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Problem Formulation for Optimization
Published in Yogesh Jaluria, Design and Optimization of Thermal Systems, 2019
Another approach, which has found widespread use in engineering systems, including thermal systems, is that of response surfaces. As mentioned earlier, response surface or surrogate models are approximate models that reduce the simulation effort by using the responses at intelligently selected points. The basic approach is similar to curve fitting, discussed in Chapter 3. The response surface methodology (RSM) comprises a group of statistical techniques for empirical model building, followed by the use of the model in the design and development of new products and also in the improvement of existing designs (Box and Draper, 1987, 2007). RSM is used when only a small number of computational or physical experiments can be conducted due to the high costs (monetary or computational) involved. Response surfaces are fitted to the limited data collected and are used to estimate the location of the optimum. RSM gives a fast approximation to the model, which can be used to identify important variables, visualize the relationship of the input to the output, and quantify trade-offs between multiple objectives. This approach has been found to be valuable in developing new processes and systems, optimizing their performance, and improving the design and formulation of new products (Myers and Montgomery, 2016).
Spray Drying for Production of Food Colors from Natural Sources
Published in M. Selvamuthukumaran, Handbook on Spray Drying Applications for Food Industries, 2019
Mehmet Koç, Feyza Elmas, Ulaş Baysan, Hilal Şahin Nadeem, Figen Kaymak Ertekin
The basis of traditional optimization methods is to keep the other variable constant, while changing only one parameter over time. This approach brings significant disadvantages both in terms of cost and time. In addition, it is difficult to obtain sufficient data to determine the interactions between various process parameters and the process. The optimization can be carried out by using multivariate statistical techniques. At a large level, full factorial design, D-optimal design, response surface methodology, and combined design are the most commonly preferred and used techniques. Response surface methodology (RSM), is a multivariate technique, used in the optimization process involving two or more variables for statistical observation and analysis, is widely used due to overcoming these limitations (Bezerra et al. 2008). The response surface method simultaneously examines a large number of variables that are affecting the response of the system. Thus, the best process variables, which is defined as the optimum point in the direction of the targets, can be determined.
Different Methodologies for the Parametric Optimization of Welding Processes
Published in Jaykumar J. Vora, Vishvesh J. Badheka, Advances in Welding Technologies for Process Development, 2019
Jaykumar J. Vora, Kumar Abhishek, PL Ramkumar
The RSM approach can be considered a step ahead of the Taguchi method as they provide a mathematical relationship between input and output parameters. RSM is a collection of mathematical and statistical techniques that are useful for the modeling and analysis of problems in which output or the response is influenced by several input variables and the objective is to optimize this response. RSM also reduces the number of experimental trials by using either CCD or BBD approach. The research survey showed that RSM determines the relationship between various process parameters with the various machining criteria. However, RSM technique gives the set of the optimum level of input parameters without considering the constraints. Hence, an optimum parameter setting with constraints is the requirement for the process which can satisfy all such conflicting objectives at the same time. Such situations can be tackled conveniently by making use of meta-heuristic optimization techniques for the parameters optimization. The relations between the input and output of the RSM method are used as an input data to be fed to meta-heuristics methods to simultaneously optimize more than one output parameters.
Optimisation of recycled concrete aggregates for cement-treated bases by response surface method
Published in International Journal of Pavement Engineering, 2023
Kondeti Chiranjeevi, Doma Hemanth Kumar, Anil Sagar Srinivasa, A. U. Ravi Shankar
In the present study, RSM is used to develop a relationship between variables and outcomes and examine the effect of RCA and cement contents on the performance of CTRCA mixtures. The RSM is an essential statistical technique connecting each response to many variables to identify the interactions, relationships, and effects between the variables and responses. It has the benefit of examining the influence of numerous variables on the responses and optimising the response value (Kockal and Ozturan 2011, Martinez-Conesa et al.2017). The design, numerical modelling, statistical analysis, and optimisation of the process factors were done using the Design-Expert software. In the present investigation, mix design formulations of CTRCA mixtures are chosen randomly based on the FCCD for two independent variables. The RCA content ranges from 0 to 100%, and cement content ranges from 3% to 7% by dry weight of aggregate is considered, and the variation has been presented in Table 2. The interaction and relationship between the process variables, RCA proportion, cement content, and the response may be ascertained using Analysis of Variance (ANOVA) (Rezaifar et al.2016).
An investigation of hybrid models FEA coupled with AHP-ELECTRE, RSM-GA, and ANN-GA into the process parameter optimization of high-quality deep-drawn cylindrical copper cups
Published in Mechanics Based Design of Structures and Machines, 2022
S. P. Sundar Singh Sivam, R. Rajendran, N. Harshavardhana
From the above Table 6, the P-Value for the model is <0.0001 for all 4 responses which are lesser than the significance value of 0.05. Hence, the model is significant to proceed further. The lack-of-fit has a P-value of 0.042 and 0.01132 hence, it is insignificant, which is desirable. Clearance is found to be the most influential parameter affecting all the responses with the lowest P-value (0.0626, significant) among all parameters. RSM uses second-order polynomial equations for model fitting and regression (Grüner and Merklein 2014; Kalaimathi, Venkatachalam, and Sivakumar 2014; Bhardwaj et al., 2014; Gopalakannan and Senthilvelan 2013; Priyadarshi and Sharma 2016; Lin et al. 2012). Backward elimination was used to compute ANOVA in Table 6, this result demonstrates the impact of process factors on forming quality. The “Predicted (Pred) R-Squared" of 0.8039 is in reasonable agreement with the “Adjusted (Adj) R-Squared" of 0.8752, likewise, the same trend was followed in other responses and the same listed in Table 7.
Study on the use of lightweight expanded perlite and vermiculite aggregates in blended cement mortars
Published in European Journal of Environmental and Civil Engineering, 2022
Tzer Sheng Tie, Kim Hung Mo, U. Johnson Alengaram, Senthil Kumar Kaliyavaradhan, Tung-Chai Ling
Response surface methodology (RSM) is a statistical technique used for modelling, optimizing and analyzing problems in which a response is influenced by several variables (Kumar & Baskar, 2014; Rooholamini et al., 2018). In this study, RSM was adopted to predict the properties of mortar, namely flow, density, and compressive strength as the responses based on the materials that were used. Face-centered central composite design with α = 1 was used in this study (Kumar & Baskar, 2014). The content of SCM (GGBS or fly ash) was coded as A and amount of sand replacement by EP or EV was coded as B; both were selected as the factors and studied based on the 3 different types of properties for mortar as its response variables. The factors and factor levels are shown in Table 4. The experiment runs were summarised as shown in Table 5. Equation (1) shows the full quadratic model in terms of coded factors: where, y = predicted response, β0 = intercept, β1, β2 = linear effect coefficients, β11, β22 = quadratic effect coefficients, β12 = interaction effect coefficient, A and B = independent variables, ε = residual.