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Objective In the current autoclave systems , several temperature sensors are primarily used to control the forming temperature of composite components . This point-measurement method makes it difficult to measure the spatial temperature field . Additionally , this contact-based temperature measurement approach directly affects the temperature distribution at the interface between the mold and the components. These limitations significantly impact the quality of component formation. Accurately measuring the gas temperature field in the forming of large-scale s patial components has become a pressing challenge in the curing process of aerospace composite material parts. Therefore, this study explores a method for distributed ultrasonic detection of the two-dimensional gas temperature field.

Methods This study first employs 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 . Subsequently, the analysis is extended to ultrasonic propagation characteristics under varying temperature fields . Based on these analyses , a distributed ultrasonic gas temperature measurement model is established using time-of-flight characteristics.To address 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 temperature resolution is low—a two-dimensional temperature field reconstruction algorithm based on logarithmic-quadratic (LQ) functions and singular value decomposition (SVD) is developed for autoclave conditions. The core idea of this algorithm is to first fit the distribution of the reciprocal of sound speed using a linear combination of LQ functions to establish an inversion model. Then, SVD is used to address the ill-posedness in the inversion process, enabling the solution of the model.The accuracy of the LQ-SVD algorithm is then 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 are compared with those of three other common algorithms. To account for practical errors, white noise is added to the theoretical true values to simulate system errors, and the noi se resistance of the algorithm is tested based on this.Finally, a distributed ultrasonic temperature measurement system is set up in the autoclave for experimental validation. Several thermocouples are used to measure the true temperature field, and the reconstruction error between the experimental system's reconstructed values and the true values is analyzed to verify the effectiveness of the proposed method.

Results and Discussions In the propagation of ultrasound within the gas space of an autoclave , besides the primary longitudinal wave pulses , multiple reflection waves and wave interferences exist , resulting in complex propagation behaviors . Additionally, due to different temperature distributions, the propagation time of ultrasound along its path varies . In this study, the "time-of-flight characteristics" are at the microsecond level, influenced by factors such as medium properties, temperature fields, and the propagation distance of ultrasound.The LQ-SVD algorithm demonstrates the following reconstruction metrics for different types of temperature fields : for a single-peak symmetric temperature field, the maximum absolute error, errormean, and root mean square error are 0.8123 K, 0.1611K, and 0.0574%, respectively; for a single-peak biased temperature field, these metrics are 0.0431 K, 0.0087K, and 0.0026%; for a double-peak biased temperature field, they are 9.9829K, 0.8283K, and 0.3175%; for a triple-peak biased temperature field, they are 16.3017K, 2.1250K, and 0.6516%; and for a quadruple-peak biased temperature field, they are 95.1638K, 11.1843K, and 3.8784%. 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 s ingle-peak symmetric temperature fields are 0.0583%, 1.2490%, and 0.5291%, respectively; for single-peak biased temperature fields, these errors are 0.2030%, 0.5017%, and 0.0494%; for double-peak biased temperature fields, they are 0.5887%, 1.2208%, and 1.8002%; for triple-peak biased temperature fields, they are 1.2387%, 1.8017%, and 3.6965%; and for quadruple-peak biased temperature fields, they are 3.8843%, 3.9644%, and 10.7357%. These results indicate that regardless of the temperature field model, the LQ-SVD algorithm consistently achieves 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 are 22.4090 K, 3.9659K, and 1.3386%; for single-peak biased temperature fields, they are 21.1747K, 3.5079K, and 1.0903%; for double-peak biased temperature fields, they are 20.7577K, 3.4176K, and 1.0510%; for triple-peak biased temperature fields, they are 25.5889K, 4.6634K, and 1.3835%; and for quadruple-peak biased temperature fields, they are 85.4804K, 11.7046K, and 3.9158%. With a noise standard deviation of 1 us, these metrics for single-peak symmetric temperature fields are 36.5781 K, 5.7792K, and 1.9563%; for single-peak biased temperature fields, they are 46.6511K, 7.2609K, and 2.5816%; for double-peak biased temperature fields, they are 67.9445K, 8.3718K, and 2.6470%; for triple-peak biased temperature fields, they are 59.3418K, 7.2211K, and 2.3339%; and for quadruple-peak biased temperature fields, they are 90.7384K, 14.3979K, and 4.4350%. In the on-site experimental validation within the autoclave, the average relative error between reconstructed temperatures and thermocouple measurements is 4.48%, indicating effective performance of the distributed ultrasound temperature measurement system in temperature field reconstruction.

Conclusions The results demonstrate that the method established in this study for distributed ultrasound detection of two-dimensional gas temperature fields can precisely describe the propagation characteristics of ultrasound under thermal/acoustic coupling effects within the autoclave . This method can accurately reconstruct the temperature field distribution in the autoclave space . Its effectiveness significantly alleviates the current limitation of using only a few sensor points to measure temperature in autoclaves. It preliminarily meets the need for accurately measuring the temperature field of forming gas in large spatial components during the molding and curing of aerospace composite material parts , providing robust support for improving the quality of component formation in the future.