CN109323757B - A method for estimating the suppression effect of air bubbles on the characteristic frequency of propeller sound source - Google Patents
A method for estimating the suppression effect of air bubbles on the characteristic frequency of propeller sound source Download PDFInfo
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Abstract
本发明公开了一种估计气泡群对螺旋桨声源特征频率抑制作用的方法，包括：(1)采集不同工况的螺旋桨噪声信号；(2)将噪声信号用循环平稳特征函数计算，得到循环密度谱；(3)将两种工况对应的循环密度谱进行点除，或采用最小二范数法，得到气泡传递函数的循环密度谱；(4)根据步骤(2)得到的循环密度谱，计算循环相干谱，构建对数坐标下的增强包络谱；(5)根据增强包络谱判断特征频率，对气泡传递函数的循环密度谱做特征频率对应的切片，得到气泡群传递函数；(6)根据气泡群传递函数，估计气泡群对螺旋桨声源特征频率抑制作用的大小。利用本发明，可以得到更加准确的传递函数，从而更好的分析气泡群隔离效果。
The invention discloses a method for estimating the suppressing effect of bubble groups on the characteristic frequency of propeller sound source, comprising: (1) collecting propeller noise signals in different working conditions; (2) calculating the noise signal with a cyclostationary characteristic function to obtain the circulation density (3) divide the cyclic density spectra corresponding to the two working conditions, or adopt the least square norm method to obtain the cyclic density spectrum of the bubble transfer function; (4) obtain the cyclic density spectrum according to step (2), Calculate the cyclic coherence spectrum, construct the enhanced envelope spectrum under the logarithmic coordinates; (5) judge the characteristic frequency according to the enhanced envelope spectrum, do the slice corresponding to the characteristic frequency to the circular density spectrum of the bubble transfer function, and obtain the bubble group transfer function; ( 6) According to the transfer function of the bubble group, estimate the suppression effect of the bubble group on the characteristic frequency of the sound source of the propeller. By using the present invention, a more accurate transfer function can be obtained, thereby better analyzing the bubble group isolation effect.
Description
技术领域technical field
本发明属于信号处理与特征提取领域，尤其是涉及一种估计气泡群对螺旋桨声源特征频率抑制作用的方法。The invention belongs to the field of signal processing and feature extraction, in particular to a method for estimating the suppression effect of bubble groups on the characteristic frequency of propeller sound source.
背景技术Background technique
水中透明的气泡具有易于形变、分裂、融合等特点，含气泡水体的声学特性也与纯水有着明显的差别。由于气泡群是水中的强散射体，它对透过的声波有很强的衰减和散射作用。水中气泡在共振时，对接近气泡共振频率上的声波衰减作用更加明显。但气泡群的传递函数特性很难用数学公式直接描述。因此，研究水中气泡群的声学特性具有极其重要的科学意义和应用前景。Transparent air bubbles in water are easy to deform, split, and fuse, and the acoustic characteristics of water containing air bubbles are also significantly different from those of pure water. Since the bubble group is a strong scatterer in water, it has a strong attenuation and scattering effect on the transmitted sound waves. When the bubbles in the water resonate, the attenuation effect on the sound wave near the resonance frequency of the bubbles is more obvious. However, the transfer function characteristics of the bubble group are difficult to be directly described by mathematical formulas. Therefore, the study of the acoustic properties of bubble groups in water has extremely important scientific significance and application prospects.
一种近似的思路是，优先关心特征频率上的气泡传递函数，因此需要一种三维的分析工具，来同时体现特征频率和传递函数的连续特性，这时循环平稳成为了一个好的选择。An approximate idea is to give priority to the bubble transfer function at the characteristic frequency, so a three-dimensional analysis tool is needed to reflect the continuous characteristics of the characteristic frequency and the transfer function at the same time. At this time, cyclostationary becomes a good choice.
循环平稳信号处理是近来兴起的信号处理的一种新兴技术。循环平稳信号即信号中包含着隐藏的周期信息的信号。循环平稳信号是非平稳信号的一种，相比于传统检测方式，更接近实际信号，尤其是旋转机械产生的信号。Cyclostationary signal processing is a newly emerging technology of signal processing. A cyclostationary signal is a signal that contains hidden periodic information. The cyclostationary signal is a kind of non-stationary signal, which is closer to the actual signal than the traditional detection method, especially the signal generated by the rotating machinery.
目前信号处理领域常用的旋转机械故障检测方法主要有傅立叶变换、短时傅立叶变换、小波变换、第二代小波变换和多小波变换等，可以说都是基于内积原理的特征波形基函数信号分解，旨在灵活运用与特征波形相匹配的基函数去更好地处理信号，提取故障特征，从而实现故障诊断。At present, the commonly used rotating machinery fault detection methods in the field of signal processing mainly include Fourier transform, short-time Fourier transform, wavelet transform, second-generation wavelet transform and multi-wavelet transform, etc., which can be said to be based on the principle of inner product. The characteristic waveform basis function signal decomposition , which aims to flexibly use the basis function that matches the characteristic waveform to process the signal better, extract fault features, and realize fault diagnosis.
但是，现有技术中存在以下缺点和不足：傅立叶变换、短时傅立叶变换、小波变换、第二代小波变换和多小波变换等故障检测的方法都建立在假设信号是平稳信号的基础上，而现实中往往是非平稳信号，从而这些检测方法都有不合理的地方，不合实际。同时，这些传统检测方法由于理论上的限制，很难检测到旋转机械的一些重要特征，如叶片通过频率BPF、叶片比频率BRF等，有很大的局限性。However, there are following shortcomings and deficiencies in the prior art: Fault detection methods such as Fourier transform, short-time Fourier transform, wavelet transform, second-generation wavelet transform and multi-wavelet transform are all based on the assumption that the signal is a stationary signal, and In reality, there are often non-stationary signals, so these detection methods are unreasonable and unrealistic. At the same time, due to theoretical limitations, these traditional detection methods are difficult to detect some important features of rotating machinery, such as blade passing frequency BPF, blade ratio frequency BRF, etc., which have great limitations.
发明内容Contents of the invention
本发明提供了一种估计气泡群对螺旋桨声源特征频率抑制作用的方法，能将螺旋桨在气泡群下的声隔离效果的更多特征表现出来，得到的传递函数更加准确，对进一步的信号处理和气泡群声隔离效果的验证都具有现实的指导意义。The invention provides a method for estimating the suppressing effect of bubble groups on the characteristic frequency of sound source of the propeller, which can show more characteristics of the sound isolation effect of the propeller under the bubble group, and the obtained transfer function is more accurate, which is useful for further signal processing And the verification of bubble group sound isolation effect has practical guiding significance.
一种估计气泡群对螺旋桨声源特征频率抑制作用的方法，包括以下步骤：A method for estimating the suppression effect of bubble groups on the characteristic frequency of propeller sound source, comprising the following steps:
(1)采集水下有气泡和无气泡两种工况的螺旋桨噪声信号；(1) Acquisition of propeller noise signals under two working conditions with and without bubbles underwater;
(2)将采集的噪声信号导入程序，用循环平稳特征函数计算，得到两种工况的循环密度谱；(2) Import the collected noise signal into the program, calculate with the cyclostationary characteristic function, and obtain the cyclic density spectra of the two working conditions;
(3)将有气泡和无气泡工况中对应的循环密度谱进行点除，或采用最小二范数法，得到气泡传递函数的循环密度谱；(3) Carry out point division of the corresponding cyclic density spectra in the working conditions with and without bubbles, or use the least square norm method to obtain the cyclic density spectrum of the bubble transfer function;
(4)根据步骤(2)得到的两种工况的循环密度谱，进行归一化后得到两种工况的循环相干谱，然后进一步构建对数坐标下的增强包络谱；(4) According to the cyclic density spectra of the two working conditions obtained in step (2), the cyclic coherence spectra of the two working conditions are obtained after normalization, and then the enhanced envelope spectrum under the logarithmic coordinates is further constructed;
(5)根据得到的增强包络谱判断特征频率，并对气泡传递函数的循环密度谱做特征频率对应的切片，得到气泡群传递函数；(5) Judging the characteristic frequency according to the enhanced envelope spectrum obtained, and doing slices corresponding to the characteristic frequency to the circular density spectrum of the bubble transfer function, to obtain the bubble group transfer function;
(6)根据得到的气泡群传递函数，估计气泡群对螺旋桨声源特征频率抑制作用的大小。(6) According to the obtained transfer function of the bubble group, estimate the suppression effect of the bubble group on the characteristic frequency of the sound source of the propeller.
本发明的方法能将螺旋桨在气泡群下的声隔离效果的更多特征表现出来，得到的特征频率更加贴近螺旋桨噪声的本质，通过得到的气泡群传递函数，可以分析气泡群对螺旋桨声源特征频率抑制作用的大小。The method of the present invention can show more characteristics of the sound isolation effect of the propeller under the bubble group, and the obtained characteristic frequency is closer to the essence of the propeller noise. Through the obtained bubble group transfer function, the sound source characteristics of the bubble group to the propeller can be analyzed. The magnitude of frequency suppression.
步骤(2)中，所述的循环平稳特征函数为：In step (2), described cyclostationary characteristic function is:
α为循环频率、f为频谱频率；x为待测信号；X为信号x的频谱；X*表示的X共轭复数。α is the cycle frequency, f is the spectrum frequency; x is the signal to be tested; X is the spectrum of the signal x; X * represents the complex conjugate of X.
其中，x的调幅模型的数学表达为：Among them, the mathematical expression of the amplitude modulation model of x is:
Ai为各特征频率对应的幅度；αi为特征频率的2倍；t为表示时间；N表示数目。A i is the amplitude corresponding to each characteristic frequency; α i is twice the characteristic frequency; t is time; N is number.
步骤(3)中，所依据的传递模型的数学公式为：In step (3), the mathematical formula of the transfer model based on is:
y(t)＝x(t)*h(t)+v(t)y(t)=x(t)*h(t)+v(t)
其中，y(t)为接收信号，x(t)为声源噪声信号，h(t)为传递函数时域模型,v(t)为背景噪声信号，*为卷积符号。Among them, y(t) is the received signal, x(t) is the noise signal of the sound source, h(t) is the time domain model of the transfer function, v(t) is the background noise signal, and * is the convolution symbol.
对应的循环平稳关系的数学公式为：The mathematical formula for the corresponding cyclostationary relationship is:
其中：
其推导如下：Its derivation is as follows:
根据傅里叶变换的卷积性质和线性性质，有：According to the convolutional and linear properties of the Fourier transform, there are:
根据背景噪声平稳性，有
当H(f)为宽频带时，近似认为
特别的，在消声水池中可以认为C接近0时有：In particular, it can be considered that when C is close to 0 in the anechoic pool:
故对于气泡传递函数的循环密度谱，可近似认为有：Therefore, for the cyclic density spectrum of the bubble transfer function, it can be approximated as:
注：其中，为气泡传递函数的循环密度谱，
此外，还可以采用最小二范数法，即使得下述计算量最小来估计
其中，为气泡传递函数的循环密度谱的最优估计，
步骤(4)中，所述的循环相干谱的数学表达式为：In step (4), the mathematical expression of described cyclic coherence spectrum is:
其中，为有气泡工况对应的循环相干谱，
步骤(4)中，构建对数坐标下的增强包络谱的详细步骤为：In step (4), the detailed steps for constructing the enhanced envelope spectrum under logarithmic coordinates are:
(4-1)计算增强包络谱各个循环频率对应的函数值；所述的增强包络谱的数学表达式为：(4-1) Calculate the function value corresponding to each cycle frequency of the enhanced envelope spectrum; the mathematical expression of the enhanced envelope spectrum is:
其中，
(4-2)将函数值通过取10的对数计算得到声压级，根据得到的对数函数值范围，设置取值区间，将剩余的对数函数值赋值为对应的最值；(4-2) Calculate the sound pressure level by taking the logarithm of 10 for the function value, set the value interval according to the obtained logarithmic function value range, and assign the remaining logarithmic function value to the corresponding maximum value;
(4-3)根据对应的坐标点和函数值，构建对数坐标下的增强包络谱。(4-3) Construct an enhanced envelope spectrum in logarithmic coordinates according to the corresponding coordinate points and function values.
步骤(5)中，所述的特征频率根据增强包络谱的明显峰值、干涉频率和谐波频率等进行综合判断。In step (5), the characteristic frequency is comprehensively judged according to the obvious peak of the enhanced envelope spectrum, interference frequency and harmonic frequency.
本发明克服了传统检测方法在处理循环平稳信号时，叶片通过频率和叶片比频率检测不到或不明显的困难，能将螺旋桨在气泡群下的声隔离效果的更多特征表现出来，同时，借助循环平稳分析进一步可以得到传递函数，从而分析气泡群隔离效果。The invention overcomes the difficulty that the blade passing frequency and the blade ratio frequency cannot be detected or is not obvious when the traditional detection method processes the cyclostationary signal, and can show more characteristics of the sound isolation effect of the propeller under the air bubble group, and at the same time, With the help of cyclostationary analysis, the transfer function can be further obtained, so as to analyze the effect of bubble group isolation.
按照调幅模型得到的特征频率更贴近螺旋桨噪声的本质，能在一定程度上还原螺旋桨噪声信号，得到的传递函数更加准确，对进一步的信号处理和气泡群声隔离效果的验证都具有现实的指导意义。The characteristic frequency obtained according to the amplitude modulation model is closer to the essence of propeller noise, and can restore the propeller noise signal to a certain extent, and the obtained transfer function is more accurate, which has practical guiding significance for further signal processing and verification of bubble group sound isolation effect .
附图说明Description of drawings
图1为本发明一种估计气泡群对螺旋桨声源特征频率抑制作用的方法流程示意图；Fig. 1 is a schematic flow chart of a method for estimating the suppressing effect of bubble groups on the propeller sound source characteristic frequency of the present invention;
图2为四叶螺旋桨在5Hz转频下无气泡群的频谱图；Figure 2 is the frequency spectrum of the four-bladed propeller without bubbles at 5Hz;
图3为四叶螺旋桨在5Hz转频下有气泡群的频谱图；Figure 3 is the frequency spectrum of the four-blade propeller with bubbles at 5Hz;
图4为四叶螺旋桨在5Hz转频下无气泡群的增强包络谱；Figure 4 is the enhanced envelope spectrum of the four-bladed propeller without bubbles at 5 Hz;
图5为四叶螺旋桨在5Hz转频下有气泡群的增强包络谱；Fig. 5 is the enhanced envelope spectrum of the four-bladed propeller with bubble groups at 5Hz rotation frequency;
图6为四叶螺旋桨在20Hz转频下无气泡群的增强包络谱；Figure 6 is the enhanced envelope spectrum of the four-bladed propeller without bubbles at 20Hz;
图7为四叶螺旋桨在20Hz转频下有气泡群的增强包络谱；Figure 7 is the enhanced envelope spectrum of the four-bladed propeller with bubble groups at 20Hz rotation frequency;
图8为四叶螺旋桨在5Hz转频下气泡群计算得到的传递函数图；Fig. 8 is the transfer function diagram calculated by the bubble group of the four-blade propeller at 5Hz rotation frequency;
图9为四叶螺旋桨在20Hz转频下气泡群计算得到的传递函数图。Fig. 9 is a diagram of the transfer function calculated by the bubble group of the four-bladed propeller at a rotational frequency of 20 Hz.
具体实施方式Detailed ways
为了更为具体地描述本发明，下面结合附图及具体实施方式对本发明的技术方案进行详细说明。In order to describe the present invention more specifically, the technical solutions of the present invention will be described in detail below in conjunction with the accompanying drawings and specific embodiments.
如图1所示，一种估计气泡群对螺旋桨声源特征频率抑制作用的方法，包括以下步骤：As shown in Figure 1, a method for estimating the suppression effect of bubble groups on the characteristic frequency of propeller sound source includes the following steps:
S01，使用水听器采集水下不同工况的噪声，包括无气泡群的工况和有气泡群的工况。S01, use hydrophones to collect the noise of different underwater working conditions, including the working conditions without bubble groups and the working conditions with bubble groups.
S02，在程序中设定好相应的参数，将采集到的信号导入到程序中，计算循环密度谱：S02, set the corresponding parameters in the program, import the collected signal into the program, and calculate the cyclic density spectrum:
其中：α为循环频率、f为频谱频率；x为待测信号；X为信号x的频谱；X*表示的X共轭复数。Among them: α is the cycle frequency, f is the spectrum frequency; x is the signal to be tested; X is the spectrum of the signal x; X * represents the complex conjugate of X.
其中x的调幅模型的数学表达为：The mathematical expression of the amplitude modulation model of x is:
其中：Ai为各特征频率对应的幅度；αi为特征频率的2倍；t为表示时间；N表示数目。Among them: A i is the amplitude corresponding to each characteristic frequency; α i is twice the characteristic frequency; t is the time; N is the number.
S03，将有气泡工况的循环密度谱的点一一对应的除以无气泡工况的循环密度谱的点，或最小二范数进行估计，得到气泡传递函数的循环密度谱。S03, divide the points of the cyclic density spectrum of the bubble working condition by the points of the cyclic density spectrum of the non-bubbling working condition one by one, or estimate the least square norm to obtain the cyclic density spectrum of the bubble transfer function.
将有气泡工况的循环密度谱的点一一对应的除以无气泡工况的循环密度谱的点时，气泡传递函数的循环密度谱可近似认为：When the points of the cyclic density spectrum of the condition with bubbles are divided one by one by the points of the cyclic density spectrum of the non-bubble condition, the cyclic density spectrum of the bubble transfer function can be approximated as:
其中，
采用最小二范数法的公式为：The formula using the least square norm method is:
其中，
S04，由S02中循环平稳特征函数计算得到的循环密度函数，根据下述公式计算增强包络谱各个循环频率对应的函数值：S04, the cyclic density function calculated by the cyclostationary characteristic function in S02, calculates the function value corresponding to each cyclic frequency of the enhanced envelope spectrum according to the following formula:
S05，将函数值通过取10的对数计算等得到声压级，根据得到的对数函数值范围，设置最值限制，根据对应的坐标点和函数值，构建对数坐标下的增强包络谱。S05, the function value is calculated by taking the logarithm of 10 to obtain the sound pressure level, according to the range of the obtained logarithmic function value, the maximum value limit is set, and the enhanced envelope under the logarithmic coordinates is constructed according to the corresponding coordinate points and function values Spectrum.
S06，保存得到实际数据的增强包络谱，包括无气泡群和有气泡群两种工况，以及计算得到的气泡群性质的增强包络谱；依据增强包络谱的明显峰值，并根据干涉频率，谐波频率等特征，推断特征频率。S06, save the enhanced envelope spectrum obtained from the actual data, including two working conditions without bubble group and with bubble group, and the enhanced envelope spectrum of the calculated properties of the bubble group; based on the obvious peak of the enhanced envelope spectrum, and according to the Features such as frequency, harmonic frequency, etc., infer the characteristic frequency.
S07，在S06的基础上，直接对比增强包络谱上特征频率、干涉频率、谐波频率等典型频率上的声压级，并做气泡群增强包络谱在对应循环频率上的切片，得到气泡群的传递函数。S07, on the basis of S06, directly compare the sound pressure levels at typical frequencies such as the characteristic frequency, interference frequency, and harmonic frequency on the enhanced envelope spectrum, and slice the bubble group enhanced envelope spectrum at the corresponding cycle frequency to obtain The transfer function of the bubble population.
S08，由所得特征频率构造仿真信号，经循环平稳处理后，与保存的实际数据的检测结果对比验证提取特征的正确性。S08, constructing a simulation signal from the obtained characteristic frequency, and after cyclostationary processing, comparing with the detection result of the stored actual data to verify the correctness of the extracted characteristic.
为了具体表现本方法在气泡群对泵噪声隔离效果检测领域的优势和特征，采用四叶螺旋桨进行试验。In order to specifically demonstrate the advantages and characteristics of this method in the field of detection of the isolation effect of bubble groups on pump noise, a four-bladed propeller was used for the test.
首先对螺旋桨在5Hz正常工况下的无气泡群和有气泡群噪声信号分别进行了采集和处理，经过传统的快速傅立叶变换得到的无气泡群频谱图如图2所示，有气泡群的频谱图如图3所示，可以看出，使用传统的快速傅立叶变换，特征频率及某些倍频检测效果不好；经过循环平稳处理后的得到的增强包络谱分别如图4和图5所示，得到的图形符合对螺旋桨旋转机械属性的预期，分别检测出了轴频5Hz，以及四叶螺旋桨对应的叶频20Hz，及其谐波频率、干涉频率等。此外，通过图4和图5的对比，可以明显看出在低频段，气泡群对螺旋桨噪声有明显的抑制作用。Firstly, the noise signals of the propeller without bubble group and with bubble group under the normal working condition of 5 Hz were collected and processed respectively. As shown in Figure 3, it can be seen that using the traditional fast Fourier transform, the detection effect of the characteristic frequency and some multiplied frequencies is not good; the enhanced envelope spectrum obtained after cyclostationary processing is shown in Figure 4 and Figure 5 respectively It is shown that the obtained graph conforms to the expectation of the mechanical properties of the propeller rotation, and the shaft frequency of 5 Hz and the corresponding blade frequency of the four-bladed propeller of 20 Hz, as well as its harmonic frequency and interference frequency are detected. In addition, through the comparison of Figure 4 and Figure 5, it can be clearly seen that in the low frequency band, the bubble group has a significant inhibitory effect on the propeller noise.
进一步，按照上述方法，对该采集到的噪声信号进行了特征提取，仿真另一个工况信号
通过对比发现，在增强包络谱上，幅值和频率都有一定的相似，但并不完全一致。考虑到仿真信号与实际信号的差异以及频率特征提取的不完全性，该仿真信号在一定程度上，从本质上揭示了气泡群对泵噪声隔离效果的模型的正确性以及特征提取的优越性，对进一步的数据处理以及生产实践具有实际指导意义。Through comparison, it is found that on the enhanced envelope spectrum, the amplitude and frequency are somewhat similar, but not completely consistent. Considering the difference between the simulated signal and the actual signal and the incompleteness of frequency feature extraction, the simulated signal, to a certain extent, essentially reveals the correctness of the model of the bubble group’s effect on pump noise isolation and the superiority of feature extraction. It has practical guiding significance for further data processing and production practice.
本说明书实施例所述的内容仅仅是对发明的解释说明，并不是对本发明进行限制，本发明的保护范围不应当被视为仅限于实施例所述的具体内容，在本发明的精神和原则之内所作的任何修改、替换和改变等，均包含在本发明的保护范围内。The content described in the embodiments of this specification is only an explanation of the invention, not a limitation on the present invention. The protection scope of the present invention should not be regarded as limited to the specific content described in the embodiments. In the spirit and principles of the present invention Any modifications, substitutions and changes made within are included within the protection scope of the present invention.
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