ANNs as On-Line Quality Models for SHMPC

Artificial neural networks arose from efforts to model the functioning of the mammalian brain. The most popular ANN — the feedforward ANN — has deeper roots in statistics than in neurobiology, though. A form of ANN (a Probability Neural Network) has been used within a QPA context to improve sensor data reliability, but not as an on-line quality model [57]. The best way to represent a feedforward ANN as an on-line quality model for SHMPC is 

Let A be an m x p matrix, abias be an m x 1 vector, B be an n x m matrix, and bbias be an n x 1 vector. Vectors x and q are then p x 1 and n x 1 vectors, respectively, and m becomes an arbitrarily determined number equal to the rows in A, the length of abias, and the columns in B. The total fitted parameters in Equation 9.6 is then m(p + n + l) + n as such, an upper limit for m) is set by the number of x, q data records available for parameter fitting. A corresponding lower limit for m is determined empirically That lower limit is reached when is so low that Equation 9.6 can no longer map x to q with the required degree of accuracy. 

Backpropagation is currently the most popular method of fitting the m(p + n + 1) + n parameters in Equation 9.6. Backpropagation is a gradient descent-based procedure that addresses the problem 

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