On the prediction of the time-varying behaviour of dynamic systems by interpolating state-space models

• Published in: Journal of physics. Conference series 2024-02, Vol.2698 (1), p.12009
• Main Authors: Dias, R S O, Martarelli, M, Chiariotti, P
• Format: Article
• Language: English
• Subjects: Accelerometers; Algorithms; Chambers; Climate; Dynamic structural analysis; Dynamical systems; Dynamics; Frequency response functions; Joint input-state estimation; Linear Parameter Varying models; Load Identification; Parameter identification; Rubber; State estimation; State space models; Structural Dynamic Measurements; System Identification; Temperature; Time dependence
• ISSN: 1742-6588; 1742-6596
• DOI: 10.1088/1742-6596/2698/1/012009

In this article, a local Linear Parameter Varying (LPV) model identification approach is exploited to analyze the dynamic behaviour of a structure whose dynamics varies over time. This structure is composed by two aluminum crosses connected by a rubber mount. To observe time-dependent variations on the dynamics of this assembly, it is placed in a climate chamber and submitted to a six minute temperature run-up. During this run-up the structure is continuously excited by a shaker. The load provided by this device is measured by a load cell, while six accelerometers are measuring the responses of the system. The temperatures of the air inside the climate chamber and at the surface of the mount are also continuously measured. It is found that during the performed temperature run-up, the rubber mount temperature increased from, roughly, 14℃ to, approximately, 35.2℃. By using the measured load provided by the shaker and the measured accelerations, Frequency Response Functions (FRFs) at five different rubber mount temperatures are computed. From each of these sets of FRFs, state-space models are estimated. Afterwards, these models are used to define an interpolating LPV model, which enables the computation of interpolated state-space models representative of the dynamics of the system at each time sample. It is found that by feeding the interpolated state-space models with the measured load, an accurate simulation of the measured accelerations is obtained. Moreover, by exploiting a joint input-state estimation algorithm with the interpolated state-space models and with the measured accelerations, a very good prediction of the applied load can be obtained. It is also shown that if the time dependency of the dynamics of the system is ignored, the results are less accurate.