The Reaction process is basically a map, beetween the reaction input conditions and process outputs, by Multiple Linear Regression modeling applied to data collected by DOE framework, you generate a low order polynomial model, that gives an approximation to this map, as function of input variables which are actively varied in their levels during DOE setup, and conditional on those process factors who remain at fixed level during DOE procedure, so in a chemical reaction if you want to predict rxn yield as a function of catalyst properties as well, your data collection process must include levels involving change in catalyst , a response model generated using a particular fixed catalyst, may not be able predict well rxn yield of a reaction , involving the same experimental space w.r.t. other input process variables but a different catalyst.

DOE involve experimental data collection using specific designs, symmetries in which reduce the prediction variance over the experimental space, a non DOE based experimental scheme to collect data, in general, lead to a higher prediction variance.

In ANN the idea of using the training set is to obtain the optimal set of network parameters that provide the best agreement beetween observed response and predicted response, it is a form of non-linear calibration, any data collected, using any experimental design, can be used to generate a response model over the experimental space encompassing the design, the question is how good that model is, therefore, the obtained model need to be iteratively modified, by measuring its agreement with observed response, using appropriately chosen evolutionary algorithm, till a threshold level of agreement beetween predicted and observed response is obtained.

Dear Debopam Ghosh, Thank you very much for comprehensive explanation. There are some unclear points regarding my case that I would love to make clear with your further help. Actually, the data I am going to use involves a set of same catalyst (10-15) with the same support, promoter, loading, but each one having different particle size and pore sizes in a certain range. At the same time space velocity is changed to adjust the conversion (to keep conversion at certain level constant for all catalysts to compare products selectivity results), at the fixed other operating conditions, such as temperature, pressure. I would like to know is it feasible to develop such a model by RSM that predicts selectivity taking pore, particle size, space velocity as variables. The data is taken from literature and actually have not been collected with the aim of model development, but just for investigation of catalyst properties on selectivity. Furthermore, as far as I know in RSM the x-variables must be independent of each other. But in this case particle size and pore size are related to each other, on the other hand the selectivity depends on both of these parameters. So, I am a little bit confused about the feasibility of such model.

When it comes to ANN, there are some cases in literature that the experimental data which is used for modelling is trained for RSM firstly by ANN just because the data were not collected by DOE method. Central composite design is employed to create DOE points, subsequently used to fit model by RSM. However there are also such cases that the experimental data have been used directly for RSM without using ANN. I would love to make it clear, which method I should use, just taking experimental data and applying directly RSM and multiple linear regression or firstly definitely making ANN, Central composite design and then RSM. Thanks for your time and consideration!

In case there are known mathematical relationships, which interrelate particle size, pore size and space velocity, selecting any one of the three as independent variable x will fix the factor levels for other two, based on these relationships. you need to consider only one as input factor in that case.

However, if these variables are known to be correlated but no such known mathematical interrelationship exist between them, i suggest you can use Multivariate Regression tools in this case, in particular Principal component Regression (Single y variable case) or Partial Least squares Regression (multiple response variables), in these procedures, it is better to cover a wide range of experimental space , in terms of these three input variables, as training set to get a reasonable insight into input-output behavior of the process modeled.

The problem , as you already mention, is basically of constrained iterative evolution in the factor space, where all factor compositions are not feasible because of this intrinsic correlation among inputs, we know from optimization theory, it is possible to optimize an objective function subjected to constraints, the following book does discuss some cases of constrained optimization in RSM:

Response Surface Methodology: Process and Product Optimization Using Designed Experiments (Wiley Series in Probability and Statistics) 4th Edition

by Raymond H. Myers (Author), Douglas C. Montgomery (Author), Christine M. Anderson-Cook (Author)

As for your second query, in my opinion, you can use experimental data directly for RSM.

Dear Debopam Ghosh , There are some works in literature in which selectivity models are developed in Minitab software by response surface methodology based on the data that have been collected by other researchers and optimization is performed to propose optimal conditions to maximize the selectivity for desirable products. I take the same data just to check how response surface methodology works, but I never get the same model that have been obtained in this works. The coefficients in the model for regressors and their interactions don't match. Even in such cases that R square and adjusted R square values are the same. Even in the case that I check some data points withy model and get the same responses as they get, but the coefficients are totally different. I don't know exactly whether I miss something or I don't use the software rightly or something else. I want to note that, in Minitab I go to Stay>DOE>Response surface and choose regressors in uncoded versions, as well as their lower and higher values, then responses at the same time. I think the problem might be in coded variables, are uncoded variables converted into coded ones in the same way, or it might be done differently? Or the problem might be with the way I interpret the results after I run RSM. What do you think, is the problem related to it or any other factors?

Dear Nuran,

Without having a detailed look at the dataset, the precise methodology of the algorithms used and flexibility it provides in iterative routes for optimization it is very difficult to pinpoint where the problem lies, also i personally have never worked with minitab software, i do most of my DOE/RSM computations in Scilab platform so i will not be able to tell whether software input is the problem. I suggest you try discuss this issue with minitab data input with experts working with and having access to minitab software.

Good luck

Best wishes

Dear Nurlan

I deeply apologise for misspelling your name in previous post.

Regards

D.Ghosh

If you designed an experiment in Minitab and you analyze it through the 'Analyze' option in the DOE sub-menu, the software assumes that the highest level for each factor is something like '1'. The lowest level is '-1'. If you analyze the data through the Regression sub-menu, then it uses the actual levels for the analysis and creates all sorts of issues for analysis.

Under the DOE submenu, after analysis, there will be 2 sets of coefficients. One for the scaled factors levels (-1, 1) and another for the unscaled levels. When you go to optimize, use the coefficients for the coded model.

In general, ANN is useful when you have lots of data. DOE tries to minimize the amount of data you use.