CN116703323A - Bridge cantilever construction monitoring system optimization method based on grey prediction theory - Google Patents
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Abstract
The application discloses a bridge cantilever construction monitoring system optimization method based on a grey prediction theory, which comprises the steps of obtaining an original data sequence in a previous construction stage and preprocessing to obtain a target data sequence; optimizing the initial gray prediction model through a target data sequence to obtain a first gray prediction model; selecting a prediction variable, and performing prediction calculation of the variable quantity according to a first gray prediction model; updating the first gray prediction model according to the calculation result to obtain a target gray prediction model; performing model precision test on the target gray prediction model, and if the model precision is met, evaluating the prediction precision of the target gray prediction model to obtain an applicability model; and if the model precision is not met, updating the parameter estimation of the prediction model again until the model precision is checked, and evaluating the model prediction precision to obtain the applicability model. The application improves the prediction precision.
Description
Technical Field
The application belongs to the technical field of bridge cantilever construction monitoring, and particularly relates to a bridge cantilever construction monitoring system optimization method based on a gray prediction theory.
Background
The continuous rigid frame bridge pier is gradually advanced to a larger scale along the span, the phenomena of overlarge main girder deflection, crack generation of the structure and the like are more serious, and the bridge construction stage needs to be monitored and controlled. In bridge construction monitoring, the existence of both known and unknown uncertain information is a typical gray system, so that the gray prediction theory is widely applied to bridge construction monitoring.
The prior art basically does not clarify the advantages and disadvantages of the gray prediction theory applied in the construction monitoring process relative to the traditional construction monitoring method, and has the following problems: firstly, most researchers do not test initial data before modeling, and test whether the initial data can directly establish a gray prediction model with higher precision, and whether preprocessing is needed when the original data has higher discreteness; secondly, after modeling is completed, the precision inspection mode of the predicted value output by the predicted model is single, and most of the predicted value is judged by only a single method in precision grade, so that the precision can not be completely ensured to meet the requirement.
Disclosure of Invention
In order to solve the problems, the application provides the following scheme: a bridge cantilever construction monitoring system optimization method based on a grey prediction theory comprises the following steps:
acquiring an original data sequence of a previous construction stage and preprocessing to acquire a target data sequence;
constructing an initial gray prediction model based on a gray prediction theory, and optimizing the initial gray prediction model through the target data sequence to obtain a first gray prediction model;
selecting a prediction variable, and performing prediction calculation of the variable quantity according to the first gray prediction model to obtain a calculation result;
updating the first gray prediction model according to the calculation result to obtain a target gray prediction model;
performing model precision test on the target gray prediction model, and if the model precision is met, evaluating the prediction precision of the target gray prediction model to obtain an applicability model; and if the model precision is not met, updating the parameter estimation of the prediction model again until the model precision is checked, and evaluating the model prediction precision to obtain the applicability model.
Preferably, the process of obtaining the original data sequence of the previous construction stage includes,
performing linear monitoring and stress monitoring on bridge cantilever construction to obtain actual measurement data; the measured data comprise deflection measured data and stress measured data;
finite element modeling is carried out on the bridge to obtain theoretical data; the theoretical data comprise deflection theoretical data and stress theoretical data;
and obtaining an original data sequence by making a difference value or a ratio of the measured data to the theoretical data.
Preferably, the preprocessing is performed on the original data sequence, and the process of obtaining the target data sequence comprises,
processing the original data in the original data sequence by adopting a multipoint moving average method to obtain an average value sequence;
reconstructing the background value of the mean value sequence according to a new method for constructing the whitened background data sequence to obtain a target data sequence.
Preferably, the method of multipoint moving average is used to process the raw data in the raw data sequence, and the process of obtaining the average value sequence comprises,
presetting an original data sequence, and preprocessing the original data of the original data sequence by adopting the multipoint sliding average of the following formula:
X (0) (1)＝(3X (0) (1)+X (0) (2))/4
X (0) (k)＝(X (0) (k-1)+2X (0) (k)+X (0) (k+1))/4k＝2,3,…,n-1
X (0) (n)＝(X (0) (n-1)+3X (0) (n))/4
obtaining a mean value sequence, wherein the formula expression is as follows:
wherein X is (0) (k) Dividing the k value measured value by the theoretical value to obtain a quotient;
assume that n actual monitored values and n theoretical design values are respectively recorded as:
X＝{X(1),X(2),X(3)…X(n)}
Y＝{Y(1),Y(2),Y(3)…Y(n)}
the quotient of the measured value and the theoretical value is marked as an initial sequence:
X (0) ＝{X (0) (1),X (0) (2),X (0) (3)...X (0) (n)}
X (0) (k)＝X(k)÷Y(k),k＝0,1,2...n
n is the number of actual monitoring values and theoretical design values; m is algebra used in accumulation, and has no practical significance; t is the sum of X (0) The number of times of generation is accumulated.
Preferably, reconstructing the background values for the mean value series according to the new method of constructing a whitened background data sequence, the process of obtaining a target data sequence comprising,
accumulating the mean value sequence to obtain a 1-AGO data sequence, and then according to a formula
Constructing an accumulation matrix and a constant term vector, and according to the formula:
obtaining a reduction value;
wherein Y is N B is a vector and a matrix formed by the two for convenient operation; n is the number of variables; a is a development coefficient, reflecting the future development condition of the measured value; u is gray action quantity and reflects the change relation of data;representing the time response value of the original data obtained after the subtraction and the reduction;For parameter vector->
Preferably, the process of selecting the prediction variables includes predicting the state of the i+1 stage using the corresponding deformation value after each construction stage is completed.
Preferably, the first gray prediction model is updated according to the calculation result, and the process of obtaining the target gray prediction model includes,
deleting the data farthest from the prediction stage in the prediction variables, adding the subsequent measured data to update the prediction model, and repeating the iterative prediction calculation of the first gray prediction model until the model accuracy test is passed.
Preferably, performing model accuracy test on the target gray prediction model comprises residual error test, association test and posterior difference test;
the residual error test judges the precision grade of the model by calculating the relative error between the predicted value and the measured value output by the target gray predicted model;
the relevancy test is a test of relevancy of two groups of sequences, and the relevancy of the two groups of sequences is judged by judging the similarity between the two groups of sequence curves;
the posterior difference test is used for model precision grade test, and the smaller the numerical data is, the higher the precision is.
Compared with the prior art, the application has the following advantages and technical effects:
1. in actual monitoring control of a bridge, the prediction precision of the gray prediction model after optimization is improved by one level compared with that of an original model, and the prediction result is more stable. The highest fitting degree between the predicted curve and the actually measured curve reaches 0.839, the probability of small error can reach 1, and the posterior difference and the residual error test reach one level.
2. Aiming at the problem that the original data discreteness greatly affects the model prediction precision, the method provides that the original data in an initial sequence is subjected to moving average treatment, and a whitening background value is reconstructed for a mean value sequence, so that an optimized GM (1, 1) model is established; and a hybrid test method for the precision test of the prediction model is provided by combining various test modes such as association degree, posterior difference, residual error, mean square error and small probability error.
3. Compared with the original GM (1, 1) model, the residual error results of the optimization model are higher than those of the original model, the association degree and the association coefficient of the prediction curve of the optimization model and the field actual measurement value are higher, and the posterior difference ratio and the precision level of the small probability error are higher than those of the original model. Although the precision of the original model can meet the construction requirement, the model prediction precision after optimization is higher in grade, and the prediction result has small fluctuation and is more stable.
Drawings
The accompanying drawings, which are included to provide a further understanding of the application and are incorporated in and constitute a part of this specification, illustrate embodiments of the application and together with the description serve to explain the application. In the drawings:
FIG. 1 is a schematic view of a continuous rigid frame bridge structure according to an embodiment of the present application;
FIG. 2 is a flow chart illustrating modeling of a gray prediction model according to an embodiment of the present application.
Detailed Description
It should be noted that, without conflict, the embodiments of the present application and features of the embodiments may be combined with each other. The application will be described in detail below with reference to the drawings in connection with embodiments.
It should be noted that the steps illustrated in the flowcharts of the figures may be performed in a computer system such as a set of computer executable instructions, and that although a logical order is illustrated in the flowcharts, in some cases the steps illustrated or described may be performed in an order other than that illustrated herein.
As shown in fig. 1-2, the optimization method of the bridge cantilever construction monitoring system based on the gray prediction theory mainly comprises the following steps:
s1, performing linear monitoring and stress monitoring on a bridge to obtain deflection measured data and stress measured data;
s2, finite element modeling is carried out on the bridge to obtain deflection theoretical data and stress theoretical data;
s3, selecting a prediction variable, and carrying out prediction calculation of deflection variation and stress variation in an optimized GM (1, 1) model;
further optimizing the scheme, wherein the method for selecting the predicted variables comprises the following steps: and predicting the state of the i+1 stage by using the corresponding deformation value after each construction stage is finished, and respectively selecting the actually measured deflection of the 6-9 # block as the original data modeling after the concrete pouring of the 10# block is finished if the deflection value after the concrete pouring of the 10# block is to be predicted.
The specific method for bringing the optimized GM (1, 1) model is as follows:
1. constructing an initial sequence by using the ratio of the theoretical data in the S2 to the measured data in the S1;
2. processing the original data sequence by using a multipoint moving average method, and reconstructing a background value according to a new method for constructing a whitened background data sequence, thereby establishing a univariate GM (1, 1) model;
3. and constructing an accumulation matrix and a constant term vector according to the univariate GM (1, 1) model, and finally obtaining a reduction value.
Further, the monitoring of the bridge cantilever construction by using the model is a common monitoring means in engineering to predict the stress strain condition of the bridge in the later construction stage, and the GM model deduces the subsequent engineering from the data in the previous construction stage so as to achieve the purpose of improving the precision. The GM model is applied to the upper part of the main beam, and the previous construction stage is used as original data for preprocessing so as to optimize the precision of the model in construction monitoring.
In bridge construction monitoring, a GM model is established by combining and analyzing measured data and theoretical data of the first construction stages, so that parameters such as a bridge deflection value, stress and the like are effectively predicted, and prediction and guidance are carried out on the next construction stage.
The equivalent-maintenance innovation GM (1, 1) model in the gray prediction model is also called a metabolism GM (1, 1) model, and is modeled in a mode of adding new information, removing old information and keeping the sequence length unchanged, wherein the mechanism of the model is similar to that of forgetting factor adaptation modeling thought in a general modeling theory.
According to the application, the GM (1, 1) optimization model is obtained by adopting an improved method for optimizing the original data of the GM (1, 1) model, so that the prediction accuracy is finally improved. The original data is generally obtained by making a difference or making a ratio between actual measurement data of a construction site and an analog value obtained by finite element simulation analysis software, so that randomness and fluctuation of the obtained original data can be larger, and if the original data with larger discreteness is not preprocessed, a prediction model is directly built, and the model has lower precision. There are many methods for preprocessing the original data, the data processing is performed in two steps in the study, firstly, the original data sequence is processed by adopting a multi-point sliding average method, and then the background value is reconstructed according to a new method for constructing a whitened background data sequence, so that a univariate GM (1, 1) model is established. The specific method comprises the following steps:
presetting an original data sequence, and preprocessing the original data of the original data sequence by adopting the multipoint sliding average of the following formula:
X (0) (1)＝(3X (0) (1)+X (0) (2))/4
X (0) (k)＝(X (0) (k-1)+2X (0) (k)+X (0) (k+1))/4k＝2,3,…,n-1
X (0) (n)＝(X (0) (n-1)+3X (0) (n))/4
obtaining a mean value sequence, wherein the formula expression is as follows:
wherein X is (0) (k) Dividing the k value measured value by the theoretical value to obtain a quotient;
assume that n actual monitored values and n theoretical design values are respectively recorded as:
X＝{X(1),X(2),X(3)…X(n)}
Y＝{Y(1),Y(2),Y(3)…Y(n)}
the quotient of the measured value and the theoretical value is marked as an initial sequence:
X (0) ＝{X (0) (1),X (0) (2),X (0) (3)...X (0) (n)}
X (0) (k)＝X(k)÷Y(k),k＝0,1,2...n
n is the number of actual monitoring values and theoretical design valuesThe method comprises the steps of carrying out a first treatment on the surface of the m is algebra used in accumulation, and has no practical significance; t is the sum of X (0) The number of times of generation is accumulated.
Further, preprocessing the data includes:
(1) Accumulation Generation (AGO)
For initial sequence X (0) Sequentially adding the original data to generate a new sequence, and accumulating once to generate 1-AGO to obtain a once accumulated sequence X (1) ：
X (1) ＝{X (1) (1),X (2) (2),X (3) (3)...X (4) (n)}
If to X (0) T this accumulation is performed, denoted t-AGO:
X (t) ＝{X (t) (1),X (t) (2),X (t) (3)...X (t) (n)}
with increasing numbers of accumulations, the stronger the regularity that the sequence exhibits. When the accumulated times approach infinity, the original sequence becomes a regular and definite non-random sequence. In the GM prediction model, the calculation amount and calculation accuracy are generally accumulated once, i.e., 1-AGO.
(2) Accumulation and subtraction production (IAGO)
The accumulation and subtraction are the inverse process of accumulation and subtraction, i.e. two adjacent data are subtracted, and the accumulation and subtraction generally plays a role in data reduction.
X (m-1) (t i )＝X (m) (t i )-X (m) (t i-1 )
……
X (1) (t i )＝X (2) (t i )-X (2) (t i-1 )
X (0) (t i )＝X (1) (t i )-X (1) (t i-1 )
X (0) And X is (t) Has the following relationship:
can be used for X (0) Doing t times of accumulation calculation to obtain X (t) X is taken as (t) Doing t times of subtraction calculation to obtain X (0) 。
Gray differential equation:
GM (n, h) represents an n-order gray differential equation model with h variables, namely:
wherein:
a 0 ＝1
among GM (n, h) models, GM models are used to analyze correlations between raw sequence data when h > 1, and GM (1, 1) models are used for predictive use when h=1. The predictive computation model GM (n, 1) represents a first order differential equation of n variables, namely:
in the aboveIs the rate of change of the variable X. GM (1, 1) gray when n=1The model is a univariate gray prediction model, and the GM (1, 1) model is the most widely used gray prediction model.
Preferably, reconstructing the background values for the mean value series according to the new method of constructing a whitened background data sequence, the process of obtaining a target data sequence comprising,
accumulating the mean value sequence to obtain a 1-AGO data sequence, and then according to a formula
Constructing an accumulation matrix and a constant term vector, and according to the formula:
obtaining a reduction value;
wherein Y is N B is a vector and a matrix formed by the two for convenient operation; n is the number of variables; a is a development coefficient, reflecting the future development condition of the measured value; u is gray action quantity and reflects the change relation of data;representing the time response value of the original data obtained after the subtraction and the reduction;For parameter vector->
Further, the bridge cantilever construction monitoring system optimizing method modeling complete flow based on the grey prediction theory comprises the following steps:
in an initial sequence X (0) Based on this, the sequence X is obtained by an accumulation process (1) Increasing the regularity of the data by using the new sequence X (1) Generating a sequence Z of immediately adjacent means (1) 。
Consider an initial sequence X (0) ：
X (0) ＝{X (0) (1),X (0) (2),X (0) (3)...X (0) (n)}
X (0) 1-AGO sequence of (1), i.e. one accumulation sequence of
X (1) ＝{X (1) (1),X (1) (2),X (1) (3)…X (1) (n)}
From X (1) Generating whitened background, i.e. immediately adjacent mean sequence Z (1) The method comprises the following steps:
Z (1) ＝{Z (1) (1),Z (1) (2),Z (1) (3)...Z (1) (n)}
Z (1) (i)＝0.5[X (1) (i-1)+X (1) (i)],i＝1,2,3,…,n
X (0) and Z (1) The data in (a) satisfy all the time:
X (0) (k)+aZ (1) (k)＝u(k＝1,2,…n)
thus, X is (0) (k)+aZ (1) (k) =u (k=1, 2, … n) is the gray differential equation of GM (1, 1) model, where a and u are parameters, a is the development coefficient, reflecting the future development of the measured values; u is gray action quantity, reflecting the change relation of data, X (0) (k) Is the gray derivative, Z (1) (k) Is X (0) (k) Is included in the white background value. The whitening differential equation corresponding to the univariate GM (1, 1) model is expressed as follows:
to make grey mouldWith only one variable and independent in the model, the common practice is to handleAs parameters to be identified, u is considered as an endogenous variable, namely:Meanwhile, according to the principle of the least square method, the method can be as follows:
the specific calculation process is as follows:
the first two equation subbands are taken into the third one:
k＝1
k＝2
k＝3
……
k＝n-1
the above equation can be transformed into:
the method is characterized by comprising the following steps:
the matrix expression of the above formula is:
n represents the number of data for establishing a gray prediction model, N is the number of variables, and it is known from the least square method that if (B T B) -1 The existence condition can be satisfied, and the parameter vector can be obtainedNamely:
wherein:
gray differential equation x (0) (k)+az (1) (k) The least squares parameter of =b satisfies:
dx (1) /dt+ax (1) ＝u
thereby can be obtained
Solving to obtain a time corresponding function as
Discretizing the above equation, the whitening equation for the GM (1, 1) model is:
because X is (1) (1)＝X (0) (1) Then:
the time response of the original data obtained after the subtraction and the reduction is as follows:
i.e. the final prediction model sequence of the GM (1, 1) model.
S4, updating the deflection gray model and the stress gray model;
further optimizing the scheme, the gray model updating method comprises the following steps: and in the S3 stage, selecting the data furthest from the prediction stage in the prediction variables, adding subsequent measured data, such as the construction of predicting the 11# block in the case, removing the construction data of the 6# block, adding the measured data of the 10# block after the construction to update the prediction model, and repeating the steps of carrying the optimized GM (1, 1) model.
S5, model accuracy testing, including residual error testing, association degree testing and posterior difference testing.
The residual error test is an objective precision judging mode, and the precision grade of the model is judged by calculating the relative error between the predicted value and the actually measured value output by the gray prediction model.
The relevancy test is a technical index for judging relevancy of two groups of data and is mainly used for analyzing relevancy of sample data in gray prediction. It reduces infinite convergence to approximate convergence, reduces complex infinite space problems to finite space, and replaces the concept of continuity with data sequences. For the detection of the correlation degree of the two groups of sequences, the correlation degree of the two groups of sequences is judged by judging the similarity between the two groups of sequence curves.
The posterior test is used for model accuracy grade test, and the smaller the value data is, the higher the accuracy is.
The embodiment is based on a grey prediction theory, and a GM (1, 1) model is applied to bridge construction monitoring; aiming at the problem that the original data discreteness greatly affects the model prediction precision, a scheme of carrying out moving average treatment on the original data in an initial sequence and reconstructing a whitening background value on a mean value array so as to establish an optimized GM (1, 1) model is provided; aiming at the problem of single prediction value precision test mode output by a prediction model, a hybrid test method for the prediction model precision test is provided.
Example 1
Finite element modeling is performed on a continuous rigid frame bridge example, and an elevation view of 6# blocks to 11# blocks is cut out in fig. 1. And collecting measured data from a construction site as original data, preprocessing by adopting multipoint moving average, and increasing the smoothness of the original data so as to optimize the model. Taking deflection prediction of a 10# beam block as an example, selecting data before and after pouring of a working condition I and before and after tensioning of a working condition II to calculate, wherein the data is specifically as follows:
initial sequence X for establishing deflection prediction model on 10# block small mileage side under working condition one condition (0) The method comprises the following steps:
X (0) (k)＝(0.606,0.663,0.835,0.809)
processing the original data sequence by using a multipoint moving average method, reconstructing background values according to a new method for constructing a whitened background data sequence, and preprocessing the initial sequence:
X (0) (1)＝(3X (0) (1)+X (0) (2))/4
X (0) (k)＝(X (0) (k-1)+2X (0) (k)+X (0) (k+1))/4k＝2,3,…,n-1
X (0) (n)＝(X (0) (n-1)+3X (0) (n))/4
X (0) (1)＝0.620X (0) (2)＝0.691X (0) (3)＝0.786X (0) (4)＝0.816
constructing a new initial sequence X from the processed data (0) The method comprises the following steps:
X (0) (k)＝(0.620,0.691,0.786,0.816)
the subsequent calculation flow is similar to the model described above. After calculation, the time corresponding sequence of the optimized GM (1, 1) model, namely a gray prediction model is obtained as follows:
the predicted value obtained after the subtraction reduction is calculated is as follows:
10# concrete casting front-back deflection theoretical value 7.74mm, output value lambda of gray prediction model i 0.951, the deflection predicted value isTheory value lambda i The product was 7.36mm and the measured value was 6.85mm.
Similar to the calculation of the 10# block deflection predicted value under the second working condition, the initial sequence X (0) The method comprises the following steps:
X (0) (k)＝(0.620,0.691,0.786,0.816)
the initial sequence after the moving average treatment is as follows:
X (0) (k)＝(1.423,1.357,1.251,1.177)
the subsequent calculation flow is similar to the model described above. After calculation, the time corresponding sequence of the optimized GM (1, 1) model, namely a gray prediction model is obtained as follows:
the predicted value obtained after the subtraction reduction is calculated is as follows:
10# concrete casting front-back deflection theoretical value 6.53mm, output value lambda of gray prediction model i 1.121, the deflection predicted value is theoretical value and lambda i The product was 7.32mm and the measured value was 7.18mm. The deflection predicted values of the final 10# block under the optimization model calculation are shown in table 1.
TABLE 1
And updating the optimized prediction model after the deflection of the 10# beam block is predicted so as to predict the deflection of the 11# beam block and guide the construction of the 11# beam block. Initial sequence X of deflection prediction of 10# block under condition one (0) The method comprises the following steps:
X (0) (k)＝(0.606,0.663,0.835,0.809)
the construction data of the six blocks with smaller influence is shown, the data of the 10# beam block is newly added, and a new initial sequence X is obtained (0) The method comprises the following steps:
X (0) (k)＝(0.663,0.835,0.809，0.885)
and carrying out moving average treatment on the new sequence, wherein the initial sequence after treatment is as follows:
X (0) (k)＝(0.706,0.786,0.835，0.866)
the initial sequence is used for establishing an optimized prediction model as follows:
the predicted value obtained after the subtraction reduction is calculated is as follows:
theoretical value of deflection before and after 11# concrete pouring is 8.51mm, and output value lambda of gray prediction model i 0.968, the deflection predicted value is theoretical and lambda i The product was 8.24mm and the measured value was 7.64mm.
Under the second working condition, the deflection prediction of the 11# beam block is similar to that of the first initial sequence X (0) Metabolism treatment, initial sequence X (0) The method comprises the following steps:
X (0) (k)＝(1.437,1.380,1.232,1.158)
removing the data of the 6# beam block, and updating the initial sequence of the data of the newly added 10# beam block to obtain the following steps:
X (0) (k)＝(1.380,1.232,1.158,1.100)
and then carrying out moving average treatment according to a formula to obtain a treated initial sequence which is as follows:
X (0) (k)＝(1.343,1.251,1.162,1.115)
the initial sequence is used for establishing an optimized prediction model as follows:
the predicted value obtained after the subtraction reduction is calculated is as follows:
theoretical value of deflection 7.17mm before and after 11# concrete pouring, output value lambda of gray prediction model i 1.071, the deflection predicted value is theoretical value and lambda i The product was 7.68mm and the measured value was 7.53mm. The deflection predicted values of the final 11# block under the optimization model calculation are shown in table 2.
TABLE 2
Taking the working condition-deflection of the 10# beam block construction as an example, calculating the precision of the prediction result, and checking a table of residual precision as shown in table 3.
TABLE 3 Table 3
Restoring data residual error checking
Posterior test:
mean square error ratioThe small error probability is p=0.95.
Performing correlation coefficient and correlation degree test calculation on deflection under the action of a first working condition, and setting an actual measurement value as a reference sequence to be Y 0 The method comprises the steps of carrying out a first treatment on the surface of the Theoretical deflection value is set as Y 1 The method comprises the steps of carrying out a first treatment on the surface of the The predicted deflection value is set as Y 2 . The following table of correlation coefficients is calculated according to the following formula:
wherein: i X 0 (k)-X i (k)|＝Δ i (k) Called k point X 0 And X is i Is the absolute difference of (2);is the two-stage minimum difference value;Is the two-stage maximum difference value; ρ is a resolution coefficient, the value is between 0 and 1, generally 0.5, the association coefficients of all points are integrated, and the whole X can be obtained by calculation i Curve and reference curve X 0 Is related to the degree r of correlation i . Wherein:
the relationship table is shown in Table 4.
TABLE 4 Table 4
The present application is not limited to the above-mentioned embodiments, and any changes or substitutions that can be easily understood by those skilled in the art within the technical scope of the present application are intended to be included in the scope of the present application. Therefore, the protection scope of the present application should be subject to the protection scope of the claims.
Claims (8)
1. The optimization method of the bridge cantilever construction monitoring system based on the grey prediction theory is characterized by comprising the following steps of:
acquiring an original data sequence of a previous construction stage and preprocessing to acquire a target data sequence;
constructing an initial gray prediction model based on a gray prediction theory, and optimizing the initial gray prediction model through the target data sequence to obtain a first gray prediction model;
selecting a prediction variable, and performing prediction calculation of the variable quantity according to the first gray prediction model to obtain a calculation result;
updating the first gray prediction model according to the calculation result to obtain a target gray prediction model;
performing model precision test on the target gray prediction model, and if the model precision is met, evaluating the prediction precision of the target gray prediction model to obtain an applicability model; and if the model precision is not met, updating the parameter estimation of the prediction model again until the model precision is checked, and evaluating the model prediction precision to obtain the applicability model.
2. The method of optimizing a bridge cantilever construction monitoring system based on gray prediction theory according to claim 1, wherein the process of obtaining the original data sequence of the previous construction stage comprises,
performing linear monitoring and stress monitoring on bridge cantilever construction to obtain actual measurement data; the measured data comprise deflection measured data and stress measured data;
finite element modeling is carried out on the bridge to obtain theoretical data; the theoretical data comprise deflection theoretical data and stress theoretical data;
and obtaining an original data sequence by making a difference value or a ratio of the measured data to the theoretical data.
3. The optimization method of the bridge cantilever construction monitoring system based on the grey prediction theory according to claim 1, wherein,
preprocessing the original data sequence to obtain a target data sequence,
processing the original data in the original data sequence by adopting a multipoint moving average method to obtain an average value sequence;
reconstructing the background value of the mean value sequence according to a new method for constructing the whitened background data sequence to obtain a target data sequence.
4. The optimization method of bridge cantilever construction monitoring system based on grey prediction theory according to claim 3, wherein the process of processing the original data in the original data sequence by adopting a multipoint moving average method to obtain the average value sequence comprises the following steps of,
presetting an original data sequence, and preprocessing the original data of the original data sequence by adopting the multipoint sliding average of the following formula:
X (0) (1)＝(3X (0) (1)+X (0) (2))/4
X (0) (k)＝(X (0) (k-1)+2X (0) (k)+X (0) (k+1))/4k＝2,3,…,n-1
X (0) (n)＝(X (0) (n-1)+3X (0) (n))/4
obtaining a mean value sequence, wherein the formula expression is as follows:
wherein X is (0) (k) Dividing the k value measured value by the theoretical value to obtain a quotient;
assume that n actual monitored values and n theoretical design values are respectively recorded as:
X＝{X(1),X(2),X(3)…X(n)}
Y＝{Y(1),Y(2),Y(3)…Y(n)}
the quotient of the measured value and the theoretical value is marked as an initial sequence:
X (0) ＝{X (0) (1),X (0) (2),X (0) (3)...X (0) (n)}
X (0) (k)＝X(k)÷Y(k),k＝0,1,2...n
n is the number of actual monitoring values and theoretical design values; m is algebra used in accumulation, and has no practical significance; t is the sum of X (0) The number of times of generation is accumulated.
5. The method for optimizing a monitoring system for cantilever construction of a bridge based on gray prediction theory according to claim 3, wherein reconstructing the background value of the mean value series according to the new method for constructing a whitened background data series, obtaining the target data series comprises,
accumulating the mean value sequence to obtain a 1-AGO data sequence, and then according to a formula
Constructing an accumulation matrix and a constant term vector, and according to the formula:
obtaining a reduction value;
wherein Y is N B is a vector and a matrix formed by the two for convenient operation; n is the number of variables; a is a development coefficient, reflecting the future development condition of the measured value; u is gray action quantity and reflects the change relation of data;representing the time response value of the original data obtained after the subtraction and the reduction;For parameter vector->
6. The optimization method of bridge cantilever construction monitoring system based on gray prediction theory according to claim 1, wherein the process of selecting the prediction variables includes predicting the state of the i+1 stage by using the corresponding deformation value after each construction stage is completed.
7. The optimization method of the bridge cantilever construction monitoring system based on the gray prediction theory according to claim 1, wherein the process of updating the first gray prediction model according to the calculation result to obtain the target gray prediction model comprises,
deleting the data farthest from the prediction stage in the prediction variables, adding the subsequent measured data to update the prediction model, and repeating the iterative prediction calculation of the first gray prediction model until the model accuracy test is passed.
8. The optimization method of the bridge cantilever construction monitoring system based on the gray prediction theory according to claim 1, wherein the model accuracy test of the target gray prediction model comprises residual error test, association test and posterior difference test;
the residual error test judges the precision grade of the model by calculating the relative error between the predicted value and the measured value output by the target gray predicted model;
the relevancy test is a test of relevancy of two groups of sequences, and the relevancy of the two groups of sequences is judged by judging the similarity between the two groups of sequence curves;
the posterior difference test is used for model precision grade test, and the smaller the numerical data is, the higher the precision is.
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN117391546A (en) * | 2023-12-11 | 2024-01-12 | 山东萌山钢构工程有限公司 | Method, system, device and storage medium for monitoring fabricated building construction |
| CN117634924A (en) * | 2023-12-07 | 2024-03-01 | 沧州经济开发区武理工京津冀协同产业科技研究院 | Method, device, equipment and medium for predicting dissolved gas in transformer oil |
Citations (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN105868556A (en) * | 2016-03-29 | 2016-08-17 | 武汉福天通科技有限公司 | Bridge safety assessment method based on Beidou bridge safety monitoring system |
-
2023
- 2023-06-15 CN CN202310710841.0A patent/CN116703323A/en active Pending
Patent Citations (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN105868556A (en) * | 2016-03-29 | 2016-08-17 | 武汉福天通科技有限公司 | Bridge safety assessment method based on Beidou bridge safety monitoring system |
Non-Patent Citations (3)
| Title |
|---|
| 包仪军;王常峰;赵继康;: "基于改进灰色预测GM(1, 1)模型的大跨度桥梁施工控制", 铁道建筑, no. 02, pages 18 * |
| 包龙生;周子博;于玲: "基于累积法的GM(1, 1)模型在桥梁施工监控上的应用", 沈阳建筑大学学报(自然科学版), no. 002, pages 240 - 246 * |
| 张丽萍;刘晓林;张德宝;: "粉喷桩复合地基极限承载力灰色预测研究", 辽东学院学报(自然科学版), no. 02, pages 114 - 119 * |
Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN117634924A (en) * | 2023-12-07 | 2024-03-01 | 沧州经济开发区武理工京津冀协同产业科技研究院 | Method, device, equipment and medium for predicting dissolved gas in transformer oil |
| CN117391546A (en) * | 2023-12-11 | 2024-01-12 | 山东萌山钢构工程有限公司 | Method, system, device and storage medium for monitoring fabricated building construction |
| CN117391546B (en) * | 2023-12-11 | 2024-02-27 | 山东萌山钢构工程有限公司 | Method, system, device and storage medium for monitoring fabricated building construction |
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