CN110163134A - A kind of structural damage area recognizing method based on weighted band-wise least square - Google Patents
A kind of structural damage area recognizing method based on weighted band-wise least square Download PDFInfo
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Abstract
The invention belongs to structural health Examined effect fields, provide a kind of structural damage area recognizing method based on weighted band-wise least square, output and input response of the structure under geological process is divided into several frequency separations within the scope of certain frequency, the TIME HISTORY SIGNAL of different frequency sections is obtained using Chebyshev's bandpass filter, least-squares parameter identification is carried out to each frequency band signals, then respectively using the energy of each frequency band as weight, weight is found out with using common Kriging technique, modal parameter is weighted.Beneficial effects of the present invention: (1) frequency dividing weighting improves accuracy；(2) pass through the variation identification of damage region of the vibration shape, it is more intuitive accurate.
Description
Technical Field
The invention belongs to the technical field of structural health examination, and particularly relates to a structural modal parameter and damage region identification method.
Background
Environmental loads such as strong wind, earthquakes and the like and various human factors such as fire, explosion and the like can cause damage to buildings in different degrees, the performance of the structure can be changed along with the environmental loads, and the change of the mechanical property of the structure can cause the change of dynamic fingerprints such as self frequency, damping and the like. Therefore, timely and accurate identification of the modal parameters of the structure is an important prerequisite for structural health monitoring and damage identification.
In actual engineering, it is a practical method to directly identify a damage by using the modal information before and after the damage. Although the existing damage identification method can realize the positioning of damage on a numerical simulation or a laboratory structure, the existing damage identification method still has a plurality of defects, such as serious misjudgment of high-order modes of a mode-shape curvature method, no clear standard for the number of orders selected by a flexibility curvature method, and the like. In view of the above disadvantages, the present invention provides a new method for identifying structural parameters and identifying damaged areas.
The invention has two purposes, namely, providing an accurate and efficient structure modal parameter identification method; secondly, the structural damage area can be identified through the change of the structural modal parameters before and after damage.
Disclosure of Invention
The invention provides a structure damage area identification method based on sub-band weighted least square, which divides input and output signals of a structure under the action of an earthquake into a plurality of frequency intervals in a certain frequency range, adopts a Chebyshev band-pass filter to obtain time-course signals of different frequency bands, carries out least square parameter identification on the signals, then respectively takes the energy of each frequency band as a weight and adopts a common Kriging method to calculate the weight, and carries out weighted calculation on modal parameters.
The technical scheme of the invention is as follows:
a structural damage region identification method based on sub-band weighted least squares comprises the following steps:
step 1, adopting a Chebyshev band-pass filter to divide input and output signals of the structure into p frequency band intervals according to the frequency for filtering, and obtaining input and output signals under each frequency band.
Step 2, performing structural parameter least square identification on each frequency band signal
Applying the formulas (3) to (7) to each obtained filtered input and output signal time course to calculate the unit mass stiffness of the multi-degree-of-freedom system<ki>jAnd unit mass damping<ci>jJ is 1, …, p, and the subscript j represents the j-th band interval;
the dynamic equation of the single-degree-of-freedom system under the earthquake load is as follows:
namely, it is
Wherein m, c and k are respectively the mass, the damping and the rigidity of the structure; a isg(t) is the seismic acceleration time course, ξ and ωnDamping ratio and natural angular velocity of the structure, respectively;
solving the following equation set, and identifying system parameters by applying a least square method to the multi-degree-of-freedom system, which is equivalent to solving the formula (3):
Hθ＝Z (3)
wherein,
θ＝[<c1>,…,<cq>,<k1>,…,<kq>](5)
the least squares estimation solution for the parameter θ is:
wherein, N is the number of sampling points, and q represents the number of nodes of the multi-degree-of-freedom system; subscript i represents the ith node; unit mass rigidity of system with multiple degrees of freedom identified by formula (7)<ki>And unit mass damping<ci>；
Step 3, weighting and summing the structural modal parameters identified by the frequency bands by adopting the method, wherein the weighting method can adopt an energy weighting method or a weight calculation method based on a common Krigin model;
(1) energy weighting method
Obtaining the variance sum MD of the filtered time interval j of each frequency band interval of the input and output signalsj(representing the energy of the signal), the weight λ of each frequency interval is calculated by the sum of the variances using equation (9) and equation (10)j；
Wherein,stiffness per unit mass for multi-degree-of-freedom system<ki>And unit mass damping<ci>An estimated value of (d);
(2) weight calculation method based on common kriging model
First, an unbiased estimation condition is defined:
wherein E (-) is the expected value, θ0Is the expected value;
then define target J:
in the formula, Var (. cndot.) is a variance, and the weight λ of each frequency interval is obtained by calculating formula (12)j；
Step 4, structural mode identification method
The unit mass stiffness of the multi-degree-of-freedom system is identified by the method<ki>And unit mass damping<ci>Obtaining a unit mass array, a unit mass rigidity array and a unit mass damping array of the system as shown in the formula (13) to carry out modal calculation identification, and directly carrying out modal calculation identification when the damping is smaller<K>Solving the characteristic value to obtain the identification values of the natural frequency and the vibration mode of the structure;
step 5, identifying method of structural damage area
Selecting a plurality of monitoring points in the horizontal direction or the vertical direction of the structure, dividing the structure into a plurality of regions through the monitoring points, performing frequency band least square identification on the monitoring points of the structure by adopting the method to obtain the natural frequency and the vibration mode of the structure, and identifying the damaged region of the structure through the time course curve of the natural frequency and the change of the vibration mode of the structure before and after damage.
The invention has the beneficial effects that:
(1) frequency division weighting to improve accuracy
According to the invention, the Chebyshev filter is adopted to carry out frequency division on the input and output signals of the structure, and after least square identification is carried out on the signals of each frequency band, weighting summation is carried out based on the energy of each frequency band or a common Kriging method, so that compared with the mode parameters of structure identification directly by adopting the least square method, the method has higher accuracy.
(2) The damage area is identified through the change of the vibration mode, and the method is more visual and accurate
In order to use the method for identifying a time-varying system, the invention uses 50 data points in a time period of 0.5s as identification points, carries out mode identification on the structure by using the method, and can accurately identify the damaged area of the structure through the change of the structure normalized mode shape in time.
Drawings
Fig. 1 is a schematic diagram of structural modal parameter identification and lesion region identification.
FIG. 2 is a Koyna gravity dam finite element model.
FIG. 3 is the acceleration time course of Koyna seismic waves in the horizontal direction.
FIG. 4 is the acceleration time course of Koyna seismic waves in the vertical direction.
FIG. 5 is a normalized vibration mode versus elevation relationship for a Koyna gravity dam line elastic model.
FIG. 6 is a first order natural frequency time course identified by the Koyna gravity dam elasto-plastic model monitoring point vertical direction response.
FIG. 7 is a first order natural frequency time course identified by the horizontal directional response of the monitoring points of the Koyna gravity dam elasto-plastic model.
FIG. 8(a) is a graph of the damage distribution of the elastoplastic model of Koyna gravity dam at 0.03 s.
FIG. 8(b) is a graph of the damage distribution of the elastoplastic model of Koyna gravity dam at 3.30 s.
FIG. 8(c) is a graph of the damage distribution of the Koyna gravity dam elastoplastic model at 5.70 s.
FIG. 8(d) is a graph of the damage distribution of the elastoplastic model of Koyna gravity dam at 9.20 s.
FIG. 9 is a comparison graph of normalized vibration modes before and after damage in the elastoplastic model of the Koyna gravity dam.
Detailed Description
The technical scheme of the invention is further explained in detail by combining the drawings and the specific embodiments:
a structural damage region identification method based on sub-band weighted least squares has a specific flow diagram as shown in (1).
1 identification method
1.1 Modal parameter identification method
Selecting a plurality of monitoring points in the vertical direction of the structure, dividing the structure into a plurality of areas through the elevations of the monitoring points, equally dividing input and output signals of the structure into five frequency sections in the frequency range of 1-100 Hz by adopting a Chebyshev band-pass filter, and carrying out weighted least square parameter identification by taking the energy of each frequency section as a weight; and solving the weight value based on a common Kriging method to carry out least square identification, and finally carrying out weighted summation.
1.2 damaged area identification method
And identifying the damage area of the dam body according to the normalized vibration mode conversion condition identified by the response signals of the monitoring points at the initial time and 9.5 seconds.
2 koyna example of gravity dam
2.1 koyan dam structure modal parameter identification
The Koyna dam is 103.0m high, the top width is 14.8m, the bottom width is 70m, and the dam body downstream slope is bent at 66.5m high. The concrete constitutive model adopts a concrete linear elastic model, and the material parameters are as follows: the concrete has an elastic modulus of 31GPa, a Poisson ratio of 0.2 and a density of 2643kg/m3The finite element model is shown in FIG. 2.
The calculated loads include gravity and seismic loads. The horizontal and vertical accelerations of the seismic load are shown in fig. 3 and 4. Five monitoring points are taken on the upstream surface of the dam body, and the elevations of the monitoring points are respectively as follows: 9.267m, 31.06m, 45.6m, 76.5m and 103m, calculating the horizontal and vertical displacement, speed and acceleration response under the action of Koyna seismic motion, and introducing the response signals into a mode identification method to obtain identified mode parameters.
Comparing the fifth-order natural frequency of the dam structure identified by using the horizontal response as the output signal with the tenth-order natural frequency of the dam identified by using the finite element mode, finding that the fifth-order natural frequency identified by adopting the sub-band weighted least square method has a corresponding relation with the first-order, second-order, third-order, fifth-order and eighth-order frequencies of the finite element mode analysis, and the comparison result is shown in table 1. It can be seen that the structural natural frequency can be identified more accurately by sub-band least square method identification based on the weighting of the common kriging model.
TABLE 1 structural natural frequency identification comparison
The vibration mode parameters of the Koyna gravity dam can be accurately identified by adopting two methods, based on the horizontal response signals of the observation points, the first-order vibration modes of the structure are identified by respectively adopting a least square method and a frequency division least square method based on common Kriging weighting, normalization is carried out, and the theoretical value of the first-order vibration modes and the finite element calculation result is shown in figure 5.
2.2 Koyna gravity dam damage area identification method under earthquake response
The Koyna gravity dam concrete constitutive model adopts a concrete elastic-plastic damage model, and the material parameters are as follows: the concrete has an elastic modulus of 31GPa, a Poisson ratio of 0.2 and a density of 2643kg/m3The expansion angle is 36.31 degrees, the initial compressive yield stress is 13MPa, the compressive strength is 24.1MPa, the initial tensile strength is 2.9MPa, the damping ratio is 0.05, and a finite element model is shown in figure 2.
The calculated loads include gravity and seismic loads, and the horizontal and vertical accelerations of the seismic loads are shown in fig. 2. And taking monitoring points which are the same as the 2.1 midline elastic model on the upstream surface of the dam body, dividing the dam body into five regions in the vertical direction, calculating the horizontal and vertical displacement, speed and acceleration response of each observation point under the action of Koyna earthquake, and identifying corresponding structural modal parameters by a least square method and a frequency division least square method based on common Kriging weighting.
Taking 50 time-course data points of five monitoring points on the upstream face of the dam within 0.5 second of a time period as identification data, namely, the corresponding relation between the first-order natural frequency time course of 9.5 seconds before the dam identified by the two methods and the damage distribution map calculated by a finite element, wherein the first-order natural frequency time course map identified by vertical response of an observation point is shown in figure 6, the first-order natural frequency time course map identified by horizontal response of the observation point is shown in figure 7, and the damage distribution map of the Koyna gravity dam elastic-plastic model under the action of an earthquake is shown in figure 8.
The damage development condition of the dam body can be accurately described through the natural frequency time course. As can be seen from fig. 6 to 8, the vertical recognition result shows a minimum value in 0.3 second, and the horizontal recognition result shows a larger descending trend in 0.03 second, and the finite element calculation result shows that the structure starts to have a damaged area at the backward slope of the dam body in 0.03 second, which is consistent with the recognition structure of the horizontal response signal; in 3.3 seconds, the natural frequencies in the (a) and (b) graphs are both reduced to a large extent, and compared with finite element results, the finite element results show that after 3.3 seconds, the crack of the dam body at the backward bending slope is rapidly expanded along the horizontal direction, and a large damage area is formed at the upstream position of the dam body within 4.25 seconds; at 5.7 seconds, the natural frequency identified by the response signals in the vertical direction and the horizontal direction does not decrease any more, and the dam body structure almost forms a penetrated main crack region at 5.7 seconds by comparing the finite element damage distribution diagram; the natural frequency time course curve generates larger amplitude oscillation after 7 seconds and 7.2 seconds respectively, and compared with a finite element structure, a through crack is formed in the dam body structure at the moment, and the structure above the crack is in a free vibration state, so that the natural frequency identification value has larger fluctuation. From the above analysis it follows that: response signals in the horizontal direction and the vertical direction of the dam body can be used for better describing the structural damage development condition, wherein a structural natural frequency time-course curve identified by the response signals in the horizontal direction is smoother than that in the vertical direction, the curve descending amplitude of the structural natural frequency time-course curve at the dam body damage expansion moment is larger, and the initial damage occurrence moment can be identified more accurately.
The structural first-order normalized vibration mode identified by the least square method and the sub-frequency least square based on the common Kriging weighting is obtained by taking the horizontal structural response of the monitoring point as an output signal, and the damage area of the dam body can be effectively and accurately identified according to the transformation condition of the normalized vibration mode (figure 9) identified by the response signal of the monitoring point at the initial moment and 9.5 seconds. As can be seen from fig. 6, after 9.5 seconds, the identified first-order vibration pattern of the structure has obvious inflection points at the positions with the elevation of 45.6m and 76.5m, because after 9.5 seconds, a through crack appears at the rear slope of the dam body, and response signals of the upper and lower monitoring points are obviously changed, so that the identified first-order vibration pattern of the structure is changed, and thus, the damaged area of the structure can be identified.
Claims (1)
1. A structural damage region identification method based on sub-band weighted least square is characterized in that structural damage region identification is carried out by directly utilizing modal information before and after damage, and the steps are as follows:
step 1, dividing an input/output signal of a structure into p frequency band sections according to the frequency by adopting a Chebyshev band-pass filter for filtering to obtain input/output signals under each frequency band;
step 2, performing structural parameter least square identification on each frequency band signal
Filtering the obtained signalApplying the formulas (3) to (7) to each input/output signal time course, and calculating the unit mass stiffness of the multi-degree-of-freedom system<ki>jAnd unit mass damping<ci>jJ is 1, …, p, and the subscript j represents the j-th band interval;
the dynamic equation of the single-degree-of-freedom system under the earthquake load is as follows:
namely, it is
Wherein m, c and k are respectively the mass, the damping and the rigidity of the structure; a isg(t) is the seismic acceleration time course, ξ and ωnDamping ratio and natural angular velocity of the structure, respectively;
solving the following equation set, and identifying system parameters by applying a least square method to the multi-degree-of-freedom system, which is equivalent to solving the formula (3):
Hθ＝Z (3)
wherein,
θ＝[<c1>,…,<cq>,<k1>,…,<kq>](5)
the least squares estimation solution for the parameter θ is:
wherein, N is the number of sampling points, and q represents the number of nodes of the multi-degree-of-freedom system; subscript i represents the ith node; identification of multiple origins by the formula (7)Stiffness per unit mass of a system of degrees of freedom<ki>And unit mass damping<ci>；
Step 3, weighting and summing the structural modal parameters identified by the frequency band signals by adopting the method, wherein the weighting method can adopt an energy weighting method or a weight calculation method based on a common Krigin model;
(1) energy weighting method
Obtaining the variance sum MD of the filtered time interval j of each frequency band interval of the input and output signalsj(representing the energy of the signal), the weight λ of each frequency interval is calculated by the sum of the variances using equation (9) and equation (10)j；
Wherein,stiffness per unit mass for multi-degree-of-freedom system<ki>And unit mass damping<ci>An estimated value of (d);
(2) weight calculation method based on common kriging model
First, an unbiased estimation condition is defined:
wherein E (-) is the expected value, θ0Is the expected value;
then define target J:
in the formula, Var (. cndot.) is a variance, and the weight λ of each frequency interval is obtained by calculating formula (12)j；
Step 4, structural mode identification method
The unit mass stiffness of the multi-degree-of-freedom system is identified by the method<ki>And unit mass damping<ci>Obtaining a unit mass array, a unit mass rigidity array and a unit mass damping array of the system as shown in the formula (13) to carry out modal calculation identification, and directly carrying out modal calculation identification when the damping is smaller<K>Solving the characteristic value to obtain the identification values of the natural frequency and the vibration mode of the structure;
step 5, identifying method of structural damage area
Selecting a plurality of monitoring points in the horizontal direction or the vertical direction of the structure, dividing the structure into a plurality of regions through the monitoring points, performing sub-band weighted least square identification on the monitoring points of the structure by adopting the method to obtain the natural frequency and the vibration mode of the structure, and identifying the damaged region of the structure through the time course curve of the natural frequency and the change of the vibration mode of the structure before and after damage.
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