Failure discrimination, reliability analysis and design method of concrete filled steel tube member

Abstract

The invention discloses a failure discrimination, reliability analysis and design method of a concrete-filled steel tube member, and belongs to the field of anti-collision design of the concrete-filled steel tube member. The method comprises the following steps: collecting impact samples of the concrete-filled steel tube member to obtain an impact sample set; based on the impact sample set, training a BP neural network to obtain a maximum deflection prediction model used for predicting maximum deflection information; acquiring a to-be-tested impact sample, and performing deflection prediction on the to-be-tested impact sample based on the maximum deflection prediction model to obtain maximum deflection information of the to-be-tested impact sample; according to the maximum deflection information of the to-be-detected impact sample, calculating a near-end support section corner, and according to the near-end support section corner and based on the set near-end support section corner threshold value of each failure level, determining the damage level of the concrete-filled steel tube member under the impact effect, and completing failure judgment. The method solves the problems that an existing method is tedious in program, and failure level judgment and reliability evaluation cannot be carried out.

Description

Technical Field

[0001] The present invention belongs to the field of anti-collision design of steel tube concrete components, and in particular relates to a failure judgment, reliability analysis and design method of steel tube concrete components. Background Art

[0002] Thanks to the synergistic effect of the steel tube and core concrete, concrete-filled steel tube (CFST) components offer advantages such as high bearing capacity, light weight, and excellent ductility. They are widely used in civil engineering structures such as submarine pipelines, building garages, overpass columns, airport terminals, and high-speed rail stations. These structures are subject to impact loads during their design lifespans. For example, buildings in mountainous areas are vulnerable to natural disasters such as debris flows and rockfalls, inland waterway bridge piers are subject to ship impacts, and high-speed rail station frame columns are subject to unexpected train derailments. Current structural design codes lack comprehensive provisions for incidental loads such as impact loads, posing a challenge for structural engineers in appropriately designing and enhancing the impact resistance of structures.

[0003] Impact loading scene Figure 1 As shown in the figure, an impact body with a mass of M and an initial velocity of V hits the CFST column laterally. The distance between the impact point and the proximal support and the clear span are l and L respectively. The impact position P is defined as the ratio of l and L. The outer diameter of the cross section is D, and the thickness, yield strength, and elastic modulus of the steel pipe are t, f respectively. y 、E s , the compressive strength of concrete cube is f cu The time history curve of the deflection δ at the impact point under the impact of the mass block includes a rising stage and a residual stage, where δ max is the maximum deflection. Figure 2 As shown in Figure 2, experimental results indicate that CFST columns experience bending failure under lateral impact. This failure can be categorized by degree of damage as overall bending deformation (no cracking in the cross section), cracking (bending cracks that do not penetrate the entire cross section), and fracture (cracks that penetrate the entire cross section). Severe impact damage to CFST columns results in a significant loss of axial bearing capacity, leading to the progressive collapse of the entire structure. Therefore, identifying CFST failure under impact is crucial for ensuring structural safety and guiding engineering design. While existing research has qualitatively analyzed the dynamic impact response of CFST using experiments and finite element methods, precise identification of CFST failure levels has yet to be reported.

[0004] For the bending failure of concrete-filled steel tubes (CFST) under impact, the deflection at the impact point can be used to macroscopically characterize the degree of damage to the component. The mass-spring equivalent two-degree-of-freedom model is usually used to solve the lateral deflection, such as Figure 3As shown in Figure 1, the impact body and the beam are regarded as two mass blocks, thus simplifying the impact system into a two-degree-of-freedom motion system, where the impact body is block 1, the impact point is block 2, m1 and V are the mass and initial velocity of the impact body, m2 is the participating mass of the CFST component, c1 and k1 are the local contact damping and local compression stiffness of the impact body and the component, respectively, c2 and k2 are the component recovery damping and overall deformation stiffness, respectively, and the system motion equation is:

[0005]

[0006] in, and are the velocity and acceleration of the impact body, and are the velocity and acceleration of the beam impact point, respectively. After determining the parameters m1, V, c1, k1, m2, c2, and k2, the system motion equation is iteratively solved by the central difference method to obtain the maximum deflection δ of the impact point. max .

[0007] The disadvantages of the above method are:

[0008] (1) The solution procedure is tedious and complicated.

[0009] The parameters m1, V, c1, k1, m2, c2, and k2 must be determined first. In particular, establishing the local compression stiffness k1 and the global deformation stiffness k2 requires considering the confining pressure effect of the steel tube, the material hardening caused by the strain rate effect under dynamic loads, the change in beam mass due to stress wave propagation, and the elastic-plastic properties of the concrete. Solving these parameters is extremely complex.

[0010] (2) Calculations must be completed using a computer.

[0011] The system's motion equations are a set of second-order differential equations. The mathematical analytical solution cannot be obtained directly by solving the equations. Instead, the numerical solution must be obtained through multiple iterations of the difference method using computer programming, which is not conducive to on-site operation by engineers.

[0012] (3) Failure to identify failure levels and conduct reliability assessment.

[0013] The maximum deflection obtained through the two-degree-of-freedom method cannot accurately classify the CFST failure level; due to the random distribution of material properties and geometric dimensions in the real world, the probabilistic analysis of CFST damage failure cannot be performed. Summary of the Invention

[0014] In view of the above-mentioned deficiencies in the prior art, the present invention provides a method for failure identification, reliability analysis and design of steel tube concrete components, which solves the problem that the existing methods are cumbersome and fail to identify failure levels and perform reliability assessment.

[0015] In order to achieve the above-mentioned purpose, the present invention adopts the following technical solution: a failure determination method for concrete-filled steel tube components, comprising:

[0016] Impact samples of steel tube concrete components are collected to obtain an impact sample set; each impact sample includes the impact load parameters, component size parameters, material parameters, boundary conditions and maximum deflection information of the component;

[0017] Based on the impact sample set, the BP neural network is trained to obtain the maximum deflection prediction model based on the constructed impact load parameters, component size parameters, material parameters and boundary conditions to predict the maximum deflection information;

[0018] Obtaining an impact sample to be tested, performing deflection prediction on the impact sample to be tested based on a maximum deflection prediction model, and obtaining maximum deflection information of the impact sample to be tested;

[0019] The proximal support section rotation angle is calculated based on the maximum deflection information of the impact sample to be tested. Based on the proximal support section rotation angle and the set proximal support section rotation angle thresholds for each failure level, the damage level of the steel tube concrete component under impact is determined to complete the failure judgment.

[0020] The beneficial effects of the present invention are as follows: based on machine learning, a simplified formula for predicting the deflection of CFST subjected to lateral impact is proposed. This formula does not rely on an in-depth understanding of the dynamic response principle, and does not need to consider physical phenomena such as complex material constitutive properties, steel pipe confining pressure, and stress wave propagation, which significantly improves the calculation efficiency; the established formula covers comprehensive input parameters, and the input parameter range basically covers the CFST design values. This scientific and effective sample selection, combined with the inherent ability of the artificial intelligence model to learn complex nonlinear mapping relationships, not only ensures the successful capture of the dynamic behavior of CFST under impact loads, but also promotes the wider application of the proposed method; based on the deformation criterion, the support section angle is used to determine the failure degree of CFST columns under impact loads, and the prediction accuracy exceeds 90%; the proposed method does not require computer assistance, and engineers can quickly and easily perform impact-resistant design, while filling the technical gap in existing research that has failed to classify CFST failure levels.

[0021] Furthermore, the BP neural network is trained based on the impact sample set to obtain a maximum deflection prediction model for predicting maximum deflection information based on the constructed impact load parameters, component size parameters, material parameters and boundary conditions, specifically:

[0022] Normalize the parameters of each impact sample in the impact sample set to obtain the normalized matrix:

[0023] x=(x 1p ,x 2p ,x 3p ,x4p ,x 5p ,x 6p ,x 7p ,x 8p ,x 9p ,x 10p ,x 11p )

[0024]

[0025] Among them, x is the normalized matrix; x 11p is the normalized value of the 11th parameter; x ip is the normalized value of the i-th parameter; x i is the original value of the i-th parameter; x i,min is the minimum value of the i-th parameter; x i,max is the maximum value of the i-th parameter;

[0026] According to the normalized matrix, the BP neural network is trained to obtain the maximum deflection prediction model based on the constructed impact load parameters, component size parameters, material parameters and boundary conditions to predict the maximum deflection information.

[0027] The beneficial effects of the above further solution are: eliminating the data range and dimension differences between input parameters and converting the data set into a compatible format for the machine learning model.

[0028] Furthermore, the hidden layer of the BP neural network adopts the logsig function; the output signal matrix of the hidden layer is:

[0029] b=logsig(xv+γ)

[0030] Where b is the output signal matrix of the hidden layer; logsig is the activation function of the hidden layer; v is the weight matrix from the input layer to the hidden layer; γ is the bias matrix from the input layer to the hidden layer;

[0031] The output layer of the BP neural network adopts the purelin function; the output of the output layer is:

[0032] β=purelin(bw+θ)=bw+θ

[0033] Among them, β is the output of the output layer; purelin is the activation function of the output layer; w is the weight matrix from the hidden layer to the output layer; θ is the bias matrix from the hidden layer to the output layer.

[0034] The beneficial effect of the above further solution is that based on the neural network forward propagation principle and network parameters, the derivation process of the maximum deflection calculation model of steel tube concrete components is presented.

[0035] Furthermore, the expression of the maximum deflection prediction model is:

[0036]

[0037] in, is the predicted value of the maximum deflection information; y max is the maximum deflection of the impact sample set; y min is the minimum deflection in the impact sample set; logsig is the hidden layer activation function; x is the normalization matrix; v is the weight matrix from the input layer to the hidden layer; γ is the bias matrix from the input layer to the hidden layer; w is the weight matrix from the hidden layer to the output layer; θ is the bias matrix from the hidden layer to the output layer.

[0038] The beneficial effect of the above further solution is: by combining the above formulas, a unified expression for the maximum deflection calculation model of steel tube concrete components is finally established.

[0039] Furthermore, the expression of the cross-sectional rotation angle of the proximal support is:

[0040]

[0041] Where θ is the cross-sectional rotation angle of the proximal support; δ max is the predicted value of the maximum deflection information; l is the distance between the impact point and the proximal support.

[0042] The beneficial effect of the above further solution is that the maximum deflection information prediction value is converted into a basis for damage judgment, which facilitates the determination of the damage level.

[0043] The present invention provides a reliability analysis method for a steel tube concrete member, comprising:

[0044] Using the maximum deflection prediction model, the maximum deflection information prediction value and failure level of the impact sample to be tested are calculated;

[0045] According to the predicted value of the maximum deflection information and the proximal support section angle threshold corresponding to the failure level, the reliability and failure probability of the impact sample to be tested are calculated based on the failure function to complete the reliability analysis.

[0046] The beneficial effects of the present invention are: providing CFST failure probability prediction based on machine learning technology and reliability. The highlight of this workflow is to perform performance-based CFST column safety assessment and design, emphasizing the necessity of integrating uncertainty input features into machine learning models.

[0047] Furthermore, the expression of the failure function is:

[0048] G(D,t,f y ,f cu ,Es )=l·tan([θ])-δ max,pre

[0049] Where G(·) is the failure function; D is the outer diameter of the cross section; t is the thickness of the steel pipe; f y is the yield strength of steel; f cu is the compressive strength of concrete; E s is the elastic modulus of steel; l is the distance between the impact point and the proximal support; [θ] is the proximal support angle threshold corresponding to the failure level; δ max,pre is the predicted value of the maximum deflection information, indicating the deformation demand; l·tan([θ]) is the deformation capacity of the component.

[0050] The beneficial effect of the above further solution is: the predicted maximum deflection of steel tube concrete δ max,pre It is used to establish the failure function of the component and further evaluate the damage reliability of the steel tube concrete component under the impact load.

[0051] Furthermore, the reliability and failure probability of the impact sample to be tested are expressed as follows:

[0052]

[0053] ψ=Φ(-κ)

[0054] Wherein, κ is the reliability of the impact sample to be tested; l is the distance between the impact point and the proximal support; [θ] is the proximal support angle threshold corresponding to the failure level; δ max,pre is the predicted value of the maximum deflection information; l·tan([θ]) is the deformation capacity of the component; D is the outer diameter of the section; δ max,pre is the predicted value of the maximum deflection information, indicating the deformation demand; t is the thickness of the steel pipe; f y is the yield strength of steel; f cu is the compressive strength of concrete; E s is the elastic modulus of steel; σ D is the standard deviation of the normal distribution function of the cross-section outer diameter; σ t is the standard deviation of the normal distribution function of steel pipe thickness; is the standard deviation of the normal distribution function of steel yield strength; is the standard deviation of the normal distribution function of concrete compressive strength; σ Es is the standard deviation of the normal distribution function of the elastic modulus of steel; ψ is the failure probability; Φ is the cumulative function of the standard normal distribution function.

[0055] The beneficial effect of the above further solution is that a calculation expression for the damage reliability and damage probability of steel tube concrete components under impact load is established.

[0056] The present invention provides a method for designing steel tube concrete components against impact, comprising:

[0057] Collect several groups of impact conditions and use the reliability analysis method of steel tube concrete components to calculate the failure probability of each impact condition at the highest damage level;

[0058] Calculate the Pearson correlation coefficient of each parameter of the impact condition and the failure probability under the highest damage level respectively;

[0059] Based on the set parameter adjustment quantity, several component attribute parameters with the largest absolute value of the Pearson correlation coefficient are selected as parameter adjustment items;

[0060] Determine the impact parameters, and calculate the predicted value of the maximum deflection information of the current steel tube concrete component under the impact based on the impact parameters;

[0061] The reliability analysis method of steel tube concrete components is used to calculate the reliability of current steel tube concrete components under impact parameters;

[0062] Determine whether the reliability of the current CFST component under impact parameters is greater than the reliability threshold corresponding to the damage level. If so, the current CFST component parameters meet the performance design requirements. Otherwise, increase the parameter adjustment item and return to calculate the reliability of the current CFST component under impact parameters again.

[0063] The beneficial effects of the present invention include providing CFST failure probability prediction based on machine learning technology and reliability. The highlight of this workflow is the implementation of performance-based CFST column safety assessment and design, emphasizing the necessity of integrating uncertainty input features into the machine learning model. Users can set CFST protection standards and design parameters based on the structural safety level and reliability threshold to meet the safety, applicability and durability standards of contemporary engineering practice.

[0064] Furthermore, the component attribute parameters include component size parameters, material parameters and boundary conditions.

[0065] The beneficial effect of the above further scheme is that the established steel tube concrete failure probability assessment model takes into account the component size, material and support constraints, which are all key factors affecting the impact response of the component. Therefore, the multi-dimensional input parameters make the proposed model have a wide range of application scenarios and improve the applicability of the assessment model. BRIEF DESCRIPTION OF THE DRAWINGS

[0066] Figure 1 Schematic diagram of CFST lateral impact.

[0067] Figure 2 Schematic diagram of CFST failure mode.

[0068] Figure 3 Schematic diagram of the equivalent two-degree-of-freedom model.

[0069] Figure 4 This is a flow chart of the failure judgment method of the steel tube concrete component of the present invention.

[0070] Figure 5 Schematic diagram of comparison between predicted values ​​and true values ​​in an embodiment of the present invention.

[0071] Figure 6 This is a deformation diagram of CFST under impact in an embodiment of the present invention.

[0072] Figure 7 This is a schematic diagram of sorting the correlation coefficients of input variables and failure probabilities in an embodiment of the present invention. DETAILED DESCRIPTION

[0073] The specific embodiments of the present invention are described below to facilitate understanding of the present invention by those skilled in the art. However, it should be clear that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the appended claims, these changes are obvious, and all inventions and creations utilizing the concepts of the present invention are protected.

[0074] Example 1

[0075] like Figure 4 As shown, in one embodiment of the present invention, a failure determination method for a concrete-filled steel tube member includes:

[0076] Impact samples of steel tube concrete components are collected to obtain an impact sample set; each impact sample includes the impact load parameters, component size parameters, material parameters, boundary conditions and maximum deflection information of the component;

[0077] Based on the impact sample set, the BP neural network is trained to obtain the maximum deflection prediction model based on the constructed impact load parameters, component size parameters, material parameters and boundary conditions to predict the maximum deflection information;

[0078] Obtaining an impact sample to be tested, performing deflection prediction on the impact sample to be tested based on a maximum deflection prediction model, and obtaining maximum deflection information of the impact sample to be tested;

[0079] The proximal support section rotation angle is calculated based on the maximum deflection information of the impact sample to be tested. Based on the proximal support section rotation angle and the set proximal support section rotation angle thresholds for each failure level, the damage level of the steel tube concrete component under impact is determined to complete the failure judgment.

[0080] The BP neural network is trained based on the impact sample set to obtain a maximum deflection prediction model that predicts the maximum deflection information based on the constructed impact load parameters, component size parameters, material parameters and boundary conditions, specifically:

[0081] Normalize the parameters of each impact sample in the impact sample set to obtain the normalized matrix:

[0082] x=(x 1p ,x 2p ,x 3p ,x 4p ,x 5p ,x 6p ,x 7p ,x 8p ,x 9p ,x 10p ,x 11p )

[0083]

[0084] Among them, x is the normalized matrix; x 11p is the normalized value of the 11th parameter; x ip is the normalized value of the i-th parameter; x i is the original value of the i-th parameter; x i,min is the minimum value of the i-th parameter; x i,max is the maximum value of the i-th parameter;

[0085] According to the normalized matrix, the BP neural network is trained to obtain the maximum deflection prediction model based on the constructed impact load parameters, component size parameters, material parameters and boundary conditions to predict the maximum deflection information.

[0086] In this embodiment, a BP (Back-propagation) neural network is used to identify the failure mode of the CFST under lateral impact.

[0087] (1) Preparation for machine learning

[0088] The successful application of machine learning algorithms requires the compilation of a comprehensive database. Due to the identical moment of inertia in all directions, circular cross-section steel tube concrete CFST columns are widely used; in addition, the two ends of the conventional frame structure CFST columns can be regarded as fixed constraints, so this embodiment is aimed at fixed circular cross-section CFST components. The impact response is affected by multiple factors, so the input parameters involve multi-dimensional independent variables as much as possible, including 11 input variables, namely impact load (impact mass M, impact velocity V, impact position P), geometric dimensions (column length L, cross-section outer diameter D, steel tube thickness t), material properties (steel tube yield strength f y , concrete cube compressive strength f cu , steel elastic modulus Es ) and boundary conditions (constraint type B, axial compression ratio n). In order to quantify B, the concept of effective length in structural design is adopted, and B is taken as the calculation length coefficient, that is, B for simple support, fixed-simple support and fixed constraint conditions is 1.0, 0.7 and 0.5 respectively. Finally, 410 impact samples (from existing impact tests and finite element analysis) were collected to build a database. Each impact sample includes the impact load parameters, component size parameters, material parameters, boundary conditions and maximum deflection δ of the component. max Information. The ranges of the research parameters are as follows: (1) Impact load properties. Impact mass M = 70 ~ 920 kg, impact velocity V = 3 ~ 24 m / s, impact position P = 0.1 ~ 0.5; (2) CFST size properties. This machine learning study is based on 1:10 scale components, so the length of the steel tube concrete CFST column L = 750 ~ 3150 mm, the corresponding dimensionless parameters length-to-diameter ratio L / D = 5 ~ 15.5, diameter-to-thickness ratio D / t = 19.88 ~ 76, which basically cover the CFST parameter values ​​in the design specifications; (3) CFST material properties. The yield strength of the steel tube f y =200~924MPa, cubic concrete compressive strength f cu =31~102MPa, steel elastic modulus E s =190~320GPa; (4) Boundary conditions: axial compression ratio n = 0~0.8, constraint type B includes simple support, fixed-simple support, and fixed constraint. Overall, the parameter values ​​of the established database cover the commonly used range of engineering design. These geometric features, material properties, and loading conditions cover the range used by current design codes. Therefore, this database can be used in the development of machine learning algorithms with deformation prediction capabilities and ensure the successful capture of the potential relationship between characteristic input and deformation output of CFST under the combined action of impact and axial load.

[0089] (2) Machine learning prediction feature parameters

[0090] In this machine learning, the above 11 parameters are used as independent variables to reflect the maximum deflection δ of the CFST deformation parameters. max These parameters, used as predictor variables, were obtained from the collected samples. Of the 410 samples in the database, 80% (328 components) were randomly selected as the training set for network training, and the remaining 20% ​​(82 components) were used as the test set to verify the model's generalization ability. To eliminate dimensional differences between the input parameters, each parameter was first normalized.

[0091] The hidden layer of the BP neural network uses the logsig function; the output signal matrix of the hidden layer is:

[0092] b=logsig(xv+γ)

[0093] Where b is the output signal matrix of the hidden layer; logsig is the activation function of the hidden layer; v is the weight matrix from the input layer to the hidden layer; γ is the bias matrix from the input layer to the hidden layer;

[0094] The output layer of the BP neural network adopts the purelin function; the output of the output layer is:

[0095] β=purelin(bw+θ)=bw+θ

[0096] Among them, β is the output of the output layer; purelin is the activation function of the output layer; w is the weight matrix from the hidden layer to the output layer; θ is the bias matrix from the hidden layer to the output layer.

[0097] In this embodiment, the development max The optimal neural network architecture is achieved by trial and error when predicting the model, including the number of hidden layer neurons, transfer function type, learning rate and number of iterations. max ,The optimal number of hidden layer neurons, hidden layer transfer function type, output layer transfer function type, learning rate, and number of iterations are 12, logarithmic sigmoid transfer function (logsig), linear transfer function (purelin), 0.01, and 500, respectively.

[0098] The trained BP neural network configuration is used to establish δ max Computational model.

[0099] The expression of the maximum deflection prediction model is:

[0100]

[0101] in, is the predicted value of the maximum deflection information; y max is the maximum deflection of the impact sample set; y min is the minimum deflection in the impact sample set; logsig is the hidden layer activation function; x is the normalization matrix; v is the weight matrix from the input layer to the hidden layer; γ is the bias matrix from the input layer to the hidden layer; w is the weight matrix from the hidden layer to the output layer; θ is the bias matrix from the hidden layer to the output layer.

[0102] In this embodiment, in the maximum deflection model training, the solved neural network v, γ, w and θ values ​​are substituted into the expression of the deflection prediction model to obtain the maximum deflection prediction model δ max,pre :

[0103]

[0104] Among them, y1~y 12 is the linear combination of 11 variables in the hidden layer of the neural network, which are:

[0105] y1=-0.00261M-0.145V-1.02P+2.53e -4 L+1.39e -4 D-0.284t-0.00194f y +0.0557f cu -9.62e -3 E s +5.55n-3.06B+5.61

[0106] y2=-9.55e -4 M-0.136V-3.05P-1.61e -4 L+0.0184D-0.524t-0.00281f y +0.0223f cu +0.0166E s -1.32n+1.8B+2.39

[0107] y3=0.00452M+0.247V-0.178P+0.00235L+0.00547D-0.858t-1.3e -5 f y -0.0014f cu +0.0158E s +0.262n-0.788B-8.24

[0108] y4=-0.00121M+0.21V-10.9P-3.06e -4 L+0.00392D-0.0826t+7.86e -4 f y +0.0253f cu +0.0276E s +2.77n-0.739B-8.97

[0109] y5=-0.00428M-0.0556V-2.31P+0.00154L+0.0239D+0.234t-8.36e -4 f y +0.0205f cu +0.00544E s -1.1n+4.86B-10.3

[0110] <h2 style=";text-align:left;direction:ltr">y6 = -0.00397M + 0.0587V - 3.2P - 0.00124L - 0.0103D + 0.171t + 0.00165f<h2 style=";text-align:left;direction:ltr"> y <h2 style=";text-align:left;direction:ltr"> -0.019f<h2 style=";text-align:left;direction:ltr"> cu <h2 style=";text-align:left;direction:ltr"> -0.0135E<h2 style=";text-align:left;direction:ltr"> s <h2 style=";text-align:left;direction:ltr"> -0.863n+2.2B+8.93<h2 style=";text-align:left;direction:ltr"> <h2 style=";text-align:left;direction:ltr">

[0111] <h2 style=";text-align:left;direction:ltr"> y7=0.0044M-0.225V+7.66P-5.85e<h2 style=";text-align:left;direction:ltr"> -4 <h2 style=";text-align:left;direction:ltr"> L+0.00771D+0.682t-0.00222f<h2 style=";text-align:left;direction:ltr"> y <h2 style=";text-align:left;direction:ltr"> +0.0221f<h2 style=";text-align:left;direction:ltr"> cu <h2 style=";text-align:left;direction:ltr"> -0.00229E<h2 style=";text-align:left;direction:ltr"> s <h2 style=";text-align:left;direction:ltr"> -1.54n-6.12B+0.251<h2 style=";text-align:left;direction:ltr"> <h2 style=";text-align:left;direction:ltr">

[0112] <h2 style=";text-align:left;direction:ltr"> y8 = 0.00871M - 0.187V - 1.33P - 7.73e<h2 style=";text-align:left;direction:ltr"> -5 <h2 style=";text-align:left;direction:ltr"> L+0.013D-0.303t-0.00504f<h2 style=";text-align:left;direction:ltr"> y <h2 style=";text-align:left;direction:ltr"> -0.0598f<h2 style=";text-align:left;direction:ltr"> cu <h2 style=";text-align:left;direction:ltr"> -0.014E<h2 style=";text-align:left;direction:ltr"> s <h2 style=";text-align:left;direction:ltr"> +3.56n+5.4B+2.55<h2 style=";text-align:left;direction:ltr"> <h2 style=";text-align:left;direction:ltr">

[0113] <h2 style=";text-align:left;direction:ltr"> y9 = -0.00812M - 0.211V + 1.24P + 5.39e<h2 style=";text-align:left;direction:ltr"> -5 <h2 style=";text-align:left;direction:ltr"> L+0.0419D+0.615t+0.00406f<h2 style=";text-align:left;direction:ltr"> y <h2 style=";text-align:left;direction:ltr"> -0.0288f<h2 style=";text-align:left;direction:ltr"> cu <h2 style=";text-align:left;direction:ltr"> +0.00252E<h2 style=";text-align:left;direction:ltr"> s <h2 style=";text-align:left;direction:ltr"> -1.71n-5.75B+1.98<h2 style=";text-align:left;direction:ltr"> <h2 style=";text-align:left;direction:ltr">

[0114] <h2 style=";text-align:left;direction:ltr"> y<h2 style=";text-align:left;direction:ltr"> 10 <h2 style=";text-align:left;direction:ltr"> <1.49e<h2 style=";text-align:left;direction:ltr"> -5 <h2 style=";text-align:left;direction:ltr"> M-0.0282V+1.85P+8.3e<h2 style=";text-align:left;direction:ltr"> -5 <h2 style=";text-align:left;direction:ltr"> L-4.08e<h2 style=";text-align:left;direction:ltr"> -3 <h2 style=";text-align:left;direction:ltr"> D-0.569t-0.00391f<h2 style=";text-align:left;direction:ltr"> y <h2 style=";text-align:left;direction:ltr"> -0.0444f<h2 style=";text-align:left;direction:ltr"> cu <h2 style=";text-align:left;direction:ltr"> +0.0167E<h2 style=";text-align:left;direction:ltr"> s <h2 style=";text-align:left;direction:ltr"> -1.67n+5.63B-0.24<h2 style=";text-align:left;direction:ltr"> <h2 style=";text-align:left;direction:ltr">

[0115] <h2 style=";text-align:left;direction:ltr"> y<h2 style=";text-align:left;direction:ltr"> 11 <h2 style=";text-align:left;direction:ltr"> =0.00301M-0.0184V+8.84P+3.75e<h2 style=";text-align:left;direction:ltr"> -4 <h2 style=";text-align:left;direction:ltr"> L+0.0182D+0.571t-3.73e<h2 style=";text-align:left;direction:ltr"> -4 <h2 style=";text-align:left;direction:ltr"> f<h2 style=";text-align:left;direction:ltr"> y <h2 style=";text-align:left;direction:ltr"> +0.0292f<h2 style=";text-align:left;direction:ltr"> cu <h2 style=";text-align:left;direction:ltr"> -0.0285E<h2 style=";text-align:left;direction:ltr"> s-1.07n-7.94B+3.7

[0116]

[0117] In this embodiment, the prediction model δ of the maximum deflection is used. max,pre Calculate the maximum deflection of the training and test set samples and compare it with the true deflection value δ max,true For comparison, such as Figure 5 As shown. The correlation coefficient R of the training set (328 samples) and the test set (82 samples) is 2 They are 0.91 and 0.90 respectively. The predicted data points are basically symmetrically distributed along the 45° oblique line, showing unbiased prediction, indicating that the developed prediction model has excellent accuracy.

[0118] The expression of the cross-sectional rotation angle of the proximal support is:

[0119]

[0120] Where θ is the cross-sectional rotation angle of the proximal support; δ max is the predicted value of the maximum deflection information; l is the distance between the impact point and the proximal support.

[0121] In this embodiment, the CFST damage level under impact is determined as follows:

[0122] Taking deformation as the criterion, Figure 6 As shown in Figure 2, the proximal support section rotation angle θ is used as an evaluation indicator to classify the CFST damage degree into three levels: mild (θ ≥ 2°), moderate (θ ≥ 5°), and severe damage (θ ≥ 10°). Since plastic hinges appear in the impact section and the fixed support section, and rigid rotation occurs in the remaining parts, θ can be approximately calculated as follows:

[0123] The prediction model of maximum deflection δ based on machine learning max,pre and the expression of the cross-sectional rotation angle of the proximal support, the damage level judgment process of CFST under impact can be summarized as follows: Figure 4 .

[0124] Example 2

[0125] A reliability analysis method for a concrete-filled steel tube member, comprising:

[0126] Using the maximum deflection prediction model, the maximum deflection information prediction value and failure level of the impact sample to be tested are calculated;

[0127] According to the predicted value of the maximum deflection information and the proximal support section angle threshold corresponding to each failure level, the reliability and failure probability of the impact sample to be tested are calculated based on the failure function to complete the reliability analysis.

[0128] The expression of the failure function is:

[0129] G(D,t,f y ,f cu ,E s )=l·tan([θ])-δ max,pre

[0130] Where G(·) is the failure function; D is the outer diameter of the cross section; t is the thickness of the steel pipe; f y is the yield strength of steel; f cu is the compressive strength of concrete; E s is the elastic modulus of steel; l is the distance between the impact point and the proximal support; [θ] is the proximal support section angle threshold corresponding to the failure level; δ max,pre is the predicted value of the maximum deflection information, indicating the deformation demand; l·tan([θ]) is the deformation capacity of the component.

[0131] In this embodiment, due to the great uncertainty of the impact scenario, the structural design under such extreme effects should be based on probabilistic analysis. Due to the influence of factors such as manufacturing process, construction error, and external environment, the geometric dimensions and material properties of components in the real world can be regarded as random variables obeying the normal distribution. Referring to existing research, the cross-section outer diameter D, steel pipe thickness t, and steel yield strength f y , concrete compressive strength f cu and steel elastic modulus E s The variability of the standard normal distribution function can be taken as 0.02, 0.02, 0.05, 0.11, and 0.05. Factors affecting structural reliability include the deformation demand and deformation capacity of the component. In this study, the deformation demand can be recorded as the maximum deflection δ max,true , the deformation capacity is l·tan([θ]), then the CFST failure function G(D,t,f y ,f cu ,E s ) can be expressed as: G(D,t,f y ,f cu ,E s )=l·tan([θ])-δ max,pre .

[0132] where δ max,pre The expression is shown in Example 1. The first-order second moment method performs Taylor series expansion on the nonlinear function and takes its first-order term, and solves the failure probability according to the reliability index, G(D, t, f y ,f cu ,E s ) with respect to each random variable are:

[0133]

[0134]

[0135] Among them, y1~y 12 These are the linear expressions of the 11 input parameters, see Example 1.

[0136] The expressions for the reliability and failure probability of the impact sample to be tested are:

[0137]

[0138] ψ=Φ(-κ)

[0139] Wherein, κ is the reliability of the impact sample to be tested; l is the distance between the impact point and the proximal support; [θ] is the proximal support section angle threshold corresponding to the failure level; δ max,pre is the predicted value of the maximum deflection information; l·tan([θ]) is the deformation capacity of the component; D is the outer diameter of the section; δ max,pre is the predicted value of the maximum deflection information, indicating the deformation demand; t is the thickness of the steel pipe; f y is the yield strength of steel; f cu is the compressive strength of concrete; E s is the elastic modulus of steel; σ D is the standard deviation of the normal distribution function of the cross-section outer diameter; σ t is the standard deviation of the normal distribution function of steel pipe thickness; is the standard deviation of the normal distribution function of steel yield strength; is the standard deviation of the normal distribution function of concrete compressive strength; is the standard deviation of the normal distribution function of the elastic modulus of steel; ψ is the failure probability; Φ is the cumulative function of the standard normal distribution function.

[0140] In this embodiment, the CFST failure function G(D,t,f y ,f cu ,E s ) can calculate the reliability and failure probability of CFST failure:

[0141]

[0142] ψ=Φ(-κ)

[0143] Among them, σ D ,σ t , and where [θ] is the standard deviation of the normal distribution function (mean multiplied by the coefficient of variation) for the cross-section outer diameter, steel pipe thickness, steel yield strength, concrete compressive strength, and steel elastic modulus, respectively. Φ is the cumulative function of the standard normal distribution function. For the reliability calculations for mild, moderate, and severe damage, [θ] is set to 2°, 5°, and 10°, respectively.

[0144] Example 3

[0145] A method for anti-impact design of steel tube concrete components, comprising:

[0146] Collect several groups of impact conditions and use the reliability analysis method of steel tube concrete components to calculate the failure probability of each impact condition at the highest damage level;

[0147] Calculate the Pearson correlation coefficient of each parameter of the impact condition and the failure probability under the highest damage level respectively;

[0148] Based on the set parameter adjustment quantity, several component attribute parameters with the largest absolute value of the Pearson correlation coefficient are selected as parameter adjustment items;

[0149] Determine the impact parameters, and calculate the predicted value of the maximum deflection information of the current steel tube concrete component under the impact based on the impact parameters;

[0150] The reliability analysis method of steel tube concrete components is used to calculate the reliability of current steel tube concrete components under impact parameters;

[0151] Determine whether the reliability of the current CFST component under impact parameters is greater than the reliability threshold corresponding to the damage level. If so, the current CFST component parameters meet the performance design requirements. Otherwise, increase the parameter adjustment item and return to calculate the reliability of the current CFST component under impact parameters again.

[0152] The component attribute parameters include component size parameters, material parameters and boundary conditions.

[0153] In this embodiment, 10,000 impact conditions are formed by randomly selecting values ​​within the database input parameter range, and the above method is used to calculate the failure probability ψ of severe damage. By calculating the Pearson correlation coefficient between each input parameter and the failure probability ψ in the 10,000 conditions, a sensitivity analysis of the failure probability is performed. The absolute values ​​of the correlation coefficients between the 11 input variables and the failure probability ψ are calculated and sorted, as shown in the following example: Figure 7 As shown in Figure 2. For impact load parameters, V and M have the greatest influence, ranking second and third among all factors respectively. For the properties of the component itself, D, f y , L and t have a greater impact, ranking first, fourth, sixth and seventh respectively. Therefore, these four parameters can be adjusted in sequence when strengthening CFST against impact.

[0154] Under the action of lateral impact, for the properties of the component itself, D, f y , L and t have a greater impact on component damage. For the impact reinforcement of specific components, the column length L is often determined by factors such as architectural space and visual aesthetics. Therefore, L is usually not adjusted. The most feasible solution is to increase the D, f and t of CFST in sequence. y The allowable reliability [κ] of a building structure is often determined by factors such as the structural safety level, environmental conditions, and material properties. In anti-collision design, the component parameters (D, f) can be adjusted based on the [κ] of the structural column. y and t) so that the structure can meet the expected function under the above conditions. Therefore, based on the BP neural network to predict deformation and the first-order moment to solve the failure reliability, the proposed CFST impact resistance design process is as follows:

[0155] Step 1: Determine the impact parameters (impact mass M, impact velocity V, impact position P), component size parameters (column length L, section outer diameter D, steel pipe thickness t), material parameters (steel pipe yield strength f y , concrete cube compressive strength f cu , steel elastic modulus E s ) and boundary conditions (restraint type B, axial compression ratio n);

[0156] Step 2: Use the method proposed in Example 1 to predict the maximum deflection δ of the component under impact max,pre ;

[0157] Step 3: The support section rotation angle thresholds [θ] for mild, moderate, and severe failure are set to 2°, 5°, and 10°, respectively. The reliability κ of the damage level of the component under the impact load is calculated according to the method of Example 2.

[0158] Step 4: Determine the reliability threshold [κ] according to the structural safety level. If κ>[κ], the CFST parameter meets the performance design requirements; otherwise, increase D, f y and t, return to the first step and recalculate.

[0159] In summary, this paper proposes a method for identifying the failure level of CFST under lateral impact, and a reliability calculation theory based on a BP neural network algorithm. Currently, no methods for identifying the failure level of CFST have been reported. Although the BP algorithm is a traditional machine learning method, this paper proposes a method more suitable for engineering calculations, achieving high-precision prediction of CFST deformation and simplifying the calculation method. This has crucial engineering significance for preventing progressive building collapse caused by severe CFST damage and improving structural safety.

Claims

1. A method for determining failure of a concrete-filled steel tube member, characterized in that: include: Impact samples of steel tube concrete components are collected to obtain an impact sample set; each impact sample includes the impact load parameters, component size parameters, material parameters, boundary conditions and maximum deflection information of the component; Based on the impact sample set, the BP neural network is trained to obtain the maximum deflection prediction model based on the constructed impact load parameters, component size parameters, material parameters and boundary conditions to predict the maximum deflection information; Obtaining an impact sample to be tested, performing deflection prediction on the impact sample to be tested based on a maximum deflection prediction model, and obtaining maximum deflection information of the impact sample to be tested; The proximal support section rotation angle is calculated based on the maximum deflection information of the impact sample to be tested. Based on the proximal support section rotation angle and the set proximal support section rotation angle thresholds for each failure level, the damage level of the steel tube concrete component under impact is determined to complete the failure judgment.

2. The failure determination method for concrete-filled steel tube components according to claim 1, characterized in that: The BP neural network is trained based on the impact sample set to obtain a maximum deflection prediction model that predicts the maximum deflection information based on the constructed impact load parameters, component size parameters, material parameters and boundary conditions, specifically: Normalize the parameters of each impact sample in the impact sample set to obtain the normalized matrix: x=(x 1p ,x 2p ,x 3p ,x 4p ,x 5p ,x 6p ,x 7p ,x 8p ,x 9p ,x 10p ,x 11p ) Among them, x is the normalized matrix; x 11p is the normalized value of the 11th parameter; x ip is the normalized value of the i-th parameter; x i is the original value of the i-th parameter; x i,min is the minimum value of the i-th parameter; x i,max is the maximum value of the i-th parameter; According to the normalized matrix, the BP neural network is trained to obtain the maximum deflection prediction model based on the constructed impact load parameters, component size parameters, material parameters and boundary conditions to predict the maximum deflection information.

3. The failure determination method for concrete-filled steel tube components according to claim 2, characterized in that: The hidden layer of the BP neural network uses the logsig function; the output signal matrix of the hidden layer is: b=logsig(xv+γ) Where b is the output signal matrix of the hidden layer; logsig is the activation function of the hidden layer; v is the weight matrix from the input layer to the hidden layer; γ is the bias matrix from the input layer to the hidden layer; The output layer of the BP neural network adopts the purelin function; the output of the output layer is: β=purelin(bw+θ)=bw+θ Among them, β is the output of the output layer; purelin is the activation function of the output layer; w is the weight matrix from the hidden layer to the output layer; θ is the bias matrix from the hidden layer to the output layer.

4. The failure determination method for concrete-filled steel tube members according to claim 2, characterized in that: The expression of the maximum deflection prediction model is: in, is the predicted value of the maximum deflection information; y max is the maximum deflection of the impact sample set; y min is the minimum deflection in the impact sample set; logsig is the hidden layer activation function; x is the normalization matrix; v is the weight matrix from the input layer to the hidden layer; γ is the bias matrix from the input layer to the hidden layer; w is the weight matrix from the hidden layer to the output layer; θ is the bias matrix from the hidden layer to the output layer.

5. The failure determination method for concrete-filled steel tube components according to claim 1, characterized in that: The expression of the cross-sectional rotation angle of the proximal support is: Where θ is the cross-sectional rotation angle of the proximal support; δ max is the predicted value of the maximum deflection information; l is the distance between the impact point and the proximal support.

6. A reliability analysis method for a concrete-filled steel tube member using the failure judgment method for a concrete-filled steel tube member according to any one of claims 1 to 5, characterized in that: include: Using the maximum deflection prediction model, the maximum deflection information prediction value and failure level of the impact sample to be tested are calculated; According to the predicted value of the maximum deflection information and the proximal support section angle threshold corresponding to the failure level, the reliability and failure probability of the impact sample to be tested are calculated based on the failure function to complete the reliability analysis.

7. The reliability analysis method of concrete-filled steel tube members according to claim 6, characterized in that: The expression of the failure function is: G(D,t,f y ,f cu ,AND s )=l·tan([θ])-δ max,pre Where G(·) is the failure function; D is the outer diameter of the cross section; t is the thickness of the steel pipe; f y is the yield strength of steel; f cu is the compressive strength of concrete; E s is the elastic modulus of steel; l is the distance between the impact point and the proximal support; [θ] is the proximal support angle threshold corresponding to the failure level; δ max,pre is the predicted value of the maximum deflection information, indicating the deformation demand; l·tan([θ]) is the deformation capacity of the component.

8. The reliability analysis method of concrete-filled steel tube members according to claim 6, characterized in that: The expressions for the reliability and failure probability of the impact sample to be tested are: ψ=Φ(-κ) Wherein, κ is the reliability of the impact sample to be tested; l is the distance between the impact point and the proximal support; [θ] is the proximal support angle threshold corresponding to the failure level; δ max,pre is the predicted value of the maximum deflection information; l·tan([θ]) is the deformation capacity of the component; D is the outer diameter of the section; δ max,pre is the predicted value of the maximum deflection information, indicating the deformation demand; t is the thickness of the steel pipe; f y is the yield strength of steel; f cu is the compressive strength of concrete; E s is the elastic modulus of steel; σ D is the standard deviation of the normal distribution function of the cross-section outer diameter; σ t is the standard deviation of the normal distribution function of steel pipe thickness; is the standard deviation of the normal distribution function of steel yield strength; is the standard deviation of the normal distribution function of concrete compressive strength; is the standard deviation of the normal distribution function of the elastic modulus of steel; ψ is the failure probability; Φ is the cumulative function of the standard normal distribution function.

9. A method for anti-impact design of steel tube concrete members based on the reliability analysis method of steel tube concrete members according to any one of claims 6 to 8, characterized in that: include: Collect several groups of impact conditions and use the reliability analysis method of steel tube concrete components to calculate the failure probability of each impact condition at the highest damage level; Calculate the Pearson correlation coefficient of each parameter of the impact condition and the failure probability under the highest damage level respectively; Based on the set parameter adjustment quantity, several component attribute parameters with the largest absolute value of the Pearson correlation coefficient are selected as parameter adjustment items; Determine the impact parameters, and calculate the predicted value of the maximum deflection information of the current steel tube concrete component under the impact based on the impact parameters; The reliability analysis method of steel tube concrete components is used to calculate the reliability of current steel tube concrete components under impact parameters; Determine whether the reliability of the current CFST component under impact parameters is greater than the reliability threshold corresponding to the damage level. If so, the current CFST component parameters meet the performance design requirements. Otherwise, increase the parameter adjustment item and return to calculate the reliability of the current CFST component under impact parameters again.

10. The impact resistance design method for concrete-filled steel tube members according to claim 9, characterized in that: The component attribute parameters include component size parameters, material parameters and boundary conditions.

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