WO2025236261A1 - 一种空中直升机噪声测量方法、装置、介质及产品 - Google Patents

一种空中直升机噪声测量方法、装置、介质及产品

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Publication number
WO2025236261A1
WO2025236261A1 PCT/CN2024/093788 CN2024093788W WO2025236261A1 WO 2025236261 A1 WO2025236261 A1 WO 2025236261A1 CN 2024093788 W CN2024093788 W CN 2024093788W WO 2025236261 A1 WO2025236261 A1 WO 2025236261A1
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Prior art keywords
noise
iteration number
correlation matrix
sampling point
spatiotemporal correlation
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English (en)
French (fr)
Inventor
朱清华
王睿杰
李奥北
涂泽强
招启军
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Nanjing University of Aeronautics and Astronautics
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Nanjing University of Aeronautics and Astronautics
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Priority to PCT/CN2024/093788 priority Critical patent/WO2025236261A1/zh
Priority to CN202480001088.0A priority patent/CN118765368B/zh
Publication of WO2025236261A1 publication Critical patent/WO2025236261A1/zh
Pending legal-status Critical Current
Anticipated expiration legal-status Critical

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Classifications

    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B64—AIRCRAFT; AVIATION; COSMONAUTICS
    • B64F—GROUND OR AIRCRAFT-CARRIER-DECK INSTALLATIONS SPECIALLY ADAPTED FOR USE IN CONNECTION WITH AIRCRAFT; DESIGNING, MANUFACTURING, ASSEMBLING, CLEANING, MAINTAINING OR REPAIRING AIRCRAFT, NOT OTHERWISE PROVIDED FOR; HANDLING, TRANSPORTING, TESTING OR INSPECTING AIRCRAFT COMPONENTS, NOT OTHERWISE PROVIDED FOR
    • B64F5/00—Designing, manufacturing, assembling, cleaning, maintaining or repairing aircraft, not otherwise provided for; Handling, transporting, testing or inspecting aircraft components, not otherwise provided for
    • B64F5/60—Testing or inspecting aircraft components or systems
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01H—MEASUREMENT OF MECHANICAL VIBRATIONS OR ULTRASONIC, SONIC OR INFRASONIC WAVES
    • G01H11/00—Measuring mechanical vibrations or ultrasonic, sonic or infrasonic waves by detecting changes in electric or magnetic properties
    • G01H11/06—Measuring mechanical vibrations or ultrasonic, sonic or infrasonic waves by detecting changes in electric or magnetic properties by electric means
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01H—MEASUREMENT OF MECHANICAL VIBRATIONS OR ULTRASONIC, SONIC OR INFRASONIC WAVES
    • G01H17/00—Measuring mechanical vibrations or ultrasonic, sonic or infrasonic waves, not provided for in the other groups of this subclass
    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/14—Fourier, Walsh or analogous domain transformations, e.g. Laplace, Hilbert, Karhunen-Loeve, transforms
    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/16—Matrix or vector computation, e.g. matrix-matrix or matrix-vector multiplication, matrix factorization
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T90/00—Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation

Definitions

  • This invention relates to the field of noise measurement technology, and in particular to a method, apparatus, medium, and product for measuring noise from an aerial helicopter.
  • Helicopters typically fly at low and very low altitudes, making them suitable for various low- and medium-speed military or civilian missions.
  • aerodynamic noise due to the periodic aerodynamic vibrations of helicopter components such as the rotor, aerodynamic noise is unavoidable. Reducing the noise level of helicopters can significantly improve their overall performance; therefore, aerodynamic noise characteristics research has become an indispensable design factor in the new design phase.
  • helicopter external noise radiation has a large impact range, strong directivity, uneven sound field distribution on the ground and in the air, and is highly correlated with flight status, atmospheric conditions, terrain, and other factors affecting sound speed.
  • Traditional helicopter aerodynamic noise measurement mainly involves two methods: installing random microphones on the target helicopter and installing ground microphone arrays along the target helicopter's flight path.
  • Airborne microphones can quickly obtain the near-field noise characteristics of the helicopter with relatively little environmental interference.
  • fixed installations are affected by mechanical vibrations, require high-quality sensors, cannot collect far-field noise, and have weak perception capabilities for rotor thickness noise.
  • Ground microphone arrays can directly obtain the ground noise radiation level and the overall helicopter noise level, but various noise signals can cause superposition interference in the time and frequency domains. Overall, there is a lack of measurement for aerial noise, and a new method for measuring aerial helicopter noise is needed.
  • the purpose of this invention is to provide a method, device, medium, and product for measuring the noise of helicopters in the air, thereby realizing the measurement of the noise of helicopters in the air.
  • the present invention provides the following solution:
  • a method for measuring noise from an aerial helicopter includes:
  • the raw noise observation signals from multiple sampling points collected by each UAV are acquired; each UAV and the helicopter under test are at the same altitude, and there is at least one UAV; each sampling point corresponds to a time and a frequency; the raw noise observation signals include: the noise of the UAV and the noise of the helicopter under test;
  • the original noise observation signals of each sampling point are transformed into non-negative values to obtain the non-negative noise observation signals of the corresponding sampling points.
  • the target spatiotemporal correlation matrix of each sampling point is estimated based on the nonnegative noise observation signal of each sampling point;
  • the short-time Fourier transform coefficient vector of the noise of the helicopter under test at the corresponding sampling point is determined.
  • the noise intensity of the helicopter under test at the corresponding sampling point is determined.
  • the target spatiotemporal correlation matrix estimate for the corresponding sampling point is determined, including:
  • the spatiotemporal correlation matrix estimation is determined based on the spatial characteristic matrix and the weights, magnitudes, and gains of the NMF basis;
  • the spatiotemporal correlation matrix of the current sampling point is estimated and updated multiple times to obtain the target spatiotemporal correlation matrix estimate of the current sampling point.
  • the update process at any current iteration number includes:
  • the spatiotemporal correlation matrix estimate under the current iteration number is determined as the target spatiotemporal correlation matrix estimate
  • the estimated spatiotemporal correlation matrix for the next iteration number is determined, including:
  • the estimated spatiotemporal correlation matrix at the current iteration number Based on the actual spatiotemporal correlation matrix, the estimated spatiotemporal correlation matrix at the current iteration number, the magnitude of the NMF basis at the current iteration number, and the gain of the NMF basis at the current iteration number, the weight of the NMF basis at the next iteration number is determined.
  • the estimated spatiotemporal correlation matrix at the current iteration number Based on the actual spatiotemporal correlation matrix, the estimated spatiotemporal correlation matrix at the current iteration number, the weights of the NMF basis at the current iteration number, and the gain of the NMF basis at the current iteration number, the magnitude of the NMF basis at the next iteration number is determined.
  • the spatial characteristic matrix at the next iteration number is determined.
  • the spatiotemporal correlation matrix estimate for the next iteration is determined.
  • the UAV is equipped with eight microphone sensors, each of which collects raw noise from one channel to form the raw noise observation signal.
  • the noise intensity of the helicopter under test at the corresponding sampling point is determined, including:
  • the short-time Fourier transform coefficient vector of the noise of the helicopter under test at each sampling point is subjected to inverse short-time Fourier transform to obtain the noise intensity of the helicopter under test at the corresponding sampling point.
  • a computer device includes: a memory, a processor, and a computer program stored in the memory and executable on the processor, the processor executing the computer program to... Implement the aerial helicopter noise measurement method described in any of the above-mentioned methods.
  • a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the aerial helicopter noise measurement method described in any of the preceding claims.
  • a computer program product includes a computer program that, when executed by a processor, implements the aerial helicopter noise measurement method described in any of the preceding claims.
  • the present invention discloses the following technical effects:
  • This invention discloses a method, apparatus, medium, and product for measuring the noise of an aerial helicopter.
  • First it acquires raw noise observation signals from multiple sampling points collected by various unmanned aerial vehicles (UAVs). Each UAV is at the same altitude as the helicopter under test, and there is at least one UAV. Each sampling point corresponds to a time and a frequency.
  • the raw noise observation signals include the noise of the UAVs and the noise of the helicopter under test.
  • the raw noise observation signals of each sampling point are converted to non-negative values to obtain the non-negative noise observation signals for the corresponding sampling points.
  • Second using a non-negative matrix factorization algorithm, based on the non-negative noise observation signals of each sampling point, the target spatiotemporal correlation matrix estimate for the corresponding sampling point is determined.
  • this invention uses a negative matrix factorization algorithm, which is lower in cost and has better directivity. It can effectively separate the noise of UAVs and the noise of the helicopter under test, and realize the measurement of helicopter noise.
  • FIG. 1 is a schematic flowchart of the helicopter noise measurement method provided in Embodiment 1 of the present invention.
  • Figure 2 is a schematic diagram of the airborne helicopter noise measurement array architecture
  • Figure 3 is a schematic diagram of the UAV structure.
  • the purpose of this invention is to provide a method, device, medium, and product for measuring the noise of helicopters in the air, with the aim of achieving the measurement of helicopter noise.
  • the method for measuring helicopter noise in this embodiment includes:
  • Step 1 Obtain the original noise observation signals from multiple sampling points collected by each UAV.
  • each UAV and the helicopter under test are at the same altitude, with at least one UAV; each sampling point corresponds to one time and one frequency; the original noise observation signal includes the noise of the UAV and the noise of the helicopter under test.
  • the UAV is equipped with eight microphone sensors, each of which collects the raw noise of one channel to form the raw noise observation signal.
  • the flight path of the helicopter under test passes through the center point.
  • the four drones are tested from different locations.
  • the flight path is set according to the experimental requirements and can be a straight line, a vertical take-off and landing, or an arc.
  • the UAV includes: fuselage 1, low-noise propellers 2, coaxial variable pitch control mechanism 3, data acquisition board 4, microphone measurement array 5, landing gear 6, Beidou antenna 7, and fixed... 8. Center axis and 9. Automatic tilting device.
  • the fuselage 1 is composed of carbon fiber composite material and aluminum profile. It adopts a " ⁇ "-shaped coaxial counter-rotating rotor configuration and is connected to the motor shaft and low-noise blades 2.
  • the fuselage 1 is connected to the coaxial pitch control mechanism 3 through the fixed central shaft 8.
  • the coaxial pitch control mechanism 3 is connected to the low-noise blades 2 through two automatic swashplates 9 to realize the periodic pitch control of the blades.
  • the fuselage contains a lithium battery that provides power to the system.
  • the microphone measurement array 5 and the acquisition board 4 are mounted on the lower part of the body 1.
  • the acquisition board 4 is directly connected to the microphone measurement array 5 through an internal data cable.
  • the microphone measurement array 5 consists of 8 microphone sensors and is mounted under the body 1 via a set of carbon fiber tubes.
  • the Beidou antenna 7 is installed on the mounting platform on the top of the fuselage 1 to achieve synchronous standard time synchronization between multiple platforms.
  • Step 2 Convert the original noise observation signals of each sampling point into non-negative values to obtain the non-negative noise observation signals of the corresponding sampling points.
  • Step 3 Using the non-negative matrix factorization algorithm, based on the non-negative noise observation signals of each sampling point, determine the target spatiotemporal correlation matrix estimate for the corresponding sampling point.
  • step 3 includes:
  • Step 31 Determine any sampling point as the current sampling point.
  • Step 32 Determine the actual spatiotemporal correlation matrix of the current sampling point based on the non-negative noise observation signal of the current sampling point.
  • X ⁇ sub>il ⁇ /sub> is the actual spatiotemporal correlation matrix of the i-th frequency at time l; for The transpose of .
  • the diagonal elements of the spatiotemporal correlation matrix are composed of the amplitudes of non-negative noise observation signals, while the off-diagonal elements represent the phase difference (imaginary part) and amplitude correlation between two microphone sensors.
  • Step 33 Initialize the spatiotemporal correlation matrix estimation for the current sampling point; the spatiotemporal correlation matrix estimation is determined based on the spatial characteristic matrix and the weights, magnitudes, and gains of the NMF basis.
  • K is the number of non-negative matrix factorization (NMF) bases
  • Hip is the spatial characteristic matrix of the p-th signal source at the i-th frequency
  • zpk is the weight of the k-th NMF base belonging to the p-th signal source
  • tik is the amplitude of the k-th NMF base at the i-th frequency
  • vkl is the gain of the k-th NMF base at time l.
  • Step 34 Using the gradient descent method, based on the actual spatiotemporal correlation matrix of the current sampling point, the estimated spatiotemporal correlation matrix of the current sampling point is updated multiple times to obtain the estimated target spatiotemporal correlation matrix of the current sampling point.
  • the update process at any current iteration number includes:
  • Step 341 Calculate the cost for the current iteration number based on the actual spatiotemporal correlation matrix of the current sampling point and the estimated spatiotemporal correlation matrix for the current iteration number.
  • the degree of approximation to Xil is determined by defining a cost function based on different metric criteria.
  • the expression for the cost function is as follows:
  • T is the magnitude matrix of the NMF basis
  • V is the gain matrix of the NMF basis
  • H is the matrix composed of the spatial characteristic matrices
  • Z is the weight matrix of the NMF basis
  • tr( ⁇ ) is the trace of the matrix. for The inverse of ; det is the determinant of the matrix.
  • Step 342 Based on the cost at the previous iteration number and the cost at the current iteration number, Determine the gradient at the current iteration number.
  • Step 343 Determine whether the gradient at the current iteration number is less than the threshold.
  • a gradient less than a threshold indicates that the NMF basis can cluster well.
  • Step 344 If so, then the spatiotemporal correlation matrix estimate under the current iteration number is determined as the target spatiotemporal correlation matrix estimate.
  • Step 345 If not, then based on the actual spatiotemporal correlation matrix and the estimated spatiotemporal correlation matrix under the current iteration number, determine the estimated spatiotemporal correlation matrix under the next iteration number, update the estimated spatiotemporal correlation matrix under the current iteration number to the estimated spatiotemporal correlation matrix under the next iteration number, update the cost under the current iteration number to the cost under the current iteration number, and return to step 341.
  • the estimated spatiotemporal correlation matrix for the next iteration number is determined, including:
  • Step 3451 Based on the actual spatiotemporal correlation matrix, the estimated spatiotemporal correlation matrix at the current iteration number, the magnitude of the NMF basis at the current iteration number, and the gain of the NMF basis at the current iteration number, determine the weight of the NMF basis at the next iteration number.
  • z ⁇ sub>pk ⁇ /sub> (j+1) is the weight of the k-th NMF basis belonging to the p-th signal source in the (j+1)-th iteration
  • z ⁇ sub>pk ⁇ /sub> (j) is the weight of the k-th NMF basis belonging to the p-th signal source in the j-th iteration
  • t ⁇ sub>ik ⁇ /sub>(j) is the amplitude of the k-th NMF basis at the i-th frequency in the j-th iteration
  • v ⁇ sub>kl ⁇ /sub> (j) is the gain of the k-th NMF basis at time l in the j-th iteration.
  • Hip (j) is the spatial characteristic matrix of the p-th signal source at the i-th frequency under the j-th iteration.
  • Step 3452 Based on the actual spatiotemporal correlation matrix, the estimated spatiotemporal correlation matrix at the current iteration number, the weights of the NMF basis at the current iteration number, and the gain of the NMF basis at the current iteration number, determine the magnitude of the NMF basis at the next iteration number.
  • the formula for updating the magnitude of the NMF basis is:
  • t ⁇ sub>ik ⁇ /sub> (j+1) is the amplitude of the k-th NMF basis at the i-th frequency in the (j+1)-th iteration.
  • Step 3453 Based on the actual spatiotemporal correlation matrix, the estimated spatiotemporal correlation matrix at the current iteration number, the weights of the NMF basis at the current iteration number, and the magnitude of the NMF basis at the current iteration number, determine the gain of the NMF basis at the next iteration number.
  • the update formula for the gain of the NMF base is:
  • v_kl (j+1) is the gain of the k-th NMF basis at time l under the (j+1)-th iteration.
  • Step 3454 Based on the actual spatiotemporal correlation matrix, the estimated spatiotemporal correlation matrix at the current iteration number, the weights of the NMF basis at the next iteration number, the magnitudes of the NMF basis at the next iteration number, and the gains of the NMF basis at the next iteration number, determine the spatial characteristic matrix at the next iteration number.
  • Step 3455 Based on the weights, amplitudes, gains, and spatial characteristic matrices of the NMF basis in the next iteration, determine the estimated spatiotemporal correlation matrix for the next iteration.
  • Step 4 Based on the non-negative noise observation signals at each sampling point and the estimated spatiotemporal correlation matrix of the target, determine the short-time Fourier transform of the noise of the helicopter under test at the corresponding sampling point. Coefficient vector.
  • STFT short-time Fourier transform
  • Step 5 Based on the short-time Fourier transform coefficient vector of the noise of the helicopter under test at each sampling point, determine the noise intensity of the helicopter under test at the corresponding sampling point.
  • step 5 includes:
  • the short-time Fourier transform coefficient vector of the noise of the helicopter under test at each sampling point is subjected to inverse short-time Fourier transform to obtain the noise intensity of the helicopter under test at the corresponding sampling point.
  • the spatial aerodynamic noise distribution characteristics of the helicopter under test can be analyzed by measuring the noise intensity of the helicopter at all sampling points corresponding to the UAVs at different positions.
  • This invention provides a coaxial UAV solution for measuring noise from an aerial helicopter. Utilizing a coaxial inverted layout, this layout can achieve a lower blade tip speed compared to a quadcopter layout, and its slender overall shape allows the microphone sensor to be kept as far away from the noise source as possible, thereby reducing the noise of the UAV itself. Furthermore, the use of low-noise blades further reduces the interference of the UAV's own noise on signal acquisition.
  • the present invention adopts a sound source separation algorithm based on negative matrix decomposition. Based on the algorithm requirements, an eight-microphone array design is adopted. Compared with general noise signal separation algorithms, it has lower cost and better directivity. It can effectively separate the noise of the UAV body and the noise of the helicopter under test. The test method of aerial array measurement is adopted to effectively solve the noise collection and measurement problem in the design process of new helicopters.
  • the present invention uses a drone to carry the acquisition module, which allows the signal acquisition point to be higher off the ground, ensuring flight safety during the test while also expanding the spatial range of data acquisition.
  • a computer device includes: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the aerial helicopter noise measurement method of Embodiment 1.
  • a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the aerial helicopter noise measurement method of Embodiment 1.
  • a computer program product includes a computer program that, when executed by a processor, implements the aerial helicopter noise measurement method of Embodiment 1.
  • a computer device which may be a database, includes a processor, memory, input/output (I/O) interfaces, and a communication interface.
  • the processor, memory, and I/O interfaces are connected via a system bus, and the communication interface is also connected to the system bus via the I/O interfaces.
  • the processor provides computational and control capabilities.
  • the memory includes a non-volatile storage medium and internal memory.
  • the non-volatile storage medium stores an operating system, computer programs, and a database.
  • the internal memory provides an environment for the operation of the operating system and computer programs stored in the non-volatile storage medium.
  • the database stores pending transactions.
  • the I/O interfaces facilitate information exchange between the processor and external devices.
  • the communication interface allows communication with external terminals via a network connection. When executed by the processor, the computer program implements the helicopter noise measurement method of Embodiment 1.
  • object information including but not limited to object device information, object personal information, etc.
  • data including but not limited to data used for analysis, data stored, data displayed, etc.
  • object information and data involved in this invention are all information and data authorized by the object or fully authorized by all parties, and the collection, use and processing of related data must comply with the relevant laws, regulations and standards of the relevant countries and regions.
  • Non-volatile memory may include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc.
  • ROM read-only memory
  • MRAM magnetic random access memory
  • FRAM ferroelectric random access memory
  • PCM phase change memory
  • Volatile memory may include random access memory (RAM) or external cache memory, etc.
  • RAM random access memory
  • SRAM static random access memory
  • DRAM dynamic random access memory
  • the databases involved in the embodiments provided by this invention may include at least one of relational databases and non-relational databases.
  • Non-relational databases may include, but are not limited to, blockchain-based distributed databases.
  • the processors involved in the embodiments provided in this invention may be general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic devices, quantum computing-based data processing logic devices, etc., and are not limited to these.

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Abstract

一种空中直升机噪声测量方法，包括：（1）获取各无人机采集的多个采样点的原始噪声观测信号；（2）将各采样点的原始噪声观测信号进行非负值转化，得到对应采样点的非负值噪声观测信号；（3）利用非负矩阵分解算法，基于各采样点的非负值噪声观测信号，确定对应采样点的目标时空关联矩阵估计；（4）基于各采样点的非负值噪声观测信号和目标时空关联矩阵估计，确定对应采样点的待测空中直升机的噪声的短时傅里叶变换系数向量；（5）基于各采样点的待测空中直升机的噪声的短时傅里叶变换系数向量，确定对应采样点的待测空中直升机的噪声的强度。实现了空中直升机噪声的测量。还公开了一种计算机装置、一种计算机可读存储介质及一种计算机程序产品。

Description

一种空中直升机噪声测量方法、装置、介质及产品 技术领域
本发明涉及噪声测量技术领域，特别是涉及一种空中直升机噪声测量方法、装置、介质及产品。
背景技术
直升机一般飞行在低空和超低空空间，适合执行各类中低速军用或民用任务。而由于直升机旋翼等各类部件存在各类周期性的气动振动，不可避免的存在气动噪声。降低直升机的噪声水平可以极大提高直升机的各类使用性能，因此在新型的设计阶段，气动噪声特性研究已经成为设计中不可忽视的设计因素。然而一般来说，直升机外部噪声辐射影响范围大、噪声特征指向性强，地面和空中声场分布不均匀，与飞行状态、大气条件、地形等音速相关性大。传统直升机气动噪声的测量主要分为两种方法：一是在目标直升机上安装随机麦克风，二是在目标直升机航道上安装地面麦克风阵列。机载麦克风可以快速获得直升机近场噪声特性，环境干扰相对较小。但是固定安装会受到机械振动的影响，对传感器的要求较高，且无法收集远场噪声，对于旋翼厚度噪声的感知能力弱。地面麦克风整列可以直接获得地面噪声辐射水平，可以得到直升机整体噪声水平，但是各类噪声信号会在时频域产生叠加干扰。整体来说，缺乏对于空中噪声的测量，需要一种新型的空中直升机噪声测量方法。
发明内容
本发明的目的是提供一种空中直升机噪声测量方法、装置、介质及产品，实现了空中直升机噪声的测量。
为实现上述目的，本发明提供了如下方案：
一种空中直升机噪声测量方法，包括：
获取各无人机采集的多个采样点的原始噪声观测信号；各所述无人机与待测空中直升机处于同一高度，所述无人机至少为1架；一个所述采样点对应一个时刻和一个频率；所述原始噪声观测信号包括：无人机的噪声和待测空中直升机的噪声；
将各采样点的原始噪声观测信号进行非负值转化，得到对应采样点的非负值噪声观测信号；
利用非负矩阵分解算法，基于各采样点的非负值噪声观测信号，确定对应采样点的目标时空关联矩阵估计；
基于各采样点的非负值噪声观测信号和目标时空关联矩阵估计，确定对应采样点的待测空中直升机的噪声的短时傅里叶变换系数向量；
基于各采样点的待测空中直升机的噪声的短时傅里叶变换系数向量，确定对应采样点的待测空中直升机的噪声的强度。
可选地，利用非负矩阵分解算法，基于各采样点的非负值噪声观测信号，确定对应采样点的目标时空关联矩阵估计，包括：
将任一采样点确定为当前采样点；
根据当前采样点的非负值噪声观测信号，确定当前采样点的实际时空关联矩阵；
初始化当前采样点的时空关联矩阵估计；时空关联矩阵估计是基于空间特性矩阵以及NMF基的权重、幅度和增益确定的；
利用梯度下降方法，基于当前采样点的实际时空关联矩阵，对当前采样点的时空关联矩阵估计进行多次迭代更新，得到当前采样点的目标时空关联矩阵估计。
可选地，任一当前迭代次数下的更新过程，包括：
基于当前采样点的实际时空关联矩阵和当前迭代次数下的时空关联矩阵估计，计算当前迭代次数下的代价；
根据上一迭代次数下的代价和当前迭代次数下的代价，确定当前迭代次数下的梯度；
判断当前迭代次数下的梯度是否小于阈值；
若是，则将当前迭代次数下的时空关联矩阵估计确定为目标时空关联矩阵估计；
若否，则基于所述实际时空关联矩阵和当前迭代次数下的时空关联矩阵估计，确定下一迭代次数下的时空关联矩阵估计，将当前迭代次数下的时空关联矩阵估计更新为下一迭代次数下的时空关联矩阵 估计，将当前迭代次数下的代价更新为当前迭代次数下的代价，并返回“基于当前采样点的实际时空关联矩阵和当前迭代次数下的时空关联矩阵估计，计算当前迭代次数下的代价”。
可选地，基于所述实际时空关联矩阵和当前迭代次数下的时空关联矩阵估计，确定下一迭代次数下的时空关联矩阵估计，包括：
基于所述实际时空关联矩阵、当前迭代次数下的时空关联矩阵估计、当前迭代次数下的NMF基的幅度和当前迭代次数下的NMF基的增益，确定下一迭代次数下的NMF基的权重；
基于所述实际时空关联矩阵、当前迭代次数下的时空关联矩阵估计、当前迭代次数下的NMF基的权重和当前迭代次数下的NMF基的增益，确定下一迭代次数下的NMF基的幅度；
基于所述实际时空关联矩阵、当前迭代次数下的时空关联矩阵估计、当前迭代次数下的NMF基的权重和当前迭代次数下的NMF基的幅度，确定下一迭代次数下的NMF基的增益；
基于所述实际时空关联矩阵、当前迭代次数下的时空关联矩阵估计、下一迭代次数下的NMF基的权重、下一迭代次数下的NMF基的幅度和下一迭代次数下的NMF基的增益，确定下一迭代次数下的空间特性矩阵；
基于下一迭代次数下的NMF基的权重、下一迭代次数下的NMF基的幅度、下一迭代次数下的NMF基的增益和下一迭代次数下的空间特性矩阵，确定下一迭代次数下的时空关联矩阵估计。
可选地，所述无人机上设置8个麦克风传感器，各所述麦克风传感器分别采集1个通道的原始噪声，从而构成所述原始噪声观测信号。
可选地，基于各采样点的待测空中直升机的噪声的短时傅里叶变换系数向量，确定对应采样点的待测空中直升机的噪声的强度，包括：
对各采样点的待测空中直升机的噪声的短时傅里叶变换系数向量进行短时傅里叶逆变换，得到对应采样点的待测空中直升机的噪声的强度。
一种计算机装置，包括：存储器、处理器以及存储在存储器上并可在处理器上运行的计算机程序，所述处理器执行所述计算机程序以 实现上述任一项所述的空中直升机噪声测量方法。
一种计算机可读存储介质，其上存储有计算机程序，该计算机程序被处理器执行时实现上述任一项所述的空中直升机噪声测量方法。
一种计算机程序产品，包括计算机程序，该计算机程序被处理器执行时实现上述任一项所述的空中直升机噪声测量方法。
根据本发明提供的具体实施例，本发明公开了以下技术效果：
本发明公开了一种空中直升机噪声测量方法、装置、介质及产品，首先，获取各无人机采集的多个采样点的原始噪声观测信号；各无人机与待测空中直升机处于同一高度，无人机至少为1架；一个采样点对应一个时刻和一个频率；原始噪声观测信号包括：无人机的噪声和待测空中直升机的噪声；将各采样点的原始噪声观测信号进行非负值转化，得到对应采样点的非负值噪声观测信号；其次，利用非负矩阵分解算法，基于各采样点的非负值噪声观测信号，确定对应采样点的目标时空关联矩阵估计；再次，基于各采样点的非负值噪声观测信号和目标时空关联矩阵估计，确定对应采样点的待测空中直升机的噪声的短时傅里叶变换系数向量；最后，基于各采样点的待测空中直升机的噪声的短时傅里叶变换系数向量，确定对应采样点的待测空中直升机的噪声的强度。相对于一般的噪声信号分离算法，本发明采用负矩阵分解算法，成本更低，指向性更优，可以有效地将无人机的噪声和待测空中直升机的噪声进行分离，实现了空中直升机噪声的测量。
附图说明
为了更清楚地说明本发明实施例或现有技术中的技术方案，下面将对实施例中所需要使用的附图作简单地介绍，显而易见地，下面描述中的附图仅仅是本发明的一些实施例，对于本领域普通技术人员来讲，在不付出创造性劳动的前提下，还可以根据这些附图获得其他的附图。
图1为本发明实施例1提供的空中直升机噪声测量方法流程示意图；
图2为空中直升机噪声测量阵列架构示意图；
图3为无人机结构示意图。
符号说明：
机身—1、低噪声桨叶—2、共轴变距控制机构—3、采集板—4、
麦克风测量阵列—5、起落架—6、北斗天线—7、固定中轴—8、自动倾斜器—9。
具体实施方式
下面将结合本发明实施例中的附图，对本发明实施例中的技术方案进行清楚、完整地描述，显然，所描述的实施例仅仅是本发明一部分实施例，而不是全部的实施例。基于本发明中的实施例，本领域普通技术人员在没有做出创造性劳动前提下所获得的所有其他实施例，都属于本发明保护的范围。
本发明的目的是提供一种空中直升机噪声测量方法、装置、介质及产品，旨在实现空中直升机噪声的测量。
为使本发明的上述目的、特征和优点能够更加明显易懂，下面结合附图和具体实施方式对本发明作进一步详细的说明。
实施例1
如图1所示，本实施例中的空中直升机噪声测量方法，包括：
步骤1：获取各无人机采集的多个采样点的原始噪声观测信号。
其中，各无人机与待测空中直升机处于同一高度，无人机至少为1架；一个采样点对应一个时刻和一个频率；原始噪声观测信号包括：无人机的噪声和待测空中直升机的噪声。
作为一种可选的实施方式，无人机上设置8个麦克风传感器，各麦克风传感器分别采集1个通道的原始噪声，从而构成原始噪声观测信号。
具体的，当设置4架无人机进行采集时，4架无人机按正面宽50m，纵深25m的矩形于空中可构成如图2所示的空中测量阵列，待测空中直升机的航线从中心点穿过。四架无人机分别在不同位置进行测试。航线按照试验需求设置，可以是直线，也可以是垂直升降，也可以是弧线。
如图3所示，无人机包括：机身1、低噪声桨叶2、共轴变距控制机构3、采集板4、麦克风测量阵列5、起落架6、北斗天线7、固 定中轴8和自动倾斜器9。
机身1由碳纤维复合材料和铝型材组成，采用“干”字型共轴反转旋翼构型，通过电机转轴和低噪声桨叶2连接，机身1通过固定中轴8与共轴变距控制机构3连接，共轴变距控制机构3通过两副自动倾斜器9与低噪声桨叶2连接，实现对桨叶的周期变距操纵。
机身1内部有锂电池为系统提供电力。
机身1下挂载有麦克风测量阵列5和采集板4，采集板4直接与麦克风测量阵列5通过内部数据线连接。
麦克风测量阵列5由8个麦克风传感器组成，并通过一组碳纤维管安装于机身1下方。
北斗天线7安装于机身1顶部的安装平台上，实现多平台间同步标准授时。
步骤2：将各采样点的原始噪声观测信号进行非负值转化，得到对应采样点的非负值噪声观测信号。
具体的，取原始噪声观测信号的平方值，得到非负值噪声观测信号，计算公式为：
其中，为第l时刻的第i个频率的非负值噪声观测信号，第l时刻的第i个频率对应一个采样点；为第l时刻的第i个频率的原始噪声观测信号，为第1个通道的原始噪声，为第M个通道的原始噪声，M为麦克风传感器的数量即原始噪声的通道数量，M＝8；为xil的转置。
步骤3：利用非负矩阵分解算法，基于各采样点的非负值噪声观测信号，确定对应采样点的目标时空关联矩阵估计。
作为一种可选的实施方式，步骤3，包括：
步骤31：将任一采样点确定为当前采样点。
步骤32：根据当前采样点的非负值噪声观测信号，确定当前采样点的实际时空关联矩阵。
具体的，实际时空关联矩阵的表达式为：
其中，Xil为第l时刻的第i个频率的实际时空关联矩阵；为的转置。
实际上，时空关联矩阵的对角线元素由非负值噪声观测信号的幅值构成，非对角线元素表示两个麦克风传感器的之间的相位差(虚部)和幅度关联。
步骤33：初始化当前采样点的时空关联矩阵估计；时空关联矩阵估计是基于空间特性矩阵以及NMF基的权重、幅度和增益确定的。
具体的，时空关联矩阵估计的表达式为：
其中，为第l时刻的第i个频率的时空关联矩阵估计；K为非负矩阵分解(Non-Negative Matrix Factorization，NMF)基的数量；P为信号源的数量，信号源包括：无人机和待测空中直升机，P＝2；Hip为第i个频率的第p个信号源的空间特性矩阵；zpk为第k个NMF基属于第p个信号源的权重；tik为第i个频率的第k个NMF基的幅度；vkl为第l时刻的第k个NMF基的增益。
步骤34：利用梯度下降方法，基于当前采样点的实际时空关联矩阵，对当前采样点的时空关联矩阵估计进行多次迭代更新，得到当前采样点的目标时空关联矩阵估计。
作为一种可选的实施方式，任一当前迭代次数下的更新过程，包括：
步骤341：基于当前采样点的实际时空关联矩阵和当前迭代次数下的时空关联矩阵估计，计算当前迭代次数下的代价。
具体的，为评估与Xil之间近似程度，根据不同度量准则来定义代价函数，代价函数的表达式为：
其中，f(T,V,H,Z)为代价，T为NMF基的幅度矩阵，V为NMF基的增益矩阵，H为各空间特性矩阵构成的矩阵，Z为NMF基的权重矩阵；tr(·)为矩阵的迹；为的逆；det为矩阵构成的行列式。
步骤342：根据上一迭代次数下的代价和当前迭代次数下的代价， 确定当前迭代次数下的梯度。
步骤343：判断当前迭代次数下的梯度是否小于阈值。
具体的，梯度小于阈值代表NMF基能良好聚类。
步骤344：若是，则将当前迭代次数下的时空关联矩阵估计确定为目标时空关联矩阵估计。
步骤345：若否，则基于实际时空关联矩阵和当前迭代次数下的时空关联矩阵估计，确定下一迭代次数下的时空关联矩阵估计，将当前迭代次数下的时空关联矩阵估计更新为下一迭代次数下的时空关联矩阵估计，将当前迭代次数下的代价更新为当前迭代次数下的代价，并返回步骤341。
作为一种可选的实施方式，基于实际时空关联矩阵和当前迭代次数下的时空关联矩阵估计，确定下一迭代次数下的时空关联矩阵估计，包括：
步骤3451：基于实际时空关联矩阵、当前迭代次数下的时空关联矩阵估计、当前迭代次数下的NMF基的幅度和当前迭代次数下的NMF基的增益，确定下一迭代次数下的NMF基的权重。
具体的，NMF基的权重的更新公式为：
其中，zpk(j+1)为第j+1次迭代下的第k个NMF基属于第p个信号源的权重；zpk(j)为第j次迭代下的第k个NMF基属于第p个信号源的权重；tik(j)为第j次迭代下的第i个频率的第k个NMF基的幅度；vkl(j)为第j次迭代下的第l时刻的第k个NMF基的增益；为第j次迭代下的的逆；Hip(j)为第j次迭代下的第i个频率的第p个信号源的空间特性矩阵。
步骤3452：基于实际时空关联矩阵、当前迭代次数下的时空关联矩阵估计、当前迭代次数下的NMF基的权重和当前迭代次数下的NMF基的增益，确定下一迭代次数下的NMF基的幅度。
具体的，NMF基的幅度的更新公式为：
其中，tik(j+1)为第j+1次迭代下的第i个频率的第k个NMF基的幅度。
步骤3453：基于实际时空关联矩阵、当前迭代次数下的时空关联矩阵估计、当前迭代次数下的NMF基的权重和当前迭代次数下的NMF基的幅度，确定下一迭代次数下的NMF基的增益。
具体的，NMF基的增益的更新公式为：
其中，vkl(j+1)为第j+1次迭代下的第l时刻的第k个NMF基的增益。
步骤3454：基于实际时空关联矩阵、当前迭代次数下的时空关联矩阵估计、下一迭代次数下的NMF基的权重、下一迭代次数下的NMF基的幅度和下一迭代次数下的NMF基的增益，确定下一迭代次数下的空间特性矩阵。
具体的，空间特性矩阵的更新公式为：
Hip(j+1)AHip(j+1)＝B。

其中，Hip(j+1)为第j+1次迭代下的第i个频率的第p个信号源的空间特性矩阵；A和B为中间矩阵。
步骤3455：基于下一迭代次数下的NMF基的权重、下一迭代次数下的NMF基的幅度、下一迭代次数下的NMF基的增益和下一迭代次数下的空间特性矩阵，确定下一迭代次数下的时空关联矩阵估计。
步骤4：基于各采样点的非负值噪声观测信号和目标时空关联矩阵估计，确定对应采样点的待测空中直升机的噪声的短时傅里叶变换 系数向量。
具体的，短时傅里叶变换系数向量的计算公式为：
其中，为第p个信号源的第l时刻的第i个频率的短时傅里叶变换(Short-TimeFouriertransform，STFT)系数向量。
步骤5：基于各采样点的待测空中直升机的噪声的短时傅里叶变换系数向量，确定对应采样点的待测空中直升机的噪声的强度。
作为一种可选的实施方式，步骤5，包括：
对各采样点的待测空中直升机的噪声的短时傅里叶变换系数向量进行短时傅里叶逆变换，得到对应采样点的待测空中直升机的噪声的强度。
进一步，在待测空中直升机飞行穿过无人机构成的测量阵列期间，通过处于不同位置的无人机对应的所有采样点的待测空中直升机的噪声的强度，可分析得到待测空中直升机的空间气动噪声的分布特征。
本发明的技术效果：
(1)本发明提供了一种空中直升机噪声测量共轴无人机方案。利用共轴反转式布局，该布局相对四旋翼布局可以做到桨尖速度更较小，且整体细长可以做到麦克风传感器尽可能远离噪声源，实现本体噪声的降低，且采用低噪音桨叶，进一步压低了无人机本体噪声对信号采集的干扰。
(2)本发明采用基于负矩阵分解的声源分离算法，基于算法需求采用了八麦克风阵列设计，相对于一般的噪声信号分离算法，其成本更低，指向性更优，可以有效地将无人机本体噪声和待测空中直升机的噪声进行分离，并采用空中阵列测量的测试方法，有效解决新型直升机设计过程中的噪声收集和测量问题。
(3)本发明采用无人机搭载采集模块的方式，使得信号采集点可以离地面更高，保证试验过程中的飞行安全的同时也可以拓展数据采集的空间范围。
实施例2
一种计算机装置，包括：存储器、处理器以及存储在存储器上并可在处理器上运行的计算机程序，处理器执行计算机程序以实现实施例1中的空中直升机噪声测量方法。
实施例3
一种计算机可读存储介质，其上存储有计算机程序，该计算机程序被处理器执行时实现实施例1中的空中直升机噪声测量方法。
实施例4
一种计算机程序产品，包括计算机程序，该计算机程序被处理器执行时实现实施例1中的空中直升机噪声测量方法。
实施例5
一种计算机设备，该计算机设备可以是数据库。该计算机设备包括处理器、存储器、输入/输出接口(Input/Output，简称I/O)和通信接口。其中，处理器、存储器和输入/输出接口通过系统总线连接，通信接口通过输入/输出接口连接到系统总线。其中，该计算机设备的处理器用于提供计算和控制能力。该计算机设备的存储器包括非易失性存储介质和内存储器。该非易失性存储介质存储有操作系统、计算机程序和数据库。该内存储器为非易失性存储介质中的操作系统和计算机程序的运行提供环境。该计算机设备的数据库用于存储待处理事务。该计算机设备的输入/输出接口用于处理器与外部设备之间交换信息。该计算机设备的通信接口用于与外部的终端通过网络连接通信。该计算机程序被处理器执行时以实现实施例1中的空中直升机噪声测量方法。
需要说明的是，本发明所涉及的对象信息(包括但不限于对象设备信息、对象个人信息等)和数据(包括但不限于用于分析的数据、存储的数据、展示的数据等)，均为经对象授权或者经过各方充分授权的信息和数据，且相关数据的收集、使用和处理需要遵守相关国家和地区的相关法律法规和标准。
本领域普通技术人员可以理解实现上述实施例方法中的全部或部分流程，是可以通过计算机程序来指令相关的硬件来完成，所述的计算机程序可存储于一非易失性计算机可读取存储介质中，该计算机 程序在执行时，可包括如上述各方法的实施例的流程。其中，本发明所提供的各实施例中所使用的对存储器、数据库或其它介质的任何引用，均可包括非易失性和易失性存储器中的至少一种。非易失性存储器可包括只读存储器(Read-OnlyMemory，ROM)、磁带、软盘、闪存、光存储器、高密度嵌入式非易失性存储器、阻变存储器(ReRAM)、磁变存储器(Magnetoresistive Random Access Memory，MRAM)、铁电存储器(Ferroelectric Random Access Memory，FRAM)、相变存储器(Phase Change Memory，PCM)、石墨烯存储器等。易失性存储器可包括随机存取存储器(Random Access Memory，RAM)或外部高速缓冲存储器等。作为说明而非局限，RAM可以是多种形式，比如静态随机存取存储器(Static Random AccessMemory，SRAM)或动态随机存取存储器(Dynamic Random Access Memory，DRAM)等。本发明所提供的各实施例中所涉及的数据库可包括关系型数据库和非关系型数据库中至少一种。非关系型数据库可包括基于区块链的分布式数据库等，不限于此。本发明所提供的各实施例中所涉及的处理器可为通用处理器、中央处理器、图形处理器、数字信号处理器、可编程逻辑器、基于量子计算的数据处理逻辑器等，不限于此。
以上实施例的各技术特征可以进行任意的组合，为使描述简洁，未对上述实施例中的各个技术特征所有可能的组合都进行描述，然而，只要这些技术特征的组合不存在矛盾，都应当认为是本说明书记载的范围。
本文中应用了具体个例对本发明的原理及实施方式进行了阐述，以上实施例的说明只是用于帮助理解本发明的方法及其核心思想；同时，对于本领域的一般技术人员，依据本发明的思想，在具体实施方式及应用范围上均会有改变之处。综上所述，本说明书内容不应理解为对本发明的限制。

Claims (9)

  1. 一种空中直升机噪声测量方法，其特征在于，所述方法包括：
    获取各无人机采集的多个采样点的原始噪声观测信号；各所述无人机与待测空中直升机处于同一高度，所述无人机至少为1架；一个所述采样点对应一个时刻和一个频率；所述原始噪声观测信号包括：无人机的噪声和待测空中直升机的噪声；
    将各采样点的原始噪声观测信号进行非负值转化，得到对应采样点的非负值噪声观测信号；
    利用非负矩阵分解算法，基于各采样点的非负值噪声观测信号，确定对应采样点的目标时空关联矩阵估计；
    基于各采样点的非负值噪声观测信号和目标时空关联矩阵估计，确定对应采样点的待测空中直升机的噪声的短时傅里叶变换系数向量；
    基于各采样点的待测空中直升机的噪声的短时傅里叶变换系数向量，确定对应采样点的待测空中直升机的噪声的强度。
  2. 根据权利要求1所述的空中直升机噪声测量方法，其特征在于，利用非负矩阵分解算法，基于各采样点的非负值噪声观测信号，确定对应采样点的目标时空关联矩阵估计，包括：
    将任一采样点确定为当前采样点；
    根据当前采样点的非负值噪声观测信号，确定当前采样点的实际时空关联矩阵；
    初始化当前采样点的时空关联矩阵估计；时空关联矩阵估计是基于空间特性矩阵以及NMF基的权重、幅度和增益确定的；
    利用梯度下降方法，基于当前采样点的实际时空关联矩阵，对当前采样点的时空关联矩阵估计进行多次迭代更新，得到当前采样点的目标时空关联矩阵估计。
  3. 根据权利要求2所述的空中直升机噪声测量方法，其特征在于，任一当前迭代次数下的更新过程，包括：
    基于当前采样点的实际时空关联矩阵和当前迭代次数下的时空关联矩阵估计，计算当前迭代次数下的代价；
    根据上一迭代次数下的代价和当前迭代次数下的代价，确定当前 迭代次数下的梯度；
    判断当前迭代次数下的梯度是否小于阈值；
    若是，则将当前迭代次数下的时空关联矩阵估计确定为目标时空关联矩阵估计；
    若否，则基于所述实际时空关联矩阵和当前迭代次数下的时空关联矩阵估计，确定下一迭代次数下的时空关联矩阵估计，将当前迭代次数下的时空关联矩阵估计更新为下一迭代次数下的时空关联矩阵估计，将当前迭代次数下的代价更新为当前迭代次数下的代价，并返回“基于当前采样点的实际时空关联矩阵和当前迭代次数下的时空关联矩阵估计，计算当前迭代次数下的代价”。
  4. 根据权利要求3所述的空中直升机噪声测量方法，其特征在于，基于所述实际时空关联矩阵和当前迭代次数下的时空关联矩阵估计，确定下一迭代次数下的时空关联矩阵估计，包括：
    基于所述实际时空关联矩阵、当前迭代次数下的时空关联矩阵估计、当前迭代次数下的NMF基的幅度和当前迭代次数下的NMF基的增益，确定下一迭代次数下的NMF基的权重；
    基于所述实际时空关联矩阵、当前迭代次数下的时空关联矩阵估计、当前迭代次数下的NMF基的权重和当前迭代次数下的NMF基的增益，确定下一迭代次数下的NMF基的幅度；
    基于所述实际时空关联矩阵、当前迭代次数下的时空关联矩阵估计、当前迭代次数下的NMF基的权重和当前迭代次数下的NMF基的幅度，确定下一迭代次数下的NMF基的增益；
    基于所述实际时空关联矩阵、当前迭代次数下的时空关联矩阵估计、下一迭代次数下的NMF基的权重、下一迭代次数下的NMF基的幅度和下一迭代次数下的NMF基的增益，确定下一迭代次数下的空间特性矩阵；
    基于下一迭代次数下的NMF基的权重、下一迭代次数下的NMF基的幅度、下一迭代次数下的NMF基的增益和下一迭代次数下的空间特性矩阵，确定下一迭代次数下的时空关联矩阵估计。
  5. 根据权利要求1所述的空中直升机噪声测量方法，其特征在于， 所述无人机上设置8个麦克风传感器，各所述麦克风传感器分别采集1个通道的原始噪声，从而构成所述原始噪声观测信号。
  6. 根据权利要求1所述的空中直升机噪声测量方法，其特征在于，基于各采样点的待测空中直升机的噪声的短时傅里叶变换系数向量，确定对应采样点的待测空中直升机的噪声的强度，包括：
    对各采样点的待测空中直升机的噪声的短时傅里叶变换系数向量进行短时傅里叶逆变换，得到对应采样点的待测空中直升机的噪声的强度。
  7. 一种计算机装置，包括：存储器、处理器以及存储在存储器上并可在处理器上运行的计算机程序，其特征在于，所述处理器执行所述计算机程序以实现权利要求1-6中任一项所述空中直升机噪声测量方法。
  8. 一种计算机可读存储介质，其上存储有计算机程序，其特征在于，该计算机程序被处理器执行时实现权利要求1-6中任一项所述空中直升机噪声测量方法。
  9. 一种计算机程序产品，包括计算机程序，其特征在于，该计算机程序被处理器执行时实现权利要求1-6中任一项所述空中直升机噪声测量方法。
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