Fault Detection and Diagnostics for Rooftop Air Conditioners

2.2.3 Back-propagation neural network
Neural networks are composed of simple elements operating in parallel. These elements
are inspired by biological nervous systems. As in nature, the network function is
determined largely by the connections between elements. A neural network can be trained
to perform a particular function by adjusting the values of the connections between
elements. Commonly neural networks are adjusted, or trained, so that a particular input
leads to a specific target output.
Back-propagation (BP) neural networks are used most often and were created by
generalizing the Widrow-Hoff learning rule to multiple-layer networks and nonlinear
differentiable transfer functions. Input vectors and the corresponding output vectors are
used to train a network until it can approximate a function or associate input vectors with
specific output vectors. Networks with biases, a sigmoid layer, and a linear output layer are
capable of approximating any function with a finite number of discontinuities. Standard
backpropagation is a gradient descent algorithm, as is the Widrow-Hoff learning rule. The
term backpropagation refers to the manner in which the gradient is computed for
nonlinear multilayer networks. Properly trained backpropagation networks tend to give
reasonable answers when presented with inputs that they have never seen. Typically, a new
input will lead to an output similar to the correct output for input vectors used in training
that are similar to the new input being presented. This generalization property makes it
possible to train a network on a representative set of input/output pairs.
The oldest algorithm is a gradient descent algorithm, for which the weights and biases are
moved in the direction of the negative gradient of the performance function. However, this
algorithm is often too slow for practical problems. So many improved algorithms such as
variable learning rate, resilient backpropagation, conjugate gradient and reduced memory
Levenberg-marquardt, have been proposed to increase training speed and reduce the
memory requirements. Another problem that occurs during neural network training is
called overfitting. The error on the training set is driven to a very small value, but when
new data is presented to the network the error is large. The network has memorized the
training examples, but it has not learned to generalize to new situations.
Since BP artificial neural networks can be used to build classifiers that directly classify input
vectors, they are often used to build both the model and classifier as a whole for FDD use.
In a paper by Li, X., H. Hvaezi-Nejad (1996), an artificial neural network (ANN) prototype
for fault detection and diagnosis (FDD) in complex heating systems was presented. The
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