Double-engine propeller noise prediction and optimization method based on analytical method

Abstract

The invention relates to a double-engine propeller noise prediction and optimization method based on an analytical method, and belongs to the field of aviation acoustics. The method disclosed by the invention comprises a noise prediction method and a noise optimization method, the noise prediction method establishes a noise prediction model based on an improved propeller characteristic theory, and the noise optimization method comprises the following steps: S1, establishing a noise objective function based on the noise prediction model, solving a first-order partial derivative and a Hessian matrix of the noise objective function, and obtaining a first-order partial derivative of the noise objective function; the method comprises the steps of S1, providing a noise target function, S2, providing a new Euler formula transformation method, and converting a triangular polynomial corresponding to a first-order partial derivative of the noise target function into a zero-equivalent algebraic polynomial, S3, analyzing and solving the zero point of the algebraic polynomial by using a Fourier-Frobenius matrix method, and S4, realizing synchronous maximum noise reduction control. According to the method, an improved propeller characteristic value theory and a Hessian + Fourier-Frobenius matrix method are used for rapidly and accurately solving an analytical solution of the minimum noise, and the method is combined with synchronous control, so that the limitation on the time and precision of predicting the minimum noise is overcome.

Description

Technical Field

[0001] The present invention relates to a method for predicting and optimizing the noise of a twin-engine propeller based on an analytical method, and belongs to the field of aeroacoustics. Background Art

[0002] Quickly and accurately determining the optimal synchronization phase angle is the key to the synchronization phase control of a low-noise multi-propeller aircraft. Turboprop aircraft have many advantages such as low fuel consumption rate, good low-speed performance, and high flight efficiency, and are widely used in fields such as short-haul transportation. However, the noise problem is an important factor restricting its application range. Without adding extra weight, the propeller synchronization phase control provides an active method to reduce the noise level of turboprop aircraft. By utilizing the sound source of the multi-rotor aircraft itself, the propeller synchronization phase method can effectively reduce noise by using the principle of coherent cancellation of the same frequency. However, the application of the synchronization phase noise reduction control on aircraft has not achieved the expected effect. This is mainly due to two reasons: First, a reasonable and credible real-time acoustic feedback online prediction model has not been established. Second, the optimal synchronization phase angle that minimizes noise is affected by airspeed, altitude, thrust, flight attitude, and the shape of the aircraft propeller, and it is difficult to obtain the current optimal synchronization phase angle.

[0003] CFD numerical simulation methods (such as large eddy simulation combined with the FW-H equation, acoustic boundary element method) have high precision and the ability to restore physical details in noise prediction. The invention patent CN 103530482 B proposes a numerical prediction method for the noise of a propeller in non-uniform inflow, and its advantage lies in being able to accurately capture the transient flow field and acoustic field characteristics in a complex flow field, and perform acoustic boundary element numerical calculations to calculate the propeller load noise. The invention patent CN 106777542 A proposes a method for predicting the flow noise of an elastic blade propeller, and the influence of the deformation of the propeller on the noise can be simulated by combining fluid-structure interaction analysis. The main disadvantage of the CFD method is the high calculation cost and poor real-time performance. It requires fine grid division and tiny time steps to ensure accuracy, resulting in a single simulation taking up to several hours or even several days. CFD has strict requirements for hardware resources and is difficult to meet the single-step calculation requirements of 10 ms to 20 ms for rapid iterative design or real-time noise monitoring. However, its essence is still limited by the inherent calculation amount of numerical solution.

[0004] To make up for the real-time defect of CFD, the invention patent CN 118965597 A proposes a method for the comprehensive design of aircraft propeller blades, their aerodynamics, noise and stiffness. According to the Hanson frequency-domain noise calculation method, after obtaining the blade shape and the discrete aerodynamic force distribution on the blade surface during the operation of the propeller, the near-field and far-field noise of the propeller can be obtained. Its single-step single-point calculation speed is 10 ms to 20 ms faster, which is suitable for preliminary design. Although it is difficult to capture non-linear effects such as turbulence. The invention patent CN116384270 A proposes a multi-propeller noise prediction method based on eigenvalue theory. By directly decomposing the single-propeller noise data through Fourier transform and extracting the amplitude and phase at the blade passing frequency (BPF) as eigenvalues, the deviation existing in the traditional method of solving the eigenvalue matrix using the least squares method can be solved. However, only making a single propeller rotate easily leads to flight instability, and this method has great limitations and can only be used for experimental research on the ground.

[0005] Once the noise prediction model is determined, then finding the "optimal" set of synchronous phase angles is crucial. Unfortunately, not many scholars have studied the optimal synchronous phase angle corresponding to the minimum noise in the noise prediction function. The data-driven propeller eigenvalue noise model is a continuous function, and together they make noise optimization a problem of finding the extreme value of a composite trigonometric function, which is solved by solving within the field of mathematics, such as solving for its minimum noise position through online Hessian matrix estimation. Frobenius proved more than a century ago that the roots of an algebraic polynomial are the eigenvalues of a matrix, called the "Frobenius companion matrix". The current challenge is to effectively represent the composite trigonometric function as a Fourier series and then use Euler's formula transformation to convert these Fourier series into algebraic polynomials.

[0006] To sum up, reducing the noise prediction error of the propeller and finding the optimal synchronous angle as quickly as possible are the technical bottlenecks of the current synchronous angle noise reduction control. Summary of the Invention

[0007] The purpose of the present invention is to provide a method for dual-engine propeller noise prediction and optimization based on the analytical method, aiming to explore a new noise reduction strategy. This scheme uses the analytical solution of the continuous acoustic prediction model to obtain the optimal synchronous phase angle most quickly and accurately, and feeds it back to the controller. The controller will respond in real time and achieve the optimal synchronous angle noise reduction control.

[0008] To achieve the above purpose, the present invention provides the following technical solutions:

[0009] A method for predicting and optimizing the noise of a twin-engine propeller based on the analytical method, including a noise prediction method and a noise optimization method. The steps of the noise prediction method are as follows: S0. Establish a noise prediction model based on the improved propeller characteristic theory, and use the noise data at a few identical synchronous phase angles obtained in the simulation or test environment to predict the noise data at all identical synchronous phase angles. The steps of the noise optimization method are as follows: S1. Establish a noise objective function based on the noise prediction model, and solve the first-order partial derivative and the Hessian matrix. S2. A new Euler formula transformation method is proposed to convert the trigonometric polynomial corresponding to the first-order partial derivative of the noise objective function into an algebraic polynomial, so that the zeros of the trigonometric polynomial become the zeros of the algebraic polynomial. S3. Use the Fourier-Frobenius matrix method to solve the zeros of the algebraic polynomial. S4. Achieve the maximum noise reduction control at the same step, overcoming the limitations in terms of time and accuracy for predicting the minimum noise;

[0010] The noise data described in S0 is obtained by CFD simulation or experimental measurement using an audio data acquisition box and a microphone array;

[0011] The noise prediction model described in S0 is improved based on the propeller eigenvalue theory. The propeller eigenvalue theory assumes that the sound pressure of each propeller is an eigenvalue vector with direction and magnitude, and the eigenvalue vector of the noise is solved by the least squares method. The improved propeller characteristic theory is based on the basic assumption that the turbulent noise does not have vector characteristics. Compared with the original theory, it adds a broadband noise factor and replaces the least squares solution with an analytical solution, improving the noise prediction accuracy;

[0012] The noise objective function described in S1 is a continuous function with a mathematical expression. Since the noise objective function is established based on the noise prediction model, the characteristics of the composite trigonometric function are retained. According to the steps, the first-order partial derivative and the Hessian matrix of the noise objective function are solved respectively. The noise objective function The minimum value is always found at the zero of the first-order partial derivative. Then, according to the Hessian matrix extreme value criterion, it is determined whether the sought synchronous phase angle is optimal;

[0013] A new Euler formula transformation method described in S2 converts the trigonometric polynomial corresponding to the first-order partial derivative of the noise objective function into an algebraic polynomial, so that the zeros of the trigonometric polynomial become the zeros of the algebraic polynomial;

[0014] The use of the Fourier-Frobenius matrix method to analytically solve the zeros of the algebraic polynomial described in S3. The eigenvalues of the Frobenius companion matrix correspond to the roots of the algebraic polynomial, and its elements are the coefficients of the polynomial. Using the Euler formula transformation, this method is applied to solve the zeros of the trigonometric series and is called the Fourier-Frobenius matrix method;

[0015] The synchronous maximum noise reduction control described in S4. Once the optimal synchronous angle corresponding to the minimum noise is obtained, the controller immediately controls the synchronous angle to the optimal angle to achieve the maximum noise reduction.

[0016] A method for predicting and optimizing the noise of a twin-engine propeller based on the analytical method, characterized in that the noise prediction model adds a broadband noise factor Has the following expression:

[0017]

[0018] Based on the basic assumption that "the difference between the broadband noise and the harmonic elements is an acoustic vector that allows mutual cancellation. In particular, the broadband noise generated by turbulence exhibits poor vector characteristics", a broadband noise factor is added The difference in the expressions between the original propeller eigenvalue theory and the improved propeller eigenvalue theory is as follows:

[0019]

[0020] Here, Represents the sound pressure eigenvalue of the nth harmonic at the acoustic receiving point M k At, A k,n，m Represents the sound pressure amplitude of the nth harmonic of the mth group at the acoustic receiving point M k At, Represents the acoustic receiving point M k The broadband noise factor of the sound pressure of the nth harmonic at the acoustic receiving point M Represents the acoustic receiving point M k At, the sound pressure phase of the nth harmonic, θ m Represents the mth group of synchronous angles;

[0021] The noise prediction model has the following steps in its modeling method:

[0022] S01. First, use the Fourier transform to obtain the sound pressure components of each harmonic at each acoustic receiving point under three groups of synchronous angles;

[0023] S02. Input the components of the sound pressure of each harmonic into the mathematical expression of the noise prediction model, and use Cramer's rule to solve for the sound pressure eigenvalue Broadband noise factor of sound pressure Sound pressure phase The solution calculation formula is as follows:

[0024]

[0025] S03. The solved sound pressure eigenvalue Broadband noise factor of sound pressure Sound pressure phase Substitute back into the noise prediction model expression (1.1) to obtain the noise level at any same synchronous angle, and use the noise synthesis formula to calculate the total average sound pressure level at all harmonic components and acoustic receiving points. The noise synthesis formula is as follows:

[0026]

[0027] where N is the number of selected harmonics, K is the total number of selected acoustic receiving points, p k,n is the sound pressure of the nth harmonic component at position k, ζ is the phase angle, SPL k is the sound pressure level at position k, and OASPL is the overall average sound pressure level at all selected positions.

[0028] The described method for predicting and optimizing the noise of a twin-engine propeller based on the analytical method is characterized in that the noise optimization method has the following steps:

[0029] S11. Taking the total average sound pressure level as the final noise target, simplify it to obtain the noise objective function of the composite trigonometric function. The specific expression is as follows:

[0030]

[0031] S12. Solve the first-order partial derivative of the noise objective function. The specific expression is:

[0032]

[0033] Solve the Hessian matrix of the noise objective function. The specific expression is:

[0034]

[0035]

[0036] Noise objective function The minimum value of is found at the zero of the first-order partial derivative. Then, according to the following Hessian matrix criterion, determine whether the sought synchronous phase angle is optimal: If at the Hessian matrix at the point is a positive definite matrix, then is the minimum value of; If at the point the Hessian matrix at is a positive semi-definite matrix, then may be the minimum value of, or may not be. Since one eigenvalue of the Hessian matrix is zero, so

[0037] S2. Solve the zero - point equation of the first - order partial derivative of the noise objective function, and its expression is:

[0038]

[0039] Convert the two multiplicative sub - terms of the zero - point equation into standard Fourier series.

[0040]

[0041] Using a newly proposed Euler formula transformation method, convert the trigonometric polynomial corresponding to the zero - point equation into an algebraic polynomial, so that the zeros of the trigonometric polynomial become the zeros of the algebraic polynomial. The conversion expression is as follows:

[0042]

[0043] where

[0044] is the conjugate complex number of d j and is the conjugate complex number of d′ j The conjugate complex number of d j and d′ j The expressions are as follows:

[0045]

[0046] Since the Euler formula transformation does not satisfy additivity, does not satisfy additivity. Therefore, when solving certain simplifications are required. The summations ∑ k and ∑ n are exchanged to obtain the approximate function

[0047]

[0048] S3. Solve the zeros of the algebraic polynomial using the Fourier - Frobenius matrix method. The eigenvalues of the Frobenius companion matrix correspond to the roots of the algebraic polynomial. Using the Euler formula transformation, apply this method to solve the zeros of the trigonometric series, and it is called the Fourier - Frobenius matrix method. The Fourier - Frobenius matrix expression is:

[0049] Sound pressure level SPL at a single acoustic receiving point:

[0050] The approximate overall average sound pressure level OASPL of all acoustic receiving points:

[0051] where δ mn represents the Kronecker symbol function, defined as δ mn = 0 if m ≠ n, otherwise δ mm = 1 for all m and n, the expression of D ij is shown in Equation (9), and the expression of D ij * is obtained by solving Equation (9) for a n , b n , a' n , b' n , and when adding the summation ∑ k ;

[0052] Solve the eigenvalues of the Fourier - Frobenius matrix to obtain the same synchronous angle corresponding to the minimum noise for the sound pressure level SPL of a single acoustic receiving point and the approximate overall average sound pressure level OASPL of all acoustic receiving points respectively;

[0053] S4. Input the difference between the optimal synchronous angle corresponding to the minimum noise and the measured feedback synchronous angle into the controller. The controller will immediately control the synchronous angle to the optimal angle to achieve the maximum noise reduction. The control algorithm is the PID algorithm or the active disturbance rejection control algorithm. The optimization accuracy of the optimal synchronous angle and the control maintenance ability of the synchronous angle jointly affect the level of noise reduction control.

[0054] Compared with the prior art, the advantages of the present invention are: a new synchronous phase - controlled acoustic feedback mechanism is proposed, including online noise prediction and feedback control of the optimal synchronous angle for minimizing noise. An improved propeller characteristic theory is proposed in noise prediction, obtaining a more accurate noise prediction ability than the original propeller eigenvalue theory. In the analytical solution of the optimal synchronous angle, the coefficient expressions of the algebraic polynomial of the improved propeller characteristic theory are derived. The analytical solution does not require repeated iteration like Newton iteration, thus obtaining the optimal synchronous angle more quickly, overcoming the control limitations in accuracy and time for predicting the optimal noise. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Figure 1 is the schematic diagram of the double - propeller noise prediction, minimum noise optimization and synchronous control of the present invention.

[0056] Figure 2 is the microphone layout and reference system of the double - propeller of the present invention.

[0057] Figure 3 is the synchronous noise reduction test bench of the present invention.

[0058] Figure 4 This is a schematic diagram of the principle of the synchronous noise reduction acoustic test bench of the present invention.

[0059] Figure 5 This is a comparison between the improved propeller eigenvalue theory and the original propeller eigenvalue theory proposed by the present invention.

[0060] Figure 6 This is the measurement of sound pressure and Fourier transform of the present invention.

[0061] Figure 7 This is the prediction of SPL at a single acoustic receiving point and the prediction of OASPL at all acoustic receiving points of the present invention.

[0062] Figure 8 This is the present invention at M 4 Analysis of the minimum value of SPL and polynomial zeros.

[0063] Figure 9 This is the analysis of the minimum value of OASPL and polynomial zeros on all receivers of the present invention.

[0064] Figure 10 This is the analytical solution accuracy and time consumption of the extreme value point of the noise objective function of the present invention.

[0065] Figure 11 This is a schematic diagram of the synchronous control of the present invention to achieve the best noise reduction effect. Detailed implementation manners

[0066] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0067] Please refer to Figure 1, in the embodiments of the present invention, a method for predicting and optimizing the noise of a twin-engine propeller based on the analytical method includes a noise prediction method and a noise optimization method. The steps of the noise prediction method are as follows: S0. Establish a noise prediction model based on the improved propeller characteristic theory, and use the noise data obtained under the simulation or test environment at a few same phase angles to predict the noise levels at all the same phase angles. The noise optimization method has the following steps: S1. Establish a noise objective function based on the noise prediction model, and solve the first-order partial derivatives and the Hessian matrix. S2. A new Euler's formula transformation method is proposed to convert the trigonometric polynomial corresponding to the first-order partial derivative of the noise objective function into an algebraic polynomial, so that the zeros of the trigonometric polynomial become the zeros of the algebraic polynomial. S3. Use the Fourier-Frobenius matrix method to solve the zeros of the algebraic polynomial. S4. Achieve the maximum noise reduction control at the same step, overcoming the limitations in terms of time and accuracy for predicting the minimum noise;

[0068] The noise data described in S0 is obtained by CFD simulation or measured by an audio data acquisition box and a microphone array. Please refer to Figure 2 , Figure 3 and Figure 4 , in the embodiments of the present invention, taking the test environment as an example, an audio data acquisition box and a microphone are used for acoustic measurement. The object considered is a 10-blade propeller with a diameter of 250 mm rotating in the same direction for a twin-engine. Please refer to Figure 2 , assuming that the starboard propeller is the main propeller, the test is carried out in an anechoic chamber with a diameter ten times that of the propeller to meet the requirements of avoiding near-field effects and reflection interference. Please refer to Figure 3 , acoustic measurement is carried out using an audio data acquisition box and a microphone. The analog microphone is arranged at the internal position of the engine room. A microphone M 3 is placed at the midpoint connection between the centers of the two propellers, in the plane of the propeller rotation. A circular microphone array tangent to the connection line of the propellers, with an interval from 0 degrees to 360 degrees. The distance between the two propellers is 360 mm, the radius of the circular array where the microphone is located is 40 mm, the audio acquisition frequency is 44.1 kHz, and the acquisition time is the time for 4 full rotations of the propeller, about 0.2 s to 0.4 s. In order to reduce sound reflection, acoustic absorption cones are applied to all the reflecting walls. The calculation frequency of OASPL is from 10 Hz to 10 kHz. Please refer to Figure 4, which shows the schematic diagram of the proposed acoustic measurement and synchronous phase control platform. The controller operates with a control period of 10 ms to 20 ms. The axial position and rotational speed of the acoustic wheel are also controlled by the STM32 microprocessor to drive the stepper motor and servo motor. The initial signals from the two probes are modulated into square waves through a signal conditioning circuit. When the square waves corresponding to the two propellers are transmitted to the STM32 for analysis, the rising edge of the square wave is captured using input capture. A new acoustic wheel with "eight"-shaped marked teeth is used for rotational speed and phase angle measurement. The measurement algorithm is the period measurement method. The phase angles of the two propellers are determined based on the position of the marked teeth. The period measurement method calculates the rotational speed and phase angle by processing the full propeller rotation signal for the synchronous control of the propellers.

[0069] The noise prediction model described in S0 is improved based on the propeller eigenvalue theory. The propeller eigenvalue theory assumes that the sound pressure of each propeller is an eigenvalue vector with direction and magnitude, and the eigenvalue vector of the noise is solved by the least squares method. The improved propeller theory is based on the basic assumption that the proposed turbulent noise does not have vector characteristics. Compared with the original theory, it adds a broadband noise factor and replaces the least squares solution with an analytical solution, improving the noise prediction accuracy.

[0070] The noise objective function described in S1 is a continuous function with a mathematical expression. Since the noise objective function is established based on the noise prediction model, it retains the characteristics of composite trigonometric functions. The first-order partial derivative and Hessian matrix of the noise objective function are solved respectively according to the steps. The noise objective function The minimum value is always found at the zero of the first-order partial derivative. Then, according to the Hessian matrix extreme value criterion, it is determined whether the sought synchronous phase angle is optimal.

[0071] A new Euler formula transformation method described in S2 converts the trigonometric polynomial corresponding to the first-order partial derivative of the noise objective function into an algebraic polynomial, thus changing the zeros of the trigonometric polynomial into the zeros of the algebraic polynomial.

[0072] The method of analytically solving the zeros of the algebraic polynomial using the Fourier - Frobenius matrix method described in S3. The eigenvalues of the Frobenius companion matrix correspond to the roots of the algebraic polynomial, and its elements are the coefficients of the polynomial. Using the Euler formula transformation, this method is applied to solve the zeros of the Fourier series and is called the Fourier - Frobenius matrix method.

[0073] The synchronous maximum noise reduction control described in S4. Once the optimal synchronous angle corresponding to the minimum noise is obtained, the controller immediately controls the synchronous angle to the optimal angle to achieve the maximum noise reduction.

[0074] Please refer to Figure 5 , in the embodiment of the present invention, for the method for predicting and optimizing the noise of a twin-engine propeller based on the analytical method, it is characterized in that, for the noise prediction model, a broadband noise factor is added and has the following expression:

[0075]

[0076] Based on the basic assumption that "the difference between the broadband noise and the harmonic elements is the acoustic vector that allows mutual cancellation. In particular, the broadband noise generated by turbulence exhibits poor vector characteristics", a broadband noise factor is added The difference in the expressions between the original propeller eigenvalue theory and the improved propeller eigenvalue theory is as follows:

[0077]

[0078] Here, represents the sound pressure eigenvalue of the nth harmonic at the acoustic receiving point M k , A k，n,m represents the sound pressure amplitude of the nth harmonic of the mth group at the acoustic receiving point M k , represents the broadband noise factor of the sound pressure of the nth harmonic at the acoustic receiving point M k , represents the sound pressure phase of the nth harmonic at the acoustic receiving point M k , θ m represents the mth group of the same synchronous angle;

[0079] Please refer to Figure 6 and Figure 7 , in the embodiment of the present invention, for the noise prediction model, its modeling method has the following steps:

[0080] S01. First, use the Fourier transform to obtain the sound pressure components of each harmonic of each acoustic receiving point under three groups of the same synchronous angles;

[0081] S02. Input the components of the sound pressure of each harmonic into the mathematical expression of the noise prediction model, and use Cramer's rule to solve the sound pressure eigenvalue Broadband noise factor of sound pressure Sound pressure phase The solution calculation formula is as follows:

[0082]

[0083] S03. The solved sound pressure eigenvalue Broadband noise factor of sound pressure Sound pressure phase Substitute back into the noise prediction model expression (1.1) to obtain the noise level at any same synchronous angle, and calculate the total average sound pressure level at all harmonic components and acoustic receiving points using the noise synthesis formula. The noise synthesis formula is as follows:

[0084]

[0085] where N is the number of selected harmonics, K is the total number of selected acoustic receiving points, p k,n is the sound pressure of the nth harmonic component at position k, ζ is the phase angle, SPL k is the sound pressure level at position k, and OASPL is the overall average sound pressure level at all selected positions.

[0086] Please refer to Figure 8 and Figure 9 , in the embodiment of the present invention, for the method for predicting and optimizing the noise of a twin-engine propeller based on the analytical method, it is characterized in that the noise optimization method has the following steps:

[0087] S11. Taking the total average sound pressure level as the final noise target, simplify it to obtain the noise objective function of the composite trigonometric function. The specific expression is as follows:

[0088]

[0089] S12. Solve the first-order partial derivative of the noise objective function. The specific expression is:

[0090]

[0091] Solve the Hessian matrix of the noise objective function. The specific expression is:

[0092]

[0093]

[0094] The noise objective function The minimum value is found at the zero of the first-order partial derivative. Then, determine whether the sought synchronous phase angle is optimal according to the following Hessian matrix criterion: If at the point, the Hessian matrix is a positive definite matrix, then is the minimum value; if at the point the Hessian matrix is a positive semi-definite matrix, then may be The minimum value may not be either. Since one eigenvalue of the Hessian matrix is zero, so

[0095] S2. Solve the zero-point equation of the first-order partial derivative of the noise objective function, and its expression is:

[0096]

[0097] Convert the two multiplicative subterms of the zero-point equation into standard Fourier series,

[0098]

[0099] Using a newly proposed Euler's formula transformation method, convert the trigonometric polynomial corresponding to the zero-point equation into an algebraic polynomial, so that the zeros of the trigonometric polynomial become the zeros of the algebraic polynomial. The conversion expression is as follows:

[0100]

[0101] where

[0102] is the conjugate complex number of d j , is the conjugate complex number of d′ j , d j and d′ j The expressions of are as follows:

[0103]

[0104] Since the Euler's formula transformation does not satisfy additivity, so does not satisfy additivity. Therefore, when solving , certain simplifications are needed. The summations ∑ k and ∑ n are exchanged to obtain the approximate function

[0105]

[0106] S3. Use the Fourier-Frobenius matrix method to solve the zeros of the algebraic polynomial. The eigenvalues of the Frobenius companion matrix correspond to the roots of the algebraic polynomial. Using the Euler's formula transformation, apply this method to solve the zeros of the trigonometric series, and it is called the Fourier-Frobenius matrix method. The Fourier-Frobenius matrix expression is:

[0107] Sound pressure level SPL at a single acoustic receiving point:

[0108] The approximate total average sound pressure level OASPL of all acoustic receiving points:

[0109] where δ mn represents the Kronecker symbol function, and δ is defined as mn = 0 if m ≠ n, otherwise δ mm = 1 for all m and n. The expression of D ij can be seen in Equation (9). The expression of D ij * is to solve for a n , b n , a' n , b’ n in Equation (9). When adding the summation ∑ k ;

[0110] Please refer to Figure 10 . In the embodiments of the present invention, when solving the eigenvalues of the Fourier-Frobenius matrix, the same synchronous angles corresponding to the minimum noise of the sound pressure level SPL of a single acoustic receiving point and the approximate total average sound pressure level OASPL of all acoustic receiving points are obtained respectively. Taking the acoustic receiving point M 4 and all receiving points as examples, compared with the original propeller eigenvalue theory, the analytical solution accuracy is increased by 4 times. However, since the number of roots to be solved doubles, the calculation time doubles.

[0111] S4. Input the difference between the optimal synchronous angle corresponding to the minimum noise and the measured feedback synchronous angle into the controller. Please refer to Figure 11 . In the embodiments of the present invention, the controller will immediately control the synchronous angle to the optimal angle to achieve the maximum noise reduction. The control algorithm is the PID algorithm or the active disturbance rejection control algorithm. The optimization accuracy of the optimal synchronous angle and the control maintenance ability of the synchronous angle jointly affect the noise reduction control level.

[0112] The present invention is not limited to the above embodiments. Based on the technical solutions disclosed in the present invention, those skilled in the art can make some simple modifications, equivalent changes and modifications to some technical features without creative labor according to the disclosed technical content, which all fall within the scope of the technical solutions of the present invention.

Claims

1. A noise prediction and optimization method for a twin-engine propeller based on an analytical method, comprising a noise prediction method and a noise optimization method, wherein the steps of the noise prediction method are as follows: S0. A noise prediction model is established based on an improved propeller characteristic theory, and noise data at a few phase-synchronous phase angles obtained under a simulation or test environment are used to predict the noise level at all phase-synchronous phase angles. The noise optimization method has the following steps: S1. A noise target function is established based on the noise prediction model, and the first-order partial derivative and the Hessian matrix are solved. S2. A new Euler formula transformation method is proposed to convert the trigonometric polynomial corresponding to the first-order partial derivative of the noise target function into an algebraic polynomial, thereby converting the zero point of the trigonometric polynomial into the zero point of the algebraic polynomial. S3. The analytical zero point of the algebraic polynomial is solved by the Fourier-Frobenius matrix method. S4. The maximum phase-synchronous noise reduction control is realized, thereby overcoming the limitations of the time and accuracy of predicting the minimum noise. The noise data described in S0 is obtained by CFD simulation or experimental measurement using an audio data acquisition box and a microphone array; The noise prediction model described in S0 is improved based on the propeller eigenvalue theory. The propeller eigenvalue theory assumes that the sound pressure of each propeller is an eigenvalue vector with direction and magnitude, and solves the eigenvalue vector of the noise by the least square method. The improved propeller characteristic theory is based on the basic assumption that the turbulent noise does not have vector characteristics. Compared with the original theory, the broadband noise factor is added, and the least square solution is replaced by an analytical solution, thereby improving the noise prediction accuracy. The noise objective function described in S1 is a continuous function with a mathematical expression. Since the noise objective function is established based on the noise prediction model, the characteristics of the composite trigonometric function are retained. According to the steps, the first-order partial derivative and the Hessian matrix of the noise objective function are solved respectively. The noise objective function The minimum value of is always found at the zero of the first-order partial derivative, and then, the Hessian matrix extreme value criterion is used to determine whether the synchronization phase angle sought is optimal; A new Euler formula transformation method described in S2 converts the trigonometric polynomial corresponding to the first-order partial derivative of the noise objective function into an algebraic polynomial, thereby converting the zero point of the trigonometric polynomial into the zero point of the algebraic polynomial; S3 uses the Fourier-Frobenius matrix method to analytically solve the zeros of the algebraic polynomial, the eigenvalues ​​of the Frobenius companion matrix correspond to the roots of the algebraic polynomial, and its elements are the coefficients of the polynomial. The method is applied to solve the zeros of the Fourier series using the Euler formula transformation, and is called the Fourier-Frobenius matrix method; The phase synchronization maximum noise reduction control described in S4, once the optimal phase synchronization angle corresponding to the minimum noise is obtained, the controller will immediately control the phase synchronization angle to the optimal angle to achieve maximum noise reduction.

2. A method for predicting and optimizing twin-engine propeller noise based on analytical method as claimed in claim 1, characterized in that: The noise prediction model described above adds a broadband noise factor With the following expression: Based on the basic assumption that "the distinction between broadband noise and harmonic elements is a sound vector that allows mutual cancellation, in particular, broadband noise generated by turbulence exhibits poor vector characteristics", the broadband noise factor is increased. The differences between the expressions of the original propeller eigenvalue theory and the improved propeller eigenvalue theory are as follows: here, Represents the acoustic receiving point M k The sound pressure characteristic value of the nth order harmonic at A k，n,m Represents the acoustic receiving point M k The sound pressure amplitude of the nth order harmonic of the mth group at Represents the acoustic receiving point M k The broadband noise factor of the sound pressure of the nth-order harmonic at Represents the acoustic receiving point M k The sound pressure phase of the nth harmonic at m represents the phase synchronization angle of the mth group; The noise prediction model, the modeling method thereof has the following steps: S01. First, use Fourier transform to obtain each order harmonic sound pressure component of each acoustic receiving point under three groups of phase synchronization angles; S02. Input the components of each order harmonic sound pressure into the mathematical expression of the noise prediction model, and use Cramer's law to solve the sound pressure characteristic value Sound pressure broadband noise factor Sound pressure phase The solution formula is as follows: S03. The sound pressure eigenvalue to be solved Sound pressure broadband noise factor Sound pressure phase Substitute the noise prediction model expression (1.1) to obtain the noise level at any phase angle, and use the noise synthesis formula to calculate the total average sound pressure level of all harmonic components and acoustic receiving points. The noise synthesis formula is as follows: Where N is the selected harmonic number, K is the total number of selected acoustic receiving points, and p k,n is the sound pressure of the nth harmonic component at position k, ζ is the phase angle, SPL k is the sound pressure level at location k and OASPL is the overall average sound pressure level of all selected locations.

3. The method for predicting and optimizing twin-engine propeller noise based on analytical method according to claim 1, characterized in that: The noise optimization method comprises the following steps: S11. Taking the total average sound pressure level as the final noise target, the noise target function of the composite trigonometric function is simplified and the specific expression is as follows: S12. Solve the first-order partial derivative of the noise objective function. The specific expression is: Solve the Hessian matrix of the noise objective function. The specific expression is: Noise objective function The minimum value of is found at the zero of the first-order partial derivative, and then the optimal synchronization phase angle is determined according to the following Hessian matrix criterion: exist The Hessian matrix at the point is a positive definite matrix, then for The minimum value of At the point The Hessian matrix at is a positive semidefinite matrix, then may be The minimum value of may not be, because one eigenvalue of the Hessian matrix is ​​zero, so S2. Solve the zero-point equation of the first-order partial derivative of the noise objective function, which is expressed as: Convert the two multiplication terms of the zero-point equation into a standard Fourier series: By using a new Euler formula transformation method proposed, the trigonometric polynomial corresponding to the zero-point equation is converted into an algebraic polynomial, thereby converting the zero point of the trigonometric polynomial into the zero point of the algebraic polynomial. The conversion expression is as follows: in, Yes j The complex conjugate of is d′ j The complex conjugate of j and d′ j The expression is as follows: Since the Euler formula transformation does not satisfy additivity, does not satisfy additivity, so in solving Some simplification is required, and the sum ∑ k and∑ n are exchanged, and the approximate function is obtained S3. The Fourier-Frobenius matrix method is used to solve the zeros of the algebraic polynomial. The eigenvalues ​​of the Frobenius companion matrix correspond to the roots of the algebraic polynomial. The method is applied to solve the zeros of the Fourier series using the Euler formula transformation, and is called the Fourier-Frobenius matrix method. The Fourier-Frobenius matrix expression is: Sound pressure level SPL at a single acoustic receiving point: The approximate overall average sound pressure level OASPL of all acoustic receiving points is: Among them, δ mn represents the Kronecker sign function, and defines δ mn =0 if m≠n, otherwise δ mm = 1 for all m and n, D ij The expression of D is shown in equation (9). ij *The expression is equation (9) to solve for a n , b n , a' n , b' n When increasing the sum ∑ k ; Solve the eigenvalues ​​of the Fourier-Frobenius matrix to obtain the minimum noise phase synchronization angle of the sound pressure level SPL of a single acoustic receiving point and the approximate total average sound pressure level OASPL of all acoustic receiving points; S4. The difference between the optimal phase synchronization angle corresponding to the minimum noise and the phase synchronization angle of the measured feedback is input into the controller. The controller will immediately control the phase synchronization angle to the optimal angle to achieve the maximum noise reduction. The control algorithm is PID algorithm or self-anti-disturbance control algorithm. The optimization accuracy of the optimal phase synchronization angle and the control and maintenance ability of the phase synchronization angle jointly affect the level of noise reduction control.

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