Study on Distributed Ultrasonic Detection Method of Two-dimensional Gas Temperature Field

ObjectiveThis study applies several temperature sensors in current autoclave systems to control the forming temperature of composite components. This point-measurement method presents challenges in capturing the spatial temperature field. In addition, this contact-based temperature measurement approach directly influences the temperature distribution at the interface between the mold and the components. These limitations significantly affect the quality of component formation. Accurately capturing the gas temperature field during the forming of large-scale spatial components remains a critical challenge in the curing process of aerospace composite material parts. This study investigates a method for distributed ultrasonic detection of the two-dimensional gas temperature field.MethodsThis study first employed numerical simulation software to analyze the ultrasonic propagation characteristics in an autoclave under steady-state temperature field conditions from the perspective of thermo-acoustic coupling. The analysis was then extended to ultrasonic propagation characteristics under varying temperature fields. Based on these analyses, a distributed ultrasonic gas temperature measurement model was established using time-of-flight characteristics. In addressing issues associated with inverse problems, such as the limitations of least squares and algebraic iterative methods, where the number of discrete points cannot exceed the number of propagation paths and the temperature resolution is low, a two-dimensional temperature field reconstruction algorithm based on logarithmic-quadratic (LQ) functions and singular value decomposition (SVD) was developed for autoclave conditions. The core idea of this algorithm was to fit the distribution of the reciprocal of sound speed using a linear combination of LQ functions to establish an inversion model. SVD was then employed to address the ill-posedness in the inversion process, which enabled the model to be solved. The accuracy of the LQ‒SVD algorithm was analyzed by evaluating the maximum absolute error, mean error, and root mean square error between the reconstructed temperature field and the original temperature field, and the results were compared to those of three other common algorithms. In accounting for practical errors, white noise was added to the theoretical actual values to simulate system errors, and the noise resistance of the algorithm was tested based on this. A distributed ultrasonic temperature measurement system was finally set up in the autoclave for experimental validation. Several thermocouples were utilized to measure the actual temperature field, and the reconstruction error between the experimental system's reconstructed values and the actual values was analyzed to verify the effectiveness of the proposed method.Results and DiscussionsIn addition to the primary longitudinal wave pulses in the propagation of ultrasound within the gas space of an autoclave, multiple reflection waves and wave interferences were present, resulting in complex propagation behaviors. Due to varying temperature distributions, the propagation time of ultrasound along its path differed. This study examined the “time-of-flight characteristics” at the microsecond level, which were influenced by factors such as medium properties, temperature fields, and the propagation distance of ultrasound. The LQ‒SVD algorithm demonstrated the following reconstruction metrics for different types of temperature fields: for a single-peak symmetric temperature field, the maximum absolute error, mean error, and root mean square error were 0.812 3 K, 0.161 1 K, and 0.057 4%, respectively; for a single-peak biased temperature field, these metrics were 0.043 1 K, 0.008 7 K, and 0.002 6%; for a double-peak biased temperature field, they were 9.982 9 K, 0.828 3 K, and 0.317 5%; for a triple-peak biased temperature field, they were 16.301 7 K, 2.125 0 K, and 0.651 6%; and for a quadruple-peak biased temperature field, they were 95.163 8 K, 11.184 3 K, and 3.878 4%. Based on root mean square error, the temperature field reconstruction errors for the Multi-Quadratic (MQ), Markov radial basis function (MK), and Gaussian function-based (GS) algorithms for single-peak symmetric temperature fields were 0.058 3%, 1.249 0%, and 0.529 1%, respectively; for single-peak biased temperature fields, these errors were 0.203 0%, 0.501 7%, and 0.049 4%; for double-peak biased temperature fields, they were 0.588 7%, 1.220 8%, and 1.800 2%; for triple-peak biased temperature fields, they were 1.238 7%, 1.801 7%, and 3.696 5%; and for the quadruple-peak biased temperature fields, they were 3.884 3%, 3.964 4%, and 10.735 7%. These results indicated that regardless of the temperature field model, the LQ‒SVD algorithm consistently achieved the best reconstruction performance. In the noise resistance test of the LQ‒SVD algorithm, with a noise standard deviation of 0.5 us, the three reconstruction metrics for single-peak symmetric temperature fields were 22.409 0 K, 3.965 9 K, and 1.338 6%; for single-peak biased temperature fields, they were 21.174 7 K, 3.507 9 K, and 1.090 3%; for double-peak biased temperature fields, they were 20.757 7 K, 3.417 6 K, and 1.051 0%; for triple-peak biased temperature fields, they were 25.588 9 K, 4.663 4 K, and 1.383 5%; and for quadruple-peak biased temperature fields, they were 85.480 4 K, 11.704 6 K, and 3.9158%. With a noise standard deviation of 1 us, these metrics for single-peak symmetric temperature fields were 36.578 1 K, 5.779 2 K, and 1.956 3%; for single-peak biased temperature fields, they were 46.651 1 K, 7.260 9 K, and 2.581 6%; for double-peak biased temperature fields, they were 67.944 5 K, 8.371 8 K, and 2.647 0%; for triple-peak biased temperature fields, they were 59.341 8 K, 7.221 1 K, and 2.333 9%; and for quadruple-peak biased temperature fields, they were 90.738 4 K, 14.397 9 K, and 4.435 0%. In the on-site experimental validation within the autoclave, the average relative error between reconstructed temperatures and thermocouple measurements was 4.48%, which indicated the effective performance of the distributed ultrasound temperature measurement system in temperature field reconstruction.ConclusionsThe results demonstrate that the method established in this study for distributed ultrasound detection of two-dimensional gas temperature fields precisely describes the propagation characteristics of ultrasound under thermal/acoustic coupling effects within the autoclave. This method accurately reconstructs the temperature field distribution in the autoclave space. Its effectiveness significantly alleviates the current limitation of relying solely on a few sensor points for temperature measurement in autoclaves. It preliminarily fulfills the requirement for accurate measurement of the temperature field of forming gas in significant spatial components during the molding and curing of aerospace composite material parts, providing robust support for enhancing the quality of component formation in the future.