Research On Temperature Field Reconstruction Of Acoustic Tomography Based On Compressed Sensing Theory

Acoustic Tomography(AT),used for temperature field reconstruction,offers the advantages of non-contact and non-interference measurement in the measured temperature field,which has a wide measurement range,cost-effectiveness,and strong environmental adaptability.This technology has already been successfully utilized in measuring high-temperature gas temperature fields in various environments,such as power plant boilers and furnace combustion chambers.Moreover,the application of this technology to monitor the hydrothermal vents at the seabed,the atmospheric environment,and the temperature distribution in stored grain is in progress.When reconstructing the temperature field using AT technology,arranging several acoustic transceivers around the measured area and discretizing the measured area into grids is necessary.The process involves measuring the time of flight of sound waves between transceivers and employing appropriate reconstruction algorithms to reconstruct a sound slowness value,i.e.,reciprocal of sound speed,for each grid.The temperature distribution is subsequently obtained using the relationship between sound velocity and temperature.The reconstruction of the temperature field by AT belongs to the study of an inverse problem based on the reverse effect.Due to the limited availability of acoustic time-of-flight data,high-precision reconstruction of the AT temperature field is challenging.Hence,this study introduces the theory of compressive sensing(CS)into the AT temperature field reconstruction to improve the accuracy of the AT temperature field reconstruction.Taking the three key elements of CS-based high-precision reconstruction,including reconstruction algorithm,dictionary,and measurement matrix,as the starting point,this study conducts in-depth and systematic research on CS-based AT temperature field reconstruction.Then,three independent algorithms are proposed to accomplish the following tasks:(1)To enhance the accuracy of temperature field description,the field is discretized into more grids,which increases the complexity of reconstruction.To address this challenge,CS theory is introduced into AT temperature field reconstruction.The sparsity of the signal in the transform domain reduces the data volume to be reconstructed and mitigates the difficulty of solving the underdetermined inverse problem.Through comparative,this study determined that the sound slowness signal serves as the measured signal,while the acoustic flight time represents the measured value.Consequently,a CS measurement matrix for the AT system is established.The orthogonal matching pursuit(OMP)algorithm is selected as the basic reconstruction algorithm.The study provides an overview of the process for the AT temperature field reconstruction based on CS,laying the foundation for subsequent research.(2)Using the improved CS reconstruction algorithm as the starting point,an improved OMP-based AT temperature field reconstruction algorithm,namely the CS-IMOMP algorithm,is proposed.Firstly,Discrete Fourier Transform(DFT)is determined as the best choice among commonly used analytical dictionaries based on the coherence between the dictionary and the measurement matrix,as well as the dictionary’s sparsity ability for sound slowness signals.Then,two improvements are proposed to the OMP algorithm: 1)Introducing iteration termination conditions related to the measurement noise level,eliminating the sparsity prediction process,and reconstructing as many non-zero elements of sound slowness signals as possible in the sparse representation of the dictionary domain,and 2)Changing the single-column selection strategy to a multi-column selection strategy with a variable number of columns to boost the reconstruction speed without reducing quality.The reconstruction results demonstrate that the reconstruction error of the CS-IMOMP algorithm is significantly lower than the least squares method(LSM)and the simultaneous iterative reconstruction technique(SIRT).Compared to the CS-OMP algorithm with single column selection,the reconstruction error of CS-IMOMP is similar to the CS-OMP algorithm,while the time consumption of CS-IMOMP is reduced by nearly half of CS-OMP.(3)An AT temperature field reconstruction algorithm based on the union dictionary(UD),namely the CS-UD algorithm,is proposed to address the limited sparsity ability of a single dictionary for sound slowness signals and the limitation of the accuracy of AT temperature field reconstruction based on CS.This algorithm utilizes the K-Singular Value Decomposition(KSVD)method to learn several specialized dictionaries for common temperature field types.During the reconstructing process,the acoustic wave flight time characteristics are extracted by through Principal Component Analysis(PCA).Then,the K-Nearest Neighbor(KNN)algorithm is used to identify the temperature field type and give the recognition credibility.For temperature fields with highly reliable peak patterns,a specialized dictionary corresponding to the recognition results is selected.In contrast,a DFT dictionary is chosen for temperature fields with low-reliability peak patterns and uncertainty.Finally,the OMP algorithm is used to complete sparse reconstruction and achieve temperature field reconstruction.The CS-UD algorithm takes into account the dictionary specificity and coverage,and learning a new type of temperature field dictionary does not affect the existing dictionary.The CS-UD algorithm has lower reconstruction error and faster reconstruction speed compared with the CS-OMP algorithm using the DFT dictionary and the CS-SLD algorithm employing a single learning dictionary.(4)In response to the issue of weak CS measurement randomness caused by the structured nature of the AT temperature field reconstruction system,the measurement "randomness" is equivalent to an "unbiased" selection of sampling points.In this case,a method is proposed to indirectly enhance the randomness of measurement by improving the Adequacy and Uniformity(AU)of sound path layout,abbreviated as AU method.The optimization objective is to maximize the AU of the sound path layout and optimize the position of the acoustic transceiver using a genetic algorithm.Compared to the measurement matrix corresponding to the standard symmetric transceiver layout,the measurement matrix optimized by the AU method exhibits better randomness and less coherence with the dictionary.Thus,an AT temperature field reconstruction algorithm is introduced based on measurement matrix optimization,called the CS-AU algorithm.The CS-AU algorithm leverages the AU method to optimize the measurement matrix,employing DFT as the dictionary and OMP as the CS reconstruction algorithm.In this scenario,the reconstruction error of the CS-AU algorithm is lower,and the impact of changes in hot spot positions on the reconstruction error of the temperature field is also smaller than the CS-OMP algorithm.(5)To validate the effectiveness of the proposed AT temperature field reconstruction algorithm,temperature field reconstruction experiments are conducted using a self-developed AT temperature field reconstruction system in the air.The results show that the reconstruction quality of the CS-IMOMP,CS-UD,and CS-AU algorithms,based on the CS reconstruction algorithm,dictionary,and observation matrix,respectively,is significantly superior to the classical LSM and SIRT algorithms.All three algorithms exhibit promising real-time performance.Subsequently,the necessity of the independent existence of these three reconstruction algorithms is analyzed,and a cross-comparison is performed among them.The CS-IMOMP algorithm exhibits a reduced reconstruction time and does not require learning dictionaries or optimizing transceiver positions.Consequently,it stands out as the easiest to implement and widely applicable.CS-UD attains the highest reconstruction quality with the shortest time consumption.However,it requires constructing sample sets for application scenarios,learning dictionaries,and training dictionary selectors.While the CS-AU has good reconstruction quality,it needs to optimize the position of the transceiver,demanding a high degree of freedom in the layout of the transceiver.Finally,the improved sparse signal reconstruction algorithm(IMOMP),union dictionary(UD),and AU method are combined,forming three new reconstruction algorithms and conducting temperature field reconstruction experiments.The findings show that the UD significantly enhances the quality and time of temperature field reconstruction.Furthermore,the reconstruction algorithm that simultaneously uses IMOMP,UD,and AU has a better reconstruction quality and shorter reconstruction time.