Artificial neural networks (ANNs) have found increasing usage in regression
problems because of their ability to map complex nonlinear relationships. In
recent years, ANN regression model applications have rapidly increased in the
engine calibration and controls area. The data used to build ANN models in
engine calibration and controls area generally consists of noise due to
instrument error, sensor precision, human error, stochastic process, etc.
Filtering the data helps in reducing noise due to instrument error, but noise
due to other sources still exist in data. Furthermore, many researchers have
found that ANNs are susceptible to learning from noise. Also ANNs cannot
quantify the uncertainty of their output in critical applications. Hence, a
methodology is developed in the present manuscript which computes the
noise-based confidence interval using engine test data. Moreover, a method to
assess the risk of ANN learning from noise is also developed. The noise-based
confidence prediction methodology does not make any unreasonable assumptions
about the data and explores the parameter space. The developed method is based
on the Bayesian neural network (BNN), and a key input parameter to the BNN is
the likelihood standard deviation. A novel method is developed to predict the
noise standard deviation, and when this noise standard deviation is inputted as
likelihood standard deviation, the noise-based confidence interval is computed
by the BNN. The risk assessment methodology of ANN learning from noise is based
on the BNN distribution of the regression metric used for the ANN. The developed
methodology is illustrated on two engine datasets: an engine friction dataset
and an engine torque dataset. The datasets were used to compare the confidence
interval of the developed method with confidence interval predictions of the
stochastic Kriging regression model. From the study, it can be seen that the
present methodology neither makes stationary noise nor minimum noise at training
points assumptions which are present in the Kriging model. Moreover, from the
engine torque dataset, it has been shown that even though two models can have
similar regression metrics, their risk of learning from noise can be vastly
different.
