Page - 77 - in Adaptive and Intelligent Temperature Control of Microwave Heating Systems with Multiple Sources

3.3. Black-boxModeling The output of the NN estimator YNN(k) has the same dimension as the measured temperature vector Yr(k). The cost function is defined as inequation 3.75withYd(k) =Yr(k). Compared with the batch learning approach, the online learning ap- proach is more suitable for the real time system identification of the plant. It has a stochastic nature that makes the weight update less likely to be trapped in a local minimum [HDB+96]. Nevertheless, on- line learning itself suffers from a problem that is called ”catastrophic interference” or ”stability-plasticity dilemma” [MC89] [Rob95]. This problem is caused by the fact that the minimum of the cost function 3.75basedonthesingledatapairmaybefarawayfromtheminimum that isbasedonthewhole trainingdataset (theminimumofequation 3.72), which leads to the network completely drops all information provides by former training data pairs (prior to the current time k). In order to reduce the effect of ”catastrophic interference”, additional strategies are taken during the training of the NN estimator, which willbe introducedin thenextsection. OnlineSupervisedLearningAlgorithmsinNeuralNetworks The most common supervised learning algorithm used in neural net- works is the backpropagation (BP) algorithm [HDB+96]. The term ”backpropagation”, short for the back propagation of error, refers to the process that errors at the output layer are feed back to for- mer hidden layers and used to adjust weights accordingly. The on- line stochastic gradient descent backpropagation (SGBP) algorithm [HDB+96], which combines principles of online backpropagation and the aforementioned gradient descent method (see equation 3.73). is presentedinthissection(thedetailedderivationprocesscanbefound in appendix A.2). In order to reduce the effect of ”catastrophic in- terference”, three online learning algorithms evolving from the clas- sical online SGBP algorithm are applied in this dissertation, includ- ing the BP with momentum (BPM) algorithm, extended Kalman filter (EKF) algorithm based BP and the so-called sliding window based BP (SWBP) algorithm. Their principles are introduced in the end of this section. 77