"""Surrogate Model based on second order response surface equations."""
from numpy import matrix, linalg, power, multiply, concatenate, ones
from openmdao.main.api import Container
from openmdao.main.interfaces import implements,ISurrogate
from openmdao.lib.datatypes.api import Float, Bool
[docs]class ResponseSurface(Container):
implements(ISurrogate)
def __init__(self,X=None,Y=None):
# must call HasTraits init to set up Traits stuff
super(ResponseSurface, self).__init__()
self.m = None #number of training points
self.n = None #number of independents
self.betas = None #vector of response surface equation coefficients
if X is not None and Y is not None:
self.train(X,Y)
[docs] def get_uncertain_value(self,value):
"""Returns the value iself. Response surface equations don't have uncertainty."""
return value
[docs] def train(self,X,Y):
""" Calculate response surface equation coefficients using least squares regression. """
X = matrix(X)
Y = matrix(Y).T
self.m = X.shape[0]
self.n = X.shape[1]
# Modify X to include constant, squared terms and cross terms
X = concatenate((matrix(ones((self.m,1))),X),1)
for i in range(1,self.n+1):
X = concatenate((X,power(X[:,i],2)),1)
for i in range(1,self.n):
for j in range(i+1,self.n+1):
X = concatenate((X,multiply(X[:,i],X[:,j])),1)
# Determine response surface equation coefficients (betas) using least squares
self.betas, rs, r, s = linalg.lstsq(X,Y)
[docs] def predict(self,new_x):
"""Calculates a predicted value of the response based on the current response surface model for the supplied list of inputs. """
new_x = matrix(new_x)
# Modify new_x to include constant, squared terms and cross terms
new_x = concatenate((matrix(ones((1,1))),new_x),1)
for i in range(1,self.n+1):
new_x = concatenate((new_x,power(new_x[:,i],2)),1)
for i in range(1,self.n):
for j in range(i+1,self.n+1):
new_x = concatenate((new_x,multiply(new_x[:,i],new_x[:,j])),1)
# Predict new_y using new_x and betas
new_y = new_x*self.betas
return new_y[0,0]
if __name__ == "__main__":
import time
tt = time.time()
# X = [[2.26,0.65],[6.11,9.53],[7.92,2.88],[2.03,9.97],[9.16,7.18],[2.98,2.5],[8.2,5.58],[6.37,4.92],[1.12,5.7],[4.76,0.9],[8.16,6.98],[6.06,1.54],\
# [4.54,5.82],[5.24,8.66],[7.8,2.41],[2.94,1.77],[8.84,6.64],[5.16,7.62],[9.14,6.51],[1.5,7.75],[7.62,5.45],[9.98,1.39],[3.15,5.25],[1.75,9.9],\
# [1.27,1.96],[3.63,1.64],[8.73,9.15],[8.34,9.45],[9.46,4.09],[9.61,4.18],[9.01,6.4],[3.69,4],[8.2,8.43],[6.81,6.1],[6.67,6.11]]
# Y = [11.031825,278.8868,115.772,185.305,279.3373,36.6028,197.9325,137.621475,64.4913,33.1837,243.8833,58.042,124.4148,223.8245,102.401125,26.901425,\
# 250.4164,188.2781,254.037625,113.640625,180.029425,117.424825,86.495,176.559375,15.700075,31.741075,344.5268,344.435825,181.506625,187.824175,\
# 246.523075,69.922075,298.858125,180.836575,177.8742]
X = [[3000,2,1,1,0],\
[3000,2,1,1,5],\
[3000,2,1,1,10],\
[3000,2,1,1,15],\
[3000,2,1,1,20],\
[3000,2,1,2,0],\
[3000,2,1,2,5],\
[3000,2,1,2,10],\
[3000,2,1,2,15],\
[3000,2,1,2,20],\
[3000,2,1,3,0],\
[3000,2,1,3,5],\
[3000,2,1,3,10],\
[3000,2,1,3,15],\
[3000,2,1,3,20],\
[3000,2,1,4,0],\
[3000,2,1,4,5],\
[3000,2,1,4,10],\
[3000,2,1,4,15],\
[3000,2,1,4,20],\
[3000,2,1,5,0],\
[3000,2,1,5,5],\
[3000,2,1,5,10],\
[3000,2,1,5,15],\
[3000,2,1,5,20],\
[3000,2,1.375,1,0],\
[3000,2,1.375,1,5],\
[3000,2,1.375,1,10],\
[3000,2,1.375,1,15],\
[3000,2,1.375,1,20],\
[3000,2,1.375,2,0],\
[3000,2,1.375,2,5],\
[3000,2,1.375,2,10],\
[3000,2,1.375,2,15],\
[3000,2,1.375,2,20],\
[3000,2,1.375,3,0],\
[3000,2,1.375,3,5],\
[3000,2,1.375,3,10],\
[3000,2,1.375,3,15],\
[3000,2,1.375,3,20],\
[3000,2,1.375,4,0],\
[3000,2,1.375,4,5],\
[3000,2,1.375,4,10],\
[3000,2,1.375,4,15],\
[3000,2,1.375,4,20],\
[3000,2,1.375,5,0],\
[3000,2,1.375,5,5],\
[3000,2,1.375,5,10],\
[3000,2,1.375,5,15],\
[3000,2,1.375,5,20],\
[3000,2,1.75,1,0],\
[3000,2,1.75,1,5],\
[3000,2,1.75,1,10],\
[3000,2,1.75,1,15],\
[3000,2,1.75,1,20],\
[3000,2,1.75,2,0],\
[3000,2,1.75,2,5],\
[3000,2,1.75,2,10],\
[3000,2,1.75,2,15],\
[3000,2,1.75,2,20],\
[3000,2,1.75,3,0],\
[3000,2,1.75,3,5],\
[3000,2,1.75,3,10],\
[3000,2,1.75,3,15],\
[3000,2,1.75,3,20],\
[3000,2,1.75,4,0],\
[3000,2,1.75,4,5],\
[3000,2,1.75,4,10],\
[3000,2,1.75,4,15],\
[3000,2,1.75,4,20],\
[3000,2,1.75,5,0],\
[3000,2,1.75,5,5],\
[3000,2,1.75,5,10],\
[3000,2,1.75,5,15],\
[3000,2,1.75,5,20],\
[3000,2,2.125,1,0],\
[3000,2,2.125,1,5],\
[3000,2,2.125,1,10],\
[3000,2,2.125,1,15],\
[3000,2,2.125,1,20],\
[3000,2,2.125,2,0],\
[3000,2,2.125,2,5],\
[3000,2,2.125,2,10],\
[3000,2,2.125,2,15],\
[3000,2,2.125,2,20],\
[3000,2,2.125,3,0],\
[3000,2,2.125,3,5],\
[3000,2,2.125,3,10],\
[3000,2,2.125,3,15],\
[3000,2,2.125,3,20],\
[3000,2,2.125,4,0],\
[3000,2,2.125,4,5],\
[3000,2,2.125,4,10],\
[3000,2,2.125,4,15],\
[3000,2,2.125,4,20],\
[3000,2,2.125,5,0],\
[3000,2,2.125,5,5],\
[3000,2,2.125,5,10],\
[3000,2,2.125,5,15],\
[3000,2,2.125,5,20],\
[3000,2,2.5,1,0],\
[3000,2,2.5,1,5],\
[3000,2,2.5,1,10],\
[3000,2,2.5,1,15],\
[3000,2,2.5,1,20],\
[3000,2,2.5,2,0],\
[3000,2,2.5,2,5],\
[3000,2,2.5,2,10],\
[3000,2,2.5,2,15],\
[3000,2,2.5,2,20],\
[3000,2,2.5,3,0],\
[3000,2,2.5,3,5],\
[3000,2,2.5,3,10],\
[3000,2,2.5,3,15],\
[3000,2,2.5,3,20],\
[3000,2,2.5,4,0],\
[3000,2,2.5,4,5],\
[3000,2,2.5,4,10],\
[3000,2,2.5,4,15],\
[3000,2,2.5,4,20],\
[3000,2,2.5,5,0],\
[3000,2,2.5,5,5],\
[3000,2,2.5,5,10],\
[3000,2,2.5,5,15],\
[3000,2,2.5,5,20],\
[3000,5,1,1,0],\
[3000,5,1,1,5],\
[3000,5,1,1,10],\
[3000,5,1,1,15],\
[3000,5,1,1,20],\
[3000,5,1,2,0],\
[3000,5,1,2,5],\
[3000,5,1,2,10],\
[3000,5,1,2,15],\
[3000,5,1,2,20],\
[3000,5,1,3,0],\
[3000,5,1,3,5],\
[3000,5,1,3,10],\
[3000,5,1,3,15],\
[3000,5,1,3,20],\
[3000,5,1,4,0],\
[3000,5,1,4,5],\
[3000,5,1,4,10],\
[3000,5,1,4,15],\
[3000,5,1,4,20],\
[3000,5,1,5,0],\
[3000,5,1,5,5],\
[3000,5,1,5,10],\
[3000,5,1,5,15],\
[3000,5,1,5,20],\
[3000,5,1.375,1,0],\
[3000,5,1.375,1,5],\
[3000,5,1.375,1,10],\
[3000,5,1.375,1,15],\
[3000,5,1.375,1,20],\
[3000,5,1.375,2,0],\
[3000,5,1.375,2,5],\
[3000,5,1.375,2,10],\
[3000,5,1.375,2,15],\
[3000,5,1.375,2,20],\
[3000,5,1.375,3,0],\
[3000,5,1.375,3,5],\
[3000,5,1.375,3,10],\
[3000,5,1.375,3,15],\
[3000,5,1.375,3,20],\
[3000,5,1.375,4,0],\
[3000,5,1.375,4,5],\
[3000,5,1.375,4,10],\
[3000,5,1.375,4,15],\
[3000,5,1.375,4,20],\
[3000,5,1.375,5,0],\
[3000,5,1.375,5,5],\
[3000,5,1.375,5,10],\
[3000,5,1.375,5,15],\
[3000,5,1.375,5,20],\
[3000,5,1.75,1,0],\
[3000,5,1.75,1,5],\
[3000,5,1.75,1,10],\
[3000,5,1.75,1,15],\
[3000,5,1.75,1,20],\
[3000,5,1.75,2,0],\
[3000,5,1.75,2,5],\
[3000,5,1.75,2,10],\
[3000,5,1.75,2,15],\
[3000,5,1.75,2,20],\
[3000,5,1.75,3,0],\
[3000,5,1.75,3,5],\
[3000,5,1.75,3,10],\
[3000,5,1.75,3,15],\
[3000,5,1.75,3,20],\
[3000,5,1.75,4,0],\
[3000,5,1.75,4,5],\
[3000,5,1.75,4,10],\
[3000,5,1.75,4,15],\
[3000,5,1.75,4,20],\
[3000,5,1.75,5,0],\
[3000,5,1.75,5,5],\
[3000,5,1.75,5,10],\
[3000,5,1.75,5,15],\
[3000,5,1.75,5,20],\
[3000,5,2.125,1,0],\
[3000,5,2.125,1,5],\
[3000,5,2.125,1,10],\
[3000,5,2.125,1,15],\
[3000,5,2.125,1,20],\
[3000,5,2.125,2,0],\
[3000,5,2.125,2,5],\
[3000,5,2.125,2,10],\
[3000,5,2.125,2,15],\
[3000,5,2.125,2,20],\
[3000,5,2.125,3,0],\
[3000,5,2.125,3,5],\
[3000,5,2.125,3,10],\
[3000,5,2.125,3,15],\
[3000,5,2.125,3,20],\
[3000,5,2.125,4,0],\
[3000,5,2.125,4,5],\
[3000,5,2.125,4,10],\
[3000,5,2.125,4,15],\
[3000,5,2.125,4,20],\
[3000,5,2.125,5,0],\
[3000,5,2.125,5,5],\
[3000,5,2.125,5,10],\
[3000,5,2.125,5,15],\
[3000,5,2.125,5,20],\
[3000,5,2.5,1,0],\
[3000,5,2.5,1,5],\
[3000,5,2.5,1,10],\
[3000,5,2.5,1,15],\
[3000,5,2.5,1,20],\
[3000,5,2.5,2,0],\
[3000,5,2.5,2,5],\
[3000,5,2.5,2,10],\
[3000,5,2.5,2,15],\
[3000,5,2.5,2,20],\
[3000,5,2.5,3,0],\
[3000,5,2.5,3,5],\
[3000,5,2.5,3,10],\
[3000,5,2.5,3,15],\
[3000,5,2.5,3,20],\
[3000,5,2.5,4,0],\
[3000,5,2.5,4,5],\
[3000,5,2.5,4,10],\
[3000,5,2.5,4,15],\
[3000,5,2.5,4,20],\
[3000,5,2.5,5,0],\
[3000,5,2.5,5,5],\
[3000,5,2.5,5,10],\
[3000,5,2.5,5,15],\
[3000,5,2.5,5,20],\
[3000,8,1,1,0],\
[3000,8,1,1,5],\
[3000,8,1,1,10],\
[3000,8,1,1,15],\
[3000,8,1,1,20],\
[3000,8,1,2,0],\
[3000,8,1,2,5],\
[3000,8,1,2,10],\
[3000,8,1,2,15],\
[3000,8,1,2,20],\
[3000,8,1,3,0],\
[3000,8,1,3,5],\
[3000,8,1,3,10],\
[3000,8,1,3,15],\
[3000,8,1,3,20],\
[3000,8,1,4,0],\
[3000,8,1,4,5],\
[3000,8,1,4,10],\
[3000,8,1,4,15],\
[3000,8,1,4,20],\
[3000,8,1,5,0],\
[3000,8,1,5,5],\
[3000,8,1,5,10],\
[3000,8,1,5,15],\
[3000,8,1,5,20],\
[3000,8,1.375,1,0],\
[3000,8,1.375,1,5],\
[3000,8,1.375,1,10],\
[3000,8,1.375,1,15],\
[3000,8,1.375,1,20],\
[3000,8,1.375,2,0],\
[3000,8,1.375,2,5],\
[3000,8,1.375,2,10],\
[3000,8,1.375,2,15],\
[3000,8,1.375,2,20],\
[3000,8,1.375,3,0],\
[3000,8,1.375,3,5],\
[3000,8,1.375,3,10],\
[3000,8,1.375,3,15],\
[3000,8,1.375,3,20],\
[3000,8,1.375,4,0],\
[3000,8,1.375,4,5],\
[3000,8,1.375,4,10],\
[3000,8,1.375,4,15],\
[3000,8,1.375,4,20],\
[3000,8,1.375,5,0],\
[3000,8,1.375,5,5],\
[3000,8,1.375,5,10],\
[3000,8,1.375,5,15],\
[3000,8,1.375,5,20],\
[3000,8,1.75,1,0],\
[3000,8,1.75,1,5],\
[3000,8,1.75,1,10],\
[3000,8,1.75,1,15],\
[3000,8,1.75,1,20],\
[3000,8,1.75,2,0],\
[3000,8,1.75,2,5],\
[3000,8,1.75,2,10],\
[3000,8,1.75,2,15],\
[3000,8,1.75,2,20],\
[3000,8,1.75,3,0],\
[3000,8,1.75,3,5],\
[3000,8,1.75,3,10],\
[3000,8,1.75,3,15],\
[3000,8,1.75,3,20],\
[3000,8,1.75,4,0],\
[3000,8,1.75,4,5],\
[3000,8,1.75,4,10],\
[3000,8,1.75,4,15],\
[3000,8,1.75,4,20],\
[3000,8,1.75,5,0],\
[3000,8,1.75,5,5],\
[3000,8,1.75,5,10],\
[3000,8,1.75,5,15],\
[3000,8,1.75,5,20],\
[3000,8,2.125,1,0],\
[3000,8,2.125,1,5],\
[3000,8,2.125,1,10],\
[3000,8,2.125,1,15],\
[3000,8,2.125,1,20],\
[3000,8,2.125,2,0],\
[3000,8,2.125,2,5],\
[3000,8,2.125,2,10],\
[3000,8,2.125,2,15],\
[3000,8,2.125,2,20],\
[3000,8,2.125,3,0],\
[3000,8,2.125,3,5],\
[3000,8,2.125,3,10],\
[3000,8,2.125,3,15],\
[3000,8,2.125,3,20],\
[3000,8,2.125,4,0],\
[3000,8,2.125,4,5],\
[3000,8,2.125,4,10],\
[3000,8,2.125,4,15],\
[3000,8,2.125,4,20],\
[3000,8,2.125,5,0],\
[3000,8,2.125,5,5],\
[3000,8,2.125,5,10],\
[3000,8,2.125,5,15],\
[3000,8,2.125,5,20],\
[3000,8,2.5,1,0],\
[3000,8,2.5,1,5],\
[3000,8,2.5,1,10],\
[3000,8,2.5,1,15],\
[3000,8,2.5,1,20],\
[3000,8,2.5,2,0],\
[3000,8,2.5,2,5],\
[3000,8,2.5,2,10],\
[3000,8,2.5,2,15],\
[3000,8,2.5,2,20],\
[3000,8,2.5,3,0],\
[3000,8,2.5,3,5],\
[3000,8,2.5,3,10],\
[3000,8,2.5,3,15],\
[3000,8,2.5,3,20],\
[3000,8,2.5,4,0],\
[3000,8,2.5,4,5],\
[3000,8,2.5,4,10],\
[3000,8,2.5,4,15],\
[3000,8,2.5,4,20],\
[3000,8,2.5,5,0],\
[3000,8,2.5,5,5],\
[3000,8,2.5,5,10],\
[3000,8,2.5,5,15],\
[3000,8,2.5,5,20],\
[3000,11,1,1,0],\
[3000,11,1,1,5],\
[3000,11,1,1,10],\
[3000,11,1,1,15],\
[3000,11,1,1,20],\
[3000,11,1,2,0],\
[3000,11,1,2,5],\
[3000,11,1,2,10],\
[3000,11,1,2,15],\
[3000,11,1,2,20],\
[3000,11,1,3,0],\
[3000,11,1,3,5],\
[3000,11,1,3,10],\
[3000,11,1,3,15],\
[3000,11,1,3,20],\
[3000,11,1,4,0],\
[3000,11,1,4,5],\
[3000,11,1,4,10],\
[3000,11,1,4,15],\
[3000,11,1,4,20],\
[3000,11,1,5,0],\
[3000,11,1,5,5],\
[3000,11,1,5,10],\
[3000,11,1,5,15],\
[3000,11,1,5,20],\
[3000,11,1.375,1,0],\
[3000,11,1.375,1,5],\
[3000,11,1.375,1,10],\
[3000,11,1.375,1,15],\
[3000,11,1.375,1,20],\
[3000,11,1.375,2,0],\
[3000,11,1.375,2,5],\
[3000,11,1.375,2,10],\
[3000,11,1.375,2,15],\
[3000,11,1.375,2,20],\
[3000,11,1.375,3,0],\
[3000,11,1.375,3,5],\
[3000,11,1.375,3,10],\
[3000,11,1.375,3,15],\
[3000,11,1.375,3,20],\
[3000,11,1.375,4,0],\
[3000,11,1.375,4,5],\
[3000,11,1.375,4,10],\
[3000,11,1.375,4,15],\
[3000,11,1.375,4,20],\
[3000,11,1.375,5,0],\
[3000,11,1.375,5,5],\
[3000,11,1.375,5,10],\
[3000,11,1.375,5,15],\
[3000,11,1.375,5,20],\
[3000,11,1.75,1,0],\
[3000,11,1.75,1,5],\
[3000,11,1.75,1,10],\
[3000,11,1.75,1,15],\
[3000,11,1.75,1,20],\
[3000,11,1.75,2,0],\
[3000,11,1.75,2,5],\
[3000,11,1.75,2,10],\
[3000,11,1.75,2,15],\
[3000,11,1.75,2,20],\
[3000,11,1.75,3,0],\
[3000,11,1.75,3,5],\
[3000,11,1.75,3,10],\
[3000,11,1.75,3,15],\
[3000,11,1.75,3,20],\
[3000,11,1.75,4,0],\
[3000,11,1.75,4,5],\
[3000,11,1.75,4,10],\
[3000,11,1.75,4,15],\
[3000,11,1.75,4,20],\
[3000,11,1.75,5,0],\
[3000,11,1.75,5,5],\
[3000,11,1.75,5,10],\
[3000,11,1.75,5,15],\
[3000,11,1.75,5,20],\
[3000,11,2.125,1,0],\
[3000,11,2.125,1,5],\
[3000,11,2.125,1,10],\
[3000,11,2.125,1,15],\
[3000,11,2.125,1,20],\
[3000,11,2.125,2,0],\
[3000,11,2.125,2,5],\
[3000,11,2.125,2,10],\
[3000,11,2.125,2,15],\
[3000,11,2.125,2,20],\
[3000,11,2.125,3,0],\
[3000,11,2.125,3,5],\
[3000,11,2.125,3,10],\
[3000,11,2.125,3,15],\
[3000,11,2.125,3,20],\
[3000,11,2.125,4,0],\
[3000,11,2.125,4,5],\
[3000,11,2.125,4,10],\
[3000,11,2.125,4,15],\
[3000,11,2.125,4,20],\
[3000,11,2.125,5,0],\
[3000,11,2.125,5,5],\
[3000,11,2.125,5,10],\
[3000,11,2.125,5,15],\
[3000,11,2.125,5,20],\
[3000,11,2.5,1,0],\
[3000,11,2.5,1,5],\
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39547.5047,\
34795.5242,\
39553.8111,\
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39555.8992,\
39550.8922,\
34797.9502,\
39555.8215,\
39555.8996,\
39555.8996,\
39551.5096]
bob = ResponseSurface()
bob.train(X,Y)
print "Coefficients: ", bob.betas
# new_y = bob.predict([1., 5.])
new_y = bob.predict([3125.,7.0,2.1, 2.5, 7.0])
print "Predicted: ", new_y
print "Elapsed time: ", time.time()-tt, "seconds"
