Response spatiotemporal correlation and transient temperature field direct reconstruction for heat conduction system

Abstract

In this paper, according to a spatiotemporal correlation characteristic of the temperature response of a transient heat conduction system, a response spatiotemporal correlation (RSTC) model of the temperatures between measurement space and estimation space of the system is proposed. Furthermore, a RSTC based direct reconstruction (RSTC-DR) method is developed for a transient temperature field reconstruction problem of a heat conduction system with unknown heat sources. In the offline stage, firstly, mapping eigenvectors of a heat conduction system are determined by the transfer equations without specific heat source information. Then, according to the correlation degree between the mapping eigenvectors, a finite number of representative spatial points (RPs) are extracted. Meanwhile, a fuzzy membership relationship between the mapping characteristics of the RPs and that of the temperature field is determined. Namely, effective mapping characteristic coverage of the RPs to the whole temperature field is realized. Moreover, a RSTC model between the measurement spatial points (MPs) and the RPs is obtained by the step response model of the temperature field. In the online stage, based on the RSTC model, the temperature responses of the RPs are estimated by employing the time series vector of the temperature measurements of the MPs. Next, according to the fuzzy membership relationship, the temperature field can be reconstructed in real time by synthesizing the temperature estimations of the RPs. The RSTC-DR method is employed to achieve the non-destructive reconstruction of the transient temperature field of a two-dimensional heat conduction system. The temperature field is reconstructed by the numerical experiment to verify the effectiveness of the proposed method and to discuss its adaptability. Furthermore, the practical effectiveness of the method is demonstrated by applying the existing experimental data.