CN115099110A - Large-span structure space net rack health monitoring point arrangement optimization method - Google Patents
Large-span structure space net rack health monitoring point arrangement optimization method Download PDFInfo
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Abstract
The invention relates to a method for optimizing the arrangement of space grid health monitoring points of a large-span structure, which comprises the following steps: establishing a three-dimensional finite element model of the large-span structure space net rack, and calculating a corresponding vibration mode according to actual calculation parameters; calculating the maximum value of the off-diagonal elements after each adding of the measuring point by using a modal confidence matrix, and optimizing the number of the sensors according to the result; a matrix is constructed from the Fisher information matrix, and then smaller data locations in the matrix are removed in iterations until the remaining sensors meet the requirements. The optimization method comprehensively considers the maximum value and the mean value of off-diagonal elements of the modal confidence matrix to optimize the number of the sensors, and finally optimizes the arrangement positions of the sensors based on an effective independent method.
Description
Technical Field
The invention relates to the technical field of building monitoring, in particular to a method for optimizing the arrangement of space grid health monitoring points of a large-span structure.
Background
The large-span space steel structure has the characteristics of various forms, strong spanning capability, high rigidity, light dead weight and the like, and is widely applied to civil and industrial buildings such as gymnasiums, terminal buildings, convention and exhibition centers, large-span industrial factory buildings and the like. In recent years, as the requirements of construction units for building shapes and space utilization are increased, more and more complicated large-span space steel structures are designed and constructed more and more. However, the complex large-span space structure has many problems in health detection, on one hand, real-time construction monitoring and health monitoring are needed to master the actual construction quality and the later safety performance of the structure, and on the other hand, the deformation condition of the structure needs to be analyzed in many vibration modes to predict, analyze and solve the difficulty of measuring point selection. The monitoring of a general long-span space steel structure is mainly in the construction and unloading process, the investment in the structural health monitoring is far less than that in the construction process, the health monitoring is redundant in arrangement of monitoring points due to more vibration modes, and the phenomenon of waste of measuring points arranged during the health monitoring is avoided. It is therefore desirable to provide a new solution.
Disclosure of Invention
The invention aims to overcome the defects of the prior art, provides a method for optimizing the arrangement of the health monitoring points of a large-span structure space network frame, and solves the problem of waste caused by redundant arrangement of the monitoring points due to more vibration modes in the conventional health monitoring.
The technical scheme for realizing the purpose is as follows:
the invention provides a method for optimizing the arrangement of space grid health monitoring points of a large-span structure, which comprises the following steps:
establishing a three-dimensional finite element model of the large-span structure space net rack, and calculating a corresponding vibration mode according to actual calculation parameters;
using modal confidence matrices
Calculating the maximum value of the non-diagonal elements after each measuring point is added, and optimizing the number of the sensors according to the result, wherein a ii 、a jj 、a ij For the value of the element, phi, corresponding to i column and j column in the Fisher information matrix ki 、φ kj I order and j order modal vectors of a kth measuring point;
constructing a matrix according to the Fisher information matrix
Wherein phi is s Is the S-th order modal vector value, λ is the eigenvalue of Fisher information matrix, which can be expressed as Ψ -ker (A- λ I), Ψ is the kernel of the matrix (A- λ I), and Φ s For the target mode matrix, the smaller data locations in the matrix are then removed in iterations until the remaining sensors meet the requirements.
The optimization method comprehensively considers the maximum value and the mean value of the off-diagonal elements of the modal confidence matrix to optimize the number of the sensors, and finally optimizes the arrangement positions of the sensors based on an effective independent method.
The large-span structure space net rack health monitoring points are optimally arrangedThe method is further improved in that the measuring points are selected based on the spatial intersection angle to reserve the vibration characteristics of the model, and the spatial intersection angle is utilized
Is evaluated, wherein phi i ,φ j I and j columns of the modal vector matrix, a ii 、a jj 、a ij Element values corresponding to i columns and j columns in the Fisher information matrix;
denotes the initial mode vector matrix by phi (n x m),
a modal vector matrix representing the points to be measured, wherein m is the number of optimized modes, n is the selected measured point,
subtracting the rest points to be measured from the selected measuring points for all measuring points;
will be in
Adding the kth measuring point to phi to obtain
Wherein
Representing the modal vector value of ith order and j order of a kth measuring point;
each time a point is added to the modal vector matrix, the maximum of the non-diagonal elements in the matrix is taken as the objective function
And finding the measuring points which reduce the objective function value to the maximum extent and adding the measuring points into phi, adding all the measuring points into phi through iterative calculation, calculating the maximum value of the off-diagonal elements after each adding of the measuring points, and optimizing the number of the sensors according to the result.
The large-span structure space net rack health monitoring points are optimally arrangedThe further improvement of the quantization method is that the Fisher information matrix
Can be expressed as
Wherein phi s Is a matrix composed of the modal vectors,
for a matrix of i-th modal vectors, Q i The number of the sensors is the number of the sensors, wherein the number of the sensors is the number of the sensors, and the number of the sensors is the number of the sensors;
solving the eigen equation (Q- λ I) Ψ ═ 0 of the matrix Q, where I is the identity matrix;
construction matrix
The position where E is 0 is removed by iteration.
The invention further improves the method for optimizing the arrangement of the space grid health monitoring points of the large-span structure, and further comprises the following steps: preliminarily arranging the structure monitoring points, and constructing a Fisher matrix
And measuring the information content contained in the Q by using the 2-norm of the Q, and calculating to obtain the target modal number.
The method for optimizing the arrangement of the spatial grid health monitoring points of the large-span structure is further improved in that the vibration response of the structure of S sensors arranged on the structure is S based on the modal superposition theory
Wherein u is s For structural response information, phi i Being modal vectors of the i-th order of the structure, q i Is the i-th order modal coordinate, phi s A matrix formed by modal vectors of all orders, wherein S is the number of sensors;
least squares to solve structural response informationSolution (II)
Rewriting the minimum v-quadratic solution to u taking into account the measured effect s ＝φ s q + v, wherein v is represented by σ 2 Gauss noise of variance;
computing the sum of q using covariance
Error, covariance calculation formula is
Wherein
Q is a Fisher information matrix formed by vibration mode modal vectors;
according to the formula of rate of change
Calculating the value of i when ROC approaches 0 or changes extremely small as the target mode number, wherein Q i And n is the number of selected modes.
Detailed Description
The present invention will be further described with reference to the following specific examples.
The invention provides a health monitoring point arrangement optimization method for a large-span structure space net rack, and aims to provide a steel structure health monitoring optimization method with high precision and high economic benefit. Aiming at the health monitoring of the large-span space steel structure, the invention optimizes the modal quantity, the sensor quantity and the sensor positions by adopting a multiple optimization method. Firstly, optimizing the target modal quantity by using the change rate of 2-norm of a Fisher information matrix, secondly, optimizing the quantity of sensors by comprehensively considering the maximum value and the mean value of off-diagonal elements of a modal confidence matrix, and finally optimizing the arrangement position of the sensors based on an effective independent method. The following explains the method for optimizing the arrangement of the space network frame health monitoring points of the large-span structure.
The invention provides a method for optimizing the arrangement of space grid health monitoring points of a large-span structure, which comprises the following steps:
establishing a three-dimensional finite element model of the large-span structure space net rack, and calculating a corresponding vibration mode according to actual calculation parameters;
using modal confidence matrices
Calculating the maximum value of the non-diagonal elements after each measuring point is added, and optimizing the number of the sensors according to the result, wherein a ii 、a jj 、a ij For the value of the element, phi, corresponding to i column and j column in the Fisher information matrix ki 、φ kj I order and j order modal vectors of a kth measuring point;
constructing a matrix from a Fisher information matrix
Wherein phi is s Is the S-th order modal vector value, λ is the eigenvalue of Fisher information matrix, which can be expressed as Ψ -ker (A- λ I), Ψ is the kernel of the matrix (A- λ I), and Φ s For the target modality matrix, the smaller data locations in the matrix are then removed in iterations until the remaining sensors meet the requirements.
In an embodiment of the present invention, a three-dimensional finite element model is established by using three-dimensional finite element software according to the actual size of the structure, and the corresponding mode shape is calculated according to the actual calculation parameters, preferably, the first 60-order mode shape is selected. The three-dimensional finite element model is preferably drawn by Solid works three-dimensional modeling software.
In one embodiment of the present invention, optimizing the number of sensors comprises the steps of:
selecting measurement points based on spatial intersection angles to preserve vibrational characteristics of the model, the spatial intersection angles utilizing
Is evaluated, wherein phi i ,φ j Being a matrix of modal vectorsi columns and j columns, a ii 、a jj 、a ij The element values corresponding to i columns and j columns in the Fisher information matrix are obtained;
denotes the initial mode vector matrix by phi (n x m),
a modal vector matrix representing the points to be measured, wherein m is the number of optimized modes, n is the selected measured point,
subtracting the remaining points to be measured from the selected measuring points from all the measuring points;
will be in
Adding the kth measuring point to phi to obtain
Wherein
Representing the modal vector value of ith order and j order of a kth measuring point;
each time a point is added to the modal vector matrix, the maximum of the non-diagonal elements in the matrix is taken as the objective function
And finding the measuring points which reduce the objective function value to the maximum extent and adding the measuring points into phi, adding all the measuring points into phi through iterative calculation, calculating the maximum value of the off-diagonal elements after each adding of the measuring points, and optimizing the number of the sensors according to the result.
When selecting measuring points, a larger space intersection angle between modal vectors to be identified is ensured, so that the vibration characteristics of the original model are reserved, and the method generally adopts
To evaluate the spatial intersection situation.
The calculation result of calculating the maximum value of the off-diagonal elements may oscillate as the number of iterations increases, but the general trend converges to the optimal value, and when the maximum off-diagonal element is stable as the number of stations increases, the value of the station is the optimal value of the number of sensors.
In one embodiment of the invention, the Fisher information matrix
Can be expressed as
Wherein phi s Is a matrix composed of the modal vectors,
for a matrix of i-th modal vectors, Q i The number of the sensors is the number of the sensors, wherein the number of the sensors is the number of the sensors, and the number of the sensors is the number of the sensors;
solving the eigen equation (Q- λ I) Ψ ═ 0 of the matrix Q, where I is the identity matrix; since Q is a symmetric matrix, after orthogonal diagonalization ψ · λ -1 ψ＝Q -1 ；
Construction matrix
The positions where E is 0 are removed by iteration.
According to the construction matrix
Available E 2 E, it follows that the eigenvalues of E are only possible to 0, 1, and the trace of E equals the rank. Wherein E ii Represents the contribution of the ith degree of freedom to the mode matrix when E ii 1, it is important to indicate that the degree of freedom at this position is linearly independent of the mode vector and that the target mode is identified, where the sensor needs to be retained when E ii A degree of freedom at this position is 0, which means that the desired target mode cannot be identified, and the sensor has an optimized space, which can be removed. Gradual removal of E by iteration ii Is smallerUntil the number of remaining sensors meets the requirements.
And (4) synthesizing the results of modal optimization, sensor quantity and position optimization to obtain the optimal arrangement of the measuring point steel structure.
In one embodiment of the present invention, the method further comprises: preliminarily arranging the structure monitoring points, and constructing a Fisher matrix
And measuring the information quantity contained in the Q by using the 2-norm of the Q, and calculating to obtain the target modal number.
Further, based on the modal stacking theory, the vibration response of the structure on which the S sensors are arranged is
Wherein u is s Is a structural response message, phi i Being modal vectors of the i-th order of the structure, q i Is the i-th order modal coordinate, phi s The matrix is formed by modal vectors of all orders, and S is the number of sensors;
solving least squares solutions to structural response information
Rewriting the minimum v-quadratic solution to u taking into account the measured effect s ＝φ s q + v, where v is represented by 2 Gauss noise of variance;
computing the sum of q using covariance
Error, covariance calculation formula of
Wherein
Q is a Fisher information matrix formed by vibration mode modal vectors; the characteristic of reflecting the sensitivity to the mode shape change requires that the Fisher information matrix Q is maximum to obtain the best estimation,the matrix 2-norm can indicate the amount of information contained in the matrix in a certain sense, so the amount of information contained in Q is measured by using the 2-norm of Q, that is, the amount of change of Q can also be measured by the amount of change of its 2-norm.
According to the formula of rate of change
Calculating the value of i when ROC approaches 0 or changes extremely small as the target mode number, wherein Q i And n is the number of selected modes. The value of n is 60.
The present invention has been described in detail with reference to the embodiments, and various modifications thereof can be made by those skilled in the art based on the above description. Therefore, certain details of the embodiments should not be construed as limitations of the invention, except insofar as the following claims are interpreted to cover the invention.
Claims (5)
1. A method for optimizing the arrangement of space grid health monitoring points of a large-span structure is characterized by comprising the following steps:
establishing a three-dimensional finite element model of the large-span structure space net rack, and calculating a corresponding vibration mode according to actual calculation parameters;
using modal confidence matrices
Calculating the maximum value of the off-diagonal elements after each measuring point is added, and optimizing the number of the sensors according to the result, wherein a ii 、a jj 、a ij For the value of the element, phi, corresponding to i column and j column in the Fisher information matrix ki 、φ kj I order and j order modal vectors of a kth measuring point;
constructing a matrix from a Fisher information matrix
Wherein phi is s Is the S-th order modal vector value, and λ is FisherThe eigenvalue of the information matrix may be denoted as Ψ — ker (a- λ I), Ψ being the kernel of the matrix (a- λ I), Φ s For the target mode matrix, the smaller data locations in the matrix are then removed in iterations until the remaining sensors meet the requirements.
2. The method for optimizing the layout of the space truss health monitoring points of the large-span structure as claimed in claim 1, wherein the measuring points are selected based on the space intersection angle, which utilizes the vibration characteristics of the model, to preserve the vibration characteristics of the model
Is evaluated, wherein phi i ,φ j I and j columns of the modal vector matrix, a ii 、a jj 、a ij The element values corresponding to i columns and j columns in the Fisher information matrix are obtained;
the initial modal vector matrix is represented by phi (n x m),
a modal vector matrix representing the points to be measured, wherein m is the optimized modal number, n is the selected measuring point,
subtracting the rest points to be measured from the selected measuring points for all measuring points;
will be in
Adding the kth measuring point to phi to obtain
Wherein
Representing the modal vector value of ith order and j order of a kth measuring point;
each time a point is added to the modal vector matrix, the maximum of the non-diagonal elements in the matrix is taken as the objective function,in that
And finding the measuring points which reduce the objective function value to the maximum extent, adding the measuring points into phi through iterative calculation, calculating the maximum value of the off-diagonal elements after each measuring point addition, and optimizing the number of the sensors according to the result.
3. The method for optimizing the arrangement of the long-span structure space network frame health monitoring points as claimed in claim 1, wherein the Fisher information matrix
Can be expressed as
Wherein phi s Is a matrix composed of the modal vectors,
for a matrix of i-th modal vectors, Q i The number of the sensors is the number of the sensors, i is a Fisher information matrix formed by vibration mode modal vectors, and the value of i is from 1 to S;
solving the eigen equation (Q- λ I) Ψ ═ 0 of the matrix Q, where I is the identity matrix;
construction matrix
The positions where E is 0 are removed by iteration.
4. The method for optimizing the arrangement of the large-span structure space grid health monitoring points as recited in claim 1, further comprising: preliminarily arranging the structure monitoring points, and constructing a Fisher matrix
Measuring the information content contained in Q by using the 2-norm of Q, and calculating to obtain a target modeNumber of the cells.
5. The method for optimizing the layout of the spatial grid health monitoring points of the large-span structure according to claim 4, wherein the vibration response of the structure with the S sensors is based on the modal superposition theory
Wherein u s For structural response information, phi i Being modal vectors of the i-th order of the structure, q i Is the i-th order modal coordinate, phi s The matrix is formed by modal vectors of all orders, and S is the number of sensors;
solving least squares solutions to structural response information
Rewriting a minimum v-quadratic solution to u in view of the measured influence s ＝φ s q + v, where v is represented by 2 Gauss noise of variance;
computing the sum of q using covariance
Error, covariance calculation formula of
Wherein
Q is a Fisher information matrix formed by vibration mode modal vectors;
according to the formula of rate of change
Calculating the value of i when ROC is close to 0 or extremely changed as the target mode number, wherein Q i And n is the number of selected modes.
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN115292792A (en) * | 2022-09-26 | 2022-11-04 | 北京云庐科技有限公司 | Monte Carlo sampling simulation-based large-span spatial structure monitoring and optimizing point distribution method |
| CN116034904A (en) * | 2023-03-31 | 2023-05-02 | 华南农业大学 | Pig health monitoring system and method based on track type inspection robot |
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2022
- 2022-07-11 CN CN202210813795.2A patent/CN115099110A/en active Pending
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN115292792A (en) * | 2022-09-26 | 2022-11-04 | 北京云庐科技有限公司 | Monte Carlo sampling simulation-based large-span spatial structure monitoring and optimizing point distribution method |
| CN116034904A (en) * | 2023-03-31 | 2023-05-02 | 华南农业大学 | Pig health monitoring system and method based on track type inspection robot |
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