CN109992815B - Support accumulated displacement calculation method based on relevance rain flow counting - Google Patents
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Abstract
The invention discloses a method for calculating accumulated displacement of a support based on relevance rain flow counting, and relates to bridge monitoring and dividingThe analysis field comprises: acquiring environmental temperature data temp of bridge health monitoring system i,origin And corresponding bridge support displacement response data in time; based on a least square method, obtaining a linear association relation between the ambient temperature and the support displacement, and separating load response to obtain the support displacement response under the influence of the ambient temperature and the train load; and calculating the accumulated support displacement under the influence of the environmental temperature by adopting a differential accumulation method, calculating the accumulated support displacement under the influence of the train load by adopting a rain flow counting method, and summing the accumulated support displacement and the accumulated support displacement to obtain the total accumulated support displacement.
Description
Technical Field
The invention relates to the field of bridge monitoring analysis, in particular to a method for calculating accumulated displacement of a support based on relevance rain flow counting.
Background
The bridge support connects the upper and lower structures of the bridge, which is an important stress member of the bridge, and the working state of the support directly relates to the safety and durability of the whole structure of the bridge. In the prior art, the bridge support has a plurality of forms, the working state and the service life of the bridge support are influenced by a plurality of factors such as construction process, material aging, environment, vehicle load and the like, the internal damage and aging fatigue degree of the support are difficult to accurately judge only by means of the appearance of the support and management and maintenance experience, and the running state of the support needs to be scientifically estimated by combining the accumulated displacement of the support.
The accumulated displacement of the support is an important index for measuring the working state and the service life of the bridge support in the bridge operation process, and is also a reliable basis for the management, maintenance and repair of the bridge support. However, at present, the research on the accurate calculation of the accumulated displacement of the support at home and abroad is insufficient, and the processing means is too rough.
Disclosure of Invention
Aiming at the defects in the prior art, the invention aims to provide a calculation method for the accumulated displacement of the support based on the relevance rain flow count, which can provide higher calculation precision than the existing calculation method.
In order to achieve the above purpose, the invention adopts the following technical scheme:
a method for calculating accumulated displacement of a support based on relevance rain flow counting comprises the following steps:
s1, respectively acquiring bridge environment temperature data temp i,origin And bridge support displacement response data, wherein i represents the measurement position of the environmental temperature data, and the environmental temperature data and the bridge support displacement response data are correlated in time;
s2, based on a least square method, obtaining a linear association relation between the ambient temperature and the support displacement, obtaining a support displacement response under the influence of the ambient temperature, and separating the support displacement response under the influence of the train load from the bridge support displacement response;
and S3, calculating the accumulated support displacement under the influence of the environmental temperature by adopting a differential accumulation method, calculating the accumulated support displacement under the influence of the train load by adopting a rain flow counting method, and summing the accumulated support displacement and the accumulated support displacement to obtain the total accumulated support displacement.
Based on the above technical solution, in step S2, the data is preprocessed by using a probability statistical method, so as to eliminate abnormal monitoring data.
Based on the technical scheme, the data preprocessing method adopting the probability statistical method specifically comprises the following steps of:
dividing the difference e into d sections in the amplitude interval, wherein d is more than 25, performing frequency histogram statistics, and recording the support displacement frequency p of each section i I represents the data position, i=1, 2,3, …, d; the difference e is the displacement of the bridge support during each measurement;
calculating the support displacement frequency p of each section by MATLAB i And various distribution function probability density integral values fre over the section length j Residual r between i ＝p i -fre i (i=1, 2,., d) using vector r i Sum of squares of 2 norms, i.e. error sum of squares
The degree of fit between the two is measured, and the optimal probability distribution of the interval samples is determined by the square of the error and the minimum value of alpha.
On the basis of the technical scheme, the step of calculating the accumulated displacement of the support under the influence of the train load by adopting the rain flow counting method comprises the following steps of:
calculating the passing time of the train according to vibration and strain data when the train passes the bridge;
recording support displacement response data of a train passing period;
and (3) counting the support displacement data of the time period when the vehicle passes each time by adopting a rain flow counting method to obtain the accumulated displacement.
On the basis of the technical scheme, the step of calculating the accumulated displacement of the support under the influence of the train load by adopting the rain flow counting method comprises the following steps of:
intercepting support displacement monitoring data f of each passing time period (wy，train),k＝1,2,3,...,N K is the train passing number, N is the train passing number for a period of time, and the change range delta wy of the single train passing support displacement amplitude is counted by adopting a rain flow counting method ii Ii=1, 2, 3..m, M is the number of magnitudes of the support displacement by the rain flow counting method, K ii For the ii-th support displacement amplitude Deltawy ii The number of times of occurrenceThe accumulated support displacement under the influence of a single train is as follows:
the cumulative seat displacement under the influence of the train is then calculated according to the following formula:
based on the above technical solution, the step S2 specifically includes:
based on the least square method, obtaining a linear correlation relationship between the ambient temperature and the displacement of the support, and marking as follows:
f wy，temp ＝a 0 +a 1 ×temp i,origin ,i＝1,2,3,...,n
e＝f wy,origin -f wy，fit
wherein a is 0 ,a 1 Is a coefficient, respectively represents intercept and slope, f wy，temp Representing the displacement of the support under the influence of temperature, e is f wy,origin And f wy，temp Difference between them.
Based on the technical proposal, the coefficient a 0 ,a 1 Calculated according to the following formula:
based on the above technical solution, in step S3, the accumulated support displacement under the influence of the environmental temperature is calculated by using a differential accumulation method according to the following formula:
diff i ＝x i+1 -x i ,i＝1,2,3,...,n-1；
wherein the support displacement f under the influence of temperature wy，temp Is diff i I=1, 2,3,..n-1, displacement_temp is the accumulated displacement of the support under the influence of temperature.
Compared with the prior art, the invention has the advantages that:
(1) According to the support accumulated displacement calculation method based on the relevance rain flow count, the load response of original support displacement monitoring data is separated by adopting a relevance analysis method, and the rain flow count method and the difference method are applied to support accumulated displacement calculation, so that more accurate support accumulated displacement is obtained, and more detailed support safety precaution is provided for bridge health monitoring.
(2) The support accumulated displacement calculation method based on the relevance rain flow count can be realized through programming of MATLAB, is convenient and quick to operate, and has stronger practicability. The method is based on bridge support displacement original monitoring data, and accurate support accumulated displacement is obtained through relevance and rain flow counting analysis, so that the method can be widely applied to support displacement calculation of various bridges, and has strong engineering and scientific research application prospects.
Drawings
FIG. 1 is a schematic diagram showing the relationship between the environmental temperature and the displacement of the support in the embodiment of the invention;
FIG. 2a is a timing chart of the displacement of the support under the influence of the ambient temperature at the first measuring point according to the embodiment of the present invention;
FIG. 2b is a graph showing the time course of displacement of the support under the influence of the ambient temperature at the second measuring point according to the embodiment of the present invention;
FIG. 3 is a timing chart of support displacement in an embodiment of the present invention;
FIG. 4 is a timing chart of accumulated displacement of a support in an embodiment of the invention;
FIG. 5 is a chart showing the displacement of the support during a typical single train pass in an embodiment of the present invention;
FIG. 6 is a schematic diagram of the basic principle of the rain flow counting method according to the embodiment of the invention;
FIG. 7 is a histogram of seat displacement under the influence of a train load in an embodiment of the invention;
fig. 8 is a graph showing the displacement spectrum of the support under the influence of the load of the train in the embodiment of the invention.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings and examples.
Referring to fig. 1, an embodiment of the present invention provides a method for calculating accumulated displacement of a support based on correlated rain flow counting, including the following steps:
the first step: acquiring environment data of the health monitoring system and support displacement response data corresponding to the environment data in time, wherein the support displacement response data adopts f in time course wy,origin Representing the environmental temperature data time course using temp i，origin，i＝1，2，...，n And (3) representing. Where i represents the data position and n represents the number of data.
And a second step of: based on the least square method, obtaining a linear correlation relationship between the ambient temperature and the displacement of the support, and marking as follows:
f wy，temp ＝a 0 +a 1 ×temp i，origin ，i＝1，2，3，...，n
e＝f wy,origin -f wy，fit
wherein a is 0 ,a 1 Is a coefficient, respectively represents intercept and slope, f wy，temp Support displacement under the influence of temperature, e is f wy,origin And f wy，temp The difference between the coefficients a 0 ,a 1 Calculated according to the following formula, namely:
let the partial derivative equal to 0, it is possible to obtain:
and a third step of: abnormal data is eliminated by adopting a probability statistical method, and a difference vector e is obtained i Statistical analysis is carried out on the values (i is more than 0 and less than or equal to N), and e is subjected to normal distribution with the mean value of 0, namely e-N (0, sigma) through distribution fitting and K-S inspection 2 ). Let the confidence interval of the monitored data be [ e ] u ,e d ]So that e u ＜e i ＜e d Satisfies 99.99% guarantee rate, and finds out the position location corresponding to the abnormal value point outside the e confidence interval j J=1, 2, 3..m, m is the number of data for which the difference falls outside the confidence interval.
The guaranteed rate is:
P(e u ＜e＜e d )＝P(z d ＜e＜z u )＝F(z u )F(z d )
wherein: f (-) is the fitted normal distribution function of the difference e.
Taking zu, wherein zd is an upper dividing point and a lower dividing point of 0.0005, and the corresponding assurance rate is as follows:
P(e u ＜e i ＜e d )＝P(z d ＜e＜z u )＝1-0.0005×2＝99.9％
at this time, the liquid crystal display device,
z u ＝F -1 (1-0.0005)，z d ＝F -1 (0.0005)
wherein: f (F) -1 (. Cndot.) fitting the inverse of the normal distribution function.
Let the original monitoring data f wy，origin 、temp i，origin，i＝1，2，...，n In the position location j J=1, 2,3, at m is nan (null), obtaining support displacement data f after removing abnormal data wy 。
Fourth step: calculating the accumulated displacement of the support under the influence of temperature by adopting a differential accumulation method, and calculating the displacement f of the support under the influence of temperature wy，temp Is diff i I=1, 2,3,..n-1, the cumulative displacement of the mount under the influence of temperature is displacement_temp, and there are:
diff i ＝x i+1 -x i ，i＝1，2，3，...，n-1；
fifth step: intercepting support displacement monitoring data f of each passing time period (wy，train)，k＝1，2，3，...,N K is the train passing number, N is the train passing number for a period of time, and the change range delta wy of the single train passing support displacement amplitude is counted by adopting a rain flow counting method ii Ii=1, 2, 3..m, M is the number of magnitudes of the support displacement by the rain flow counting method, K ii For the ii-th support displacement amplitude Deltawy ii The number of occurrences, the cumulative support displacement under the influence of a single train is:
therefore, the cumulative seat displacement under the influence of the train is:
sixth step: and calculating the support accumulated displacement displacement_all, and summing the support accumulated displacement displacement_temp under the influence of temperature and the support accumulated displacement_train under the influence of the train to obtain the support accumulated displacement_all.
displacement_all＝displacement_temp+displacement_train
The specific steps of the support accumulated displacement calculation method based on relevance rain flow counting are described below by taking a practical case of a highway and railway two-purpose Yangtze river bridge as an example:
the highway and railway two-purpose Yangtze river bridge related in the embodiment is a highway and railway combined bridge, wherein four-line railways are arranged at the lower part of the Yangtze river bridge and six-lane highways are arranged at the upper part of the highway and railway two-purpose Yangtze river bridge. The full length of the bridge is 1290 m, the main span is 630 m, the bridge spans are arranged as (90+240+630+240+90) m, and a three-truss three-cable-surface structure is adopted. The main trusses are of an N-shaped truss structure, the center-to-center spacing of the three main trusses is 17.1 meters, the total width of the trusses is 34.2 meters, the truss height is 15.5 meters, the internode length is 15 meters, and cast steel movable supports are vertically arranged between the tower and the beam and at the side piers and the auxiliary piers. The displacement monitoring of the support of the Yangtze river bridge for both the highway and the railway of the copper tomb is an important component of a health monitoring system, and the longitudinal support displacement of the main beam is obvious under the action of an uneven environment temperature field and a train load due to the large bridge span. The support displacement measuring points are arranged at the 0# piers and the 6# piers and are distributed in an upstream symmetrical mode and a downstream symmetrical mode. The health monitoring system adopts a magnetostrictive displacement meter, the sampling frequency is 1Hz, and the precision is 0.01mm.
(1) Based on the step S1, the displacement of the support seats at the upper and the lower stream of the 0# pier of the Yangtze river bridge for highway and railway and the corresponding environmental temperature data acquisition, the sampling frequency of the equipment is 1Hz. And selecting and analyzing the fourth quarter support displacement and the ambient temperature in 2017.
(2) Based on the monitoring data in the first step, calculating a linear association relation between the ambient temperature and the support displacement by adopting a least square method principle, wherein the linear association relation is shown in figure 1; the time course of the displacement of the support under the influence of the temperature separated from the correlation relationship is shown in fig. 2a and 2b, and the correlation parameter information is shown in table 1.
TABLE 1 correlation parameters between ambient temperature and support displacement
(3) Based on the association relation in the second step, eliminating abnormal data by adopting a probability statistical method, and carrying out the correlation relation on the difference vector e i Statistical analysis is carried out on the values (i is more than 0 and less than or equal to N), and e is subjected to normal distribution with the mean value of 0, namely e-N (0, sigma) through distribution fitting and K-S inspection 2 ). Let the confidence interval of the monitored data be [ e ] u ,e d ]So that e u ＜e i ＜e d Satisfies 99.99% guarantee rate, and finds out the position location corresponding to the abnormal value point outside the e confidence interval j J=1, 2, 3..m, m is the number of data for which the difference falls outside the confidence interval.
The guaranteed rate is: p (e) u ＜e＜e d )＝P(z d ＜e＜z u )＝F(z u )F(z d ) Wherein: f (-) is the fitted normal distribution function of the difference e.
Taking zu, wherein zd is an upper dividing point and a lower dividing point of 0.0005, and the corresponding assurance rate is as follows:
P(e u ＜e i ＜e d )＝P(z d ＜e＜z u )＝1-0.0005×2＝99.9％
at this time, z u ＝F -1 (1-0.0005)，z d ＝F -1 (0.0005) wherein: f (F) -1 (. Cndot.) fitting the inverse of the normal distribution function. Let the original monitoring data f wy，origin 、temp i，origin，i＝1，2，...，n In the position location j J=1, 2,3, at m is nan (null), obtaining support displacement data f after removing abnormal data wy As shown in fig. 3.
Fourth step: calculating the accumulated displacement of the support under the influence of temperature by adopting a differential accumulation method, and calculating the displacement f of the support under the influence of temperature wy，temp Is diff i I=1, 2,3,..n-1, the cumulative displacement of the mount under the influence of temperature is displacement_temp, and there are:
diff i ＝x i+1 -x i ,i＝1,2,3,...,n-1；
respectively calculating support displacement monitoring data f by adopting differential accumulation method wy,origin And temperature-affected lower support displacement monitoring data f wy，temp As shown in fig. 4.
Fifth step: intercepting support displacement monitoring data f of each passing time period (wy，train)，k＝1，2，3，...，N K is a train passing number, N is a train passing number of a period of time, the typical single train passing time period support displacement time course change is shown in figure 5, and a rain flow counting method (the statistical principle is shown in figure 6) is adopted to count the single train passing support displacement amplitude change range delta wy ii Ii=1, 2, 3..m, M is the number of magnitudes of the support displacement by the rain flow counting method, K ii For the ii-th support displacement amplitude Deltawy ii The number of occurrences, the cumulative support displacement under the influence of a single train is:
the accumulated support displacement under the influence of the train is as follows:
the support displacement histogram under the influence of the train load and the support displacement spectrum under the influence of the train load are shown in fig. 7 and 8.
Sixth step: and calculating the support accumulated displacement displacement_all, and summing the support accumulated displacement displacement_temp under the influence of temperature and the support accumulated displacement_train under the influence of the train to obtain the support accumulated displacement_all.
displacement_all＝displacement_temp+displacement_train
And counting the accumulated support displacement in the fourth quarter, wherein as shown in table 2, the accumulated displacement 0# pier is 36.55m downstream and 35.26m upstream by using a displacement differential accumulation method, the accumulated displacement 0# pier is 28.07m downstream and 27.12m upstream by using a correlation-based rain flow counting method, the average displacement of the support per day can be obtained from the accumulated displacement in the quarter and the effective time, and the accumulated displacement of the support in the missing time of the monitored data can be predicted by using the average accumulated displacement of the support per day, so that the estimated displacement in the quarter of the support can be obtained.
Table 2 quarter cumulative displacement statistics
The invention is not limited to the embodiments described above, but a number of modifications and adaptations can be made by a person skilled in the art without departing from the principle of the invention, which modifications and adaptations are also considered to be within the scope of the invention. What is not described in detail in this specification is prior art known to those skilled in the art.
Claims (6)
1. The method for calculating the accumulated displacement of the support based on the relevance rain flow count is characterized by comprising the following steps of:
s1, respectively acquiring bridge environment temperature data temp i,origin And bridge support displacement response data, wherein i represents the measurement position of the environmental temperature data, and the environmental temperature data and the bridge support displacement response data are correlated in time;
s2, based on a least square method, obtaining a linear association relation between the ambient temperature and the support displacement, obtaining a support displacement response under the influence of the ambient temperature, separating the support displacement response under the influence of the train load from the bridge support displacement response, preprocessing data by adopting a probability statistical method, and eliminating abnormal monitoring data, wherein the method comprises the following steps: dividing the difference e into d sections in the amplitude interval, wherein d is more than 25, performing frequency histogram statistics, and recording the support displacement frequency p of each section i I represents the data position, i=1, 2,3, …, d; the difference e is the displacement of the bridge support during each measurement;
calculating the support displacement frequency p of each section by MATLAB i And various distribution function probability density integral values fre over the section length j Residual r between i ＝p i -fre i I=1, 2, d, using vector r i Sum of squares of 2 norms, i.e. error sum of squares
The degree of fit between the two is measured, and the optimal probability distribution of the interval samples is determined by the square of the error and the minimum value of alpha.
And S3, calculating the accumulated support displacement under the influence of the environmental temperature by adopting a differential accumulation method, calculating the accumulated support displacement under the influence of the train load by adopting a rain flow counting method, and summing the accumulated support displacement and the accumulated support displacement to obtain the total accumulated support displacement.
2. The method for calculating the accumulated displacement of the support based on the correlative rain flow count as claimed in claim 1, wherein the step of calculating the accumulated displacement of the support under the influence of the load of the train by adopting the rain flow count method comprises the steps of:
calculating the passing time of the train according to vibration and strain data when the train passes the bridge;
recording support displacement response data of a train passing period;
and (3) counting the support displacement data of the time period when the vehicle passes each time by adopting a rain flow counting method to obtain the accumulated displacement.
3. The method for calculating the cumulative displacement of the support based on the correlative rain flow count as claimed in claim 2, wherein the step of calculating the cumulative displacement of the support under the influence of the load of the train by adopting the rain flow count method comprises the steps of:
intercepting support displacement monitoring data f of each passing time period (wy，train)，k＝1，2，3，...，N K is the train passing number, N is the train passing number for a period of time, and the change range delta wy of the single train passing support displacement amplitude is counted by adopting a rain flow counting method ii Ii=1, 2, 3..m, M is the number of magnitudes of the support displacement by the rain flow counting method, K ii For the ii-th support displacement amplitude Deltawy ii The number of occurrences, the cumulative support displacement under the influence of a single train is:
the cumulative seat displacement under the influence of the train is then calculated according to the following formula:
4. the method for calculating the cumulative displacement of the support based on the correlation rain flow count according to claim 1, wherein the step S2 specifically includes:
based on the least square method, obtaining a linear correlation relationship between the ambient temperature and the displacement of the support, and marking as follows:
f wy，temp ＝a 0 +a 1 ×temp i，origin ，i＝1，2，3，...，n
e＝f wy，origin -f wy，temp
wherein a is 0 ，a 1 Is a coefficient, respectively represents intercept and slope, f wy，temp Representing the displacement of the support under the influence of temperature, e is f wy，origin And f wy，temp Difference between them.
5. The method for calculating the accumulated displacement of the support based on the relevance rain flow count according to claim 4, wherein the method comprises the following steps: coefficient a 0 ，a 1 Calculated according to the following formula:
6. the method for calculating the accumulated displacement of the support based on the correlative rain flow count according to claim 1, wherein in the step S3, the accumulated displacement of the support under the influence of the environmental temperature is calculated by using a differential accumulation method by the following formula:
diff i ＝x i+1 -x i ，i＝1，2，3，...，n-1；
wherein the support displacement f under the influence of temperature wy，temp Is diff i I=1, 2,3,..n-1, displacement_temp is the accumulated displacement of the support under the influence of temperature.
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