Method for optimizing three-dimensional sensor in operation mode

Abstract

The invention discloses a method for optimizing a three-dimensional sensor in an operation mode, which combines an effective independence method with redundancy, sorts candidate sensors according to contribution of candidate sensor positions to linear independence of a target mode, and removes an unimportant position through iteration each time. The final sensor configuration tends to maximize the determinant of the Fisher information matrix, so that the corresponding target modal shape is linearly independent as far as possible, and meanwhile, the signal strength of the target modal response in the test data is maximized, so that the modals are distinguished as far as possible, the signal-to-noise ratio is improved, and the influence of noise on the test is reduced. According to the invention, the number of required sensors can be minimized while the accuracy of data collection is ensured, so that the potential influence of the sensors on the structure function is reduced, and the test cost is reduced.

Description

Technical Field

[0001] The present invention relates to the field of mechanical engineering, and in particular to a method for optimizing a three-dimensional sensor in an operating mode. Background Art

[0002] Rotating machinery usually works in harsh working environments such as high temperature and alternating loads. There are complex nonlinear load excitations during operation, which often lead to dynamic problems and fatigue failure of mechanical structures. Therefore, it is of great significance to carry out modal identification of rotating machinery in operation. Its dynamic characteristics are important indicators of system status monitoring, which can serve as the basis for reliable and stable operation of the rotor system, detection of mechanical system failures and damage, and early estimation of system service life.

[0003] The accuracy of modal characteristic identification depends on the number and location of sensors. For small and simple test structures, the number of test sensors and the location of measuring points can often be determined based on expert experience. However, for large and complex structures, harsh operating environments and complex spatial structures will affect the layout of sensors and the quality of data collection. In order to ensure the accuracy of data collection, it is necessary to study the optimal layout location and number of sensors to maximize the effectiveness of the measurement system.

[0004] One of the most popular sensor placement optimization methods for modal testing is the effective independence (EI) method proposed by DC Kammer, which aims to maximize the Fisher Information Matrix (FIM) corresponding to the target mode, thereby maximizing the contribution of each sensor to the observability of the mode. However, the sensor configuration obtained by the EI method is prone to information redundancy in the sensor position, especially in the case of complex structures or dense sensor configurations. In addition, this method generates a sensor configuration in each iteration and leaves the best configuration to the user to choose, and cannot directly give the optimal number and configuration of sensors. Summary of the invention

[0005] The technical problem to be solved by the present invention is to provide a method for optimizing a three-dimensional sensor in an operating mode in view of the defects involved in the background technology.

[0006] The present invention adopts the following technical solutions to solve the above technical problems:

[0007] A method for optimizing a three-dimensional sensor in an operating mode comprises the following steps:

[0008] Step 1) Establish a finite element model of the target structure, perform finite element modal analysis on the finite element model, and obtain the required number of modes n and modal vibration shape Ф sEach node of the finite element model is taken as a candidate sensor position to establish a candidate sensor position set. The number m of candidate sensor positions in the candidate sensor position set is greater than or equal to the preset sensor number threshold t sn ;

[0009] Step 2), calculate the Fisher information matrix of all candidate sensors in the candidate sensor position set. The Fisher information matrix Q of all candidate sensors in the candidate sensor position set is expressed as:

[0010]

[0011] where Φ 3i is the three-dimensional modal vibration matrix corresponding to the i-th candidate sensor position, is the vibration mode matrix Φ 3i The transposed matrix, Q 3i is the three-dimensional information matrix of the i-th candidate sensor position, and m is the number of candidate sensor positions;

[0012] Step 3), calculate the three-axis effective independence index of each candidate sensor position in the candidate sensor position set, where the three-axis effective independence index EfI3 of the i-th candidate sensor position is i =1-det(I3-E 3i ), where det(.) represents the determinant of the matrix in brackets, I3 is the three-dimensional unit matrix; E 3i is a 3×3 fully filled matrix, which is expressed as:

[0013]

[0014] Among them, Q -1 is the inverse matrix of Q, Φ sir is the rth row of the mode shape at the i-th sensor position in the set of candidate sensor positions, r = 1, 2, 3;

[0015] Step 4), according to EfI3 i The size of the value sorts the candidate sensor positions in the candidate sensor position set from high to low;

[0016] Step 5), remove EfI3 from the set of candidate sensor locations i The candidate sensor location with the lowest value;

[0017] Step 6), calculate the three-dimensional Fisher information matrix of each candidate sensor position in the candidate sensor position set according to the following formula:

[0018]

[0019] Step 7), calculate the redundancy between the candidate sensor positions in the candidate sensor position set, and take the smallest redundancy R S , where the redundancy between the i-th candidate sensor location and the j-th candidate sensor location is R ij The calculation formula is as follows:

[0020]

[0021] In the formula, Q 3i , Q 3j are the three-dimensional Fisher information matrices of the i-th and j-th candidate sensor positions respectively;

[0022] Step 8), R S and the preset redundancy threshold t r For comparison, if R S <t r , jump to step 2), if R S >t r , execute step 9);

[0023] Step 9), the remaining sensor positions and quantities in the candidate sensor position set are regarded as the optimal sensor configuration.

[0024] Compared with the prior art, the present invention adopts the above technical solution and has the following technical effects:

[0025] The present invention optimizes sensor layout and parameter settings to improve the accuracy of structural vibration data acquisition, analysis efficiency and reduce the number of sensors used. It can minimize the number of sensors required while ensuring the accuracy of data collection, thereby reducing the potential impact of sensors on structural functions and reducing testing costs. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 It is a schematic diagram of the structure of the target object in the present invention;

[0027] Figure 2 It is a schematic diagram of the process of the present invention;

[0028] Figure 3 It is a schematic diagram of the optimization results of the three-dimensional sensor of the rotor test bench in the present invention;

[0029] Figure 4 MAC values ​​of each mode after optimization by the three-dimensional sensor optimization method. DETAILED DESCRIPTION

[0030] The technical solution of the present invention is further described in detail below in conjunction with the accompanying drawings:

[0031] The present invention can be implemented in many different forms and should not be considered to be limited to the embodiments described herein. On the contrary, these embodiments are provided to make this disclosure thorough and complete, and will fully express the scope of the present invention to those skilled in the art. In the accompanying drawings, components are enlarged for clarity.

[0032] The goal of the sensor placement strategy in the present invention is to select the optimal sensor position so that the corresponding target modal vibration shapes are as linearly independent as possible, while maximizing the signal strength of the target modal response in the test data, so as to distinguish the modes as much as possible and reduce the impact of noise on the test. Therefore, the modal analysis results of the finite element model of the target structure can be used to help place the sensor, and each node of the finite element model is used as a candidate sensor position to establish a candidate sensor position set, and the vibration shape matrix Φ of all candidate sensors in the candidate sensor position set is taken. s .

[0033] Linear independence means that at any time, the displacement output u of the target structure sensor position s =Ф s q, by solving this equation, the modal coordinate q can be estimated: in is the estimated target modal coordinate vector, Ф T s is the vibration mode matrix Ф s The transposed matrix of . [.] -1 Represents the inverse matrix of the matrix in brackets.

[0034] In order to obtain the best modal estimation, it is necessary to minimize the covariance matrix of the estimation error, so u s Written as: s =H(q)+N=Φ s q+N, where the symbol H represents the process measurement value, and the vector N represents a stationary Gaussian white noise with a mean of 0 and a variance of

[0035] For an effectively unbiased estimator, the covariance matrix of the estimation error is Where E is the expected value.

[0036] Assume H(q) = Φ s q, then the covariance matrix Where Q is the Fisher information matrix of all candidate sensors in the candidate sensor location set, Q -1 is the inverse matrix of Q. From this formula, it is found that maximizing Q will lead to minimizing the covariance matrix, thus obtaining the optimal modal coordinates.

[0037] To simplify the analysis, it is assumed that the measurement noise is uncorrelated and each sensor has the same statistical properties. The Fisher information matrix of all candidate sensors in the candidate sensor location set is For each candidate sensor's contribution to the information matrix,

[0038] Among them Ф i is the modal vibration matrix corresponding to the i-th candidate sensor position, and m is the number of candidate sensor positions. o As can be seen from the expression of , when each degree of freedom is increased or decreased on the candidate sensor set, the information in the Fisher information matrix will also be increased or decreased. Therefore, the number of sensors can be reduced by eliminating positions that do not significantly contribute to the independent information contained in the target mode.

[0039] Usually, in actual modal testing, triaxial sensors are placed at selected locations for measurement. In this case, the Fisher information matrix of all candidate sensors in the candidate sensor location set can be modified as Among them Ф 3i is the three-dimensional modal matrix corresponding to the i-th sensor position, Q 3i is the three-dimensional Fisher information matrix of the ith position, and m is the number of candidate sensor positions.

[0040] The determinant of the three-dimensional Fisher information matrix after deleting the i-th sensor position is: where det(.) represents the determinant of the matrix in brackets, I3 is the three-dimensional identity matrix, and E 3i is a 3×3 fully filled matrix:

[0041]

[0042] In the formula, Q -1 is the inverse matrix of Q, Φ sir is the r-th row of the modal shape at the i-th sensor position on the target structure, r = 1, 2, 3.

[0043] An effective independence index EfI3 of a three-axis sensor i The expression is as follows:

[0044] Ef3 i =1-det(I3-E 3i )

[0045] Effective independence index EfI3 i It represents the change ratio of the determinant of the Fisher information matrix if the i-th sensor position is deleted from the candidate set. The range of the change is: 0≤EfI3 i≤1, if a sensor position is critical to the independence of the target modality, then the corresponding EfI3 i A value of 1.0 means that the sensor position does not contribute to the independence of the target mode, and its EfI3 i The value is 0. Using this metric, the candidate sensor locations can be sorted and the least important sensor locations can be removed. It should be noted that when a sensor is removed from the candidate set, the EfI3 of the remaining sensors i To ensure that no important sensors are deleted in any iteration, the current EfI3 i The technique requires that only one sensor be removed per iteration.

[0046] Although according to EfI3 i Minimizing the estimation error of the expression for can obtain good estimates of the mode shapes, but this goal is not enough to prevent potential information redundancy between the selected sensor locations. Due to reasons such as spatial correlation, the sensors may share the same information. Therefore, it is obvious that the redundancy between sensors must be minimized.

[0047] To quantify the redundancy of information, the redundancy R between candidate sensor locations i and j is ij Defined as

[0048]

[0049] Where Q 3i and Q 3j are the three-dimensional information matrices of the i-th candidate sensor position and the j-th candidate sensor position respectively; in the above formula, the redundancy measure R ij is normalized so that when Q 3i and Q 3j When orthogonal, R ij approaches the limit value 1. In this case, it means that the two sensors do not share information. On the contrary, if the two sensors share the same information, R ij will get closer and closer to 0. Redundancy can be used as a constraint for sensor placement optimization.

[0050] In order to verify the versatility of the proposed method, we used Figure 1 The rotor test bench casing shown in the figure is verified, with an elastic modulus of 210Gpa and a density of 7850kg / m 3 , Poisson's ratio is 0.3, the number of nodes is 10926, the number of units is 3024, and the flow chart of the method for optimizing the position and number of three-dimensional sensors according to the present invention is as follows ( Figure 2 ), take the vibration mode values ​​of all nodes of the finite element model to construct the Fisher information matrix, and delete the points that contribute the least to independence one by one. When the redundancy reaches 0.4, stop the calculation and get the optimal arrangement of sensors as follows: Figure 3 As shown in the figure, the sensors are dispersedly distributed on the receiver, and there is no sensor aggregation or redundancy. In addition, the sensors are placed in the area of ​​high modal displacement, indicating that this method will ensure the linear independence of the modal vibration shape of the selected sensor position as much as possible, while maximizing the signal strength of the target modal response in the test data.

[0051] In order to measure the quality of the sensor configuration, the modal assurance criterion (MAC) is used as the evaluation criterion. The MAC value between the modes measured by the sensor configuration is as follows: Figure 4 As shown, it can be found that this method can restore the modal vibration shape of the target structure and distinguish the modes when the number of sensors is very small, and obtain a very good MAC value. The maximum value is only the MAC value between mode 1 and mode 3, which is 0.2936.

[0052] In summary, the present invention studies a method for optimizing the position and number of three-dimensional sensors for operational modal analysis. The sensor optimization method combines the effective independence method with redundancy. The method can select the optimal sensor position to make the corresponding target modal vibration shape as linearly independent as possible, while maximizing the signal strength of the target modal response in the test data, thereby distinguishing the modes as much as possible and reducing the impact of noise on the test. In addition, the number of sensors required can be minimized while ensuring the accuracy of data collection, thereby reducing the potential impact of sensors on structural functions and reducing test costs. Finally, the feasibility of the optimization method was verified by simulation data.

[0053] It will be understood by those skilled in the art that, unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as those generally understood by those skilled in the art in the art to which the present invention belongs. It should also be understood that terms such as those defined in common dictionaries should be understood to have meanings consistent with the meanings in the context of the prior art, and will not be interpreted with idealized or overly formal meanings unless defined as herein.

[0054] The specific implementation methods described above further illustrate the objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above description is only a specific implementation method of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for optimizing a three-dimensional sensor in an operating mode, characterized in that: The following steps are involved: Step 1) Establish a finite element model of the target structure, perform finite element modal analysis on the finite element model, and obtain the required number of modes n and modal vibration shape Φ s Each node of the finite element model is taken as a candidate sensor position to establish a candidate sensor position set. The number m of candidate sensor positions in the candidate sensor position set is greater than or equal to the preset sensor number threshold t sn ; Step 2), calculate the Fisher information matrix of all candidate sensors in the candidate sensor position set. The Fisher information matrix Q of all candidate sensors in the candidate sensor position set is expressed as: where Φ 3i is the three-dimensional modal vibration matrix corresponding to the i-th candidate sensor position, is the vibration mode matrix Φ 3i The transposed matrix of , Q3i is the three-dimensional information matrix of the i-th candidate sensor position, and m is the number of candidate sensor positions; Step 3), calculate the three-axis effective independence index of each candidate sensor position in the candidate sensor position set, where the three-axis effective independence index EfI3 of the i-th candidate sensor position is i =1-det(I3-E 3i ), where det(.) represents the determinant of the matrix in brackets, I3 is the three-dimensional unit matrix; E 3i is a 3×3 fully filled matrix, which is expressed as: Among them, Q -1 is the inverse matrix of Q, Φ sir is the r-th row of the mode shape at the i-th sensor position in the set of candidate sensor positions, r = 1, 2, 3; Step 4), according to EfI3 i The size of the value sorts the candidate sensor positions in the candidate sensor position set from high to low; Step 5), remove EfI3 from the set of candidate sensor locations i The candidate sensor location with the lowest value; Step 6), calculate the three-dimensional Fisher information matrix of each candidate sensor position in the candidate sensor position set according to the following formula: Step 7), calculate the redundancy between the candidate sensor positions in the candidate sensor position set, and take the smallest redundancy R S , where the redundancy between the i-th candidate sensor location and the j-th candidate sensor location is R ij The calculation formula is as follows: In the formula, Q 3i , Q 3j are the three-dimensional Fisher information matrices of the i-th and j-th candidate sensor positions respectively; Step 8), R S and the preset redundancy threshold t r For comparison, if R S <t r , jump to step 2), if R S >t r , execute step 9); Step 9), the remaining sensor positions and quantities in the candidate sensor position set are regarded as the optimal sensor configuration.

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