MIXED ORDER RESPONSE FUNCTION ESTIMATION FROM MULTIINPUT NONLINEAR-SYSTEMS

In this work a novel formalism to estimate the vector linear and leadi ng non-linear impulse response functions from the experimental data ob served from a multi-input system, allowing for correlation between the inputs, is presented. Time series statistical moments are estimated f rom the data and used as the basis of a set of simultaneous equations in the unknown response functions. These simultaneous equations are so lved using standard matrix methods for the unknown response functions. The response functions of a system provide a unique description of th e physical process under investigation, unlike many of the other time series methods available, The ability of the technique to correctly es timate the response functions of a multi-input non-linear system to a high degree of accuracy is demonstrated, using a numerical example whe re the properties of the system are known and there is strong correlat ion between the input data. This novel technique is then used to estim ate, from the time series, the first (linear) and second order respons e functions of the coupled convective and radiative processes, that ac t at the internal surface of the ceiling of a building, The estimated first and second order response functions all show discernible structu re. The area/volume under the estimated response functions of each pro cess are, respectively, the first and second order gains or heat trans fer coefficients for that process. The response functions, of each pro cess, estimated were employed to predict the surface heat flux in an o ut of sample section, given the convective and radiative driving force s, which was compared with the measured heat flux and showed an excell ent agreement.