Temperature field reconstruction from the partial measurement data using the gappy proper orthogonal decomposition

Abstract

Fast reconstruction of the temperature field from the partial temperature measurement data is highly desirable in the field of thermal engineering, in which reconstruction algorithms play a crucial role in real applications. Based on the gappy proper orthogonal decomposition technique, a promising approach that integrates the numerical simulation information and the measurement information is proposed in this study for the temperature field reconstruction from the partial measurement data, where the original reconstruction problem is formulated into an optimisation problem. An objective functional, which simultaneously considers the outliers in the measurement data and the model approximation distortions, is presented. Based on the split Bregman iteration technique, an iterative scheme is developed for solving the proposed objective functional. Numerical simulations are implemented to demonstrate the feasibility and effectiveness of the proposed algorithm.

Three‐dimensional temperature distribution reconstruction using the extreme learning machine

“…From the viewpoint of statistics, the 3DTDR problem belongs to the category of the missing data estimation. Currently, most of the development of the missing data estimation methods is focused on issues involving 1D or 2D cases, including the gappy proper orthogonal decomposition (GPOD) method or the principle component analysis (PCA) technique [1][2][3][4], the compressed sensing method [5], the matrix completion (MC) method [6][7][8] etc. It is difficult to directly extend the GPOD approach and the PCA method to 3DTDR problems due to the spatial correlations of the 3D data structure.…”

Data Driven Based Method for Field Information Sensing

“…In order to satisfy the above requirements, two kinds of approaches, including numerical simulation methods and measurement approaches, are available. Owing to the challenges, such as (1) the understanding of the complicated mechanisms of the underlying process and the acquisition of the reasonable mathematical model are challenging, (2) it is hard to provide reliable governing equations, boundary conditions, physical property parameters, and initial conditions due to the restrictions of real conditions and (3) numerical simulations are time-consuming; applying numerical simulation methods to achieve the monitoring and control of the large-scale dynamic objects may be impractical. Currently, different measurement methods, which can be approximately divided into two categories, such as point measurement methods and field measurement techniques, have been developed for acquiring such information.…”

“…It is worth emphasizing that differing from common measurement approaches and numerical methods, the FIS method is a data driven measurement data, which integrates scattered measurement method and numerical optimization approach. Presently, different methods, including the artificial neural network (ANN) technique [1], the gappy proper orthogonal decomposition (GPOD) method or the principle component analysis (PCA) technique [2][3][4][5], the compressed sensing (CS) method [6], and the matrix completion (MC) method [7,8], are available for the FIS problem. The ANN method belongs to the data driven approaches and has found wide applications in various fields.…”

Indoor physical field estimation from sparse sensor observations

“…• The other approach is to solve a linear equation formulated by sparse observations of the physical field [57][58][59]. With the PCA modes, we can easily find a linear measurement model for every single point of the physical field in terms of the PCA coefficients.…”

“…Directly minimizing Ξ n is not easy. One popular approach to find the approximated solution is the method of snapshots [57][58][59][60], which only consider the physical field (i.e., the snapsots) in the known database S. In other words, we can approximately…”