CN107357980A - A kind of damnification recognition method of axial functionally gradient beam - Google Patents

Abstract

The present invention discloses a kind of damnification recognition method of axial functionally gradient beam, and implementation process is：1. establishing the FEM model of functionally gradient beam damaged structure by Finite Element, the parameters such as intrinsic frequency, the mode of structure are extracted；2. calculating and the residual strain energy value of more each node, select suspicious unit；3. the impairment parameter α based on suspicious unit, calculate the Mixed Sensitivity matrix S and response difference DELTA H of positive model to be repaired and true model；4. solve update equation S Δs α=Δ H；5. update impairment parameter α=α+Δ α of suspicious unit；6. if not up to default required precision, returns to 3. loop iteration, impairment parameter is otherwise exported as recognition result.The concept of dynamic residual vector is the method define, damage is positioned, reduces the quantity for needing identification parameter；And the Mixed Sensitivity matrix containing frequency and dynamic response is employed, compared to common sensitivity matrix, still there is at a relatively high accuracy of identification under noise situations, this complex structure also can be identified successfully to functionally gradient beam.

Description

A damage identification method for axially functionally graded beams

technical field

The invention relates to the technical field of structural health detection damage identification, and more specifically, to a damage identification method for an axially functionally graded beam.

Background technique

With the rapid development of our society, the number of various engineering facilities has been increasing, and large-scale and complex buildings have sprung up. During the service period of these structures and infrastructure, due to the influence of environmental loads, corrosion, material aging and other adverse factors, structural fatigue and damage will inevitably accumulate over time. If these damages are ignored, once the damage of the key parts of the structure accumulates to a certain extent, the damage will expand rapidly, leading to the destruction of the entire structure. The tragedies caused by the failure to detect structures in time are numerous, not only causing significant economic damage, but also threatening the lives of people. Therefore, the detection and evaluation of the health status of the structure has become an inevitable requirement during the service period of the structure.

There are various methods for detecting structural damage. From the initial observation with the naked eye to the current use of high-tech instruments, such as ultrasonic waves, infrared rays, etc., these technologies have been widely used in engineering practice. Among the various approaches, damage identification techniques based on structural vibration characteristics have been the most widely studied. The basic idea of damage identification technology based on structural vibration characteristics is that local damage will inevitably cause changes in structural dynamic characteristics. If classified according to the data used, it can be subdivided into two categories: static identification technology and dynamic identification technology.

For static identification technology, it is the application of static measurement data for damage identification. Since the static equilibrium equation only involves structural stiffness, the identification target is relatively clear. Moreover, the static measurement data is relatively easy to obtain, and the measurement error is also small. However, most of the current static recognition technologies have problems such as complex algorithm process, large amount of calculation or insufficient accuracy. As for the dynamic identification technology, it is the application of various parameters in the power system for damage identification. At present, the main technical directions are frequency domain and time domain. The technology in the frequency domain direction is mainly applied to the frequency, mode shape, modal curvature or frequency response function in the dynamical system; the technology in the time domain direction is mainly applied to the velocity, acceleration, and displacement responses of the dynamical system. The advantage of dynamic identification technology is that there are many parameters and methods that can be used for identification, but its disadvantage is that the required measurement data is large and it is easily affected by noise.

In recent years, due to various demands in engineering and science and technology, various materials have sprung up, and functionally graded materials have been more and more widely used in aerospace, engineering and other fields because of their good thermal and mechanical properties. middle. As a link in the structure, functionally graded beams will inevitably experience fatigue and damage, and damage identification has become a very important part of engineering research.

The document "Damage Identification of Bridge Structure Based on Static Response (Foreign Building Materials Science and Technology, 2006, 27(2), 105-107)" introduces a method for identifying bridge structure. This method uses static measurement data and further solves the damage control equation to obtain the identification result. However, when the damage degree increases and the damage number is large, the identification deviation is large, and misjudgment is prone to occur. volume problem. However, the literature "Compliance Sensitivity Method for Structural Damage Identification (Journal of Sun Yat-Sen University, 2010, 49(1), 16-19)" proposed a model correction method based on vibration modes. This method uses the Neumann series expansion to derive the sensitivity formula of the structural flexibility matrix with respect to the element stiffness damage parameters, and establishes the damage identification equation of the structure, which can obtain better identification results. However, due to the application to modal data, there is a certain requirement for the number of measuring points, and the accuracy is reduced when using incomplete modal. Similarly, because the damage location is not predicted first, it will cause problems such as low recognition efficiency and misjudgment of damage.

Contents of the invention

In order to overcome at least one defect of the above-mentioned prior art, the present invention provides a damage identification method for an axially functionally graded beam. This method uses the residual force vector to locate the structural damage of the axially functionally graded beam, and then uses the sensitivity method including the mixed sensitivity matrix to identify the damage degree.

In order to solve the problems of the technologies described above, the technical solution of the present invention is as follows:

A damage identification method for an axially functionally graded beam, comprising the following steps:

1) Use the finite element method to simplify the modeling of the axially functionally graded beam structure, and divide the structure into nel units;

2) Extract the frequency and mode of the damaged structure, and obtain the residual force vector f _i of the damaged structure according to the following formula, and obtain the corresponding RFV value:

Among them, ω _di and V _di are the frequency and mode data obtained from the i-th order measurement of the damaged structure, respectively, and K and M are the stiffness matrix and mass matrix of the intact structure respectively;

Compare the value of each node corresponding to f _i , the unit corresponding to the node whose local RFV value is not equal to zero is defined as a suspicious unit that may be damaged, there are n suspicious units in total, and the initial value of its damage parameter is set to α _i =1, i=1,2,...,n, α={α ₁ ,α ₂ ,...,α _n };

3) Carry out further accurate identification of the damage parameter α corresponding to the suspicious unit obtained in step 2); Substitute the damage parameter α into the calculation stiffness matrix K _c , and calculate the calculation frequency ω _c and calculation acceleration R _c of the corrected structure;

4) Using the measured frequency ω _d and the measured acceleration R _d of the damaged structure, it can be obtained by Δω=ω _c -ω _d , ΔR=R _c -R _d

5) Establish the model correction equation SΔα=ΔH, wherein S is a mixed sensitivity matrix composed of eigenvalue sensitivity and acceleration sensitivity; use Tikhonov regularization method and L-curve method to solve this equation to obtain the value of Δα;

6) The damage parameter of the suspicious unit is updated to α=α+Δα;

If the damage parameter change amount Δα does not meet the set accuracy requirements, return to step 3) to continue iteration; otherwise, the damage parameter α obtained in step 6) is the final recognition result;

Among them, α=1 means no damage, and α=0 means complete damage; by checking the finite element model unit number corresponding to the damage parameters, the precise location of structural damage and the detailed damage degree can be obtained.

In order to improve the defects of the prior art, firstly, the present invention uses the residual force vector containing frequency domain data to locate the damage, which reduces the number of identification parameters required, and further uses the sensitivity method including the mixed sensitivity matrix to identify the damage parameters, Get the damage identification result. This method requires time domain and frequency domain data for damage identification and has high accuracy.

The beneficial effect of the present invention is that: compared with the direct solution of the document "Damage Identification of Bridge Structure Based on Static Response (Foreign Building Materials Science and Technology, 2006, 27(2), 105-107)", the present invention adopts two-part identification, Suspicious units are located, which improves recognition accuracy and calculation efficiency. In addition, in the second step of damage degree identification, this method uses a mixed sensitivity matrix including frequency and dynamic response, which is similar to the "softness sensitivity method for structural damage identification" (Journal of Sun Yat-Sen University, 2010, 49(1), 16-19 )” requires fewer measurement points than the method that requires structural modal data, but achieves greater accuracy and is still robust in the presence of noise. And this two-step method can well deal with the damage problem of the complex structure of functionally graded beams.

Description of drawings

Fig. 1 is the schematic diagram of the inventive method;

Fig. 2 is the structural representation of simply supported beam of embodiment 1 of the present invention;

Fig. 3 is the damage location of the embodiment 1 of the present invention - the display diagram of the RFV value of each degree of freedom;

FIG. 4 is a display diagram of the final recognition result of Embodiment 1 of the present invention;

Fig. 5 is a schematic diagram of the four-span beam structure of Embodiment 2 of the present invention;

Fig. 6 is a display diagram of damage location of Example 2 of the present invention-RFV values of each degree of freedom;

FIG. 7 is a display diagram of the final recognition result of Embodiment 2 of the present invention.

detailed description

The drawings are for illustrative purposes only and should not be construed as limitations on this patent; in order to better illustrate this embodiment, some parts in the drawings will be omitted, enlarged or reduced, and do not represent the size of the actual product;

For those skilled in the art, it is understandable that some well-known structures and descriptions thereof may be omitted in the drawings. The technical solutions of the present invention will be further described below in conjunction with the accompanying drawings and embodiments.

The specific process of the present invention is divided into two steps. Firstly, the concept of residual force vector is defined and the suspicious elements of the axial functionally graded beam are predicted by the finite element model method; then, the model correction method based on the mixed response sensitivity is applied to identify the damage parameters of the suspicious elements to accurately detect the damage location and extent of damage.

1) Damage location

Assuming that the axially functionally graded beam to be detected is discretized into nel units, in the damaged state, its characteristic equation is:

where K _d , M _d are the system stiffness and mass matrix, (ω _di , V _di ) is the i-th order frequency and the corresponding mode in the damaged state, ignoring the change of mass, and attribute the damage to the reduction of stiffness, in discrete The reduction of stiffness when damage occurs under the optimized condition can be described by a series of damage coefficients α _i (i=1,2...,nel), α _i ∈[0,1]. When α _i =0, the structure is not damaged, and when α _i =1, the structure is completely destroyed, so the overall stiffness matrix of the damaged structure can be written as

The overall stiffness matrix after damage can be changed from the overall stiffness matrix before damage and the stiffness matrix:

Substituting this into the characteristic equation, the residual force vector (RFV) is obtained and defined:

Since α≠0 on the damaged unit, the value of the residual force vector (RFV) on the corresponding node of the unit is not equal to zero. These units are selected as suspicious units, and their damage parameters are used for model correction.

2) Correct the damage model by using the mixed response sensitivity method to obtain the recognition result.

Initialize the damage parameter α corresponding to the suspicious unit, and substitute it into the modified stiffness matrix K _c to calculate the calculation frequency ω _c and acceleration R _c of the structure. Using the measured frequency ω _d and the measured acceleration R _d of the damaged structure, it is obtained by Δω=ω _c -ω _d , ΔR=R _c -R _d

Then solve the model correction equation SΔα=ΔH, where S is a mixed sensitivity matrix composed of eigenvalue sensitivity and acceleration sensitivity:

Where k is the number of measured data and n is the number of suspicious units. and It can be obtained by direct integration method.

Generally speaking, the model correction equation is an ill-conditioned equation, so the Tikhonov regularization method and the L-curve method are used to solve it. Obtain the Δα in the iteration, and observe whether it meets the preset accuracy requirements. If so, the damage parameter α in this iteration is the final recognition result; otherwise, enter the next iteration. The damage parameter in the next iteration becomes:

α=α+Δα

The specific identification process is shown in Figure 1 and Figure 2.

Example 1: Damage identification for axially functionally graded simply supported beams

As shown in Figure 3, the simply supported beam with a rectangular cross-section, the geometric parameters are shown in the figure, and the structural parameters are: the material on the left is pure aluminum, Young's modulus E _l = 6.9×10 ¹⁰ N/m ² , material density ρ _l ＝2700kg/m ³ , the material on the right is pure steel, Young's modulus E _r ＝2.1×10 ¹¹ N/m ² , material density ρ _r ＝7800kg/m ³ , and the power ratio of the functionally graded beam is 1.5, namely The change of elastic modulus and density from left to right is: E(x)=(E _L -E _R )(1-x/L) ^θ +E _R , ρ(x)=(ρ _L -ρ _R )( 1-x/L) ^θ + ρ _R . The simply supported beam is decomposed into 12 functionally graded beam units as shown in Fig. 3 . Assume that the loss factor of unit No. 1 is 0.05, that of unit No. 1 is 0.1, that of unit No. 6 is 0.15, and that of unit No. 10 is 0.2.

The RFV values of each degree of freedom are shown in Figure 4. The values of the degrees of freedom corresponding to nodes 1, 2, 3, 4, 6, 7, 10 and 11 are significantly larger than those of other nodes, so the corresponding 1, 2, 3, 6, 10 The unit is a suspected damaged unit.

Dynamic load acting on node 7 The acceleration responses of nodes 3, 5, 7, 9, and 10 and the first 6 natural frequency data are used to identify the damage degree, and the identification results shown in Figure 5 are obtained. It can be seen from the figure that the degree of damage at the corresponding position is accurately identified. Therefore, the two-step method can accurately identify the damage location and damage degree.

Example 2: Damage identification for a four-span functionally graded beam

For the four-span beam structure shown in Figure 6, the length of each span is l=3m. The structure is divided into 60 functionally graded beam units, the material on the left is Ti-6Al-4V alloy, Young’s modulus E _l =1.05×10 ¹¹ N/m ² , material density ρ _l =4429kg/m ³ , the right The side material is zirconium dioxide ZrO2, Young's modulus E _r =1.68×10 ¹¹ N/m ² , material density ρ _r =3000kg/m ³ , and the power ratio of the functionally graded beam is 1.5. Assume a 5% loss in unit 2, a 10% loss in unit 8, a 15% loss in unit 18, a 20% loss in unit 28, and a 5% loss in unit 33 , Unit 38 suffered a 10% loss and Unit 48 suffered a 15% loss.

The RFV values of each node are shown in Figure 7, and it can be seen that units 2, 8, 18, 28, 33, 38, and 48 are suspicious units that may be damaged.

Dynamic loads applied at nodes 8, 17, 34 and 36 Extract the displacement responses of nodes 3, 5, 12, 15, 25, 29, and 37 and the first 6 natural frequency data, add 0.5% white noise to the frequency data, and add 10% noise to the dynamic displacement to identify the damage degree. Under the influence of , the method of the present invention can still identify the damage more accurately.

The invention discloses a damage identification method for an axially functionally graded beam, which mainly relates to a damage location and degree identification method for an axially functionally graded beam based on a residual force vector (RFV) and a sensitivity method. The main steps are as follows: ①Through the finite element method Establish the finite element model of the damaged structure of the functionally graded beam, extract the natural frequency, mode and other parameters of the structure; ② calculate and compare the residual strain energy (RFV) value of each node, and the corresponding element of the node whose value is not zero is selected as suspicious unit; ③ based on the damage parameter α of the suspicious unit, calculate the mixed sensitivity matrix S and the response difference ΔH between the model to be corrected and the real model; ④ use the Tikhonov regularization method and the L-curve method to solve the correction equation SΔα = ΔH; ⑤ update the suspicious The damage parameter of the unit α=α+Δα; ⑥If the preset accuracy requirement is not met, return to ③ loop iteration, otherwise output the damage parameter as the recognition result. This method defines the concept of the residual force vector, locates the damage, and reduces the number of identification parameters; and uses a mixed sensitivity matrix including frequency and dynamic response. Compared with the ordinary sensitivity matrix, there is still The recognition accuracy is quite high, and the relatively complex structure of functionally graded beams can also be successfully recognized.

Apparently, the above-mentioned embodiments of the present invention are only examples for clearly illustrating the present invention, rather than limiting the implementation of the present invention. For those of ordinary skill in the art, on the basis of the above description, other changes or changes in different forms can also be made. It is not necessary and impossible to exhaustively enumerate all implementation modes here. All modifications, equivalent replacements and improvements made within the spirit and principles of the present invention shall be included within the protection scope of the claims of the present invention.

Claims (1)

1. A damage identification method for an axially functionally graded beam, comprising the following steps: 1) Use the finite element method to simplify the modeling of the axially functionally graded beam structure, and divide the structure into nel units; 2) Extract the frequency and mode of the damaged structure, and obtain the residual force vector f _i of the damaged structure according to the following formula, and obtain the corresponding RFV value: <mrow><msub><mi>f</mi><mi>i</mi></msub><mo>=</mo><mrow><mo>(</mo><mi>K</mi><mo>-</mo><msubsup><mi>&amp;omega;</mi><mrow><mi>d</mi><mi>i</mi></mrow><mn>2</mn></msubsup><mi>M</mi><mo>)</mo></mrow><msub><mi>V</mi><mrow><mi>d</mi><mi>i</mi></mrow></msub></mrow> Among them, ω _di and V _di are the frequency and mode data obtained from the i-th order measurement of the damaged structure, respectively, and K and M are the stiffness matrix and mass matrix of the intact structure respectively; Compare the value of each node corresponding to f _i , and the unit corresponding to the node whose local RFV value is not equal to zero is defined as a suspicious unit that may be damaged. There are n suspicious units in total, and the initial value of its damage parameter is set to α _i =1, i=1,2,...,n, α={α ₁ ,α ₂ ,...,α _n }; 3) Further accurately identify the damage parameter α corresponding to the suspicious unit obtained in step 2); substitute the damage parameter α into the calculation stiffness matrix K _c , and calculate the calculation frequency ω _c and calculation acceleration R _c of the modified structure; 4) Using the measured frequency ω _d and the measured acceleration R _d of the damaged structure, it can be obtained by Δω=ω _c -ω _d , ΔR=R _c -R _d 5) Establish a model correction equation SΔα=ΔH, where S is a mixed sensitivity matrix composed of eigenvalue sensitivity and acceleration sensitivity; use Tikhonov regularization method and L-curve method to solve this equation to obtain the value of Δα; 6) The damage parameter of the suspicious unit is updated to α=α+Δα; If the damage parameter change amount Δα does not meet the set accuracy requirement, return to step 3) to continue iteration; otherwise, the damage parameter α obtained in step 6) is the final recognition result; Among them, α=1 means no damage, and α=0 means complete damage; by checking the number of the finite element model unit corresponding to the damage parameters, the precise location of the structural damage and the detailed damage degree can be obtained.