CN116186833A - Machine learning method for identifying and diagnosing vertical deformation related modes of cable-supported bridge girder - Google Patents
Machine learning method for identifying and diagnosing vertical deformation related modes of cable-supported bridge girder Download PDFInfo
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Abstract
The invention provides a machine learning method for identifying a mode related to vertical deformation of a girder of a cable-stayed bridge and diagnosing health. According to the method, the health diagnosis of the cable-supported bridge structure is carried out according to two evaluation indexes, namely the vertical deformation ratio of the main beam and the integral ratio of the absolute value of the vertical deformation of the main beam. The main beam vertical deformation ratio and the main beam vertical deformation absolute value integration ratio of the transverse position of the vehicle are only related to the structural parameters of the cable bridge, and the effect generated by the load variation of the vehicle is eliminated, so that the cable bridge can be used for health diagnosis.
Description
Technical Field
The invention relates to the technical fields of structural health monitoring, structural state evaluation, deep learning and machine learning, which can be directly applied to intelligent bridges, intelligent operation and maintenance, intelligent infrastructure and the like, in particular to a method for identifying a mode related to vertical deformation of a girder of a cable-stayed bridge and diagnosing a machine learning.
Background
Cable-stayed bridges, suspension bridges and other cable-bearing system bridges are important components of the construction of infrastructures in China and the economic development of national countries, and the number and the scale of the cable-stayed bridges and the suspension bridges in China all jump to the front of the world at present. The rope bearing system bridge structure is inevitably subjected to the coupling action of complex factors such as environmental erosion, material aging, fatigue load, disasters, emergencies and the like in the service period of hundreds of years, and damage accumulation and resistance degradation are generated. The vertical deformation of the main girder of the cable-stayed bridge is an integral variable reflecting the structural rigidity of the cable-stayed bridge, and is an important control variable in the design, construction and operation of the cable-stayed bridge, for example, the main girder vertical deformation of different types of bridges caused by vehicle loads is definitely regulated in the 'highway cable-stayed bridge design specification'. The development of the structural health monitoring technology is mature day by day, the multi-type monitoring quantity such as cable bridge bearing environment, action, structural response, structural change and the like is monitored, and the cable bridge bearing state evaluation and health diagnosis are realized based on monitoring data analysis and mining. At present, the vertical deformation of the main girder of the cable bearing bridge is mainly compared with a standard limit value to judge the health state of the bridge, however, the standard limit value is set based on engineering experience, highly depends on statistical results, has poor adaptability to the actual vehicle load conditions of different single bridges, and has poor stability and accuracy. Therefore, there is a need for an improved conventional cable bridge status assessment method for girder vertical deformation that is compared to the specification limits.
Under the action of the same vehicle load and structural parameters, mechanical correlation necessarily exists between different types of responses of the cable-stayed bridge structure and between different measuring points of similar responses, if the structure is damaged, the correlation between the responses of the bridge structure under the action of the same vehicle load can be changed, and the health state of the cable-stayed bridge structure can be deduced by utilizing the change of the correlation. However, although the above concepts are theoretically possible, it is very difficult to ensure accurate uniformity of the vehicle load under actual complex conditions. Firstly, at present, the measurement of the vehicle load is generally based on a dynamic weighing system at two sides of a bridge, and the running process of the vehicle on a large-scale cable-supported bridge often changes the track, so that the accurate spatial distribution of the vehicle load on the bridge cannot be obtained. Secondly, although the vehicle load shows a certain rule (such as basically similar statistical rules of daily, weekly and yearly) in a certain period, the similarity is similar in statistical sense, and the time cannot be precisely the same, so that the vehicle loads of different training sets and test sets are not strictly the same. Because of the two reasons, the external factor of the vehicle load cannot be ensured to be accurately obtained and kept consistent, and the thought of carrying out state evaluation and health diagnosis based on the response correlation of the bridge structure can generate larger errors in the practical application process.
In order to solve the problems, the invention provides a cable-stayed bridge girder vertical deformation related mode identification and health diagnosis machine learning method, and the cable-stayed bridge structure health diagnosis method is carried out according to two evaluation indexes of girder vertical deformation ratio and girder vertical deformation absolute value integral ratio. The main beam vertical deformation ratio and the main beam vertical deformation absolute value integration ratio of the transverse position of the vehicle are only related to the structural parameters of the cable bridge, and the effect generated by the load variation of the vehicle is eliminated, so that the cable bridge can be used for health diagnosis.
Disclosure of Invention
The invention aims to solve the problems in the prior art and provides a machine learning method for identifying and diagnosing the vertical deformation related modes of a main girder of a cable-supported bridge.
The invention is realized by the following technical scheme, and provides a machine learning method for identifying and diagnosing the vertical deformation related modes of a cable-supported bridge girder, which specifically comprises the following steps:
step one: analyzing the independence of the vertical deformation ratio of the main beam and the external load and verifying based on actual monitoring data;
step two: analyzing the independence of the absolute value integration ratio of the vertical deformation of the main beam and the external load, and verifying based on actual monitoring data;
step three: and carrying out cluster recognition of the related modes according to the main beam vertical deformation ratio index and the main beam vertical deformation absolute value integral ratio index.
Further, the first step specifically includes the following steps:
the method comprises the following steps: considering the flat structure of the cross section of the large cable bridge-bearing steel box girder and multi-lane arrangement, the deformation of stay ropes or slings at two sides and the elastic deformation of the cross section lead to different vertical deformation of the girder at different positions of the same cross section; regarding a certain cross section of the cable-supported bridge girder, stay ropes or slings at two sides are regarded as spring supports, and the cross section is simplified into a simply supported girder with spring supports A and B at two ends; when a concentrated force is applied at 1/4 span position, two vertical displacements from the two side support a positions C and D are:
wherein k is A For the stiffness of the A-point spring support, k B The rigidity of the point B spring support, EI is the bending rigidity of the main beam, l is the length of the half span beam, a is the distance between two measuring points and the nearest support respectively, and F is the concentration force;
step two: calculating to obtain the vertical deformation ratio lambda of the measuring points at the two sides of the main beam y The method comprises the following steps:
from equation (2), the vertical deformation ratio λ of the position C, D at a distance a from the end mounts A, B y Independent of the magnitude of the concentrated force, and only dependent on the rigidity k of the support A ,k B The vertical deformation ratio of the main beam at the same vehicle load action position is only related to structural parameters and is irrelevant to vehicle load; when the transverse position of the vehicle is determined, the vertical deformation ratio of the main beam does not change with the load of the vehicle; therefore, by analyzing the independence of the girder vertical deformation ratio on the external load, the girder vertical deformation ratio is found to be related to the structural parameters only, and the girder vertical deformation ratio is used as a bridge health diagnosis index.
Further, in the first step, the verification result based on the actual monitoring data is: the vertical deformation ratio of the main beam at the upstream and downstream of the cable bridge is approximately kept constant, and the ratio or the slope of the vertical deformation ratio represents different lane positions, so that the independence of the vertical deformation ratio of the main beam on external load and the relation of the vertical deformation ratio of the main beam on structural parameters are verified based on real bridge monitoring data.
Further, in step one, when a single vehicle is traveling in the upstream lane, the upstream vertical deformation is larger than the downstream vertical deformation, i.e., λ in equation (2) y Less than 1; when a single vehicle is traveling in the downstream lane, the downstream vertical deformation is larger than the upstream vertical deformation, i.e., λ in equation (2) y Greater than 1; if the stiffness of the spring supports at the two ends is the same and the slope is lambda when the vehicle runs at a certain position at the upstream y The slope is 1/lambda when the vehicle runs at the downstream symmetrical position y The method comprises the steps of carrying out a first treatment on the surface of the To maintain symmetry of the extracted features in both the upstream and downstream directions, for λ y Taking logarithm to obtain:
ζ＝lnλ y (3)
in the formula, zeta is a main beam vertical deformation ratio index, and the values of the upstream and downstream symmetrical positions of the same section are opposite;
the main beam vertical deformation ratio index zeta is taken as a first related mode variable of the vertical deformation of the cable-supported bridge main beam, the ratio is related to the transverse action position of the load of the vehicle and the structural parameter, however, considering that the transverse positions of multiple vehicles in a lane obey normal distribution, the main beam vertical deformation ratio index zeta is only related to the structural parameter and is irrelevant to the load in a statistical sense; when the health state of the bridge structure is changed, the vertical deformation ratio index of the main beam is changed, and the bridge health diagnosis can be performed based on the change.
Further, the second step specifically includes the following steps:
step two,: considering a scene that a unit concentrated vertical load moves along a longitudinal bridge, wherein a change rule curve between a certain point of a main girder vertical deformation and a concentrated load position is a vertical deformation influence line of the point; when a single vehicle runs from one end of the bridge to the other end at a constant speed, the vertical deformation time course of a certain measuring point is approximately considered to be positively correlated with the value of the vertical deformation influence line of the measuring point; let the bridge length be L, there are F, G measuring points on the bridge, the vertical deformation influence line of the F point is F (x), the vertical deformation influence of the G pointThe line g (x), S F And S is G Line of influence integral at F, G two points respectively
Step two: consider two vehicles, denoted as Car1 and Car2, respectively, having weights w, respectively 1 And w 2 Distance of separation s (s<L) successively bridge in the same direction at the speed v 1 And v 2 Is driven at a constant speed; under the action of Car1 and Car2, the vertical deformation time interval integration ratio of the measuring point F, G is as follows:
wherein T is F ,T G Is the integral of the vertical deformation time interval of the main beams of the measuring points F and G, S F ,S G The integration of the vertical deformation influence lines of the measuring point F and the measuring point G is that, w 1 ,v 1 Weight and speed, w, of Car1 2 ,v 2 Weight and speed for Car 2;
from equation (4), T is calculated when the vehicle is passing at a constant speed F /T G ＝S F /S G I.e. the ratio of the vertical deformation time interval integrals of the measuring point F, G is equal to the ratio of the vertical deformation influence line integrals of the measuring point F, G; the vertical deformation influence line is a function of bridge rigidity and bridge geometric dimension, so that the ratio of the influence line integrals of the two measuring points is irrelevant to the vehicle load and is only relevant to the bridge state parameter, and the influence line integrals can be used as an evaluation index for bridge health diagnosis;
step two, three: the second step is that when the vehicle runs at a constant speed, the ratio of the time interval integrals of the vertical deformation of the two measuring points caused by the vehicle team is approximately equal to the ratio of the line integrals of the vertical deformation influence of the two measuring points; however, when the vehicle passes through the bridge, the possibility of non-uniform running exists, and the situation is uniformly considered to be within an error range of the line integral ratio influenced by vertical deformation; the integral ratio of the absolute values of the vertical deformation time courses of the two measuring points is used as an index for measuring the health state of the bridge:
wherein D is F Is the integral of the absolute value of the vertical deformation time interval of the measuring point F, D G Is the integral of the absolute value of the vertical deformation time interval of the measuring point G, R A The integral ratio of the absolute values of the vertical deformation of the main beams at the two measuring points;
thus, the integral ratio R of the absolute value of the vertical deformation of the main beam A As a second related mode of vertical deformation of the main girder of the cable-stayed bridge, the ratio is only related to structural parameters and is not related to external load; when the health state of the bridge structure is changed, the integral ratio of the absolute value of the vertical deformation of the main girder is changed, and the index is used for bridge health diagnosis.
Further, the third step specifically includes the following steps:
based on the two-point characteristics of the mode center points, firstly, the density of the mode center points is larger than that of other surrounding points, secondly, the distance between the mode center points and other mode center points is far, the mode quantity and the mode centers are determined for the sample points, classification is carried out, and the local density of each vertical deformation ratio sample point and the distance between each vertical deformation ratio sample point and other sample points are calculated; taking the vertical deformation ratio of the main beam as an example, the clustering algorithm for carrying out pattern recognition under the single-car working condition comprises the following steps:
step three: vertical deformation ratio set D= { ζ to be clustered i I= … N }, vertical deformation ratio ζ i Local density ρ of (2) i The calculation formula is as follows:
wherein d ij ＝|ζ i -ζ j I is the vertical deformation ratio ζ i And zeta is j Distance d of (d) c For the cut-off distance, N is the number of sample points; vertical deformation ratio ζ i Local density ρ of (2) i Represents the sum ζ of D i The distance between the two is smaller than the cutting distance d c Is the number of samples of (a); cut-off distance d c Empirically determined, selectTaking 20% fraction of all N (N-1)/2 distances;
step three, two: vertical deformation ratio ζ i Distance delta of (2) i The calculation formula is as follows:
when zeta is i With maximum local density, its distance delta i Is D is medium and ζ i Sample point with largest distance and zeta i A distance therebetween; when zeta is i Without maximum local density, its distance delta i Is that the local density in D is greater than ρ i And ζ in the sample points of (2) i Sample point with minimum distance and zeta i A distance therebetween;
and step three: all sample point densities ρ calculated from the above i And delta i Drawing ρ i -δ i A relational decision graph, in delta i Large and ρ i The relatively large points are various centers; assuming that the cluster center has n c The corresponding sample points are numbered as
I.e. < ->
Is the j-th cluster center; after various centers are determined, sequentially distributing the rest points from high to low according to the density of the sample points, wherein each point is distributed to the category to which the nearest neighbor point with higher density than the point belongs, and the distribution process can be completed once in one direction;
and step three, four: the sample points follow Gaussian mixture distribution around a straight line, and the slope of the straight line is the vertical deformation ratio of different lanes; the errors of sample points around different straight lines obey Gaussian distribution, and the Gaussian mixture model parameters are solved by using an expectation maximization algorithm.
The invention has the beneficial effects that:
(1) The invention provides two relevant mode indexes of the vertical deformation ratio of the main girder of the large cable bridge bearing and the integral ratio of the absolute value of the vertical deformation of the main girder, which are irrelevant to the load of the vehicle and are relevant to the parameters of the structural state only, so that the decoupling of the load of the vehicle and the structural state is realized;
(2) According to the invention, the change modes of different lanes can be identified through the main beam vertical deformation ratio mode identification clustering algorithm and the expectation maximization algorithm, so that the identification of different lanes with the same cross section is realized;
(3) According to the invention, the effectiveness of the method is verified through real bridge health monitoring data, and the bridge health state is analyzed and diagnosed based on a control chart of the girder vertical deformation ratio and the girder vertical deformation absolute value integration ratio;
(4) The method solves the problems of poor adaptability, poor stability and insufficient accuracy of the existing assessment method and the standard limit value, high dependence on engineering experience and poor adaptability to the actual vehicle load conditions of different single bridges in bridge health state diagnosis.
Drawings
FIG. 1 is a flow chart of a method for machine learning for identifying and diagnosing vertical deformation related modes of a girder of a cable-supported bridge.
Fig. 2 is a schematic diagram for verifying independence of the girder vertical deformation ratio on the external load based on actual monitoring data. Wherein (a) is a time chart of the vertical deformation of the upstream and downstream main beams of the bicycle through a certain section; (b) Is a correlation diagram between vertical deformation of the upstream and downstream main beams of the bicycle; (c) Is a correlation diagram between vertical deformation of the upstream and downstream main beams of multiple vehicles.
FIG. 3 is a schematic diagram showing the independence of the absolute value integration ratio of the vertical deformation of the main beam on the basis of actual monitoring data; wherein (a) is an upstream bicycle at an upstream measuring point; (b) upstream measuring point multi-vehicle.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
The invention provides a method for identifying a relevant mode and diagnosing health based on a cable-stayed bridge girder vertical deformation ratio and a girder vertical deformation absolute value integral ratio, wherein the two relevant modes are irrelevant to vehicle load and are relevant to bridge state parameters only. Therefore, the health state of the bridge structure is diagnosed by identifying the relevant modes of the vertical deformation ratio of the cable-supported bridge girder and the integral ratio of the absolute value of the vertical deformation of the girder.
The invention provides a method for identifying a vertical deformation related mode of a cable-supported bridge girder and learning a health diagnosis machine, and a flow chart of the method is shown in figure 1. The invention provides a machine learning method for identifying a vertical deformation related mode of a cable-supported bridge girder and diagnosing health, which specifically comprises the following steps:
step one: analyzing the independence of the vertical deformation ratio of the main beam and the external load and verifying based on actual monitoring data;
step two: analyzing the independence of the absolute value integration ratio of the vertical deformation of the main beam and the external load, and verifying based on actual monitoring data;
step three: and carrying out cluster recognition of the related modes according to the main beam vertical deformation ratio index and the main beam vertical deformation absolute value integral ratio index.
The first step specifically comprises the following steps:
the method comprises the following steps: considering the flat structure of the cross section of the large cable bridge-bearing steel box girder and multi-lane arrangement, the deformation of stay ropes or slings at two sides and the elastic deformation of the cross section lead to different vertical deformation of the girder at different positions of the same cross section; regarding a certain cross section of the cable-supported bridge girder, stay ropes or slings at two sides are regarded as spring supports, and the cross section is simplified into a simply supported girder with spring supports A and B at two ends; when a concentrated force is applied at 1/4 span position, two vertical displacements from the two side support a positions C and D are:
wherein k is A For the stiffness of the A-point spring support, k B The rigidity of the point B spring support, EI is the bending rigidity of the main beam, l is the length of the half span beam, a is the distance between two measuring points and the nearest support respectively, and F is the concentration force;
step two: calculating to obtain the vertical deformation ratio lambda of the measuring points at the two sides of the main beam y The method comprises the following steps:
from equation (2), the vertical deformation ratio λ of the position C, D at a distance a from the end mounts A, B y Independent of the magnitude of the concentrated force, and only dependent on the rigidity k of the support A ,k B The vertical deformation ratio of the main beam at the same vehicle load action position is only related to structural parameters and is irrelevant to vehicle load; when the transverse position of the vehicle is determined, the vertical deformation ratio of the main beam does not change with the load of the vehicle; therefore, by analyzing the independence of the girder vertical deformation ratio on the external load, the girder vertical deformation ratio is found to be related to the structural parameters only, and the girder vertical deformation ratio is used as a bridge health diagnosis index.
In the first step, analysis is performed by using the monitoring data of the vertical deformation of a girder of an actual cable-stayed bridge, where (a) in fig. 2 shows a vertical deformation time interval of an upstream girder and a downstream girder of a certain section when a single vehicle passes through the bridge, and (b) in fig. 2 shows a relationship between the vertical deformation of the upstream girder and the vertical deformation of the downstream girder. It can be seen that when the vehicle passes through the cable-stayed bridge, the upstream and downstream vertical deformations of the same section are different, the downstream vertical deformation change is larger than that of the upstream, and it is inferred that the vehicle may travel on a downstream side lane, and the upstream and downstream main girder vertical deformations are strongly linearly related. Fig. 2 (c) shows the vertical deformation relationship of the upstream and downstream girders under 30 single vehicle working conditions, and it can be seen from fig. 2 that the vertical deformation of the upstream and downstream girders under a single vehicle working condition is in a positive correlation relationship, and is basically distributed on N straight lines passing through the origin, where N represents the lane position, that is, the different values corresponding to the distances a between the vehicle load and the elastic supports at the two ends in formulas (1) and (2) (n=4 in fig. 2). The verification result based on the actual monitoring data is as follows: the vertical deformation ratio of the main beam at the upstream and downstream of the cable bridge is approximately kept constant, and the ratio or the slope of the vertical deformation ratio represents different lane positions, so that the independence of the vertical deformation ratio of the main beam on external load and the relation of the vertical deformation ratio of the main beam on structural parameters are verified based on real bridge monitoring data.
In step one, when a single vehicle is driving on the upstream lane, the upstream vertical deformation is greater than the downstream vertical deformation, i.e., λ in equation (2) y Less than 1; when a single vehicle is traveling in the downstream lane, the downstream vertical deformation is larger than the upstream vertical deformation, i.e., λ in equation (2) y Greater than 1; if the stiffness of the spring supports at the two ends is the same and the slope is lambda when the vehicle runs at a certain position at the upstream y The slope is 1/lambda when the vehicle runs at the downstream symmetrical position y The method comprises the steps of carrying out a first treatment on the surface of the To maintain symmetry of the extracted features in both the upstream and downstream directions, for λ y Taking logarithm to obtain:
ξ＝lnλ y (3)
in the formula, xi is a main beam vertical deformation ratio index, and the values of the upstream and downstream symmetrical positions of the same section are opposite numbers;
the main beam vertical deformation ratio index xi is taken as a first related mode variable of the vertical deformation of the cable-supported bridge main beam, the ratio is related to the transverse action position of the load of the vehicle and the structural parameter, however, considering that the transverse position of the multi-vehicle in the lane obeys normal distribution, the main beam vertical deformation ratio index xi is only related to the structural parameter and is unrelated to the load in the statistical sense; when the health state of the bridge structure is changed, the vertical deformation ratio index of the main beam is changed, and the bridge health diagnosis can be performed based on the change.
The second step specifically comprises the following steps:
step two,: considering a scene that a unit concentrated vertical load moves along a longitudinal bridge, wherein a change rule curve between a certain point of a main girder vertical deformation and a concentrated load position is a vertical deformation influence line of the point; when a single vehicle runs from one end of the bridge to the other end at a constant speed, the vertical deformation time course of a certain measuring point is approximately considered to be positive to the value of the vertical deformation influence line of the measuring pointCorrelation; let the bridge length be L, there are F, G measuring points on the bridge, the vertical deformation influence line of F point is F (x), the vertical deformation influence line of G point is G (x), record S F And S is G Line of influence integral at F, G two points respectively
Step two: consider two vehicles, denoted as Car1 and Car2, respectively, having weights w, respectively 1 And w 2 Distance of separation s (s<L) successively bridge in the same direction at the speed v 1 And v 2 Is driven at a constant speed; under the action of Car1 and Car2, the vertical deformation time interval integration ratio of the measuring point F, G is as follows:
wherein T is F ,T G Is the integral of the vertical deformation time interval of the main beams of the measuring points F and G, S F ,S G The integration of the vertical deformation influence lines of the measuring point F and the measuring point G is that, w 1 ,v 1 Weight and speed, w, of Car1 2 ,v 2 Weight and speed for Car 2;
from equation (4), T is calculated when the vehicle is passing at a constant speed F /T G ＝S F /S G I.e. the ratio of the vertical deformation time interval integrals of the measuring point F, G is equal to the ratio of the vertical deformation influence line integrals of the measuring point F, G; the vertical deformation influence line is a function of bridge rigidity and bridge geometric dimension, so that the ratio of the influence line integrals of the two measuring points is irrelevant to the vehicle load and is only relevant to the bridge state parameter, and the influence line integrals can be used as an evaluation index for bridge health diagnosis;
step two, three: the second step is that when the vehicle runs at a constant speed, the ratio of the time interval integrals of the vertical deformation of the two measuring points caused by the vehicle team is approximately equal to the ratio of the line integrals of the vertical deformation influence of the two measuring points; however, when the vehicle passes through the bridge, the possibility of non-uniform running exists, and the situation is uniformly considered to be within an error range of the line integral ratio influenced by vertical deformation; for the girder vertical deformation monitoring data obtained by the bridge structure health monitoring system, as the monitoring data has noise to a certain extent, the influence line and the time signal are positive and negative, and the error is larger when the positive and negative counteractions are more, the integral ratio of the absolute values of the vertical deformation time intervals of the two measuring points is used as an index for measuring the health state of the bridge:
wherein D is F Is the integral of the absolute value of the vertical deformation time interval of the measuring point F, D G Is the integral of the absolute value of the vertical deformation time interval of the measuring point G, R A The integral ratio of the absolute values of the vertical deformation of the main beams at the two measuring points;
thus, the integral ratio R of the absolute value of the vertical deformation of the main beam A As a second related mode of vertical deformation of the main girder of the cable-stayed bridge, the ratio is only related to structural parameters and is not related to external load; when the health state of the bridge structure is changed, the integral ratio of the absolute value of the vertical deformation of the main girder is changed, and the index is used for bridge health diagnosis.
And secondly, verifying the independence of the absolute value integration ratio of the vertical deformation of the main beam and the external load based on actual monitoring data, and firstly considering the condition of a bicycle. Considering the transverse width of the bridge, when the vehicles run on different lanes, the vertical deformation influence lines of the same measuring point are different, and single vehicles on different lanes are divided into an upstream class and a downstream class according to two running directions. According to monitor data of the vertical deformation of a girder of a cable-stayed bridge in 2012-2018, the integral of the absolute value of the vertical deformation of partial measuring points at the same side is shown in fig. 3 (a). And then consider a multi-car situation. Integrating the time interval absolute values of each channel of the data from 00:00 to 24:00 every day by integrating the time intervals of a plurality of sensor channels of a plurality of sections. At this time, the multi-period division does not distinguish the traveling direction, so the integration ratio calculation does not distinguish the upstream traveling from the downstream traveling as well. Fig. 3 (b) shows the result of the change in the absolute value integration ratio of the vertical deformation at the same-side measurement point in 2012-2018. Calculating the integral ratio R of the absolute values of the vertical deformation of the two measuring points by taking 2012-2015 as a reference A Mean (solid line) and standard deviation (dashed line 3 times)Standard deviation threshold line). The upstream takes the integral of the absolute value of the vertical deformation time interval of the PT5 measuring point as a denominator, and the results of different upstream measuring points PT21, PT9, PT15 and PT17 relative to the PT5 measuring point are shown. As can be seen from fig. 3, the absolute value integration ratio of the vertical deformation of each measuring point pair falls within the range of 3 times of standard deviation, which indicates that the bridge health status is diagnosed as unchanged in 2012-2018 by taking the absolute value integration ratio of the vertical deformation as an index, and the bridge health status is the same as the previous diagnosis result of the single vehicle working condition.
The third step specifically comprises the following steps:
based on the two-point characteristics of the mode center points, firstly, the density of the mode center points is larger than that of other surrounding points, secondly, the distance between the mode center points and other mode center points is far, the mode quantity and the mode centers are determined for the sample points, classification is carried out, and the local density of each vertical deformation ratio sample point and the distance between each vertical deformation ratio sample point and other sample points are calculated; taking the vertical deformation ratio of the main beam as an example, the clustering algorithm for carrying out pattern recognition under the single-car working condition comprises the following steps:
step three: vertical deformation ratio set D= { ζ to be clustered i I= … N }, vertical deformation ratio ζ i Local density ρ of (2) i The calculation formula is as follows:
wherein d i j＝|ζ i -ζ j I is the vertical deformation ratio ζ i And zeta is j Distance d of (d) c For the cut-off distance, N is the number of sample points; vertical deformation ratio ζ i Local density ρ of (2) i Represents the sum ζ of D i The distance between the two is smaller than the cutting distance d c Is the number of samples of (a); cut-off distance d c Empirically determined, the 20% quantile is chosen for all N (N-1)/2 distances;
step three, two: vertical deformation ratio ζ i Distance delta of (2) i The calculation formula is as follows:
when zeta is i With maximum local density, its distance delta i Is D is medium and ζ i Sample point with largest distance and zeta i A distance therebetween; when zeta is i Without maximum local density, its distance delta i Is that the local density in D is greater than ρ i And ζ in the sample points of (2) i Sample point with minimum distance and zeta i A distance therebetween;
and step three: all sample point densities ρ calculated from the above i And delta i Drawing ρ i -δ i A relational decision graph, in delta i Large and ρ i The relatively large points are various centers; assuming that the cluster center has n c The corresponding sample points are numbered as
I.e. < ->
Is the j-th cluster center; after various centers are determined, sequentially distributing the rest points from high to low according to the density of the sample points, wherein each point is distributed to the category to which the nearest neighbor point with higher density than the point belongs, and the distribution process can be completed once in one direction;
and step three, four: the sample points follow Gaussian mixture distribution around a straight line, and the slope of the straight line is the vertical deformation ratio of different lanes; the errors of sample points around different straight lines obey Gaussian distribution, and the Gaussian mixture model parameters are solved by using an expectation maximization algorithm.
The invention has been described in detail with respect to the method for identifying the mode related to the vertical deformation of the girder of the cable-stayed bridge and for learning the machine for diagnosing health, and specific examples are applied to illustrate the principle and the implementation of the invention, and the description of the above examples is only used to help understand the method and the core idea of the invention; meanwhile, as those skilled in the art will have variations in the specific embodiments and application scope in accordance with the ideas of the present invention, the present description should not be construed as limiting the present invention in view of the above.
Claims (6)
1. A cable-supported bridge girder vertical deformation related mode identification and health diagnosis machine learning method is characterized in that: the method specifically comprises the following steps:
step one: analyzing the independence of the vertical deformation ratio of the main beam and the external load and verifying based on actual monitoring data;
step two: analyzing the independence of the absolute value integration ratio of the vertical deformation of the main beam and the external load, and verifying based on actual monitoring data;
step three: and carrying out cluster recognition of the related modes according to the main beam vertical deformation ratio index and the main beam vertical deformation absolute value integral ratio index.
2. The method according to claim 1, wherein said step one specifically comprises the steps of:
the method comprises the following steps: considering the flat structure of the cross section of the large cable bridge-bearing steel box girder and multi-lane arrangement, the deformation of stay ropes or slings at two sides and the elastic deformation of the cross section lead to different vertical deformation of the girder at different positions of the same cross section; regarding a certain cross section of the cable-supported bridge girder, stay ropes or slings at two sides are regarded as spring supports, and the cross section is simplified into a simply supported girder with spring supports A and B at two ends; when a concentrated force is applied at 1/4 span position, two vertical displacements from the two side support a positions C and D are:
wherein k is A For the stiffness of the A-point spring support, k B The rigidity of the point B spring support, EI is the bending rigidity of the main beam, l is the length of the half span beam, a is the distance between two measuring points and the nearest support respectively, and F is the concentration force;
step two: calculating to obtain the vertical deformation ratio lambda of the measuring points at the two sides of the main beam y The method comprises the following steps:
from equation (2), the vertical deformation ratio λ of the position C, D at a distance a from the end mounts A, B y Independent of the magnitude of the concentrated force, and only dependent on the rigidity k of the support A ,k B The vertical deformation ratio of the main beam at the same vehicle load action position is only related to structural parameters and is irrelevant to vehicle load; when the transverse position of the vehicle is determined, the vertical deformation ratio of the main beam does not change with the load of the vehicle; therefore, by analyzing the independence of the girder vertical deformation ratio on the external load, the girder vertical deformation ratio is found to be related to the structural parameters only, and the girder vertical deformation ratio is used as a bridge health diagnosis index.
3. The method according to claim 2, wherein in step one, the result of verification based on the actual monitoring data is: the vertical deformation ratio of the main beam at the upstream and downstream of the cable bridge is approximately kept constant, and the ratio or the slope of the vertical deformation ratio represents different lane positions, so that the independence of the vertical deformation ratio of the main beam on external load and the relation of the vertical deformation ratio of the main beam on structural parameters are verified based on real bridge monitoring data.
4. A method according to claim 3, wherein in step one, when a single vehicle is travelling in an upstream lane, the upstream vertical deformation is greater than the downstream vertical deformation, λ in equation (2) y Less than 1; when a single vehicle is traveling in the downstream lane, the downstream vertical deformation is larger than the upstream vertical deformation, i.e., λ in equation (2) y Greater than 1; if the stiffness of the spring supports at the two ends is the same and the slope is lambda when the vehicle runs at a certain position at the upstream y The slope is 1/lambda when the vehicle runs at the downstream symmetrical position y The method comprises the steps of carrying out a first treatment on the surface of the To maintain symmetry of the extracted features in both the upstream and downstream directions, for λ y Taking logarithm to obtain:
ξ＝lnλ y (3)
in the formula, xi is a main beam vertical deformation ratio index, and the values of the upstream and downstream symmetrical positions of the same section are opposite numbers;
the main beam vertical deformation ratio index xi is taken as a first related mode variable of the vertical deformation of the cable-supported bridge main beam, the ratio is related to the transverse action position of the load of the vehicle and the structural parameter, however, considering that the transverse position of the multi-vehicle in the lane obeys normal distribution, the main beam vertical deformation ratio index xi is only related to the structural parameter and is unrelated to the load in the statistical sense; when the health state of the bridge structure is changed, the vertical deformation ratio index of the main beam is changed, and the bridge health diagnosis can be performed based on the change.
5. The method according to claim 4, wherein the second step specifically comprises the steps of:
step two,: considering a scene that a unit concentrated vertical load moves along a longitudinal bridge, wherein a change rule curve between a certain point of a main girder vertical deformation and a concentrated load position is a vertical deformation influence line of the point; when a single vehicle runs from one end of the bridge to the other end at a constant speed, the vertical deformation time course of a certain measuring point is approximately considered to be positively correlated with the value of the vertical deformation influence line of the measuring point; let the bridge length be L, there are F, G measuring points on the bridge, the vertical deformation influence line of F point is F (x), the vertical deformation influence line of G point is G (x), record S F And S is G Line of influence integral at F, G two points respectively
Step two: consider two vehicles, denoted as Car1 and Car2, respectively, having weights w, respectively 1 And w 2 Distance of separation s (s<L) successively bridge in the same direction at the speed v 1 And v 2 Is driven at a constant speed; under the action of Car1 and Car2, the vertical deformation time interval integration ratio of the measuring point F, G is as follows:
wherein T is F ,T G The integral of the vertical deformation time interval of the main beam is measured point F and measured point G，S F ,S G The integration of the vertical deformation influence lines of the measuring point F and the measuring point G is that, w 1 ,v 1 Weight and speed, w, of Car1 2 ,v 2 Weight and speed for Car 2;
from equation (4), T is calculated when the vehicle is passing at a constant speed F /T G ＝S F /S G I.e. the ratio of the vertical deformation time interval integrals of the measuring point F, G is equal to the ratio of the vertical deformation influence line integrals of the measuring point F, G; the vertical deformation influence line is a function of bridge rigidity and bridge geometric dimension, so that the ratio of the influence line integrals of the two measuring points is irrelevant to the vehicle load and is only relevant to the bridge state parameter, and the influence line integrals can be used as an evaluation index for bridge health diagnosis;
step two, three: the second step is that when the vehicle runs at a constant speed, the ratio of the time interval integrals of the vertical deformation of the two measuring points caused by the vehicle team is approximately equal to the ratio of the line integrals of the vertical deformation influence of the two measuring points; however, when the vehicle passes through the bridge, the possibility of non-uniform running exists, and the situation is uniformly considered to be within an error range of the line integral ratio influenced by vertical deformation; the integral ratio of the absolute values of the vertical deformation time courses of the two measuring points is used as an index for measuring the health state of the bridge:
wherein D is F Is the integral of the absolute value of the vertical deformation time interval of the measuring point F, D G Is the integral of the absolute value of the vertical deformation time interval of the measuring point G, R A The integral ratio of the absolute values of the vertical deformation of the main beams at the two measuring points;
thus, the integral ratio R of the absolute value of the vertical deformation of the main beam A As a second related mode of vertical deformation of the main girder of the cable-stayed bridge, the ratio is only related to structural parameters and is not related to external load; when the health state of the bridge structure is changed, the integral ratio of the absolute value of the vertical deformation of the main girder is changed, and the index is used for bridge health diagnosis.
6. The method according to claim 5, wherein the third step comprises the steps of:
based on the two-point characteristics of the mode center points, firstly, the density of the mode center points is larger than that of other surrounding points, secondly, the distance between the mode center points and other mode center points is far, the mode quantity and the mode centers are determined for the sample points, classification is carried out, and the local density of each vertical deformation ratio sample point and the distance between each vertical deformation ratio sample point and other sample points are calculated; taking the vertical deformation ratio of the main beam as an example, the clustering algorithm for carrying out pattern recognition under the single-car working condition comprises the following steps:
step three: vertical deformation ratio set D= { ζ to be clustered i I= … N }, vertical deformation ratio ζ i Local density ρ of (2) i The calculation formula is as follows:
wherein d ij ＝|ζ i -ζ j I is the vertical deformation ratio ζ i And zeta is j Distance d of (d) c For the cut-off distance, N is the number of sample points; vertical deformation ratio ζ i Local density ρ of (2) i Represents the sum ζ of D i The distance between the two is smaller than the cutting distance d c Is the number of samples of (a); cut-off distance d c Empirically determined, the 20% quantile is chosen for all N (N-1)/2 distances;
step three, two: vertical deformation ratio ζ i Distance delta of (2) i The calculation formula is as follows:
when zeta is i With maximum local density, its distance delta i Is D is medium and ζ i Sample point with largest distance and zeta i A distance therebetween; when zeta is i Without maximum local density, its distance delta i Is that the local density in D is greater than ρ i And ζ in the sample points of (2) i Sample point with minimum distance and zeta i A distance therebetween;
and step three: all sample point densities ρ calculated from the above i And delta i Drawing ρ i -δ i A relational decision graph, in delta i Large and ρ i The relatively large points are various centers; assuming that the cluster center has n c The corresponding sample points are numbered as
I.e.
Is the j-th cluster center; after various centers are determined, sequentially distributing the rest points from high to low according to the density of the sample points, wherein each point is distributed to the category to which the nearest neighbor point with higher density than the point belongs, and the distribution process can be completed once in one direction;
and step three, four: the sample points follow Gaussian mixture distribution around a straight line, and the slope of the straight line is the vertical deformation ratio of different lanes; the errors of sample points around different straight lines obey Gaussian distribution, and the Gaussian mixture model parameters are solved by using an expectation maximization algorithm.
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