Mixed order response function estimation from multi-input non-linear systems

Abstract

In this work a novel formalism to estimate the vector linear and leading non-linear impulse response functions from the experimental data observed from a multi-input system, allowing for correlation between the inputs, is presented. Time series statistical moments are estimated from the data and used as the basis of a set of simultaneous equations in the unknown response functions. These simultaneous equations are solved using standard matrix methods for the unknown response functions. The response functions of a system provide a unique description of the physical process under investigation, unlike many of the other time series methods available. The ability of the technique to correctly estimate the response functions of a multi-input non-linear system to a high degree of accuracy is demonstrated, using a numerical example where the properties of the system are known and there is strong correlation between the input data. This novel technique is then used to estimate, from the time series, the first (linear) and second order response functions of the coupled convective and radiative processes, that act at the internal surface of the ceiling of a building. The estimated first and second order response functions all show discernible structure. The area/volume under the estimated response functions of each process are, respectively, the first and second order gains or heat transfer coefficients for that process. The response functions, of each process, estimated were employed to predict the surface heat flux in an out of sample section, given the convective and radiative driving forces, which was compared with the measured heat flux and showed an excellent agreement.