Ion criterion (BIC) is used to quantify the magnitude of ond, the Bayesian data criterion

Ion criterion (BIC) is used to quantify the magnitude of ond, the Bayesian data criterion (BIC) is utilized towards the coefficients in the estimated input utput neurons within the hidden layer, which impacts quantify the magnitude of neurons within the hidden layer, which impacts the coefficientscase study are presented to verify equations. equations. Ultimately, the outcomes from the within the estimated input utput the effectiveness of Finally, the outcomes of your case NN-based presented to verify the effectiveness in the proposed the proposed study are estimation system compared with the LSM-based RSM. The graphical overview of your proposed NN-based estimation method overview NN-based estimation strategy compared using the LSM-based RSM. The graphicalis demonstrated in Figure 1. of the proposed NN-based estimation method is demonstrated in Figure 1.Figure 1. Proposed feed-forward NN-based estimation Figure 1. Proposed feed-forward NN-based estimation process. procedure.The remainderThethe study is of the study follows: Section follows: Section 2 introduces the of remainder organized as is organized as 2 introduces the convenconventional LSM-based RSM. the functional-link-NN-based dual-response dualtional LSM-based RSM. Section three describes Section three describes the functional-link-NN-based response estimation model. Section four explains the estimation model. Section four explains the outputs generatedoutputs generated by the proposed NNby the proposed NN-based primarily based estimation approach and analyzes the LSM-based RSM depending on the outcomes from the estimation strategy and analyzes the LSM-based RSM depending on the outcomes of your case study. case study. Ultimately, Section five concludes the study and describes further research. Pipamperone manufacturer Lastly, Section 5 concludes the study and describes additional research. 2. Traditional LSM-Based RSM2. Traditional LSM-Based RSM The RSM was first introduced by Box and Wilson [35] and is used to model empiricalThe RSM was 1st introduced by output and input variables. Myers [36] empirical Box and Wilson [35] and is made use of to model and Khuri and relationships among relationships among output and input variables. Myers [36] and Khuri and MukhopadMukhopadhyay [37] present insightful commentaries around the different development hyay [37] present insightful commentariesthe the distinctive development phases of difficult or is phases in the RSM. When on precise functional relationship is quite the RSM. When the exactunknown, the traditional LSM is applied to estimate the input esponse functional functional relationship is quite complicated or is unknown, the traditional LSM is utilized torelationships from the output [38,39]. In general, the estimated output [38,39]. estimate the input esponse functional relationships in the second-order response Normally, the surface functions are used to analyze RD issues. The utilized to analyze RD estimated second-order response surface functions are estimated method imply and challenges. Thestandard deviation functionsand regular deviation functions proposed by follows: estimated procedure imply proposed by Vining and Myers [8] can be defined as Vining and Myers [8] could be defined as follows: ^ ^ ^ two ^ LSM (x) = 0 + i xi + i xi +i =1 i =1 p p^ ij xi x j i=1 ijp j =pp(1)^ ^ ^ 2 ^ LSM (x) = 0 + i xi + i xi +i =1 i =pp^ ij xi x j i=1 ijj =p(2)Appl. Sci. 2021, 11, x FOR PEER REVIEW4 ofAppl. Sci. 2021, 11,four of() = +++(1)^ ^ exactly where x = x1 , . . . , xi , . . . , x j , . . . , x p is usually a vector of input variables, and and are the () = m.