 2011 IEEE Energy Conversion Congress and Exposition (ECCE). IEEE, 2011. http://dx.doi.org/10.1109/ecce.2011.6064020.

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Galvez, Juan, Martin Ordonez, Samuel Cove, and John Quaicoe. "Nonlinearity in small planar inductors: experimental characterization using multivariate response surface." In 2012 25th IEEE Canadian Conference on Electrical and Computer Engineering (CCECE). IEEE, 2012. http://dx.doi.org/10.1109/ccece.2012.6857451.

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Vaccari, David A. "Multivariate Polynomial Response Surface Analysis - Combining Advantages of Multilinear Regression and Artificial Neural Networks." In Modelling, Simulation and Identification. Calgary,AB,Canada: ACTAPRESS, 2018. http://dx.doi.org/10.2316/p.2018.857-021.

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Widodo, Edy, and Kariyam. "Estimating multivariate response surface model with data outliers, case study in enhancing surface layer properties of an aircraft aluminium alloy." In PROCEEDINGS FROM THE 14TH INTERNATIONAL SYMPOSIUM ON THERAPEUTIC ULTRASOUND. Author(s), 2017. http://dx.doi.org/10.1063/1.4978127.

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Nelson, Donald D., and Elaine Cohen. "Algebraic Surface Derivatives for Rendering Virtual Contact Force." In ASME 2000 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2000. http://dx.doi.org/10.1115/imece2000-2426.

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Abstract Previous augmented reality displays have rendered crisp virtual walls and virtual objects with finger-surface reactions through haptics feedback devices. The widely used stiffness (or impedance) methods penalize a user’s intrusion into a virtual surface with a force response dependent on the amount of penetration along the contact normal at the virtual proxy location. We present an alternative approach for computing the surface impact response that projects Lagrange multipliers associated with a unilateral surface constraint onto a multivariate surface constraint Jacobian for the case where the two objects (finger and model) do not stick together. Advantages of our method are that the surface Jacobian is already being computed from an exact NURBS-NURBS collision update algorithm previously developed by the authors, and that the force response is accurate to numerical precision; no polygonal or numerical approximations are employed.
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Zhang, T., K. K. Choi, and S. Rahman. "A Hybrid Method Using Response Surface and Pattern Search for Design Optimization." In ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/detc2005-85146.

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This paper presents a new method to construct response surface function and a new hybrid optimization method. For the response surface function, the radial basis function is used for a zeroth-order approximation, while new bases is proposed for the moving least squares method for a first-order approximation. For the new hybrid optimization method, the gradient-based algorithm and pattern search algorithm are integrated for robust and efficient optimization process. These methods are based on: (1) multi-point approximations of the objective and constraint functions; (2) a multi-quadric radial basis function for the zeroth-order function representation or radial basis function plus polynomial based moving least squares approximation for the first-order function approximation; and (3) a pattern search algorithm to impose a descent condition. Several numerical examples are presented to illustrate the accuracy and computational efficiency of the proposed method for both function approximation and design optimization. The examples for function approximation indicate that the multi-quadric radial basis function and the proposed radial basis function plus polynomial based moving least squares method can yield accurate estimates of arbitrary multivariate functions. Results also show that the hybrid method developed provides efficient and convergent solutions to both mathematical and structural optimization problems.
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Somayasa, Wayan, Ruslan Ruslan, and Desak Ketut Sutiari. "Assessing the optimum condition of multivariate second order response surface model through the asymptotic inference of the eigenvalues." In THE 3RD INTERNATIONAL CONFERENCE ON MATHEMATICS AND SCIENCES (THE 3RD ICMSc): A Brighter Future with Tropical Innovation in the Application of Industry 4.0. AIP Publishing, 2022. http://dx.doi.org/10.1063/5.0112594.

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Wahab, M. M. A., V. J. Kurian, M. S. Liew, Z. Nizamani, and D. K. Kim. "Structural Reliability Analysis Using Quadratic Polynomial Response Surface and Finite Element in MATLAB." In ASME 2016 35th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/omae2016-54543.

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Many aging jacket platforms are being pushed for continued use beyond their design life due to advancement in oil extracting technology and economic reasons. Thus reassessment to determine the platform safety is vital. But no exact guide on methods to assess the safety of the aging platforms is available. Hence, development of reliability analysis methodologies is an active research area. Meanwhile, reassessment deals with numerous uncertainties especially in the load and resistance variables of a jacket platform. Response Surface methodology, a limit state approximation technique was deployed by many in many engineering fields to apprehend inherent uncertainty. Hence in this work, a reliability analysis methodology that combines simple response surface and finite element approach in MATLAB is adopted. The approach assumes a physical transfer function utilizing explicit multivariate expressions and random variables. Also, this avoids large number of finite element simulation required for any probabilistic analysis. The methodology developed allows for reliability analysis to be performed based on easy to program procedures. It also addresses the platform and environmental specific uncertainty variables to distinguish the distinctive characteristics of the cases. Upon execution of multiple finite element simulations, response of components and systems are formulated using quadratic polynomial response surface expressions, which eventually are utilized in the limit state functions. Later using numerical techniques in a separate computational routine the reliability indices are estimated. Utilizing the developed method, component and system level reliability indices are obtained. The developed methodology also has been verified with method currently available in the practice as well as with typical simulation method i.e. Monte Carlo Simulation.
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10

Branagan, Michael, Neal Morgan, Brian Weaver, and Houston Wood. "Response Surface Mapping and Multi-Objective Optimization of Tilting Pad Bearing Designs." In ASME Turbo Expo 2017: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/gt2017-64949.

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Abstract:
Fluid film bearings for turbomachinery are designed to support the loads applied by the rotor system, often at high speeds when power loss in the bearing becomes significant and bearing temperatures can reach levels that can be detrimental to the long-term reliability of the support system. These requirements of supportive bearings require an intimate understanding of how bearing design variables affect their overall performance. Ideal bearings minimize power loss to increase machine efficiency and maintain low operating temperatures to ensure long-term reliability while meeting other design criteria such as minimum film thickness to provide proper support and avoiding high fluid pressures that can be harmful to the bearing structure. However, real world designs are often forced to sacrifice some of these design goals in order to preserve others. Therefore, further understanding of the relative opportunity costs associated with optimizing the bearing design with differently weighted performance metrics and their relationships to bearing design variables is invaluable to design engineers. This study explores the impact of eight bearing design variables on the performance of two tilting pad journal bearings supporting an eight-stage centrifugal compressor using design of experiments techniques applied to an established thermoelastohydrodynamic (TEHD) bearing model of tilting pad bearing performance. The bearing design variables analyzed include the radial clearance, pad arc spacing, pad axial length, pivot offset, preload, working fluid viscosity and viscosity index, and the number of pads. Each of the design variables — excluding the number of pads which was realistically constrained — were first varied over five levels each in a central composite design. These central composite designs were repeated for each of three values for number of pads. The responses obtained from the TEHD numerical simulations for each bearing design point were power loss, maximum pad temperature, minimum film thickness, and maximum fluid film pressure. The results from the central composite studies were fit with a multivariate least-squares regression model and a secondary series of experimental design studies were simulated around potential optimum design points to obtain a learning set to initialize direct optimization methods. Two direct multi-objective optimization methods, a sequential quadratic programming method and a multi-island genetic algorithm, were performed using Isight, a commercial software. A range of weighting parameters were selected for the optimization functions to find bearing designs that minimized power loss and pad temperature while maintaining pressure and film thickness criteria within acceptable design ranges for fluid film bearings. The resulting optimum design points allowed for a comparison between the design optimization approaches. The various strengths and weaknesses of the different methods are discussed. This study demonstrates how designers can use these approaches to view the relationships between design variables and important performance metrics to design better bearings for a wide range of applications.
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