Hi, uqlab
first of all, thanks to the developers who created the nice package.
After creating a data driven PCE model, i want to proceed with robust optimization after extracting the PCE function.
Thus, an m-file was created to solve the toy problem as shown in figure 1. In addition, a total of three input variables were entered and the distribution was input as shown in figure 2.
Thus, a PCE model was created, and the results of the model are shown in Table 1 and Table 2.
Since the coefficient is 0 from the 11th to the 20th, there is no basis for the third order.
What I am trying to do is extract the PCE function and optimize it with MATLAB fmincon.
- The PCE formula was referenced by referring to several papers. I wonder if it is right to expand in the above order(table 3).
0 1 2 3 [1,1] [1,2] [1,3] [2,2] [2,3] [3,3] …
When expand in the above order, it is different from the validation result of the model. Can i extract basis from uqlab package?
X_val = [1.7118, -2.8774, 1.9047] Y_val = [-0.0906], Y_cal = [7.024]
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x1 and x2 are Legendre polynomial and x3 is Hermite polynomial. If Legendre and Hermite are multiplied, is it simply to multiply the two polynomials? (table 2. right)
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What is the basis of arbitrary PCE? I would like to know if there are related literature.
I would be very grateful with your response.