CN116401920A - Method for predicting bearing capacity of stainless steel tube concrete shaft pressure based on extreme gradient algorithm - Google Patents
Method for predicting bearing capacity of stainless steel tube concrete shaft pressure based on extreme gradient algorithm Download PDFInfo
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Abstract
The invention discloses a method for predicting the bearing capacity of a stainless steel tube concrete shaft pressure based on an extreme gradient algorithm, which comprises the following steps: based on mechanical mechanism analysis of the stainless steel tube concrete pressed component, creating data related to the pressed bearing capacity of the round and square cross-section component by using test and numerical simulation results, and dividing a data set into a training set and a testing set by using ten times of cross validation; and respectively establishing extreme gradient lifting regression models of the compressive bearing capacity of the round section and the square section by utilizing the training set, and carrying out prediction iteration on the model by adopting the data set until the network meets the convergence condition. Inputting the test set into a regression model of the bearing capacity under pressure to obtain a predicted value of the bearing capacity under pressure; finally, the prediction precision of the regression model is analyzed by utilizing an error evaluation index, and comparison with an actual bearing capacity test value and an existing related specification calculation value shows that the method can calculate the bearing capacity of the stainless steel tube concrete faster and more accurately, and the prediction result is closer to the actual situation.
Description
Technical Field
The invention relates to the technical field of stainless steel compression detection, in particular to a method for predicting the bearing capacity of a stainless steel tube concrete shaft pressure based on an extreme gradient algorithm.
Background
The stainless steel material has excellent corrosion resistance, durability, fire resistance and fatigue resistance due to the addition of not less than 10.5% of chromium. The stainless steel pipe concrete is formed by pouring the concrete into the stainless steel pipe, and the stainless steel pipe concrete has both excellent mechanical property and excellent durability of the stainless steel, so that the stainless steel pipe concrete has wide application prospect in marine and offshore infrastructures. Stainless steel pipe concrete has been used in many large projects as a primary pressure-bearing structure. However, at present, no design rules and design clauses are provided for the stainless steel pipe concrete, and the prediction method for the compressive load capacity of the stainless steel pipe concrete is not clear and unified. The stainless steel material has obvious nonlinear characteristics and has plasticity far exceeding that of common carbon steel, so that the restraining effect of the stainless steel pipe on core concrete has complexity and obvious difference from a common steel pipe concrete structure. Meanwhile, the factors influencing the bearing capacity of the stainless steel tube concrete structure are more, and the correlation is more complex, so that the method for predicting the bearing capacity of the stainless steel tube concrete structure under pressure is very critical to the safe application of the method in actual engineering.
Disclosure of Invention
In view of the above, the invention aims to provide a method for predicting the axial pressure bearing capacity of stainless steel pipe concrete based on an extreme gradient algorithm, which can accurately, stably and efficiently predict the ultimate bearing capacity of a stainless steel pipe concrete structure under the action of a pressed load and provide a technology and a method for scientifically and rapidly predicting the structural performance of the stainless steel pipe concrete for engineers.
In order to achieve the above purpose, the invention adopts the following technical scheme: the method for predicting the bearing capacity of the stainless steel tube concrete shaft based on the extreme gradient algorithm comprises the following steps:
step 1: obtaining the existing test data of the compressive load capacity of the stainless steel tube concrete, according to a carbon steel tube concrete load capacity calculation formula, combining mechanical mechanism analysis, and solidifying out all parameters related to the compressive limit load capacity of the stainless steel tube concrete member, and obtaining a specific expression of the characteristic influence parameters;
step 2: establishing a finite element model of the stainless steel tube concrete pressed component, and carrying out parameter analysis of the system to obtain numerical simulation data under different parameters;
step 3: fully integrating the finite element data obtained in the step 2 and the test data set in the step 1 to form a database which has comprehensive coverage, reasonable parameter distribution and good generalization capability; taking the characteristic influence parameters as input parameters and the compression limit bearing capacity as output parameters, and respectively establishing a circular section stainless steel tube concrete compression bearing capacity data set and a square section stainless steel tube concrete compression bearing capacity data set;
step 4: determining a correlation coefficient value between a characteristic influence parameter and the compressive load capacity of the stainless steel tube concrete compressive load capacity data set through a Pearson correlation analysis; randomly dividing a data set into a training set and a prediction set according to the proportion of 8:2 by using a ten-time cross validation mode, training a model by using the divided training set, and establishing an extreme gradient lifting model for predicting the compressive bearing capacity of the concrete-filled stainless steel tube;
step 5: inputting the extreme gradient lifting model in the step 4 by adopting a prediction set to carry out prediction iteration until the network meets the convergence condition and the compression bearing capacity prediction precision meets the requirement; and finally outputting the bearing capacity of the stainless steel tube concrete under compression limit to finish prediction.
In a preferred embodiment: the important characteristic influence parameters influencing the compressive bearing capacity of the stainless steel tube concrete in the step 1 are the diameter D of a circular section or the width B of a square section, the wall thickness t, the length l of a component, the elastic modulus E of the stainless steel, the radius i of gyration of the section and the standard value f of the compressive strength of the concrete axle center ck Nominal yield strength sigma 0.2 Constrained effect coefficient xi, regularized slenderness ratio
Component slenderness ratio lambda, circular section diameter-thickness ratio D/t or square section width-thickness ratio B/t, ratio f of compressive strength to yield strength ck /σ 0.2 Dimensionless yield strengthDegree sigma 0.2 /E；
The constraint effect coefficient xi is expressed as follows according to the technical specification of the concrete-filled steel tube structure of Fujian province:
the regularized slenderness ratio
According to the technical specifications of the concrete filled steel tube structure, the expression is as follows:
in a preferred embodiment: the data set constructed in the step 3 is theta= [ theta ] 1 ,θ 2 ,…,θ N ]＝[(X 1 ,Y 1 ,Z 1 ),(X 2 ,Y 2 ,Z 2 ),…,(X N ,Y N ,Z N )]Where (X, Y, Z …) refers to the input parameter set for each group of components, with the training set and the prediction set being randomly generated.
In a preferred embodiment: and 4, training the polar gradient lifting model by using a randomly generated training set, and obtaining a required prediction model.
In a preferred embodiment: inputting the related parameter information into the extreme gradient lifting regression model, accumulating output information of a decision tree in the extreme gradient regression model, and determining the bearing capacity of the stainless steel pipe concrete axial compression member corresponding to the prediction set;
the preset accumulation formula is as follows:
wherein k represents the tree of the decision tree in the extreme gradient lifting regression model, represents the set of all decision trees CART, f 1 (x i ) Representing the decisionOutput information of the tree;
and the extreme gradient lifting model takes a plurality of decision trees as learning units, fits the next decision tree according to the residual error between the output result of the last decision tree and the actual value, and sums the output results of the decision trees to obtain the predicted value of the compressive load capacity of the stainless steel tube concrete.
In a preferred embodiment: the method for predicting the compressive bearing capacity of the stainless steel tube concrete based on the extreme gradient lifting algorithm further comprises the following steps: judging whether the precision of the prediction result of the extreme gradient lifting model reaches the set precision, if so, outputting a prediction value of the compressive bearing capacity of the concrete-filled stainless steel tube; otherwise, modifying the number of decision trees of the extreme gradient lifting model, and re-acquiring the predicted value of the compressive load capacity of the concrete-filled stainless steel tube.
The invention also provides a computer readable storage medium, on which a computer program is stored, which when being executed by a processor, implements the method for predicting the bearing capacity of the stainless steel tube concrete shaft based on the extreme gradient algorithm.
The invention also provides computer equipment, which comprises a memory, a processor and a computer program stored in the memory and executable by the processor, wherein the processor realizes the method for predicting the bearing capacity of the stainless steel tube concrete shaft based on the extreme gradient algorithm when executing the computer program.
Compared with the prior art, the invention has the following beneficial effects: the prediction accuracy is effectively improved, the prediction parameter range can fully cover the extreme conditions in the actual engineering, and the method has important significance for accurately predicting the performance of the stainless steel pipe concrete engineering, guaranteeing the structural safety and avoiding major engineering accidents.
Drawings
FIG. 1 is a flow chart of a preferred embodiment of the present invention;
FIG. 2 is a comparison of stress-strain curves of stainless steel and ordinary steel in finite element modeling according to a preferred embodiment of the present invention;
FIG. 3 is a schematic view showing initial defect distribution of a concrete-filled stainless steel tube member according to a preferred embodiment of the present invention;
FIG. 4 is a graph showing stress-strain relationship of core concrete in a finite element model according to a preferred embodiment of the present invention;
FIG. 5 is a finite element model schematic diagram of a stainless steel reinforced concrete compression member in a preferred embodiment of the invention;
FIG. 6 is a typical finite element parameter analysis of a stainless steel pipe concrete compression member in a preferred embodiment of the invention, wherein (1 a) is the effect of different ζ on the stainless steel pipe concrete compression load versus axial strain curve for a round stainless steel pipe concrete, wherein (1B) is the effect of different ζ on the stainless steel pipe concrete compression load versus axial strain curve for a square stainless steel pipe concrete (D/B=1), wherein (1 c) is the effect of different ζ on the stainless steel pipe concrete compression load versus axial strain curve for a rectangular stainless steel pipe concrete (D/B=1.5), wherein (1D) is the effect of different ζ on the stainless steel pipe concrete compression load versus axial strain curve for a rectangular stainless steel pipe concrete (D/B=2), wherein (2 a) is the effect of different ζ on the stainless steel pipe concrete compression stability coefficient φ -length ratio curve for a round member, wherein (2B) is the effect of different ζ 0.2 on the stainless steel pipe concrete compression stability coefficient φ -length ratio curve for a round member, wherein (2B) is the effect of a 3 on the stainless steel pipe concrete compression stability coefficient of a member cu Influence on the relation of the stress stability coefficient phi-slenderness ratio lambda of stainless steel tube concrete, wherein (3 b) is f for square members cu Influence on the relation of the stress stability coefficient phi-slenderness ratio lambda of stainless steel tube concrete, wherein (4 a) is alpha with respect to a circular member s Influence on the relation of the stress stability coefficient phi-slenderness ratio lambda of stainless steel tube concrete, wherein (4 b) is alpha with respect to square components s Influence on a relation curve of a compressive stability coefficient phi-slenderness ratio lambda of the stainless steel tube concrete;
FIG. 7 is a specific procedure of a method for predicting and cross-verifying extreme gradient lifting of compressive load of concrete-filled stainless steel tubes in accordance with a preferred embodiment of the present invention;
FIG. 8 is a root mean square error RMSE learning curve for each time period of the extreme gradient lifting model over the training and testing data set in accordance with the preferred embodiment of the invention;
FIG. 9 is a plot of predicted values of sample data for a concrete-filled stainless steel tube load-bearing portion based on an extreme gradient lifting algorithm in accordance with a preferred embodiment of the present invention;
fig. 10 is a graph showing a discrete distribution diagram of a predicted result and a normalized calculated value of a concrete-filled stainless steel tube based on an extreme gradient lifting algorithm according to a preferred embodiment of the present invention, wherein (a) is a square screenshot and (b) is a circular screenshot.
Detailed Description
The invention will be further described with reference to the accompanying drawings and examples.
It should be noted that the following detailed description is illustrative and is intended to provide further explanation of the present application. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs.
It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of example embodiments in accordance with the present application; as used herein, the singular is also intended to include the plural unless the context clearly indicates otherwise, and furthermore, it is to be understood that the terms "comprises" and/or "comprising" when used in this specification are taken to specify the presence of stated features, steps, operations, devices, components, and/or combinations thereof.
The method for predicting the bearing capacity of the stainless steel tube concrete shaft based on the extreme gradient algorithm comprises the following steps:
step 1: the existing test data of the compressive load capacity of the stainless steel tube concrete are obtained from the prior literature. And referring to a common carbon steel tube concrete bearing capacity calculation formula provided in the existing related design specification, combining mechanical mechanism analysis, solidifying out all parameters related to the compressive limit bearing capacity of the stainless steel tube concrete member, and obtaining a specific expression of the characteristic influence parameters.
Step 2: and establishing a finite element model of the stainless steel tube concrete pressed member, and carrying out parameter analysis of the system to obtain numerical simulation data under different parameters. The finite element simulation data can verify whether the parameters determined by the test data are comprehensive and accurate or not, and can effectively enlarge the parameter range of the database, so that the parameter distribution is uniform, the coverage range is comprehensive, and the generalization capability of the database is improved;
step 3: and (3) fully integrating the finite element data obtained in the step (2) and the test data set in the step (1) to form a database which has comprehensive coverage, reasonable parameter distribution and good generalization capability. Taking the characteristic influence parameters as input parameters and the compression limit bearing capacity as output parameters, and respectively establishing a circular section stainless steel tube concrete compression bearing capacity data set and a square section stainless steel tube concrete compression bearing capacity data set;
step 4: determining a correlation coefficient value between a characteristic influence parameter and the compressive load capacity of the stainless steel tube concrete compressive load capacity data set through a Pearson correlation analysis; randomly dividing a data set into a training set and a prediction set according to the proportion of 8:2 by using a ten-time cross validation mode, training a model by using the divided training set, and establishing an extreme gradient lifting model for predicting the compressive bearing capacity of the concrete-filled stainless steel tube;
step 5: and (3) inputting the extreme gradient lifting model in the step (4) by adopting a prediction set to carry out prediction iteration until the network meets the convergence condition and the compression bearing capacity prediction precision meets the requirement. And finally outputting the bearing capacity of the stainless steel tube concrete under compression limit to finish prediction.
The test data of the compressive bearing capacity of the stainless steel tube concrete collected in the step 1 are derived from test documents which are reported in the open at home and abroad in the past; the referenced prior related design specifications are specifically derived from four common carbon steel pipe concrete specifications commonly used at present: U.S. standard (ANSI/AISC 360-16), european standard EC4 (2004) Specification, chinese concrete filled Steel tube construction Specification (GB 50936-2014), fujian province concrete filled Steel tube construction Specification (DBJ/T13-51-2020).
Further, the characteristic parameters affecting the compression bearing capacity of the stainless steel tube concrete in the step 1 are respectively as follows:circular section diameter D, square section width B, stainless steel pipe wall thickness t, component length l, stainless steel elastic modulus E, section radius of gyration i and concrete axle center compressive strength standard value f ck Nominal yield strength sigma of stainless steel 0.2 Constrained effect coefficient xi, regularized slenderness ratio
Component slenderness ratio lambda, circular section diameter-thickness ratio D/t (square section width-thickness ratio B/t), ratio f of concrete compressive strength to stainless steel nominal yield strength ck /σ 0.2 Dimensionless nominal yield strength sigma 0.2 /E；
Wherein, the constraint effect coefficient xi is corrected by referring to the expression of the common carbon steel pipe concrete in the technical regulations (DBJ/T13-51-2020) of the steel pipe concrete structure of Fujian province:
the regularized slenderness ratio
The expression of (2) is:
in the step 2, since the conventional test work performed on the stainless steel pipe concrete is insufficient, the pressure bearing capacity test data of the collected stainless steel pipe concrete is less, the parameter distribution is uneven, and the parameter range required by the actual engineering is difficult to cover. If the polar gradient lifting model is trained by using only the data, inaccurate training results and poor generalization performance can be caused by fewer database samples, uneven distribution and comprehensive parameters. Therefore, the invention utilizes the finite element model verified by the test to carry out the expansion parameter analysis on the database sample so as to obtain a complete and high-applicability data set, ensures more reasonable data distribution, provides guarantee for the prediction accuracy of the extreme gradient lifting model, and is beneficial to training the prediction model which meets the actual engineering requirements.
1) And (6) building a stainless steel tube concrete compression database. Basic parameters for finishing the test data of the compressive load capacity of the stainless steel tube concrete obtained in the prior literature are collected, and a stainless steel tube concrete compressive test data set is constructed. In the embodiment of the invention, 189 test data of the compressive load capacity of the stainless steel tube concrete are collected, and the basic parameter ranges of the test data are shown in table 1.
Table 1 table of basic parameters of test data
Because the cost of the stainless steel pipe concrete physical experiment is higher, the test data which are finished at present are less, and if the extreme gradient lifting model is trained by using the data, the training result is inaccurate due to insufficient database samples, so that the generalization performance of the model is poor. Therefore, the invention utilizes the finite element model verified by the test to carry out the expansion parameter analysis on the database sample so as to obtain a complete and high-applicability data set, ensures more reasonable data distribution, provides guarantee for the prediction accuracy of the extreme gradient lifting model, and is beneficial to training the prediction model which meets the actual engineering requirements.
The concrete steps of the construction of the stainless steel tube concrete pressed finite element model are as follows:
(1) The stainless steel tube adopts a four-node complete integration-format shell unit (S4), and in order to meet certain calculation accuracy, simpson integration with 9 integration points is adopted in the thickness direction of the shell unit. The cover plate and the core concrete are three-dimensional entity units (C3D 8R) adopting eight-node reduced integral formats. And adopting a structured grid division technology provided by finite element software to carry out unit division on the finite element model.
(2) The material structure of the concrete considers the restraint effect of the stainless steel pipe, and particularly has a strong restraint effect on core concrete which can still be maintained due to the excellent plasticity of the stainless steel in the later loading stage. The influence of residual stress is not considered in the finite element model of the stainless steel member and the stainless steel tube concrete member.
Because of the addition of alloy elements, the stress-strain relationship of the stainless steel material is different from that of the common carbon steel, and the stress-strain relationship curve of the common carbon steel has obvious yield points and yield platforms; the stress-strain curve of the stainless steel material shows remarkable nonlinear characteristics at the initial stage of loading, the proportion limit is low, and the stress-strain curve of the stainless steel and the common steel is compared as shown in fig. 2. The stress-strain relation model expression of the stainless steel in the invention is as follows:
when sigma is less than or equal to sigma 0.2 When (1):
when sigma > sigma 0.2 When (1):
wherein:
wherein sigma 0.01 For a residual strain of 0.01% stress, a unified parameter value of the type of stainless steel commonly used in building structures is adopted, namely n=5.4 when the austenitic stainless steel is pulled and n=4.3 when the austenitic stainless steel is pressed.
The stainless steel tube in the finite element model adopts an isotropic elastic-plastic model, and meets the VonMIses yield criterion. Since the model requires the true stress-true plastic strain relation of the input material, the sigma-epsilon relation calculated by the formulas (3) and (4) needs to be converted into the true stress-true plastic strain relation, i.e., sigma true ＝σ(1+ε)，ε p1 true ＝ln(1+ε)-σ true /E s Wherein sigma true And epsilon p1 true True stress and true plastic strain, respectively.
The stainless steel tube of the invention considers initial defects, namely, the mode is subjected to elastic buckling mode analysis before nonlinear analysis, and then a first-order buckling mode is input as the initial defects of the component during nonlinear analysis, as shown in fig. 3, the initial defects can be expressed by the following expression:
wherein a is the plate width; l is the length of the plate; m and n are the half wave numbers of the plate buckling in the x and y directions, respectively, for example, when the aspect ratio is 1:3, m and n can be respectively 1 and 3.
For stainless steel pipes
Wherein, the liquid crystal display device comprises a liquid crystal display device,
is the elastic critical buckling stress.
The core concrete adopts a plastic damage model, the stress-strain relation model in a pressed state adopts a core concrete model with a steel pipe constraint effect, the stress-strain relation curve is shown as figure 4, and the expression is as follows:
wherein:
σ o ＝f′ c ；ε o ＝ε c +800×ξ 0.2 ×10 -6 ；ε c ＝(1300+12.5f′ c )×10 -6 ；
in the invention, parameters of the elastic stage of the concrete in the plastic damage model are determined according to ACI318-05 (2005), and the elastic modulus value of the core concrete is E c ＝4700(f c ′) 1/2 Wherein f c ' is the compressive strength of concrete cylinder, in N/mm 2 In units, the poisson ratio of the concrete in the elastic phase is 0.2.
For constitutive relation of the tensile concrete, the tensile softening performance of the concrete, namely the stress-fracture energy relation, defined by an energy failure criterion is adopted. Tensile properties of concrete using breaking energy (G f ) Description, for concrete grade C20, G f Taking 40N/m, and for concrete grade of C40 and G f Taking 120N/m, and calculating other intermediate grades according to linear interpolation. The concrete cracking stress is calculated by adopting a concrete tensile calculation formula, namely:
σ to ＝0.26×(1.25f′ c ) 2/3 (6)
(3) The interface model between the stainless steel pipe and the core concrete consists of bonding slip in the tangential direction and contact in the normal direction of the interface. The stainless steel pipe and core concrete normal contact model is simulated by using Hard contact (Hard), namely, the pressure perpendicular to the section can be completely transmitted between interfaces, and the stainless steel pipe and the concrete are allowed to separate in the loading process, and the expression is as follows:
wherein F is N Is the cell contact force; σ is the cell contact compressive stress; a is the normal cell area of the cell compressive stress.
The tangential contact model adopts a coulomb Friction (Friction) model, the interface can transmit shear stress until the shear stress reaches a critical value, the relative sliding is generated between the interfaces, and the Friction coefficient mu of the interface is 0.25.
(4) The component adopts boundary conditions that one end is fixed and the other end is free, the upper cover plate and the lower cover plate are respectively coupled with reference points (RP 1 and RP 2) during modeling, and boundary and loading conditions are set for the reference points, namely RP1 constrains X, Y and displacement in the Z axis direction, RP2 constrains displacement in the X axis direction and the Y axis direction, and rotation is allowed to occur. And (3) carrying out displacement loading on the Z-axis direction of RP2 during calculation.
(5) Before grid division, the grid division density meeting the precision is determined, and then the finite element model is subjected to unit division by adopting a structured grid division technology provided by finite element software. And (3) assembling the rigidity matrix of each unit into a total rigidity matrix, then combining the displacement matrix and the load matrix, and solving a nonlinear equation set by adopting a Newton Lapherson method to obtain the mechanical response of the stainless steel pipe concrete member under the action of compression.
(6) And carrying out parameter analysis of the system on mechanical behaviors of the component under various parameters by utilizing a finite element model. The range of parameter analysis is: stainless steel nominal yield strength (180-900 MPa), concrete cube compressive strength (30-150 MPa), section steel content (0.02-2), slenderness ratio (10-200) and the like.
A schematic diagram of the established stainless steel tube concrete finite element axial compression model is shown in FIG. 5.
Test data are used to verify the reliability and rationality of the finite element model. The test verification results of the finite element simulation of the compressive load capacity of the stainless steel tube concrete are shown in tables 2 and 3.
Table 2 table of results of finite element simulation verification of circular cross section
Table 3 table of results of finite element simulation verification of square cross section
The established finite element can simulate the actual working condition well through verification, 1200 groups of simulation data are calculated, and the parameter ranges are as follows: f (f) cu ＝30～150MPa、σ 0.2 ＝180～900MPa、λ＝10～200、α s =0.02 to 2.0. Typical finite element parameter analysis results are shown in fig. 6. And carrying out parameter expansion on the collected test results by using a finite element model, randomly combining 1200 groups of finite element simulation results with 189 groups of collected test results, and establishing a stainless steel tube concrete compression bearing capacity database.
2) And (3) referring to the definition and sources of parameters in the compression bearing capacity calculation formula provided in the conventional common steel tube concrete design specification, and finishing all parameters related to the compression bearing capacity. Determining characteristic parameters affecting the bearing capacity of the stainless steel tube concrete compression member: circular section diameter D (square section width B), wall thickness t, component length l, stainless steel elastic modulus E, section radius of gyration i and concrete axle compression strength standard value f ck Nominal yield strength sigma 0.2 . In order to achieve more accurate and stable prediction precision, seven dimensionless factors are added on the basis of the above influencing factors: constrained effect coefficient ζ, regularized slenderness ratio
Component slenderness ratio lambda, circular section diameter-thickness ratio D/t (square section width-thickness ratio B/t), ratio f of compressive strength to yield strength ck /σ 0.2 Dimensionless yield strength sigma 0.2 /E；
And taking the characteristic parameters affecting the bearing capacity of the stainless steel tube concrete compression member as input parameters and the ultimate bearing capacity of the member as output parameters to construct a data set. Wherein the constructed data set is theta= [ theta ] 1 ,θ 2 ,…,θ N ]＝[(X 1 ,Y 1 ,Z 1 ),(X 2 ,Y 2 ,Z 2 ),…,(X N ,Y N ,Z N )]Where (X, Y, Z …) refers to the input parameter set for each group of components.
3) Calculating a correlation coefficient between a characteristic parameter affecting the bearing capacity of the stainless steel tube concrete bearing member and the bearing capacity under pressure according to a Pearson correlation coefficient formula, wherein the Pearson correlation coefficient expression is as follows:
wherein P is ij A correlation coefficient between the ith characteristic parameter and the jth characteristic parameter; x is X i And X j Vectors of the ith characteristic parameter and the jth characteristic parameter respectively; the pearson correlation coefficient varies from-1 to +1, 0 representing no correlation, and-1/+1 representing an exact negative/positive linear relationship.
The correlation coefficient values of the characteristic parameters affecting the bearing capacity of the concrete filled stainless steel tube compression member calculated using the pearson correlation coefficient formula are shown in table 4. Since the correlation between the characteristic parameters of the bearing capacity of the stainless steel tube concrete compression member and the bearing capacity is studied intensively here, only absolute values of pearson correlation coefficients between the respective parameters and the bearing capacity are listed.
TABLE 4 Pelson correlation between ultimate bearing capacity and characteristic parameters of stainless steel concrete filled steel tube pressed members
4) Dividing the data set into a training set and a prediction set according to a set proportion of 8:2, and simultaneously, in order to prevent over fitting, resampling the data set by using a ten-time cross-validation verification mode, and training an extreme gradient lifting model by using the training set; the specific flow of the ten-fold cross-validation method is shown in fig. 7: dividing the samples into 10 subsets with equal size, taking one sub-sample as a training set and the rest sub-samples as test sets, and repeating the process for several times until all the samples are tested once;
5) The extreme gradient lifting model uses a decision tree as a basic learning unit, and a ten-time cross validation method is utilized to iteratively establish the decision tree to form the extreme gradient lifting model. The method comprises the steps that a stainless steel tube concrete compression bearing capacity prediction device establishes a first decision tree based on parameter information and limit bearing capacity information, calculates residual errors between a predicted value and a true value, and establishes a later decision tree based on the residual errors output by the former decision tree; and selecting the iteration number corresponding to the minimum residual error as a target iteration number within the preset iteration number, and determining the number of the decision trees based on the target iteration number so as to form an extreme gradient lifting regression model. The method comprises the following specific steps:
setting data sets
The loss function of the learning unit of the extreme gradient lifting model is that
Traversing the iteration times t and the number k of the decision trees in a set data set, verifying the precision, and selecting the iteration times t with the highest precision and the number k of the decision trees as the extreme gradient lifting model parameters; wherein x is i Is a feature vector, n is the number of data set samples, y i For actually outputting the result, < > for>
Outputting a result for the extreme gradient lifting model;
obtaining the simulation predicted value of the t-th time of the extreme gradient lifting model in the following way
Wherein the method comprises the steps of
Carry out the extreme gradientRaising the output result of the model t-1 times, f t (x i ) Outputting a result for the t-th iteration of the decision tree;
the training data set is randomly provided with a plurality of subsets K which are put back and extracted, each subset generates a decision tree, each decision tree is trained, and residual errors are obtained
The training loss function is minimized as follows:
wherein γ is a regularized term coefficient;
summing the prediction results of the decision trees to obtain a predicted value of the bearing capacity under pressure:
wherein f k Is the prediction result of a single decision tree, Φ is the set of all decision trees CART. Carrying out bearing capacity prediction on a single subset by utilizing decision trees, and obtaining a bearing capacity predicted value with higher accuracy by averaging the predicted results of the decision trees;
6) And inputting the trained extreme gradient lifting model into the divided prediction set to predict, stopping when the prediction precision of the bearing capacity meets the requirement, and outputting the bearing capacity of the stainless steel tube concrete pressed member to complete the prediction. And if the predicted result does not meet the precision requirement, modifying the number of decision trees of the extreme gradient lifting model, and re-acquiring the predicted value of the compressive bearing capacity of the stainless steel tube concrete. The predicted value is more accurate and stable through iterative optimization processes of feedback, model parameter improvement, retraining and result output until the precision requirement is met.
When the extreme gradient lifting model is trained on the training data set and the test data set, the performance of the model needs to be evaluated for each iteration of the extreme gradient lifting model, and the result is drawn into a learning curve, and the learning curve can be used for evaluating the prediction effect of the extreme gradient lifting model, so that the model can be optimized to improve the prediction performance. The root mean square error RMSE learning curve of the extreme gradient lifting model at each period on the training and testing data set in the embodiment of the present invention is shown in fig. 8; in this example, to prevent model overfitting, the polar gradient lifting model is applied with an early_stop_rounds=10 parameter at the fit stage.
7) The line graph of the partial prediction sample data and the test sample data of the bearing capacity of the stainless steel tube concrete pressed component in the embodiment of the invention is shown in fig. 9, and the prediction sample data and the test sample data are quite identical from fig. 9, which shows that the extreme gradient lifting model has better prediction effect on the bearing capacity of the stainless steel tube concrete pressed component; the prediction results of the compressive load capacity of the stainless steel tube concrete based on the extreme gradient lifting model are shown in table 5, and as can be seen from the error indexes of the prediction results of table 5, the prediction accuracy of the compressive load capacity of the stainless steel tube concrete based on the extreme gradient lifting model in the embodiment of the invention is higher, and the prediction performance of the extreme gradient lifting model is better.
The error index is an average value ave of the ratio of the predicted value to the test value, a standard deviation std of the ratio of the predicted value to the test value, and a root mean square error RMSE between the predicted value and the test value, and the formulas are respectively as follows:
wherein n is the total number of test data, χ pi And χ (x) ti The predicted and experimental values of the load bearing capacity (unit: kN) are given respectively.
TABLE 5 prediction results of compressive load capacity of concrete-filled stainless steel tube based on extreme gradient lifting model
8) The embodiment of the invention obtains a standard formula calculation value corresponding to each sample by utilizing formulas in four common carbon steel pipe concrete standards (American standard (ANSI/AISC 360-16), european standard EC4 (2004) standard, chinese steel pipe concrete structure technical specification (GB 50936-2014) and Fujian province steel pipe concrete structure technical specification (DBJ/T13-51-2020)) which are commonly used at present, and carries out error analysis on the standard formula calculation value and a predicted value of the corresponding sample, wherein the error analysis result is shown in Table 6. The average value, standard deviation and variance respectively represent the average value, standard deviation and variance of the ratio of each sample predicted value and the corresponding standard calculated value; the coefficient of variation represents the ratio of the standard deviation to the average value. From the view of the variation coefficient in table 6, the prediction accuracy of the extreme gradient lifting model adopted in the embodiment of the invention is obviously better than the standard design standard; from the average value, the predicted value and the test value of the extreme gradient lifting model adopted by the embodiment of the invention are more consistent than the calculated value and the test value of the standard formula. The extreme gradient lifting model adopted by the embodiment of the invention has good prediction performance, and can accurately predict the compression bearing capacity of the stainless steel tube concrete member.
TABLE 6 error analysis results of extreme gradient lifting model predictive value and four canonical formula calculation values
Fig. 10 shows a discrete distribution diagram between a predicted value and a test value of an extreme gradient lifting model and a discrete distribution diagram between a calculated value and a test value of the existing standard respectively, and it can be seen from fig. 10 that the prediction accuracy and the matching degree of the extreme gradient lifting model are obviously better than those of the design standard, which means that the extreme gradient lifting model adopted in the embodiment of the invention can more accurately predict the compression bearing capacity of the stainless steel pipe concrete member.
In summary, the invention provides the method for predicting the extreme gradient lifting of the compressive bearing capacity of the stainless steel tube concrete, and the calculation result shows that the method effectively improves the accuracy, the universality and the reliability of the design work, and can calculate the bearing capacity of the stainless steel tube concrete faster and more stably. With the increase of test data and the expansion of test parameter range, a more complete and wider extreme gradient lifting prediction system can be established, and the prediction precision of the model is improved, so that the method is popularized and applied in actual engineering.
The invention also provides a computer readable storage medium, on which a computer program is stored, which when being executed by a processor, realizes the steps of the method for predicting the stainless steel tube concrete bearing capacity index based on the extreme gradient lifting algorithm.
The invention also provides computer equipment, which comprises a memory, a processor and a computer program stored in the memory and executable by the processor, wherein the processor realizes the steps of the method for predicting the compressive load capacity of the stainless steel tube concrete based on the extreme gradient lifting algorithm when executing the computer program.
The present invention may be implemented in whole or in part by a computer program which, when executed by a processor, performs the steps of the various method embodiments described above, and which may be embodied in a computer readable storage medium. The present invention may take the form of a computer program product embodied on one or more storage media (including, but not limited to, magnetic disk storage, CD-ROM, optical storage, etc.) having program code embodied therein. Wherein the computer program comprises computer program code which may be in source code form, object code form, executable file or some intermediate form etc. Computer-readable storage media include both non-transitory and non-transitory, removable and non-removable media, and information storage may be implemented by any method or technology. The information may be computer readable instructions, data structures, modules of a program, or other data.
The above embodiments are only for illustrating the technical solution of the present invention, and are not limiting. Although the invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: other examples can still be carried out by using the technical solutions described in the foregoing examples or equivalent substitutions can be made on some technical features thereof, and these modifications or substitutions do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the examples of the present invention.
Claims (8)
1. The method for predicting the bearing capacity of the stainless steel tube concrete shaft based on the extreme gradient algorithm is characterized by comprising the following steps:
step 1: obtaining the existing test data of the compressive load capacity of the stainless steel tube concrete, according to a carbon steel tube concrete load capacity calculation formula, combining mechanical mechanism analysis, and solidifying out all parameters related to the compressive limit load capacity of the stainless steel tube concrete member, and obtaining a specific expression of the characteristic influence parameters;
step 2: establishing a finite element model of the stainless steel tube concrete pressed component, and carrying out parameter analysis of the system to obtain numerical simulation data under different parameters;
step 3: fully integrating the finite element data obtained in the step 2 and the test data set in the step 1 to form a database which has comprehensive coverage, reasonable parameter distribution and good generalization capability; taking the characteristic influence parameters as input parameters and the compression limit bearing capacity as output parameters, and respectively establishing a circular section stainless steel tube concrete compression bearing capacity data set and a square section stainless steel tube concrete compression bearing capacity data set;
step 4: determining a correlation coefficient value between a characteristic influence parameter and the compressive load capacity of the stainless steel tube concrete compressive load capacity data set through a Pearson correlation analysis; randomly dividing a data set into a training set and a prediction set according to the proportion of 8:2 by using a ten-time cross validation mode, training a model by using the divided training set, and establishing an extreme gradient lifting model for predicting the compressive bearing capacity of the concrete-filled stainless steel tube;
step 5: inputting the extreme gradient lifting model in the step 4 by adopting a prediction set to carry out prediction iteration until the network meets the convergence condition and the compression bearing capacity prediction precision meets the requirement; and finally outputting the bearing capacity of the stainless steel tube concrete under compression limit to finish prediction.
2. The method for predicting the axial compressive bearing capacity of the stainless steel tube concrete based on the extreme gradient algorithm according to claim 1, wherein important characteristic influence parameters influencing the compressive bearing capacity of the stainless steel tube concrete in the step 1 are a circular section diameter D or a square section width B, a wall thickness t, a component length l, a stainless steel elastic modulus E, a section turning radius i and a concrete axial compressive strength standard value f ck Nominal yield strength sigma 0.2 Constrained effect coefficient xi, regularized slenderness ratio
Component slenderness ratio lambda, circular section diameter-thickness ratio D/t or square section width-thickness ratio B/t, ratio f of compressive strength to yield strength ck /σ 0.2 Dimensionless yield strength sigma 0.2 /E；
The constraint effect coefficient xi is expressed as follows according to the technical specification of the concrete-filled steel tube structure of Fujian province:
the regularized slenderness ratio
According to the technical specifications of the concrete filled steel tube structure, the expression is as follows:
3. the method for predicting the axial bearing capacity of the concrete-filled stainless steel tube based on the extreme gradient algorithm according to claim 1, wherein the data set constructed in the step 3 is θ= [ θ ] 1 ,θ 2 ,…,θ N ]＝[(X 1 ,Y 1 ,Z 1 ),(X 2 ,Y 2 ,Z 2 ),…,(X N ,Y N ,Z N )]Where (X, Y, Z …) refers to the input parameter set for each group of components, with the training set and the prediction set being randomly generated.
4. The method for predicting the bearing capacity of the stainless steel tube concrete shaft based on the extreme gradient algorithm, which is disclosed by claim 1, is characterized in that: and 4, training the polar gradient lifting model by using a randomly generated training set, and obtaining a required prediction model.
5. The method for predicting the bearing capacity of the concrete-filled stainless steel tube shaft based on the extreme gradient algorithm according to claim 1, wherein the related parameter information is input into the extreme gradient lifting regression model, output information of decision trees in the extreme gradient regression model is accumulated, and the bearing capacity of the concrete-filled stainless steel tube shaft corresponding to the prediction set is determined;
the preset accumulation formula is as follows:
wherein k represents the tree of the decision tree in the extreme gradient lifting regression model, represents the set of all decision trees CART, f 1 (x i ) Output information representing the decision tree;
and the extreme gradient lifting model takes a plurality of decision trees as learning units, fits the next decision tree according to the residual error between the output result of the last decision tree and the actual value, and sums the output results of the decision trees to obtain the predicted value of the compressive load capacity of the stainless steel tube concrete.
6. The method for predicting the bearing capacity of the stainless steel tube concrete shaft based on the extreme gradient algorithm, which is disclosed by claim 5, is characterized in that: the method for predicting the compressive bearing capacity of the stainless steel tube concrete based on the extreme gradient lifting algorithm further comprises the following steps: judging whether the precision of the prediction result of the extreme gradient lifting model reaches the set precision, if so, outputting a prediction value of the compressive bearing capacity of the concrete-filled stainless steel tube; otherwise, modifying the number of decision trees of the extreme gradient lifting model, and re-acquiring the predicted value of the compressive load capacity of the concrete-filled stainless steel tube.
7. A computer-readable storage medium having stored thereon a computer program, characterized by: the computer program, when executed by a processor, implements the method for predicting the bearing capacity of the stainless steel tube concrete shaft based on the extreme gradient algorithm.
8. A computer device, characterized by: the method comprises a memory, a processor and a computer program stored in the memory and executable by the processor, wherein the processor realizes the method for predicting the bearing capacity of the stainless steel tube concrete shaft based on the extreme gradient algorithm when executing the computer program.
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