Estimation of sound source level of underwater acoustic transducer in shallow water

A sound source level estimation method based on the acoustic inverse frequency response function (IFRF) is proposed to solve the problem of poor accuracy of the assessment of the vibration and noise level of underwater acoustic equipment in shallow waters. This method represents the multi-channel transmission function as the interference superposition of the sound source and its multi order virtual source. The transfer matrix builds the relationship between the complex source strengths, the complex pressures at measurement points and the acoustic channel. The source strengths of underwater acoustic transducer can be estimated accurately from the radiated acoustic field measurement based on the inversion of transfer matrix. The basic principle of the IFRF method is introduced, and the influencing factors of source strength estimation errors are analyzed, including the underwater acoustic channel estimation errors, sound pressure measurement errors, and the conditions of the transfer matrix. The results of numerical simulation analysis are presented, which indicates that the proposed method is feasible and has good performance in estimating the sound source level of underwater acoustic transducer.

With the proposal and implementation of the national maritime power strategy, great attention has been paid to the development of marine cylinderical underwater transducer, ecological protection, scientific research and rights protection. The underwater acoustic equipment and unmanned underwater vehicles (UUV, UUV, AUV) and marine engineering equipment have also been rapidly developed, and the provision of accurate and effective equipment performance information will strongly support the development of various transducers. The intensity of underwater radiated sound source is an important parameter of underwater acoustic equipment when it is working, and it is related to its own performance and safety. Currently, for the testing of underwater noise sources,In most cases, the position of the noise source can be well located and identified, but it is difficult to accurately measure the intensity of the target sound source.If the radiated sound level of the noise source can be accurately measured or evaluated, it can provide guidance for equipment development or performance estimation, and extend it to underwater navigation.The evaluation of the underwater noise level of targets such as traveling vehicles or surface ships will provide effective evaluation of their noise level or the effect of acoustic treatment measures. In a shallow water environment, the reflected sound from the interface and other background interference sound sources will affect the target underwater radiated sound field test. If the direct sound of the target can be separated from the interference sound by a specific algorithm, the sound source can be accurately estimated Information, inverse frequency response matrix method(Inverse Frequency Response Function, IFRF) As a spatial transformation algorithm, it has a high Ground accuracy, and can be used to identify sound sources and visualize the sound field of complex structures, and is not limited by the acoustic system, which is a practical test method of the IFRF method in near-field sound source imaging in air medium.With more detailed theoretical analysis, scholars from various countries have also successively studied and developed the theory in the subsequent time. But there have been research masters.It must be concentrated in the air anechoic room environment and has achieved good results. If the method can be introduced into the actual shallow water environment, it can be used for testing and evaluating the radiation intensity of the vibration sound source will significantly improve the problem of poor accuracy of the target sound source intensity test in a shallow water environment.In view of the above problems, this paper takes monopole sound source as the research object, and under the assumption of spherical wave, the channel transfer function is modeled as multi-virtual source radiation.The vector superposition of radio sound propagation, the IFRF method is used to invert the target radiated sound source level value, and the factors that affect the accuracy of sound source level estimation are evaluated.Reasoning analysis, and related simulation analysis based on the established sound field model, the results show that the method estimates the sound source radiated by the underwater acoustic transducer Level is feasible and has a high degree of accuracy.

1.1 Inverse frequency response matrix method

The frequency response function establishes the relationship between the actual environmental measurement sound pressure and the target sound source. The function matrix can be directly measured or passed.The numerical model is calculated, and the sound field is measured by the hydrophone array to obtain the frequency response function matrix and the complex sound pressure of the sound field.After calculation, the intensity of the sound source can be estimated from the sound field measurement. Considering the case of a single-point sound source, the connection of the piezo element on the sound array.The receiving transducer signal is the sound source emission signal and the underwater acoustic channel response function, where q(hs,t) is the depth of the sound source at hs, and p(hm,t) is the depth.The time domain signal received at the measuring point hm, H(hs,hm) is the acoustic channel response function from the sound source to the receiving point.In order to facilitate the analysis, we choose to analyze the sound propagation relationship in the frequency domain, and use a matrix to represent the ideal array acquisition signal and sound.

The relationship between the sources, P is the M×1 order complex sound pressure vector, Q is the sound source intensity vector (including the imaginary source), H is the complex frequency response matrix, where the term Hi,j is related to the i-th sound source to the i-th sound source. Acoustic transfer function between j elements. In the actual measurement, noise interference or conditional assumptions will bring certain errors. Therefore, vector e needs to be added to the ideal measurement sound pressure. The vector e represents the deviation between the measured sound value and the ideal sound pressure value P. In order to make both To achieve the "best match", the traditional method is to use the least squares method. Define a cost function: It is easy to prove that the sound source intensity when the minimum value of equation is obtained is the best estimated solution.

1.2 Error analysis

Through error analysis, the source of the estimation error can be found, and it can provide basic guidance for the actual measurement work to reduce the error. Without loss of generality .In this case, we conduct an in-depth analysis of the estimated sound source intensity calculated in Section and considering the use of a useful property of the matrix 2-norm, that is, for the matrices A and B.The condition number of the matrix is related to the state of the matrix. When the condition is too large, the matrix is in an ill-conditioned state, and the target estimate will be given at this time .Bring great errors. The matrix condition number is defined.

2 Simulation and discussion

As the actual sound field environment is complex and changeable, different factors will affect the performance of the method to a certain extent. In order to verify the IFRF.The method is used to estimate the accuracy and applicability of the sound source intensity. The objective is to estimate the intensity of the sound source radiated by the monopole sound source, and the MATLAB software is used.To analyze the effect of the IFRF method in a noisy environment, in order to quantify the error between the estimated value and the actual value, the root mean square error is selected to represent the performance in a wide frequency band.

The simulation environment is a uniform shallow water environment with a flat bottom, a water depth of 60m, and the sound source depth is set to 10m, using 33 yuan equally spaced vertical .The linear array is used for measurement, the element spacing is 1m, the center of the base array is at a depth of 22m, and the signal is a single-frequency continuous signal in the range of 100Hz~10kHz spherical underwater acoustic transducer. In order to simulate the influence of noise interference in the actual test signal, Gaussian white noise is added to the sound pressure signal obtained by the simulation calculation. Therefore, the relationship between the difference between the estimated value of the sound source intensity and the true value with frequency and noise level is shown in Figure 1.

In order to highlight the change characteristics of the curve, the error change curve corresponding to the signal-to-noise ratio of 3dB, and 10dB is shown in Figure 2, Table The root-mean-square value of the estimation error of the sound source intensity in the corresponding frequency band of some signal-to-noise ratios .

From the results of Figure 1 and Figure 2, it can be seen that in the frequency range of 100Hz~10kHz spherical hydrophone transducer, the sound source intensity estimation error varies irregularly with the frequency. When the signal-to-noise ratio is low, the error at some frequency points exceeds 3dB preset reference value, with the improvement of the signal-to-noise ratio, this situation has been significantly weakened, and the overall error curve tends to be stable. Combined with the statistical data analysis in Table 1, the overall error in the frequency band is gradually reduced and stabilized with the increase of the signal-to-noise ratio, and it still has a higher accuracy at a lower signal-to-noise ratio, indicating the effectiveness of the IFRF method. Sex and accuracy.

(2) The influence of horizontal distance on sound source level estimation

Due to the expansion of sound waves with the increase of distance, the magnitude of the sound signal at different horizontal distances at the same depth is different. In order to analyze the influence of the measurement array at different horizontal distances on the accuracy of the sound source level estimated by the IFRF method, it is assumed that each The signal-to-noise ratio of the measuring signal at the horizontal distance is the same. According to the analysis of the text, the signal-to-noise ratio is selected as 10dB to analyze the corresponding test conditions of different test distances. Figure 3 lists the corresponding simulation results for some distances. The root mean square value of the estimation error of the sound source level in the corresponding frequency band.

Comparing and analyzing the simulation results in Figure 3, it can be seen that it has similar characteristics to noise changes. As the horizontal test distance increases, the overall sound source level estimation error curve fluctuates more sharply, and there will be more errors at frequencies. Exceeding the 3dB predetermined reference value. Combining the statistical data in Figure 4, it can be seen that the inversion deviation within the frequency band gradually rises as the test distance increases. Analyzing this trend change, the overall deviation is less than 1dB or even lower within a distance of about 200m. Considering that the actual acoustic signal has propagation attenuation and environmental noise interference, in the actual test, the test horizontal position is controlled within 100m from the target, which can improve the validity and accuracy of the test results.

3 Conclusion

This paper proposes a method for estimating the sound source intensity of underwater acoustic transducers in shallow waters based on the inverse frequency response matrix method. The feasibility and accuracy of the method are analyzed and verified from the perspective of theory and simulation. The article first derives and describes the principle of the IFRF method; and analyzes the cause of the error in the sound source intensity estimation from the theoretical derivation. Comparing with the traditional spherical wave attenuation method and beam forming method, the inverse frequency response function takes the reflected signal from each boundary surface as an effective input, and also takes into account the influence of the acoustic channel and the fluctuation of the sound field. The simulation analysis shows that the proposing method has good performance in the estimation of target sound source level in shallow water. This method is suitable for the case of shallow seas with constant sound velocity profile, and for complex hydrology or The situation of broadband signal measurement needs further study.