Layout optimization method for multi-mode vibration sensor of wind tunnel tail strut

Abstract

The invention discloses a wind tunnel tail strut multi-modal vibration sensor layout optimization method, which comprises the following steps: establishing a tail strut finite element model containing a wind tunnel test model and a balance, carrying out modal analysis, and determining a to-be-monitored vibration modal order; arranging n vibration sensors along the axis direction of the support rod, exciting the tail support rod by adopting a bandwidth random signal according to the vibration mode order to be monitored, and extracting the vibration mode frequency of the corresponding tail support rod structure; exciting the tail support rod by sine waves of each modal vibration frequency, recording an amplitude ratio sequence of the vibration sensor relative to an excitation signal, and assembling the amplitude ratio sequence of a multi-order modal to form a vibration mode matrix; and solving the optimal installation position layout of the sensor by taking the sensor layout optimization criterion as a fitness function of the position layout of the sensor. According to the method, the observation capability of the vibration mode set is maximized by adopting an optimization criterion, and meanwhile, the linear correlation between the mode vectors is minimized, so that the optimal position layout of the sensor is realized.

Description

Technical Field

[0001] The present invention relates to the field of wind tunnel model tests, and particularly relates to a method for optimizing the layout of multi-modal vibration sensors for a wind tunnel tail strut. Background Art

[0002] Full-scale wind tunnel tests are an authoritative verification means for measuring the aerodynamic parameters of an aircraft under different conditions. Among them, the tail strut support method is widely used to support the aircraft model. This support structure forms a cantilever structure and often vibrates during the large angle of attack test stage in a transonic wind tunnel, resulting in problems such as reduced accuracy of data measurement and limited test angle of attack range. Since it does not interfere with the aerodynamic shape of the tail strut, an active vibration suppression device based on piezoelectric materials is used as a vibration suppression solution for the tail strut. As the input of the active vibration suppression device, vibration sensors mainly include methods such as accelerometers, strain balances, and visual images. Some researchers use strain balances to measure the vibration of the tail strut. The strain balance has high sensitivity and can effectively measure the deformation under external loads. However, the position of the strain balance as a vibration sensor in the overall structure of the tail strut is fixed and cannot be adjusted. Some researchers also use accelerometers arranged inside the model as vibration measurement devices for the tail strut, and use a method combining visual vibration images and accelerometers embedded in the model as a vibration monitoring means for the tail strut. For example, self-luminous marking points are pasted at the front end of the aircraft model as vibration measurement points. None of the above solutions consider the position optimization of the vibration sensor, which may result in weak vibration signals of a certain order of mode being measured, low signal-to-noise ratio, and inability to effectively monitor the corresponding vibration of the wind tunnel tail strut, thus limiting the control performance of the active vibration suppression device for the tail strut.

[0003] In the prior art, there are also some examples of optimizing the layout of vibration sensors, but most of them cannot be directly applied to the vibration measurement of wind tunnel tail struts. The reason is that most vibration sensor layout optimization methods focus on a single index, that is, to optimize a group from the candidate vibration sensor combinations to maximize or minimize a certain index. For example, the modal confidence criterion mainly emphasizes the linear independence between mode shape vectors; the Fisher information matrix method emphasizes maximizing the observability of the target mode; the effective independence rule focuses on the linear independent characteristics between modes. For the vibration mode monitoring of the tail strut, it is necessary to be able to monitor multiple modes and at the same time satisfy the reduction of the linear independence between the mode shape vectors of each order, so as to be able to effectively monitor the vibration of the wind tunnel tail strut and further improve the control ability of the active vibration suppression device for the tail strut. However, no relevant research has been proposed yet. Summary of the Invention

[0004] Aiming at the deficiencies of the existing layout method of vibration sensors for wind tunnel tail struts, the purpose of the present invention is to propose an optimization method for the layout of multi-modal vibration sensors for wind tunnel tail struts. First, confirm the set of vibration modes to be observed, establish a series of candidate sensor positions, and use an optimization criterion to maximize the observation ability of the vibration mode set while minimizing the linear correlation between modal vectors, so as to achieve the optimal position layout of the sensors.

[0005] To achieve the above technical purpose, the technical solution adopted by the present invention is as follows:

[0006] An optimization method for the layout of multi-modal vibration sensors for wind tunnel tail struts, the method comprising the following steps:

[0007] S1, establish a finite element model of the tail strut including the wind tunnel test model and the balance, conduct modal analysis, and determine the order m of the vibration modes to be monitored = card(A), where A is the set of modes to be monitored and card() is the number of elements in the set;

[0008] S2, arrange n vibration sensors along the axis of the strut. The n vibration sensors form an overall monitoring set B. According to the order of the vibration modes to be monitored, use a broadband random signal to excite the tail strut and extract the vibration mode frequencies of the corresponding tail strut structure. n > m, and both n and m are positive integers greater than 1;

[0009] S3, excite the tail strut with a sine wave of each modal vibration frequency respectively, and record the amplitude ratio sequence A n×1 of the vibration sensors relative to the excitation signal, and assemble the amplitude ratio sequences of multiple orders of modes to form a mode shape matrix Φ n×m ;

[0010] S4, use the sensor layout optimization criterion as the fitness function for the sensor position layout, and solve that the installation position layout of the sensor with the minimum fitness function value is the optimal installation position layout of the sensor. The fitness function is:

[0011] ;

[0012] where, is the k-th vibration sensor; is the condition number of the matrix based on the 2-norm, defined as where is the largest eigenvalue of matrix A, and is the smallest eigenvalue of matrix A; is the mode shape matrix of m measurement points of order m; sigmoid is a smooth activation function, defined as ; represents the cosine value of the i-th mode vector and the j-th mode vector.

[0013] Furthermore, in step S1, a finite element model of the tail support rod including the wind tunnel test model and the balance is established, modal analysis is carried out, the effective modal mass of each order is extracted, and the vibration modal order to be monitored is determined according to the predetermined index of the effective modal mass; specifically, it includes the following steps:

[0014] S11. Carry out modal analysis on the finite element model of the tail support rod including the wind tunnel test model and the balance, and extract the frequency, vibration mode and effective modal mass of each order from the analysis results;

[0015] S12. Divide the effective modal mass of each order by the total mass of the tail support rod including the wind tunnel test model and the balance to obtain the ratio of the effective modal mass;

[0016] S13. Accumulate the ratios of the effective modal mass of each order from low order to high order in turn until the sum of the accumulations is greater than or equal to the set value of the ratio of the effective modal mass, obtain the set of modes to be monitored, and calculate the vibration modal order to be monitored.

[0017] Furthermore, in step S2, n vibration sensors are arranged along the axis of the support rod by using the Monte Carlo method or the equal-spacing method.

[0018] Furthermore, in step S2, the tail support rod is excited by a bandwidth random signal to extract the vibration modal frequency of the tail support rod structure; specifically, it includes the following steps:

[0019] S21. The signal generator generates a bandwidth random excitation signal, which is amplified by a piezoelectric power amplifier and then drives the piezoelectric actuator embedded in the tail support rod to make the tail support rod including the wind tunnel test model and the balance vibrate;

[0020] S22. Collect the vibration response signal through the vibration sensors arranged on the tail support rod;

[0021] S23. Combine the excitation signal and the response signal, and use the H1 estimation method to calculate the frequency response function;

[0022] S24. According to the vibration modal order to be monitored determined in step S1, extract the vibration modal frequency of the tail support rod structure.

[0023] Furthermore, in step S4, the genetic algorithm is used to optimize and determine the installation position layout of the sensors, specifically including the following steps:

[0024] S41. For the set S, use lexicographical sorting and encoding to generate an initial population, and the number of the initial population is M; select the sensor layout optimization criterion function as the fitness function, and use the penalty function method to calculate the fitness function;

[0025] S42. Use the roulette wheel selection method to select individuals;

[0026] S43. Assume the crossover probability is , randomly select to perform parental crossover on the chromosome to obtain the next generation; let the initial individuals be , , and new individuals are generated after arithmetic crossover of the two individuals:

[0027] ;

[0028] In the formula, is the arithmetic crossover parameter;

[0029] S44. Adopt uniform mutation, set the mutation rate to , for each gene of the new generation of individuals generated after crossover, randomly generate a mutation probability , if , then perform mutation operation, randomly select a candidate value in the population space to replace the original value;

[0030] S45. Loop and iterate steps S42 to S44 until the difference between the fitness function of the best individual in this generation and the fitness function of the best individual in the previous generation is less than the specified value or the maximum number of generations is satisfied, and the optimal sensor layout can be extracted.

[0031] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0032] The method for optimizing the layout of multi-modal vibration sensors on the wind tunnel tail strut of the present invention can collect more vibration modes with higher signal-to-noise ratio for the vibration sensors compared with the existing layout of vibration sensors on the wind tunnel tail strut, and can remove redundant sensors, thereby improving the multi-order modal vibration monitoring ability of the wind tunnel tail strut. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 is a schematic structural diagram of the wind tunnel tail strut model of the present invention.

[0034] Figure 2 is a data diagram of the mode shape matrix of the present invention.

[0035] Figure 3 is a flow chart of the genetic algorithm of the present invention.

[0036] Figure 4 is a convergence curve diagram of the fitness function of the genetic algorithm of the present invention.

[0037] Figure 5 is a schematic diagram of the optimized result of the vibration sensor layout of the present invention.

[0038] Figure 6 is a flow chart of the method for optimizing the layout of multi-modal vibration sensors on the wind tunnel tail strut of the present invention. Specific Embodiments

[0039] The embodiments of the present invention will be further described in detail below with reference to the accompanying drawings.

[0040] See Figure 6 , the technical solution adopted by the present invention is a method for optimizing the layout of multi-modal vibration sensors on the tail strut of a wind tunnel. The specific steps of the method are as follows:

[0041] S1. Establish a finite element model of the tail strut including the wind tunnel test model and the balance, perform modal analysis, and extract the effective modal mass of each order. According to the predetermined index of the effective modal mass, determine the number of vibration modal orders m = card(A) to be monitored, where A is the set of modes to be monitored.

[0042] In step S1, a finite element model of the tail strut including the wind tunnel test model and the balance is established, modal analysis is performed, the effective modal mass of each order is extracted, and the number of vibration modal orders to be monitored is determined according to the predetermined index of the effective modal mass; specifically, it includes the following steps:

[0043] S11. Perform modal analysis on the finite element model of the tail strut including the wind tunnel test model and the balance, and extract the frequency, vibration mode, and effective modal mass of each order from the analysis results;

[0044] S12. Divide the effective modal mass of each order by the total mass of the tail strut including the wind tunnel test model and the balance to obtain the ratio of the effective modal mass;

[0045] S13. Accumulate the ratios of the effective modal mass of each order from low order to high order until the sum of the accumulations is greater than or equal to the set value of the ratio of the effective modal mass, obtain the set of modes to be monitored, and calculate the number of vibration modal orders to be monitored.

[0046] S2. Arrange n (n > m) vibration sensors along the axis of the strut, which is called the overall monitoring set B. Use a bandwidth random signal to excite the tail strut and extract the vibration modal frequency of the tail strut structure. Optionally, perform modal analysis by the finite element method to extract the vibration modal frequency of the tail strut structure.

[0047] Preferably, use the Monte Carlo method or the equal-spacing method to arrange n vibration sensors along the axis of the strut.

[0048] In step S2, use a bandwidth random signal to excite the tail strut and extract the vibration modal frequency of the tail strut structure; specifically, it includes the following steps:

[0049] S21. The signal generator generates a bandwidth random excitation signal, which is amplified by a piezoelectric power amplifier and then drives the piezoelectric actuator embedded in the tail strut to make the tail strut including the wind tunnel test model and the balance vibrate;

[0050] S22. Collect the vibration response signals through the vibration sensors arranged on the tail strut;

[0051] S23. Combine the excitation signal and the response signal, and use the H1 estimation method to calculate the frequency response function;

[0052] S24. According to the vibration mode order to be monitored determined in step S1, extract the vibration mode frequencies of the tail strut structure.

[0053] S3. Excite the tail strut with sine waves of the actual vibration mode frequencies respectively, and record the amplitude ratio sequence A of the vibration sensors relative to the excitation signal n×1 , assemble the amplitude ratio sequences of multiple orders of modes to form the mode shape matrix Φ n×m .

[0054] Optionally, perform modal analysis by the finite element method, extract the amplitude ratio sequence A of the mode shapes at the positions of the recorded vibration sensors n×1 , assemble the amplitude ratio sequences of multiple orders of modes to form the mode shape matrix Φ n×m .

[0055] S4. Take the sensor layout optimization criterion as the fitness function of the sensor position layout, and solve that the installation position layout of the sensor with the minimum fitness function value is the optimal installation position layout of the sensor, thus completing the sensor layout optimization. The sensor layout optimization criterion function is

[0056] ;

[0057] where , according to the binomial coefficient, there are possibilities, is the condition number of the matrix based on the 2-norm, and sigmoid is the smooth activation function.

[0058] Optionally, in S4, use the genetic algorithm to optimize and determine the installation position layout of the sensors. The specific steps include:

[0059] S41. Encoding, generating the initial population. For the set S, use the lexicographical order sorting and encoding to generate the initial population.

[0060] S42. Fitness function. The fitness function is the performance index of the genetic algorithm. This optimization problem is to minimize the sensor layout optimization criterion function. Therefore, the fitness function selects the sensor layout optimization criterion function and uses the penalty function method to calculate the fitness function.

[0061] S43. Selection. Selection is to select individuals with high fitness from the population with a certain probability and copy them to the next-generation population. Individuals with high fitness have a high probability of being selected, while individuals with low fitness have a low probability of being copied to the next generation. The roulette wheel selection method is used to select individuals.

[0062] S44. Crossover. The genetic algorithm simulates the mating process through crossover and generates the next-generation individuals. The number of the initial population is M. Assuming the crossover probability is , randomly select to perform double-parent crossover on the chromosomes to obtain the next generation. Let the initial individuals be , . After arithmetic crossover of the two individuals, new individuals are generated, that is,

[0063] ;

[0064] In the formula, is the arithmetic crossover parameter.

[0065] S45. Mutation. Based on the new offspring generated in the previous step, with a small probability, a certain value or some values in the individual are forced to change, so as to expand the search range, avoid premature convergence and falling into local optimum, and maintain the diversity of the population. Uniform mutation is adopted, and the mutation rate is set as . For each gene of the new generation of individuals generated after crossover, a random mutation probability is generated. If , then the mutation operation is performed, and a candidate value is randomly selected in the population space to replace the original value.

[0066] S46. Loop and iterate S42 to S45 until the difference between the fitness function of the best individual in this generation and the fitness function of the best individual in the previous generation is less than the specified value or the maximum number of generations is satisfied, and the optimal sensor layout can be extracted.

[0067] Example

[0068] An optimization method for the vibration sensor layout of a wind tunnel tail strut includes the following steps:

[0069] (1). As Figure 1 shown, establish a finite element model of the tail strut 2 including the wind tunnel test model 1 and the balance, perform modal analysis, and extract the effective modal masses of each order. According to the predetermined index of the effective modal mass, determine the vibration modal order m = 3 to be monitored, where A = {1, 2, 3} is the modal set to be monitored.

[0070] (2). Arrange 277 vibration sensors along the axis direction of the strut, which is called the overall monitoring set B. Use a broadband random signal to excite the tail strut and extract the actual vibration modal frequencies of the tail strut structure.

[0071] (3) Sinusoidally excite the tail strut with the actual vibration modal frequencies respectively, record the amplitude ratio sequence of the vibration sensor relative to the excitation signal, and assemble the amplitude ratio sequences of multiple orders of modes to form the acceleration mode matrix Φ 277×3 , such as Figure 2 shown.

[0072] (4) Use the sensor layout optimization criterion as the fitness function for the sensor position layout, and solve that the installation position layout of the sensor with the minimum fitness function value is the optimal installation position layout of the sensor, completing the sensor layout optimization.

[0073] The sensor layout optimization criterion function is

[0074] ;

[0075] Among them, , is the k-th vibration sensor; is the condition number of the matrix based on the 2-norm, defined as , where is the largest eigenvalue of matrix A, is the smallest eigenvalue of matrix A; is the mode matrix of m measuring points of order m; sigmoid is a smooth activation function, defined as ; represents the cosine value of the i-th mode vector and the j-th mode vector.

[0076] The genetic algorithm is used to optimize and determine the installation position layout of the sensor, as Figure 3 shown, and the specific steps include:

[0077] (4-1) Encoding, generating the initial population. For the set S, use lexicographical sorting and encoding to generate the initial population. First, generate the lexicographical sorting table. When using binary encoding, the number of binary digits needs to meet the requirements of the lexicographical sorting table, that is . Therefore, d takes the value of 22.

[0078] (4-2) Fitness function. The fitness function is the performance index of the genetic algorithm. This optimization problem is to minimize the sensor layout optimization criterion function. Therefore, the fitness function selects the sensor layout optimization criterion function and calculates the fitness function using the penalty function method.

[0079] (4-3) Selection. Selection is to select individuals with high fitness from the population with a certain probability and copy them to the next generation population. Individuals with high fitness have a high probability of being selected, while individuals with low fitness have a low probability of being copied to the next generation. The roulette wheel selection method is used to select individuals.

[0080] (4-4), Crossover. The genetic algorithm simulates the mating process through crossover and generates the next generation of individuals. The number of the initial population is M, assuming the crossover probability is , randomly select pairs of chromosomes for double-parent crossover to obtain the next generation. Let the initial individuals be , , after arithmetic crossover of the two individuals, new individuals are generated, that is,

[0081] ;

[0082] In the formula, is the arithmetic crossover parameter.

[0083] (4-5), Mutation. Based on the new offspring generated in the previous step, with a relatively small probability, a certain value or some values in the individual are forcibly changed, so as to expand the search range, avoid premature convergence and falling into local optimum, and maintain the diversity of the population. Uniform mutation is adopted, and the mutation rate is set as , for each gene of the new generation of individuals generated after crossover, a random mutation probability is generated. If , then mutation operation is performed, and a candidate value is randomly selected in the population space to replace the original value.

[0084] Loop and iterate from (4-2) to (4-5) until the difference between the fitness function of the best individual in this generation and the fitness function of the best individual in the previous generation is less than the specified value or the maximum number of generations is satisfied, and the optimal sensor layout can be extracted.

[0085] Finally, the difference between the fitness functions is less than the specified value 10, and the genetic algorithm search ends. The value of the sensor layout optimization criterion function is 279.727, as Figure 4 shown. The encoding of the best individual value is 986558, and its corresponding sensor layout position is [29167 277], as Figure 5 shown.

[0086] Although the preferred embodiments of the present application have been described, those skilled in the art can make additional changes and modifications to these embodiments once they know the basic creative concept. Therefore, the appended claims are intended to be construed to include the preferred embodiments and all changes and modifications falling within the scope of the present application.

[0087] Obviously, those skilled in the art can make various changes and modifications to the present application without departing from the spirit and scope of the present application. Thus, if these modifications and variations of the present application fall within the scope of the claims of the present application and their equivalent technologies, the present application also intends to include these modifications and variations therein.

Claims

1. A method for optimizing the layout of multi-modal vibration sensors of a wind tunnel tail strut, characterized in that: The method comprises the following steps: S1, establish a finite element model of the tail strut including a wind tunnel test model and a balance, perform modal analysis, and determine the vibration mode order m=card(A) to be monitored, where A is the mode set to be monitored and card() is the number of elements in the set; S2, n vibration sensors are arranged along the axis direction of the strut, and the n vibration sensors constitute the overall monitoring set B. According to the vibration mode order to be monitored, the tail strut is excited by a broadband random signal, and the vibration mode frequency of the corresponding tail strut structure is extracted, n>m, and n and m are both positive integers greater than 1; S3, excite the tail strut with a sine wave of each modal vibration frequency, and record the amplitude ratio sequence A of the vibration sensor relative to the excitation signal n×1 , assemble the amplitude ratio sequence of multiple modes to form the vibration matrix Φ n×m ; S4, using the sensor layout optimization criterion as the fitness function of the sensor location layout, solving the sensor installation location layout with the smallest fitness function value as the optimal sensor installation location layout, the fitness function is: ； in, , is the kth vibration sensor; is the condition number of the matrix based on the 2-norm, defined as ,in is the largest eigenvalue of matrix A, is the minimum eigenvalue of matrix A; is the vibration mode matrix of m-order and m-measurement points; sigmoid is a smooth activation function, defined as ; Represents the cosine value of the i-th vibration mode vector and the j-th vibration mode vector.

2. The method for optimizing the layout of multi-modal vibration sensors of the tail strut of a wind tunnel according to claim 1, characterized in that: In step S1, a finite element model of the tail strut including a wind tunnel test model and a balance is established, modal analysis is performed, effective modal masses of each order are extracted, and the vibration modal order to be monitored is determined according to a predetermined index of the effective modal mass; specifically, the following steps are included: S11, perform modal analysis on the tail strut finite element model including the wind tunnel test model and the balance, and extract the frequency, vibration shape and effective modal mass of each mode from the analysis results; S12, dividing the effective modal mass of each mode by the total mass of the tail strut including the wind tunnel test model and the balance to obtain the ratio of the effective modal mass; S13, the ratios of the effective modal masses of each order are accumulated in sequence from low order to high order until the accumulated sum is greater than or equal to the set value of the ratio of the effective modal masses, thereby obtaining a modal set to be monitored and calculating the vibration modal order to be monitored.

3. The method for optimizing the layout of multi-modal vibration sensors of the wind tunnel tail strut according to claim 1, characterized in that: In step S2, n vibration sensors are arranged along the axis direction of the support rod by using the Monte Carlo method or the equal spacing method.

4. The method for optimizing the layout of multi-modal vibration sensors of the wind tunnel tail strut according to claim 1, characterized in that: In step S2, a broadband random signal is used to excite the tail strut to extract the vibration modal frequency of the tail strut structure; specifically, the following steps are included: S21, the signal generator generates a broadband random excitation signal, which is amplified by the piezoelectric power amplifier and drives the piezoelectric actuator embedded in the tail support rod to vibrate the tail support rod containing the wind tunnel test model and the balance; S22, collecting a vibration response signal through a vibration sensor arranged on the tail support rod; S23, combining the excitation signal and the response signal, using the H1 estimation method, and calculating the frequency response function; S24, extracting the vibration modal frequency of the tail strut structure according to the vibration modal order to be monitored determined in step S1.

5. The method for optimizing the layout of multi-modal vibration sensors of the wind tunnel tail strut according to claim 1, characterized in that: In step S4, a genetic algorithm is used to optimize the installation position layout of the sensor, which specifically includes the following steps: S41. Sorting the set S in lexicographic order and encoding the set S to generate an initial population, where the number of the initial population is M; selecting a sensor layout optimization criterion function as a fitness function, and calculating the fitness function using a penalty function method; S42, using roulette wheel selection method to select individuals; S43, assuming the crossover probability is , will randomly select The next generation is obtained by crossover of chromosomes; let the initial individual be , , a new individual is generated by performing arithmetic crossover on two individuals: ； In the formula, is the arithmetic crossover parameter; S44, use uniform mutation, set the mutation rate , for each gene of the new generation of individuals generated after crossover, randomly generate a mutation probability ,like , then a mutation operation is performed to randomly select candidate values ​​in the population space to replace the original values; S45, looping and iterating steps S42 to S44 until the difference between the fitness function of the best individual of this generation and the fitness function of the best individual of the previous generation is less than a specified value or satisfies the maximum number of generations, and the optimal sensor layout can be extracted.

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