一种两阶段声学层析成像温度分布重建方法

doi:10.12096/j.2096-4528.pgt.24056

摘要/Abstract

摘要：

目的为提高声学层析成像温度分布的重建精度，提出一种基于压缩感知与多尺度扩张卷积的两阶段重建算法。方法首先建立声学层析成像温度分布重建的压缩感知模型，并使用正交匹配追踪(orthogonal matching pursuit，OMP)算法求解得到粗网格温度分布；然后构建多尺度卷积神经网络，预测得到细网格温度分布重建结果，在网络模型中通过引入原始测量信息补偿通道提高对先验信息的利用率；分别建立3种典型温度分布的数值模型，并与OMP算法、代数重建(algebraic reconstruction technique，ART)算法、同步代数重建(simultaneous algebraic reconstruction technique，SART)算法以及Landweber算法进行对比试验。结果所提算法的平均相对误差和均方根误差分别为0.45%和0.64%，重建误差均小于其他算法。结论两阶段温度分布重建算法能够有效缓解温度分布重建问题的病态性，进而提高温度分布的重建精度。

关键词: 声学层析成像, 高分辨率重建, 压缩感知, 多尺度扩张卷积, 正交匹配追踪

Abstract:

Objectives To improve the reconstruction accuracy of temperature distribution in acoustic tomography, a two-stage reconstruction algorithm based on compressed sensing and multi-scale dilated convolution is proposed. Methods First, a compressed sensing model for reconstructing temperature distribution in acoustic tomography is developed, and the orthogonal matching pursuit (OMP) algorithm is used to obtain a coarse-grid temperature distribution. Then, a multi-scale convolutional neural network is established to predict the fine-grid temperature distribution reconstruction results, where a compensation channel for original measurement is incorporated to enhance the utilization of prior information. Three numerical models of typical temperature distributions are established and compared with the OMP, algebraic reconstruction technique (ART), simultaneous algebraic reconstruction technique (SART), and Landweber algorithms. Results The proposed algorithm achieves an average relative error and a root mean square error of 0.45% and 0.64%, respectively, with reconstruction errors lower than those of other algorithms. Conclusions The two-stage temperature distribution reconstruction algorithm can effectively alleviate the ill-posedness of the temperature distribution reconstruction problem, thereby improving the reconstruction accuracy.

Key words: acoustic tomography, high-resolution reconstruction, compressed sensing, multi-scale dilated convolution, orthogonal matching pursuit

中图分类号:

TK 31

张立峰, 董祥虎. 一种两阶段声学层析成像温度分布重建方法[J]. 发电技术, 2025, 46(5): 1050-1058.

Lifeng ZHANG, Xianghu DONG. A Two-Stage Acoustic Tomography Method for Temperature Distribution Reconstruction[J]. Power Generation Technology, 2025, 46(5): 1050-1058.

图/表 17

图1 被测区域及声波路径

Fig. 1 Measurement area and acoustic wave paths

图2 温度分布重建流程

Fig. 2 Flowchart of temperature distribution reconstruction

图3 压缩感知原理图

Fig. 3 Schematic diagram of compressed sensing

图4 OMP算法流程图

Fig. 4 Flowchart of OMP algorithm

图5 SE通道注意力机制原理图

Fig. 5 Schematic diagram of SE channel attention mechanism

图6 扩张卷积原理

Fig. 6 Principle of dilated convolution

图7 多尺度扩张卷积模块

Fig. 7 Multi-scale dilated convolution module

图8 图像的分解与重组

Fig. 8 Image decomposition and recombination

图9 网络结构图

Fig. 9 Diagram of network architecture

图10 MSDC网络训练流程

Fig. 10 MSDC network training process

图11 单峰重建

Fig. 11 Single-peak reconstruction

表1 单峰温度分布重建误差 (%)

Tab. 1 Reconstruction errors of single-peak temperature distribution

重建算法	E_ARE	E_RMSE
Landweber	4.58	6.97
ART	4.27	6.61
SART	3.77	6.46
OMP	0.57	0.88
OMP-MSDC	0.31	0.45

图12 双峰重建

Fig. 12 Double-peak reconstruction

表2 双峰温度分布重建误差 (%)

Tab. 2 Reconstruction errors of double-peak temperature distribution

重建算法	E_ARE	E_RMSE
Landweber	6.43	8.79
ART	6.39	9.30
SART	5.78	8.03
OMP	0.81	1.19
OMP-MSDC	0.44	0.64

图13 四峰重建

Fig. 13 Four-peak reconstruction

表3 四峰温度分布重建误差 (%)

Tab. 3 Reconstruction errors of four-peak temperature distribution

重建算法	E_ARE	E_RMSE
Landweber	7.21	9.13
ART	8.0	10.48
SART	6.83	8.14
OMP	1.48	1.96
OMP-MSDC	0.58	0.79

图14 不同噪声水平下温度场重建误差

Fig. 14 Reconstruction errors of temperature field at different noise levels

参考文献 16

[1]	刘厦，刘石．基于声学层析成像的炉内温度场重建算法研究[J]．动力工程学报，2017，37(7)：525-532．
	LIU S， LIU S ．Research on temperature distribution reconstruction of a boiler furnace based on acoustic tomography[J]．Journal of Chinese Society of Power Engineering，2017，37(7)：525-532．
[2]	张立峰，苗雨．炉膛声学层析测温探头分布方式研究[J]．发电技术，2021，42(3)：329-335． doi:10.12096/j.2096-4528.pgt.20050
	ZHANG L F， MIAO Y ．Study of probe distribution for furnace acoustic tomographic temperature measurement[J]．Power Generation Technology，2021，42(3)：329-335． doi:10.12096/j.2096-4528.pgt.20050
[3]	张立峰，李晶，王智．基于主成分分析和深度神经网络的声学层析成像温度分布重建[J]．发电技术，2023，44(3)：399-406．
	ZHANG L F， LI J， WANG Z ．Reconstruction of temperature distribution by acoustic tomography based on principal component analysis and deep neural network[J]．Power Generation Technology，2023，44(3)：399-406．
[4]	ZHANG S， SHEN G， AN L，et al ．Online monitoring of the two-dimensional temperature field in a boiler furnace based on acoustic computed tomography[J]．Applied Thermal Engineering，2015，75：958-966． doi:10.1016/j.applthermaleng.2014.10.085
[5]	ZHAO G， LEI B， YE G，et al ．Improved eccentricity self-detection method based on least square algorithm for polar coordinate encoder[J]．IEEE Sensors Journal，2021，21(23)：26902-26911． doi:10.1109/jsen.2021.3120328
[6]	YAN H， WEI Y， ZHOU Y，et al ．Temperature distribution reconstruction method for acoustic tomography based on compressed sensing[J]．Ultrason Imaging，2022，44(2/3)：77-95． doi:10.1177/01617346221092695
[7]	WANG J， LI P ．Recovery of sparse signals using multiple orthogonal least squares[J]．IEEE Transactions on Signal Processing，2017，65(8)：2049-2062． doi:10.1109/tsp.2016.2639467
[8]	张立峰，苗雨．一种声学层析成像温度分布高分辨率重建方法[J]．系统仿真学报，2022，34(9)：2065-2073．
	ZHANG L F， MIAO Y ．A high resolution reconstruction method of temperature distribution in acoustic tomography[J]．Journal of System Simulation，2022，34(9)：2065-2073．
[9]	刘厦，刘石，任婷．基于SA-ELM的声学层析成像温度分布重建算法[J]．化工学报，2017，68(6)：2434-2446． doi:10.11949/j.issn.0438-1157.20161597
	LIU S， LIU S， REN T ．SA-ELM based method for reconstructing temperature distribution in acoustic tomography measurement[J]．CIESC Journal，2017，68(6)：2434-2446． doi:10.11949/j.issn.0438-1157.20161597
[10]	SAHOO S K， MAKUR A ．Signal recovery from random measurements via extended orthogonal matching pursuit[J]．IEEE Transactions on Signal Processing，2015，63(10)：2572-2581． doi:10.1109/tsp.2015.2413384
[11]	CANDÈS E J， ROMBERG J K， TAO T ．Stable signal recovery from incomplete and inaccurate measurements[J]．Communications on Pure and Applied Mathematics，2006，59(8)：1207-1223． doi:10.1002/cpa.20124
[12]	ZHANG L， LI J ．Acoustic tomography temperature reconstruction based on virtual observation and residual network[J]．IEEE Sensors Journal，2022，22(17)：17054-17064． doi:10.1109/jsen.2022.3192924
[13]	HU J， SHEN L， SUN G ．Squeeze-and-excitation networks[C]//2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition．Salt Lake City，UT：IEEE，2018：7132-7141． doi:10.1109/cvpr.2018.00745
[14]	WANG Y， WANG G， CHEN C，et al ．Multi-scale dilated convolution of convolutional neural network for image denoising[J]．Multimedia Tools and Applications，2019，78(14)：19945-19960． doi:10.1007/s11042-019-7377-y
[15]	BAO Y， JIA J ．Online time-resolved reconstruction method for acoustic tomography system[J]．IEEE Transactions on Instrumentation and Measurement，2019，69(7)：4033-4041． doi:10.1109/tim.2019.2947949
[16]	LIU S， LIU S， REN T ．Acoustic tomography reconstruction method for the temperature distribution measurement[J]．IEEE Transactions on Instrumentation and Measurement，2017，66(8)：1936-1945． doi:10.1109/tim.2017.2677638