An Optimization Method for the Layout of Multi-Modal Vibration Sensors on the Wind Tunnel Tail Strut

Abstract

The present invention discloses a method for optimizing the layout of multi-modal vibration sensors on a wind tunnel tail strut, including: establishing a finite element model of the tail strut including the wind tunnel test model and the balance, performing modal analysis to determine the vibration modal orders to be monitored; arranging n vibration sensors along the axis direction of the strut. According to the vibration modal orders to be monitored, the tail strut is excited by a bandwidth random signal, and the vibration modal frequencies of the corresponding tail strut structure are extracted; the tail strut is excited by a sine wave of each modal vibration frequency respectively, the amplitude ratio sequence of the vibration sensors relative to the excitation signal is recorded, and the amplitude ratio sequences of multiple orders of modes are assembled to form a mode shape matrix; the sensor layout optimization criterion is used as the fitness function for the position layout of the sensors, and the optimal installation position layout of the sensors is solved. The present invention uses the optimization criterion to maximize the observation ability of the vibration modal set and minimize the linear correlation between the modal vectors, realizing the optimal position layout of the sensors.

Description

Technical Field

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

[0002] Full-scale wind tunnel tests are authoritative verification means for measuring the aerodynamic parameters of an aircraft in different states. 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 the vibration suppression scheme for the tail strut. As the input of the active vibration suppression device, vibration sensors mainly include accelerometers, strain balances, and visual images, etc. Some researchers use strain balances to measure the vibration of the tail strut. Strain balances have 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 the vibration measurement equipment for the tail strut, and use the method of combining visual vibration images with accelerometers embedded in the model as the 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-mentioned schemes consider the position optimization of vibration sensors, which may lead to weak vibration signals of a certain order of mode measured, low signal-to-noise ratio, and inability to effectively monitor the corresponding vibration of the wind tunnel tail strut, thus restricting 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 on the wind tunnel tail strut, the purpose of the present invention is to propose an optimization method for the layout of multi-modal vibration sensors on the wind tunnel tail strut. First, confirm the set of vibration modes to be observed, establish a series of candidate sensor positions, and use the optimization criterion to maximize the observation ability of the vibration mode set while minimizing the linear correlation between modal vectors, so as to realize 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 on a wind tunnel tail strut, 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, 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 the 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 of the vibration sensor relative to the excitation signal n×1 , 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, is the smallest eigenvalue of matrix A; is the mode shape 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.

[0013] Further, 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 performed, the effective modal mass of each order is 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:

[0014] S11. Perform 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 the low order to the high order in sequence 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] Further, 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] Further, in step S2, the tail support rod is excited by a bandwidth random signal, and the vibration modal frequency of the tail support rod structure is extracted; specifically, the following steps are included:

[0019] S21. The signal generator generates a bandwidth random excitation signal, which is amplified by a piezoelectric power amplifier and then drives a 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] Further, 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, perform 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 that the crossover probability is , randomly select to perform double-parent crossover on the chromosome to obtain the next generation; assume the initial individuals are , , 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. Detailed Embodiment

[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 for a wind tunnel tail strut. 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, conduct modal analysis, and extract the effective modal masses 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, establish a finite element model of the tail strut including the wind tunnel test model and the balance, conduct modal analysis, extract the effective modal masses of each order, and determine the number of vibration modal orders to be monitored according to the predetermined index of the effective modal mass; specifically, it includes the following steps:

[0043] S11. Conduct modal analysis on the finite element model of the tail strut including the wind tunnel test model and the balance, and extract the frequencies, vibration modes, and effective modal masses 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 masses of each order from low order to high order in sequence 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 direction 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 frequencies of the tail strut structure. Optionally, conduct modal analysis through the finite element method to extract the vibration modal frequencies 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 direction of the strut.

[0048] In step S2, use a bandwidth random signal to excite the tail strut and extract the vibration modal frequencies 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 signal through the vibration sensor 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 frequency of the tail strut structure.

[0053] S3. Sinusoidally excite the tail strut with the actual vibration mode frequency respectively, and record the amplitude ratio sequence A of the vibration sensor 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 shape at the position of the recorded vibration sensor 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's 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] Among them, , 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 sensor. 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 pick 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. Assume the crossover probability is , and randomly select to perform parental crossover on the chromosomes to obtain the next generation. Let the initial individuals be and . After performing arithmetic crossover on 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 mode 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 shape matrix Φ 277×3 , such as Figure 2 shown

[0072] (4) Take the sensor layout optimization criterion as the fitness function for the position layout of the sensors, 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

[0073] The sensor layout optimization criterion function is

[0074] ;

[0075] 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 the matrix A, is the smallest eigenvalue of the 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

[0076] Use the genetic algorithm to optimize and determine the installation position layout of the sensors, 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 bits of the binary 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 into 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 into the next generation. Use the roulette wheel selection method 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 parental 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 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 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 interpreted to include the preferred embodiments as well as all changes and modifications falling within the scope of the present application.

[0087] Obviously, those skilled in the art can make various changes and variations 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 multi-modal vibration sensor layout optimization method for a wind tunnel tail strut, characterized in that The method includes the following steps: S1. Establish a finite element model of the tail support rod with a wind tunnel test model and a balance, conduct a modal analysis, and determine the order m of the vibration modes to be monitored, where A is the set of modes to be monitored and card() is the number of elements in the set; S2. Arrange n vibration sensors along the axis of the support rod. 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 support rod, and extract the vibration mode frequencies of the corresponding tail support rod structure. n > m, and both n and m are positive integers greater than 1; S3. Excite the tail support rod with sine waves of each modal vibration frequency respectively, and record the amplitude ratio sequence A of the vibration sensor relative to the excitation signal n×1 , assemble the amplitude ratio sequences of multiple orders of modes to form a mode shape matrix Φ n×m ; S4. Use the sensor layout optimization criterion as the fitness function for the position layout of the sensors, and solve for the installation position layout of the sensors with the minimum fitness function value as the optimal installation position layout of the sensors. The fitness function is: ； 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 vibration 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 vibration mode vector and the j-th vibration mode vector.

2. The multi-modal vibration sensor layout optimization method for the wind tunnel tail strut according to claim 1, wherein In step S1, establish a finite element model of the tail support rod with a wind tunnel test model and a balance, conduct a modal analysis, extract the effective modal mass of each order, and determine the order of the vibration modes to be monitored according to the predetermined index of the effective modal mass. Specifically, it includes the following steps: S11. Conduct a modal analysis on the finite element model of the tail support rod with a wind tunnel test model and a balance, and extract the frequencies, vibration modes, and effective modal mass of each order from the analysis results; S12. Divide the effective modal mass of each order by the total mass of the tail support rod with a wind tunnel test model and a balance to obtain the ratio of the effective modal mass; S13. Accumulate the ratios of the effective modal mass of each order from the lower order to the higher 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 order of the vibration modes to be monitored.

3. The multi-modal vibration sensor layout optimization method for the wind tunnel tail strut according to claim 1, wherein In step S2, use the Monte Carlo method or the equal-spacing method to arrange n vibration sensors along the axis of the support rod.

4. The method for optimizing the layout of multi-modal vibration sensors of a wind tunnel tail strut according to claim 1, wherein, In step S2, use a broadband random signal to excite the tail support rod and extract the vibration mode frequencies of the tail support rod structure. Specifically, it includes the following steps: S21. The signal generator generates a broadband 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 with a wind tunnel test model and a balance vibrate; S22. Collect the vibration response signal through the vibration sensors arranged on the tail support rod; S23. Combine the excitation signal and the response signal, and use the H1 estimation method to calculate the frequency response function; S24. According to the order of the vibration modes to be monitored determined in step S1, extract the vibration mode frequencies of the tail support rod structure.

5. The multi-modal vibration sensor layout optimization method for the wind tunnel tail strut according to claim 1, wherein In step S4, use the genetic algorithm to optimize and determine the installation position layout of the sensors. Specifically, it includes the following steps: S41. For the set S, use the lexicographical order 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; S42. Use the roulette wheel selection method to select individuals; S43. Assume that 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: ； In the formula, is the arithmetic crossover parameter; S44. Adopt uniform mutation, and set the mutation rate to be . For each gene of the new generation of individuals generated after crossover, randomly generate a mutation probability . If , then perform the mutation operation, and randomly select a candidate value in the population space to replace the original value; 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.

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