A Legendre Polynomial Neural Network and its Application in Predicting Data Center Temperature

This paper investigates the potential of using of novel a Legendre polynomial neural network in predicting the temperature profile of a highly complex data center hosted in the University of the Aegean, Greece. The network comprises an input, a hidden and an output layer. The hidden layer consists of a number of nodes, which expand linear combinations of the input variables into truncated Legendre polynomial series. The output layer aggregates the nodes' outputs into a single sum and provides the network's output. Since Legendre polynomials are orthogonal under certain requirements, explicit mathematical analysis is carried out to provide conditions for satisfying those requirements and to take the advantage of the orthogonal polynomials' accurate performance. Moreover, it is analytically proven that the network can approximate any continuous function defined on a compact subset of the general Euclidean space to arbitrary accuracy. The modelling concerns the air temperature inside the data center server' s rack and takes place on the basis of a number of variables (i.e., input variables) that directly affect the above temperature. The network is compared to other two polynomial networks. The comparison has been conducted in terms of standard performance criterion and extensive non-parametric statistical analysis. Main results of the experimental comparison are enumerated as follows: (a) polynomial orders of 3 and 4 effectively predict the temperature profile, while higher polynomial orders deteriorate the network's performance due to possible fitting problems; (b) the statistical analysis indicates that the proposed network outperforms the other networks.