CN107796643B - Model-free rapid damage identification method based on statistical moment theory - Google Patents
Model-free rapid damage identification method based on statistical moment theory Download PDFInfo
- Publication number
- CN107796643B CN107796643B CN201710970735.0A CN201710970735A CN107796643B CN 107796643 B CN107796643 B CN 107796643B CN 201710970735 A CN201710970735 A CN 201710970735A CN 107796643 B CN107796643 B CN 107796643B
- Authority
- CN
- China
- Prior art keywords
- statistical
- moment
- damage
- acceleration
- layer
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
Images
Classifications
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
- G01M99/00—Subject matter not provided for in other groups of this subclass
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
Landscapes
- Physics & Mathematics (AREA)
- Engineering & Computer Science (AREA)
- General Physics & Mathematics (AREA)
- Theoretical Computer Science (AREA)
- Computer Hardware Design (AREA)
- Evolutionary Computation (AREA)
- Geometry (AREA)
- General Engineering & Computer Science (AREA)
- Testing Of Devices, Machine Parts, Or Other Structures Thereof (AREA)
Abstract
The invention belongs to the technical field of civil engineering structure damage identification, and particularly relates to a model-free rapid damage identification method based on a statistical moment theory, which comprises the following steps: acquiring theoretical acceleration order statistical moments of each order; secondly, selecting a proper statistical moment damage identification index through analyzing the sensitivity of different statistical moments to rigidity change; and step three, judging the damage of the structure by using the change of the acceleration eighth moment. Compared with the prior art, the method has the advantages of simple calculation in the time domain and higher identification precision.
Description
Technical Field
The invention belongs to the technical field of civil engineering structure damage identification, and particularly relates to a model-free rapid damage identification method based on a statistical moment theory.
Background
The civil engineering structure can be damaged due to various natural and artificial effects, when the damage is accumulated to a certain degree, the reduction and even destruction of the structural performance can be caused, the life and property of the country and people are seriously threatened, and the economic loss of the civil engineering structure cannot be measured. Therefore, the method has extremely important significance in judging and positioning the damage of the existing structure.
General civil engineering structures have the characteristics of large size, complex and changeable environment and operation conditions and the like, and the difficulties that artificial excitation is difficult to realize, natural excitation sources are difficult to measure and the like exist, so that the traditional damage detection method based on experimental mode technology is difficult to apply, and the damage detection method directly utilizing structural response is considered as a promising method by a plurality of researchers.
The existing damage identification method for the structure can be divided into model-free damage identification and model damage identification, wherein the model damage identification mainly comprises a characteristic structure assignment method, a strain energy method and the like, the methods can be used for positioning the damage and solving the damage degree, but the actual engineering structure is complex, and the damage identification result is also influenced by uncertain factors such as a finite element model and the like by utilizing simplified model analysis; the model damage-free identification method mainly comprises a frequency change method, a vibration mode change method, a flexibility matrix change method and the like, the methods do not need finite element modeling on the structure, and the damage identification result is not influenced by the precision of the finite element model.
Zhang et al propose a structural damage recognition method based on finite element model analysis using statistics, and when damage recognition is performed using statistical moments on the basis of a model correction method, it is necessary to continuously optimize the back-calculated structural stiffness.
Disclosure of Invention
The invention aims to: the model-free rapid damage identification method based on the statistical moment theory is simple in calculation in a time domain and has high identification precision.
In order to achieve the technical purpose, the technical scheme adopted by the invention is as follows:
a model-free rapid damage identification method based on a statistical moment theory comprises the following steps:
step one, obtaining the statistical moment of each theoretical acceleration order
The specific acquisition process is as follows:
the equation of motion for an ① multiple degree of freedom building structure may be expressed as:
wherein: m, C, K are respectively a mass matrix, a damping matrix and a stiffness matrix of the structure;
x (t) is acceleration, velocity and displacement time course response of the structure under ground excitation, and f (t) [ f ]1(t),f2(t),…,fN(t)]TFourier transform thereof into Ck(ω)；
② Rayleigh damping, the structural response mode expansion is:
X＝Φ·Z (1.2)
wherein: phi is a vibration mode matrix after structural mass normalization; z is a generalized coordinate vector of the vibration mode amplitude;
③ substituting equation (1.2) into equation of motion (1.1), and using orthogonality between mode shapes, the equation of motion for the first order mode shape reaction can be obtained by decoupling as follows:
wherein: xi1、ω1Damping ratio of 1 st order and natural vibration circle frequency;
φji(K) is the j unit mode at the ith order;
④ Fourier transform formula (1.3) and using mode superposition method, the Fourier transform expression of acceleration time-course response of i-th layer of the structure is:
⑤ use inter-layer relative acceleration statistical moments as damage indicators:
⑥ the formula of the acceleration second moment obtained by the formula of the statistical moment is:
wherein:
is composed of
The conjugate complex number of (a);
⑦ in the time domain, the structure is excited in any form, the response of the j measuring point is used
Is represented by the formula, wherein NsRepresenting the number of sampling points by statistical moments
Represents;
⑧ for a linear structure, if excited by a smooth gaussian random distribution process, the response of the structure follows the gaussian random process distribution, which can be obtained from the statistical moment relationship:
M4i＝3(M2i)2(1.9)
M6i＝15(M2i)2(1.10)
M8i＝105(M2i)2(1.11)
secondly, through the analysis of the sensitivity of different statistical moments to the change of the rigidity, selecting a proper statistical moment damage identification index and analyzing the change relation between the statistical moment with single degree of freedom and the rigidity as follows:
the high-order statistical moment is more sensitive to the response of the structure than the low-order statistical moment, when the structure is damaged, the rigidity is reduced, the acceleration statistical moment is reduced, the noise influence is considered, and after comprehensive comparison analysis, the acceleration eighth-order moment is selected as an index for damage identification;
step three, judging damage of the structure by using change of the acceleration eighth moment
When the structure is damaged, the rigidity can be changed, and the change of the structural dynamic time-course response can be caused, so that the damage of the structure can be directly judged by counting the change of the moment, and the calculation formula is as follows:
ΔM＝Md-Mu(1.16)
wherein M isdAs statistical moment under lossless conditions, MuThe statistical moment under the damage condition is obtained.
Compared with the prior art, the method has the advantages of simple calculation in the time domain and higher identification precision.
Drawings
The invention is further illustrated by the non-limiting examples given in the accompanying drawings;
FIG. 1 is a schematic diagram of a four-layer steel frame structure model in an embodiment of a model-free rapid damage identification method based on a statistical moment theory;
FIG. 2 is a comparison graph (each order moment) of the damage identification result of the embodiment of the model-free rapid damage identification method based on the statistical moment theory under the working condition 1a without noise;
FIG. 3 is a comparison graph (moments) of the damage recognition results of an embodiment of the model-free rapid damage recognition method based on the statistical moment theory under the condition of no noise in the working condition 2 a;
FIG. 4 is a comparison graph (each order moment) of the damage identification result when the signal-to-noise ratio of the working condition 1a is 30 according to the embodiment of the model-free rapid damage identification method based on the statistical moment theory;
FIG. 5 is a comparison graph (each order moment) of the damage identification result when the signal-to-noise ratio of the working condition 2a is 30 according to the embodiment of the model-free rapid damage identification method based on the statistical moment theory;
FIG. 6 is a schematic diagram of a physical structure model of a four-layer steel framework in an embodiment of a model-free rapid damage identification method based on a statistical moment theory;
FIG. 7 is a comparison graph (eighth moment) of the damage recognition results of the embodiment of the model-free rapid damage recognition method based on the statistical moment theory under the working condition 1 b;
FIG. 8a is a comparison graph (eighth moment) of the damage recognition result of the embodiment of the model-free rapid damage recognition method based on the statistical moment theory under the working condition 2 b;
FIG. 8b is a graph (eighth moment) comparing the damage recognition results of the embodiment of the model-free rapid damage recognition method based on the statistical moment theory under the working condition 3a according to the present invention;
FIG. 9 is a diagram of a twelve-layer framework structure model in an embodiment of a model-free rapid damage identification method based on a statistical moment theory according to the present invention;
FIG. 10 is a comparison graph (eighth moment) of the damage recognition numerical simulation results of the embodiment of the model-free rapid damage recognition method based on the statistical moment theory under the noiseless working conditions 1c, 2c and 3 b;
FIG. 11 is a comparison graph (eighth moment) of the damage identification numerical simulation results when the SNR is 40 under the working condition 1c, the working condition 2c and the working condition 3b according to the embodiment of the model-free rapid damage identification method based on the statistical moment theory;
FIG. 12 is a comparison graph (eighth moment) of the damage identification numerical simulation results when the SNR is 30 under the working condition 1c, the working condition 2c and the working condition 3b in an embodiment of the model-free rapid damage identification method based on the statistical moment theory of the present invention;
FIG. 13 is a schematic diagram of a vibration table test model according to an embodiment of the model-free rapid damage identification method based on the statistical moment theory;
FIG. 14 is a graph of the eighth moment damage recognition result under the working condition 16 according to an embodiment of the model-free rapid damage recognition method based on the statistical moment theory;
FIG. 15 is a graph of the eighth moment damage recognition result under the working condition 25 of an embodiment of the model-free rapid damage recognition method based on the statistical moment theory of the present invention;
fig. 16 is a graph of the eighth moment damage identification result under the working condition 34 of the model-free fast damage identification method based on the statistical moment theory according to the embodiment of the present invention.
Detailed Description
In order that those skilled in the art can better understand the present invention, the following technical solutions are further described with reference to the accompanying drawings and examples.
The invention relates to a model-free rapid damage identification method based on a statistical moment theory, which comprises the following steps of:
step one, obtaining the statistical moment of each theoretical acceleration order
The specific acquisition process is as follows:
the equation of motion for an ① multiple degree of freedom building structure may be expressed as:
wherein: m, C, K are respectively a mass matrix, a damping matrix and a stiffness matrix of the structure;x (t) is acceleration, velocity and displacement time course response of the structure under ground excitation, and f (t) [ f ]1(t),f2(t),…,fN(t)]TFourier transform thereof into Ck(ω)；
② Rayleigh damping, the structural response mode expansion is:
X＝Φ·Z (1.2)
wherein: phi is a vibration mode matrix after structural mass normalization; z is a generalized coordinate vector of the vibration mode amplitude;
③ substituting equation (1.2) into equation of motion (1.1), and using orthogonality between mode shapes, the equation of motion for the first order mode shape reaction can be obtained by decoupling as follows:
wherein: xi1、ω1Damping ratio of 1 st order and natural vibration circle frequency;
φji(K) is the j unit mode at the ith order;
④ Fourier transform formula (1.3) and using mode superposition method, the Fourier transform expression of acceleration time-course response of i-th layer of the structure is:
⑤ use inter-layer relative acceleration statistical moments as damage indicators:
⑥ the formula of the acceleration second moment obtained by the formula of the statistical moment is:
wherein:
is composed of
The conjugate complex number of (a);
⑦ in the time domain, the structure is excited in any form, the response of the j measuring point is used
Is represented by the formula, wherein NsRepresenting the number of sampling points by statistical moments
Represents;
⑧ for a linear structure, if excited by a smooth gaussian random distribution process, the response of the structure follows the gaussian random process distribution, which can be obtained from the statistical moment relationship:
M4i＝3(M2i)2(1.9)
M6i＝15(M2i)2(1.10)
M8i＝105(M2i)2(1.11)
secondly, through the analysis of the sensitivity of different statistical moments to the change of the rigidity, selecting a proper statistical moment damage identification index and analyzing the change relation between the statistical moment with single degree of freedom and the rigidity as follows:
the high-order statistical moment is more sensitive to the response of the structure than the low-order statistical moment, when the structure is damaged, the rigidity is reduced, the acceleration statistical moment is reduced, the noise influence is considered, and after comprehensive comparison analysis, the acceleration eighth-order moment is selected as an index for damage identification;
step three, judging damage of the structure by using change of the acceleration eighth moment
When the structure is damaged, the rigidity can be changed, and the change of the structural dynamic time-course response can be caused, so that the damage of the structure can be directly judged by counting the change of the moment, and the calculation formula is as follows:
ΔM＝Md-Mu(1.16)
wherein M isdAs statistical moment under lossless conditions, MuThe statistical moment under the damage condition is obtained.
Compared with the prior art, the method has the advantages of simple calculation in the time domain and higher identification precision.
The method comprises the following specific operations: the method comprises the following steps of vertically placing an acceleration sensor on each floor, preferably placing the acceleration sensor on the mass center of each floor, periodically collecting acceleration signals and time-course signals under the pulse of each floor, and extracting relative acceleration signals among the floors; analyzing the acceleration signal to obtain a first-order frequency of the structure, extracting relative acceleration signals of each floor corresponding to the first-order frequency, and filtering by adopting a frequency band in a certain range; comparing the acceleration signal statistical distances of the same floor collected at different periods under the corresponding first-order frequency, and judging damage through the acceleration signal statistical distance change rule; when the change rule of the statistical moments is not obvious, the sum of the mean value and the variance of the statistical moments of each layer is used as a reference, and when the variation of the statistical moments of the measured layer is larger than the reference value, the structural damage of the measured layer can be determined; and continuously and circularly calculating until all the statistical moments of all the layers are smaller than the reference value.
It should be noted that although the above part of theories are obtained by linear structure and stable gaussian distribution, the following actual measurement structure and analysis data are not limited to theoretical assumption, because the method does not need a specific model of an original structure, and for a long-term engineering structure without original data, a structural response can be directly obtained by a test method which is similar to pulsation periodically twice to identify model-free damage; for structures subjected to natural disasters such as typhoons, earthquakes and the like, the statistical distance comparison between the structural impulse response tested on the structure after disasters and the structural impulse response tested before disasters can be utilized, so that the damage position can be quickly identified, and the post-disaster quick evaluation can be carried out.
The damage identification method of the present invention is further described in detail below with reference to the accompanying drawings by taking a structural model of a four-layer steel frame as an example.
First, identification of each order statistical moment damage of numerical analysis model
The invention adopts a model with 12 degrees of freedom and symmetrically distributed floor quality, and supposing that the floor is completely rigid, each floor and the beam move together in a rigid manner, only the translation in the x and y directions and the rotation around the central column exist, namely, each floor has only 3 degrees of freedom. The column and the beam adopt a linear elastic Euler-Bemoulli beam model, and the inclined strut is an axial tension-compression component, and the model is shown in figure 1. The sampling duration of the numerical simulation model is 40s, the sampling step length is 0.001s, and the excitation is the environment excitation with the amplitude of 50kN along the Y-axis (weak axis) direction, which is loaded on the middle column at the north side of each floor. The acceleration sensor is arranged in the Y direction of each layer of the middle column according to the conventional dynamic test principle, namely the centroid position of each layer, and the simulation working conditions are as follows:
working condition 1 a: the headboard north-west sprag provides only 2/3 stiffness;
working condition 2 a: the first and fourth layers of west north diagonal braces provide only 2/3 stiffness.
The recognition results are shown in fig. 2 and 3, in which the abscissa represents the different orders of the simulation, and the ordinate represents the ratio of the statistical moment in each damage mode to the statistical moment in the lossless mode. As shown in fig. 2, under the working condition 1a, the variation of the fourth layer statistical moment of the second order moment and the fourth order moment is the largest, that is, the fourth layer damage is identified as an error; the variation of the first layer of statistical moment of the sixth-order moment is the largest, but the variation of the fourth layer of statistical moment is also larger and very close to the reference value, and the identification result is not obvious; the variation of the first layer of statistical moment of the eighth-order moment is obviously larger than the variation of the statistical moments of the other three layers, and the variation of the fourth layer of statistical moment is smaller than a reference value, so that the damage of the first layer can be identified. Under the working condition 2a, the fourth layer statistical moment variation of the second-order moment and the fourth-order moment is obvious relative to the statistical moments of other three layers, and the statistical moment variations of other layers are all smaller than a reference value, so that the first layer damage cannot be identified; and identifying the damage of the first layer and the fourth layer when the variation of the first layer and the fourth layer of the sixth-order moment and the eighth-order moment is more obvious than that of the other two layers of the statistical moments, and the variation of the statistical moments of the other layers is less than a reference value.
Noise levels with certain intensities are considered for the working condition input signals, and the recognition results of the statistical moment variation are shown in fig. 4 and 5. When the signal to noise ratio is 30DB, the identification effect of the statistical moment variation under the working condition 1a and the working condition 2a is basically consistent with that of the statistical moment variation under the noise-free condition. Compared with fig. 3, the eighth moment variation in fig. 5 can identify the damage variation of the first layer more than the sixth moment.
Second, eighth moment damage identification of physical model
The structure is a 4-layer 2 multiplied by 2 span steel structure frame reduced scale model, the plane size is 2.5m multiplied by 2.5m, and the height is 3.6 m. The frame component is made of hot-rolled 300W-grade steel, and the section of the frame component is designed in a reduced scale mode. The section of the frame column is 8100X39, and the section of the beam is S75X 11. Each span of each layer has a floor slab, the mass of the first layer (non-ground) slab is 4800kg, the mass of the second layer and the third layer is 4600kg, and the mass of the fourth layer slab is divided into two cases of 4400kg of symmetrical distribution and 3400kg +550kg of asymmetrical distribution. In addition, the lower floor slab can be used as a working platform of the upper floor slab, and the additional mass is 35 kg.
As shown in fig. 6, the experiment adopts the pulsating force generated by the electromagnetic exciter used on the top layer, the excitation of each working condition in the sampling time is basically equal, the sampling frequency is 200Hz, and the simulation working conditions are as follows:
under the working condition 1b, all the inclined struts on the south of the east side are removed;
under the working condition 2b, removing one or four layers of east side and one span inclined struts;
and under the working condition 3a, a layer of east-side south-leaning brace is removed.
Three sensors are arranged on each layer of the experiment, and are respectively arranged on the east side, the middle part and the west side of each layer. The eighth moment recognition results are shown in fig. 7, 8a, and 8b, where the abscissa represents the number of layers of the frame and the ordinate represents the ratio of the statistical moment in each damage mode to the statistical moment in the lossless mode. As can be seen from fig. 7, the east statistical moment variation of each layer of the frame structure is much larger than the west statistical moment variation of the middle layer, and according to the comparative analysis of the east statistical moment variation and the reference value, the damage of the east statistical moment variation of the four layers of the frame structure can be identified. As can be seen from fig. 8a, the variation of the statistical moments at the east side and the west side of the first and fourth layers of the frame structure is much larger than that at the middle and the west side, and it is recognized that the east side and the four layers of the frame structure are damaged. As can be seen from fig. 8b, the east statistical moment variation of the first layer of the frame structure is significantly greater than the middle statistical moment variation and the west statistical moment variation, and it is recognized that the east of the first layer of the frame structure is damaged. The damage mode under each working condition is matched with the recognition result of the acceleration statistical moment.
Third, eight-order moment damage identification of numerical simulation structure
As shown in FIG. 9, the modulus of elasticity of the frame beam and the frame column are 3X 1010N·m2The height of each layer is 3m, the span of the frame beam is 6m, and the damping ratio is xii0.05(i ═ 1,2,3.. N), beam line density of
The linear density of the left and right columns of the frame isThe simulation conditions are as follows:
working condition 1 c: the damage of the first layer of beam units is 20%;
working condition 2 c: the second layer beam unit is damaged by 20%;
working condition 3 b: the damage of the first layer beam unit is 20 percent, and the damage of the second layer beam unit is 15 percent.
The model performs numerical simulation under the three conditions under the condition of Gaussian white noise without considering noise, and the identification result is shown in FIG. 10. The abscissa represents the different simulated conditions, and the ordinate represents the ratio of the statistical moment in each damage mode to the statistical moment in the lossless mode. In this embodiment, only the variation of the first four layers of displacement and the statistical moment of acceleration are analyzed, and the variation of the statistical moment is gradually reduced and is very small in each layer along with the increase of the number of layers in the rest layers. As can be seen from fig. 10, under each working condition, the amount of change of the statistical moment of each damaged layer immediately adjacent to the upper layer is also large, because the beam stiffness of the damaged layer of the frame model is reduced, and the beam stiffness of the damaged layer has a large influence on the stiffness of the damaged layer and the stiffness of the upper layer. Under the condition of the working condition 1c, the variation of the statistical moment of the first layer is maximum, the variation of the statistical moment of the second layer is close to a reference value, and the variations of the statistical moments of the other layers are smaller than the reference value; under the condition of the working condition 2c, the variation of the statistical moment of the second layer is maximum, the variation of the statistical moment of the third layer is larger than a reference value, and the variations of the statistical moments of the other layers are smaller than the reference value. Because the working condition 1c and the working condition 2c are both single-point damage, the influence of the rigidity change of the damaged layer beam on the rigidity of the upper layer is considered to be large, and each damaged layer can be identified according to the acceleration statistical moment variation of each layer. Under the condition of the working condition 3b, the variation of the statistical moment of the first layer and the second layer is large, the variation of the statistical moment of the third layer is close to a reference value, and the variation of the statistical moment of the fourth layer is smaller than the reference value. According to the statistical moment variation of each layer, the first and second layers of damage can be identified, and the statistical moment variation of the second layer beam is approximately 75% of that of the first layer and is better matched with the damage degree.
Noise levels with different intensities are considered under different working conditions, and the statistical moment variation identification results are shown in fig. 11 and 12. In general, under the conditions that the signal-to-noise ratio is 40 and the signal-to-noise ratio is 30, the variation of the statistical moment of each layer is not more than 5% compared with the variation of the statistical moment of the corresponding layer in the absence of noise, and the variation rule of the acceleration eighth moment is substantially consistent with that in the absence of noise, so that the damaged layer can be identified, which indicates that the method has certain noise immunity.
Fourth, vibration table test eight-order moment damage identification
A 12-layer standard frame vibration table test is carried out in 2003 by a vibration table test room of a national emphasis laboratory of civil engineering disaster prevention of the university of unity, and as shown in fig. 13, a test model is a single-span 12-layer Reinforced Concrete (RC) frame structure and adopts an 1/10 scale model. The model material is particle concrete and galvanized iron wire. And considering the actual structure decoration and 50% live load, a mass block counterweight is arranged on the plate. Each layer on the standard layer is provided with 19.4kg of balance weight, and the roof layer is provided with 19.7kg of balance weight. In the test, white noise excitation with small amplitude is input every time the input magnitude of the acceleration is changed, and the change of the dynamic characteristic of the model system is observed. X-direction sensors (main direction) are arranged at the centers of single frame beams of 2, 4, 6, 8, 10, and 12 layers on the base top surface.
Typical working conditions described by the observation results of the test are as follows: in the first 7 conditions, no cracks were found. And after the 16 th working condition, vertical cracks are formed at the beam ends of 4-6 layers of frame beams parallel to the X vibration direction, and the width of each crack is about 0.08 mm. And after the 18 th working condition, the beam ends of the 3-6 layers of frame beams parallel to the X vibration direction are vertically penetrated through by cracks, and the maximum crack width is about 0.15mm at the 4 th layer. Then, as the input excitation is increased, the beam end crack is increased, and the position of the cracked beam develops to the upper layer and the lower layer.
The experiment is carried out under 62 working conditions in total, the first white noise input is taken in the embodiment, namely the working condition 1 is a lossless working condition, in order to ensure that the input of each working condition is consistent, the working condition 16, the working condition 25 and the working condition 34 under the white noise input after the follow-up earthquake wave are analyzed, and the identification result is shown in fig. 14 to 16. The abscissa represents the number of layers of the frame on which the sensor is located, and the ordinate represents the ratio of the statistical moment in each damage mode to the statistical moment in the lossless mode. The working condition 16 is a working condition when white noise is input for the third time, as can be seen from fig. 14, the fourth layer statistical moment is greatly changed, and the variation of the sixth layer statistical moment is larger than the reference value, i.e., the fourth layer and the periphery, and the sixth layer and the periphery damage are identified, which is consistent with the description of the test phenomenon. The working condition 25 is a working condition of the fourth input of white noise, and cracks appear at a plurality of beam ends. As can be seen in fig. 15, the acceleration statistical moment of the fourth layer varied the most, indicating the greatest damage here, corresponding to the maximum slot width described by the test. The statistical moment variation of the second layer and the sixth layer is larger than the reference value, that is, the positions are damaged. The working condition 34 is a working condition of white noise input for the fifth time, and it can be seen from fig. 16 that the variation of the statistical moment of the fourth layer is the largest, and the variations of the statistical moments of the second layer, the sixth layer and the eighth layer are all larger than the reference value, that is, the positions are damaged, just as the beam end crack described in the experiment is increased, and the cracked crack is continuously developed towards two sides. From this, it can be seen that the recognition result using the acceleration eighth moment variation as the damage index is consistent with the test description.
In conclusion, the embodiment verifies the feasibility of the method in the time domain, and the method can be used for rapidly identifying the damage position of the structure subjected to natural disasters such as typhoons, earthquakes and the like, and performing rapid evaluation after disasters.
The method has certain applicability to damage identification of the RC three-dimensional frame structure and has certain guiding significance to the application of actual engineering.
The foregoing embodiments are merely illustrative of the principles of the present invention and its efficacy, and are not to be construed as limiting the invention. Any person skilled in the art can modify or change the above-mentioned embodiments without departing from the spirit and scope of the present invention. Accordingly, it is intended that all equivalent modifications or changes which can be made by those skilled in the art without departing from the spirit and technical spirit of the present invention be covered by the claims of the present invention.
Claims (1)
1. A model-free rapid damage identification method based on a statistical moment theory is characterized by comprising the following steps:
step one, obtaining the statistical moment of each theoretical acceleration order
The specific acquisition process is as follows:
the equation of motion for an ① multiple degree of freedom building structure may be expressed as:
wherein: m, C, K are respectively a mass matrix, a damping matrix and a stiffness matrix of the structure;
x (t) is acceleration, velocity and displacement time course response of the structure under ground excitation, and f (t) [ f ]1(t),f2(t),…,fN(t)]TFourier transform thereof into Ck(ω)；
② Rayleigh damping, the structural response mode expansion is:
X＝Φ·Z (1.2)
wherein: phi is a vibration mode matrix after structural mass normalization; z is a generalized coordinate vector of the vibration mode amplitude;
③ substituting equation (1.2) into equation of motion (1.1), and using orthogonality between mode shapes, the equation of motion for the first order mode shape reaction can be obtained by decoupling as follows:
wherein: xi1、ω1Damping ratio of 1 st order and natural vibration circle frequency;
φji(K) is the j unit mode at the ith order;
④ Fourier transform formula (1.3) and using mode superposition method, the Fourier transform expression of acceleration time-course response of i-th layer of the structure is:
⑤ use inter-layer relative acceleration statistical moments as damage indicators:
⑥ the formula of the acceleration second moment obtained by the formula of the statistical moment is:
wherein:
the conjugate complex number of (a);
⑦ in the time domain, the structure is excited in any form, the response of the j measuring point is used
Is represented by the formula, wherein NsRepresenting the number of sampling points by statistical moments
Represents;
⑧ for a linear structure, if excited by a smooth gaussian random distribution process, the response of the structure follows the gaussian random process distribution, which can be obtained from the statistical moment relationship:
M4i＝3(M2i)2(1.9)
M6i＝15(M2i)2(1.10)
M8i＝105(M2i)2(1.11)
secondly, through the analysis of the sensitivity of different statistical moments to the change of the rigidity, selecting a proper statistical moment damage identification index and analyzing the change relation between the statistical moment with single degree of freedom and the rigidity as follows:
the high-order statistical moment is more sensitive to the response of the structure than the low-order statistical moment, when the structure is damaged, the rigidity is reduced, the acceleration statistical moment is reduced, the noise influence is considered, and after comprehensive comparison analysis, the acceleration eighth-order moment is selected as an index for damage identification;
step three, judging damage of the structure by using change of the acceleration eighth moment
When the structure is damaged, the rigidity can be changed, and the change of the structural dynamic time-course response can be caused, so that the damage of the structure can be directly judged by counting the change of the moment, and the calculation formula is as follows:
ΔM＝Md-Mu(1.16)
wherein M isdAs statistical moment under lossless conditions, MuThe statistical moment under the damage condition is obtained;
step four, the acceleration sensor is vertically arranged on each floor, preferably on the mass center of the floor, the acceleration signal and the time-course signal under the pulse of each floor are periodically collected, and the relative acceleration signal between each floor is extracted; analyzing the acceleration signal to obtain a first-order frequency of the structure, extracting relative acceleration signals of each floor corresponding to the first-order frequency, and filtering by adopting a frequency band in a certain range; comparing the acceleration signal statistical distances of the same floor collected at different periods under the corresponding first-order frequency, and judging damage through the acceleration signal statistical distance change rule; when the change rule of the statistical moments is not obvious, the sum of the mean value and the variance of the statistical moments of each layer is used as a reference, and when the variation of the statistical moments of the measured layer is larger than the reference value, the structural damage of the measured layer can be determined; and continuously and circularly calculating until all the statistical moments of all the layers are smaller than the reference value.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201710970735.0A CN107796643B (en) | 2017-10-18 | 2017-10-18 | Model-free rapid damage identification method based on statistical moment theory |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201710970735.0A CN107796643B (en) | 2017-10-18 | 2017-10-18 | Model-free rapid damage identification method based on statistical moment theory |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN107796643A CN107796643A (en) | 2018-03-13 |
| CN107796643B true CN107796643B (en) | 2020-01-10 |
Family
ID=61533367
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201710970735.0A Active CN107796643B (en) | 2017-10-18 | 2017-10-18 | Model-free rapid damage identification method based on statistical moment theory |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN107796643B (en) |
Families Citing this family (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109839441B (en) * | 2019-03-20 | 2021-03-30 | 合肥工业大学 | Bridge modal parameter identification method |
| CN110427716B (en) * | 2019-08-09 | 2022-09-27 | 重庆大学 | Statistical moment-based high-rise structure model-free damage identification method |
| CN113533505B (en) * | 2021-06-17 | 2023-10-20 | 北京工业大学 | Vibration damage structure damage quantification method based on Kalman filtering and elastoplastic energy consumption difference |
Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2007086834A3 (en) * | 2006-01-13 | 2009-04-09 | New Jersey Tech Inst | Method for identifying marked images using statistical moments based at least in part on a jpeg array |
| US9183333B2 (en) * | 2013-08-12 | 2015-11-10 | Synopsys, Inc. | Generalized moment based approach for variation aware timing analysis |
Family Cites Families (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN1825082B (en) * | 2006-03-31 | 2010-04-14 | 洛阳轴研科技股份有限公司 | Automatic diagnosing system for rolling bearing fault |
| WO2015145257A2 (en) * | 2014-03-28 | 2015-10-01 | Cgg Services Sa | Method and apparatus for characterizing azimuthal anisotropy using statistical moments |
| CN104517036A (en) * | 2014-12-22 | 2015-04-15 | 华中科技大学 | Simply-supported piece damage identification method based on strain statistical moment |
| CN106383959A (en) * | 2016-09-23 | 2017-02-08 | 南京航空航天大学 | Maximum entropy model-based material fatigue life prediction method |
| CN107246944B (en) * | 2017-04-07 | 2019-01-22 | 重庆大学 | A kind of Structural Damage Identification based on statistical moment theory |
-
2017
- 2017-10-18 CN CN201710970735.0A patent/CN107796643B/en active Active
Patent Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2007086834A3 (en) * | 2006-01-13 | 2009-04-09 | New Jersey Tech Inst | Method for identifying marked images using statistical moments based at least in part on a jpeg array |
| US9183333B2 (en) * | 2013-08-12 | 2015-11-10 | Synopsys, Inc. | Generalized moment based approach for variation aware timing analysis |
Also Published As
| Publication number | Publication date |
|---|---|
| CN107796643A (en) | 2018-03-13 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| Foti et al. | Ambient vibration testing, dynamic identification and model updating of a historic tower | |
| CN104198144B (en) | Middle and small bridge fast detecting method based on long-scale-distance optical fiber strain sensor | |
| Xu et al. | Damage detection for a frame structure model using vibration displacement measurement | |
| CN107796643B (en) | Model-free rapid damage identification method based on statistical moment theory | |
| Esfandiari et al. | Finite element model updating using frequency response function of incomplete strain data | |
| Diaferio et al. | Operational modal analysis of a historic tower in Bari | |
| Chandramohan et al. | Response of instrumented buildings under the 2016 Kaikoura earthquake. | |
| Casciati et al. | Dynamic behavior of a masonry civic belfry under operational conditions | |
| CN104517036A (en) | Simply-supported piece damage identification method based on strain statistical moment | |
| Diaferio et al. | Identification of the modal properties of a building of the Greek heritage | |
| CN112067116B (en) | Method for testing and analyzing impact vibration of medium and small bridges with noise resistance | |
| Wu et al. | Dynamic performance evaluation of Shanghai Tower under winds based on full‐scale data | |
| CN110427716B (en) | Statistical moment-based high-rise structure model-free damage identification method | |
| Li et al. | Seismic random vibration analysis of tall buildings | |
| He et al. | Damage assessment for structure subjected to earthquake using wavelet packet decomposition and time-varying frequency | |
| Kia et al. | Assessment the effective ground motion parameters on seismic performance of R/C buildings using artificial neural network | |
| Lu et al. | Real-time structural damage detection using wireless sensing and monitoring system | |
| CN110008520B (en) | Structural damage identification method based on displacement response covariance parameters and Bayesian fusion | |
| Zhou et al. | Modal identification of high-rise buildings under earthquake excitations via an improved subspace methodology | |
| Nie et al. | Study on dynamic behavior of single-layer reticulated dome by shaking table test | |
| Aguirre1a et al. | Damping and frequency changes induced by increasing levels of inelastic seismic demand | |
| Yeh et al. | Test of a full-scale steel frame with TADAS | |
| Feng et al. | Effects of high modes on the wind-induced response of super high-rise buildings | |
| Ponzo et al. | Localization of damage occurred on framed structures: analysis of the geometric characteristics of the fundamental mode shape | |
| Altunışık et al. | Structural response relationship between scaled and prototype concrete load bearing systems using similarity requirements |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |