CN114088052B - Building structure settlement deformation prediction method based on monitoring data fitting curve derivative - Google Patents
Building structure settlement deformation prediction method based on monitoring data fitting curve derivative Download PDFInfo
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Abstract
The invention discloses a building structure settlement deformation prediction method based on monitoring data fitting curve derivative, wherein a structural settlement model of the prediction method comprises a settlement-time prediction fitting equation f (t) and a section-deformation fitting equation g (x), and then first derivatives of the fitting equation f (t) and the fitting equation g (x) are respectively calculated. For the first derivative of the predictive fit equation f (t), the reciprocal approximation of 0 indicates that the land enters the consolidation stage, and the derivative difference value of the adjacent points exceeds the threshold value to indicate that deformation is uncoordinated, and the predictive structure has cracks. For the first derivative of the fitting equation g (x), if the absolute value of the derivative is less than the threshold, then the structure is judged to be at risk of cracking. The invention has the advantages that: the invention predicts the sedimentation deformation development trend of the building structure and can assist construction organization decision-making; meanwhile, by evaluating the state of the building structure, the hidden danger of quality and safety can be found in advance and measures can be taken to eliminate the hidden danger.
Description
Technical Field
The invention belongs to the technical field of building structure monitoring, and particularly relates to a building structure settlement deformation prediction method based on a monitored data fitting curve derivative.
Background
The settlement deformation of the building structure is due to vertical deformation or sinking of foundation soil caused by compression under the load of the building. Even settlement generally has less harm to the building, but when the settlement is too large, the elevation of the building is reduced to influence the use; uneven settlement is harmful to the building, and can cause additional stress to the building to cause cracks, even partial components to break, thereby endangering the safety of the building.
The settlement deformation of the building structure is a problem of long-term research in the fields of building engineering and geotechnical engineering, and the traditional research method is based on causal relation, and the research theory comprises a soil mechanics model of a Taisha group, an empirical formula, a finite element model and the like. In recent years, as machine learning algorithms have matured, research results have appeared in which BP neural networks, convolutional neural networks, and the like have been used as tools to search for sedimentation deformation rules from the viewpoint of correlation of data, and predict the sedimentation deformation rules.
The traditional causal relation research method is suitable for application in the structural design stage and in the condition of lacking measured data, and has the limitation that a plurality of boundary conditions are needed to be assumed, and the boundary conditions often have great changes in the construction and use stages of the building structure, so that the theoretical calculation result and the actual result have great deviation.
The machine learning algorithm does not consider the causal relationship of the research object, and only corrects the model weight based on a large amount of monitoring data, so that a prediction function is realized. However, the disadvantage is that a proper parameter combination needs to be determined to achieve a good prediction effect, while the theory of the optimal parameter combination is still not mature, and a large number of engineering practices need to be adjusted by manual trial and error.
Although a great deal of research results exist on structural sedimentation deformation rules, accurate prediction of the development trend of the structural sedimentation deformation rules is a difficult problem which plagues engineering for a long time. For example, in the construction of large-area industrial plant floors, if post-cast strips are constructed too early when the settlement and deformation of two adjacent plates are not coordinated, the resulting constraints will cause structural cracking, affect the service life of the structure, and even cause safety problems. If the settlement deformation trend can be predicted, not only the construction organization plan can be properly arranged, but also the quality and safety hidden trouble can be found in advance and measures can be taken to eliminate. Therefore, it is needed to provide a method for predicting settlement deformation of a building structure to solve the problems in the prior art.
Disclosure of Invention
According to the defects of the prior art, the invention provides the building structure settlement deformation prediction method based on the monitoring data fitting curve derivative.
The invention is realized by the following technical scheme:
the building structure settlement deformation prediction method based on the monitored data fitting curve derivative is characterized by comprising the following steps of:
step 1: arranging a plurality of monitoring points with settlement deformation monitoring sensors on a building structure to be predicted, and acquiring settlement values of the monitoring points at regular time by using the settlement deformation monitoring sensors;
step 2: preliminarily determining a fitting curve equation f (t) adopting a higher order polynomial; wherein f (t) is a sedimentation value; t is a time variable; the rest of the fitting curve equation f (t) is a plurality of coefficients to be determined;
step 3: substituting the historical sedimentation values of the monitoring points and the corresponding time variable t thereof into the fitting curve equation f (t) in the step 2 to determine various undetermined coefficients in the fitting curve equation f (t); under the same time variable t, comparing the fitted sedimentation value obtained by using the fitted curve equation f (t) of each coefficient to be determined with the actually measured sedimentation value, and evaluating the effect of the fitted curve according to a preset statistical index;
step 4: repeating the step 2 and the step 3 until a best fit curve function f (t) under the preset statistical index is obtained;
step 5: calculating a first derivative function f '(t) of the best fit curve function f (t) in the step 4 and taking the first derivative function f' (t) as a deformation development trend prediction model;
step 6: determining the time t to be predicted according to engineering requirements;
step 7: substituting the time t to be predicted in the step 6 into the first derivative function f' (t) in the step 5 to obtain the predicted sedimentation change trend of each monitoring point;
step 8: performing first-order differential operation on the predicted sedimentation change trend of each monitoring point in the step 7 to obtain change trend differences between adjacent monitoring points;
step 9: if the variation trend difference calculated in the step 8 exceeds the threshold range, deducing that settlement and deformation of the area where the adjacent monitoring points are located are inconsistent, and the structure has the risk of crack occurrence; if the variation trend difference calculated in the step 8 is within the threshold range, deducing that the soil body of the area where the adjacent monitoring point is located enters the consolidation stage;
step 10: performing curve fitting on the sedimentation values of the same monitoring section where the adjacent monitoring points are located, and preliminarily determining a fitted curve equation g (x) with the sedimentation values and the sedimentation deformation monitoring sensor positions being dependent variables and independent variables respectively; wherein g (x) is a sedimentation value; x is the abscissa of the settlement deformation monitoring sensor; the rest of the fitting curve equation g (x) is a plurality of coefficients to be determined;
step 11: substituting the monitoring point sedimentation value at the latest moment and the monitoring data of the sedimentation deformation monitoring sensor position into a fitting curve equation g (x) in the step 10 to determine each undetermined coefficient in the fitting curve equation g (x), comparing the fitting sedimentation value obtained by using the fitting curve equation g (x) with the determined undetermined coefficients with the actually measured sedimentation value at the same monitoring point, and evaluating the effect of the fitting curve according to a preset statistical index;
step 12: repeating the step 10 and the step 11 until a best fit curve equation g (x) under the preset statistical index is obtained;
step 13: calculating a first derivative function g' (x) of the best fit curve equation g (x) determined in step 12;
step 14: substituting the abscissa of each monitoring point in the step 11 into the first derivative function g' (x) in the step 13, and deducing that the monitoring point is positioned in the maximum bending moment area if the result is within the range from 0 to a set threshold value, wherein the risk of occurrence of cracks exists in a nearby structure.
And 3, determining each undetermined coefficient in the fitting curve equation f (t) through a trust domain or LM fitting algorithm.
The preset statistical index in the step 3 and the step 11 is one of the statistical indexes obtained according to SSE, RMSE, R-Squre.
And step 10, performing curve fitting on the sedimentation values of the same monitoring section, and performing fitting by adopting a 4-order Fourier equation.
The invention has the advantages that:
(1) The invention predicts the sedimentation deformation development trend of the building structure by utilizing the collected deformation monitoring data and by using a mathematical model, and can assist construction organization decision; meanwhile, by evaluating the state of the building structure, the hidden danger of quality and safety can be found in advance and measures can be taken to eliminate the hidden danger. In the full life cycle using stage of the building structure, the monitoring data of key single building or key areas of the building can be analyzed through the method, development trend is deduced, and decision is assisted.
(2) The mathematical model adopted by the invention is obtained by curve fitting the monitoring data, complex boundary conditions are not considered, the parameters of the mathematical model adopt a mature mathematical method to quickly obtain a numerical solution, manual intervention is not needed, and the obtained result is visual and easy to understand.
Drawings
FIG. 1 is a schematic flow diagram of a method for predicting sedimentation deformation of a building structure according to the present invention;
FIG. 2 is a historical dataset of a settlement deformation monitoring sensor according to the present invention;
FIG. 3 is a general form of a predictive equation for each monitoring point in the present invention;
FIG. 4 is a first derivative function f' (t) of a best fit curve function f (t) for each monitoring point in the present invention;
FIG. 5 is a graph showing deformation trend prediction analysis of each monitoring point in the invention;
FIG. 6 is a 5 month 1 day monitoring profile dataset according to the present invention;
FIG. 7 is a graph of a fit for monitoring section settlement deformation in the present invention;
FIG. 8 shows the first derivative values of each monitoring point on day 5 and day 1 in the present invention.
Detailed Description
The features of the present invention and other related features are described in further detail below by way of example in conjunction with the following drawings, to facilitate understanding by those skilled in the art:
examples: as shown in fig. 1-8, the embodiment specifically relates to a building structure settlement deformation prediction method based on monitoring data fitting curve derivative, which mainly comprises the following steps:
step 1, arranging a plurality of monitoring points with settlement deformation monitoring sensors on a building structure to be predicted, and acquiring settlement values of the monitoring points at regular time by using the settlement deformation monitoring sensors;
in this embodiment, taking a high-rise building engineering of 17 floors as an example, 20 settlement deformation monitoring sensors are arranged in a foundation slab, the interval is 1m, data are collected 1 time a day, and in this embodiment, data of 17 days in total from 4 months 15 days to 5 months 1 day are selected to form a historical data set, as shown in fig. 2.
Step 2, preliminarily determining a fitting curve equation f (t) adopting a higher-order polynomial; in this embodiment, the general form of the fitting curve equation is f (t) =p1×t≡3+p2×t≡2+p3×t+p4;
wherein:
f (t) is a sedimentation value;
t is a time variable in days;
p1, p2, p3, p4 are undetermined coefficients.
Step 3, substituting the historical sedimentation values of each monitoring point in the historical data set shown in fig. 2 and the corresponding time variable t thereof into the fitting curve equation f (t) in the step 2, and determining each undetermined coefficient (p 1, p2, p3 and p 4) in the fitting curve equation f (t) of each 20 monitoring points through fitting algorithms such as a trust domain or LM, so as to obtain a determined fitting curve equation f (t), as shown in fig. 3;
under the same time variable t, comparing a fitting sedimentation value obtained by using a fitting curve equation f (t) of each coefficient to be determined with an actual measurement sedimentation value, and evaluating the effect of a fitting curve according to a preset statistical index (SSE, RMSE, R-Squre and the like); the effect evaluation is carried out on the fitting curve equation f (t) of each monitoring point according to the method.
Step 4, repeating the step 2 and the step 3 according to preset statistical indexes such as SSE, RMSE, R-Squre and the like until the fitting effect meets the engineering error progress requirement, and obtaining a best fitting curve function f (t) under the preset statistical indexes; if not, it is considered to fit by using polynomials of other orders instead.
Step 5 the first derivative function f' (t) of the best fit curve function f (t) in step 4 is calculated and used as a deformation development trend prediction model, as shown in fig. 4.
Step 6, determining the time t to be predicted according to engineering requirements, and selecting the time t to be predicted from 5 months, 10 days to 5 months and 15 days according to the deformation development trend prediction model as shown in fig. 4, wherein the corresponding time t is 26, 27, …, 30 and 31.
Step 7, substituting the time t to be predicted in the step 6 into the first derivative function f' (t) in the step 5 to obtain the predicted sedimentation change trend of each monitoring point, as shown in fig. 5.
Step 8, performing first-order differential operation on the predicted sedimentation change trend of each monitoring point in step 7 to obtain the change trend difference between adjacent monitoring points, as shown in fig. 5.
Step 9, if the variation trend difference calculated in the step 8 exceeds a threshold value (assumed to be 1), deducing that settlement deformation of the area where the adjacent monitoring points are located is inconsistent, wherein the positions corresponding to the two monitoring points have the risk of cracking; if the variation trend difference calculated in the step 8 is within the threshold range (assumed to be between 0 and 1), the soil body of the area where the adjacent monitoring points are located is inferred to enter the consolidation stage.
Above step 10, the settlement deformation trend is predicted from the time dimension, but it is also possible that the monitoring point in a certain area is strongly constrained (for example, near the ground beam, the bearing platform, etc.), the trend of the settlement change with time is not obvious, and the data shows a "false consolidation" phenomenon, for example, point 0 in the above example. It is therefore necessary to determine the dangerous area where the crack occurs from the spatial dimension:
and then carrying out curve fitting on the sedimentation values of the same monitoring section where the adjacent monitoring points are located, preliminarily determining a fitting curve equation g (x) with the sedimentation values and the positions of the sedimentation deformation monitoring sensors as dependent variables and independent variables respectively, and fitting the sections formed by the 1 st to 20 th sedimentation deformation monitoring sensors by adopting a 4 th Fourier equation:
g(x) = a0 + a1*cos(x*w) + b1*sin(x*w) + a2*cos(2*x*w) + b2*sin(2*x*w) + a3*cos(3*x*w) + b3*sin(3*x*w) + a4*cos(4*x*w) + b4*sin(4*x*w)
wherein:
g (x) is the sedimentation value;
x is the abscissa of the settlement deformation monitoring sensor; the rest are undetermined coefficients.
Through evaluation of statistical indexes such as SSE, RMSE, R-Squre, the fitting effect of the equation is superior to that of a polynomial.
Step 11, as shown in fig. 6, is a monitoring section data set composed of monitoring points on 1 day of 5 months, and the monitoring data of the sedimentation value and the sedimentation deformation monitoring sensor position of each monitoring point at the latest moment are substituted into a fitting curve equation g (x) in step 10 to determine each undetermined coefficient in the fitting curve equation g (x), so as to obtain each undetermined coefficient shown as follows:
as shown in fig. 7, the fitted curve equation g (x) is:
g(x)=7658+1938*cos(x*0.1574)-14040*sin(x*0.1574)-8872*cos(2*x*0.1574)-2849*sin(2*x*0.1574)-1689*cos(3*x*0.1574)+4187*sin(3*x*0.1574)+766.1*cos(4*x*0.1574)+660.9*sin(4*x*0.1574)
and at the same monitoring point, comparing the fitted sedimentation value obtained by using the fitted curve equation g (x) of each determined coefficient to be determined with the measured sedimentation value, and evaluating the effect of the fitted curve according to a preset statistical index.
Step 10 and step 11 are repeated until the best fit curve equation g (x) under the preset statistical index is obtained.
Step 13, calculating the first derivative function g' (x) of the best fit curve equation g (x) determined in step 12, to obtain:
g'(x)=(5201283*cos((787*x)/1250))/12500-(2242163*cos((787*x)/2500))/2500- 276237*cos((787*x)/5000))/125+(9885507*cos((2361*x)/5000))/5000- (6029207*sin((787*x)/1250))/12500+(1745566*sin((787*x)/2500))/625- (762603*sin((787*x)/5000))/2500 + (3987729*sin((2361*x)/5000))/5000。
step 14, substituting the abscissa of each monitoring point in step 11 into the first derivative function g' (x) in step 13 to obtain the first derivative value of each monitoring point in 5 months and 1 days as shown in fig. 8; the first derivative value obtained is determined, and if the result is within the range from 0 to the set threshold (assumed to be 50), it is inferred that the monitoring point is located in the maximum bending moment region (monitoring points 1 and 16 in fig. 8), and a crack is at risk in the nearby structure.
Claims (3)
1. The building structure settlement deformation prediction method based on the monitored data fitting curve derivative is characterized by comprising the following steps of:
step 1: arranging a plurality of monitoring points with settlement deformation monitoring sensors on a building structure to be predicted, and acquiring settlement values of the monitoring points at regular time by using the settlement deformation monitoring sensors;
step 2: preliminarily determining a fitting curve equation f (t) adopting a higher order polynomial; wherein f (t) is a sedimentation value; t is a time variable; the rest of the fitting curve equation f (t) is a plurality of coefficients to be determined;
step 3: substituting the historical sedimentation values of the monitoring points and the corresponding time variable t thereof into the fitting curve equation f (t) in the step 2 to determine various undetermined coefficients in the fitting curve equation f (t); under the same time variable t, comparing the fitted sedimentation value obtained by using the fitted curve equation f (t) of each coefficient to be determined with the actually measured sedimentation value, and evaluating the effect of the fitted curve according to a preset statistical index;
step 4: repeating the step 2 and the step 3 until a best fit curve function f (t) under the preset statistical index is obtained;
step 5: calculating a first derivative function f '(t) of the best fit curve function f (t) in the step 4 and taking the first derivative function f' (t) as a deformation development trend prediction model;
step 6: determining the time t to be predicted according to engineering requirements;
step 7: substituting the time t to be predicted in the step 6 into the first derivative function f' (t) in the step 5;
step 8: performing first-order differential operation on the predicted sedimentation change trend of each monitoring point in the step 7 to obtain change trend differences between adjacent monitoring points;
step 9: if the variation trend difference calculated in the step 8 exceeds the threshold range, deducing that settlement and deformation of the area where the adjacent monitoring points are located are inconsistent, and the structure has the risk of crack occurrence; if the variation trend difference calculated in the step 8 is within the threshold range, deducing that the soil body of the area where the adjacent monitoring point is located enters the consolidation stage;
step 10: performing curve fitting on the sedimentation values of the same monitoring section, adopting 4-order Fourier equation fitting, and preliminarily determining a fitting curve equation g (x) with the sedimentation values and the sedimentation deformation monitoring sensor positions respectively as dependent variables and independent variables; wherein g (x) is a sedimentation value; x is the abscissa of the settlement deformation monitoring sensor; the rest of the fitting curve equation g (x) is a plurality of coefficients to be determined;
step 11: substituting the monitoring point sedimentation value at the latest moment and the monitoring data of the sedimentation deformation monitoring sensor position into a fitting curve equation g (x) in the step 10 to determine each undetermined coefficient in the fitting curve equation g (x), comparing the fitting sedimentation value obtained by using the fitting curve equation g (x) with the determined undetermined coefficients with the actually measured sedimentation value at the same monitoring point, and evaluating the effect of the fitting curve according to a preset statistical index;
step 12: repeating the step 10 and the step 11 until a best fit curve equation g (x) under the preset statistical index is obtained;
step 13: calculating a first derivative function g' (x) of the best fit curve equation g (x) determined in step 12;
step 14: substituting the abscissa of each monitoring point in the step 11 into the first derivative function g' (x) in the step 13, and deducing that the monitoring point is positioned in the maximum bending moment area if the result is within the range from 0 to a set threshold value, wherein the risk of occurrence of cracks exists in a nearby structure.
2. The method for predicting sedimentation deformation of a building structure based on fitting curve derivatives with monitored data according to claim 1, wherein said step 3 determines each undetermined coefficient in the fitted curve equation f (t) by a trust domain or LM fitting algorithm.
3. The method for predicting sedimentation deformation of a building structure based on fitting curve derivatives with monitored data according to claim 1, wherein the preset statistical index in the step 3 and the step 11 is one of the statistical indexes obtained according to SSE, RMSE, R-Squre.
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