Seismic analysis method using improved steel reinforcement restoring force model

Abstract

The application discloses an anti-seismic analysis method of improved steel reinforcement restoring force model, and is based on a built digital component test database, and uses the improved steel reinforcement restoring force model and a concrete constitutive model considering tensile characteristics as material constitutive, uses the fiber element based on the stiffness method to build the automatic elastic-plastic analysis model of the component fiber element, and carries out the optimal solution identification of control parameters, builds the component steel reinforcement constitutive parameter prediction model taking the component design characteristic parameters as input and taking the improved steel reinforcement restoring force model control parameters as output and carries out training. The application can consider the interaction between different materials and the influence of the component macroscopic characteristics on the material mechanical properties, and then consider the complex hysteretic characteristics of the component, and through embedding the improved steel reinforcement restoring force model in the fiber element, the component elastic-plastic analysis in the structure anti-seismic is carried out, the calculation efficiency is ensured while the elastic-plastic calculation precision is improved.

Description

Technical Field

[0001] This invention relates to the technical field of structural seismic analysis and numerical simulation, and in particular to a seismic analysis method using an improved steel reinforcement restoring force model. Background Technology

[0002] Currently, structural seismic analysis mainly involves establishing detailed finite element models of structures and conducting accurate and efficient elastoplastic analysis. Domestically and internationally, increasingly sophisticated seismic design methods have gradually emerged. Among these, performance-based seismic design methods, as the mainstream of seismic analysis, are gaining increasing favor among scholars and engineers.

[0003] The realization of seismic performance design of structures relies on reliable elastoplastic analysis methods. Selecting the element constitutive model is a crucial step in establishing a finite element elastoplastic model, and the quality of the element constitutive model directly affects the accuracy of the numerical analysis. Currently, the mainstream element constitutive models both domestically and internationally include fiber elements and concentrated plastic hinge elements. Compared with concentrated plastic hinge elements, fiber elements allow plasticity to develop at any location within the element and are widely used in simulating the elastoplastic response of beam-column members. Fiber elements simulate the elastoplastic response of reinforced concrete members under cyclic loading through the plane section assumption and the uniaxial constitutive relationship between reinforcement and concrete. However, they struggle to describe complex hysteretic characteristics caused by material interactions, such as shear effects and bond-slip, making it difficult to accurately assess the mechanical properties of finite element models using fiber elements. Although many scholars have considered bond-slip effects by adding bond-slip elements or modifying the reinforcing force model, problems such as low computational efficiency or complex parameter definitions in the modified model still exist.

[0004] In summary, the elastoplastic response of reinforced concrete members under cyclic loading is often simulated using fiber elements. To address the limitations of classical fiber models, which are constrained by uniaxial tension-compression constitutive models and cannot accurately simulate material interactions such as shear and bond-slip effects, and to further improve computational accuracy while maintaining efficiency, it is necessary to employ more efficient and accurate methods based on member test data to modify the reinforcing steel restoring force model. This would effectively improve the simulation accuracy of fiber elements and allow for consideration of interactions between different materials and the influence of macroscopic characteristics of the member on the material's mechanical properties. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of the existing technology and to provide a seismic analysis method using an improved steel reinforcement restoring force model.

[0006] The objective of this invention is achieved through the following technical solution: a seismic analysis method using an improved steel reinforcement restoring force model, comprising the following steps:

[0007] S1. Collect low-cycle reciprocating test data, perform equivalent transformation of the component loading mode on the low-cycle reciprocating test data to obtain component design characteristic parameters, then transform and extract the PEER structural performance database to obtain hysteresis curves and skeleton curves, and build a digital component test database based on the component design characteristic parameters, the hysteresis curves and the skeleton curves.

[0008] S2. Perform dimensionless transformation on the skeleton curve described in step S1 to obtain the skeleton control parameters;

[0009] S3. Perform single-factor analysis based on the hysteresis curve described in step S1 to obtain hysteresis control parameters, and use the hysteresis control parameters as the hysteresis rules for improving the steel reinforcement restoring force model.

[0010] S4. Based on the skeleton control parameters in step S2 and the hysteresis control parameters in step S3, establish the improved steel reinforcement restoring force model;

[0011] S5. Based on the concrete constitutive model and the improved steel reinforcement restoring force model described in step S4, establish an automatic elastic-plastic analysis model for the fiber element of the component. If the automatic elastic-plastic analysis model of the fiber element of the component conforms to the structural concept, proceed to step S6; otherwise, return to step S4.

[0012] S6. Determine the key target parameters of the skeleton curve in step S1. Based on the target error function of the skeleton control parameters in step S2, use the three-way search algorithm to identify the optimal solution of the skeleton control parameters of the improved steel rebar restoring force model in step S4, and obtain the optimal solution of the skeleton control parameters.

[0013] S7. Determine the key target parameters of the hysteresis curve in step S1. Based on the target error function of the hysteresis control parameters in step S3, and using the differential evolution algorithm to identify the optimal solution of the hysteresis control parameters of the improved steel reinforcement restoring force model in step S4, the optimal solution of the hysteresis control parameters is obtained.

[0014] S8. Using the component design feature parameters in step S1 as input parameters, and the optimal solutions of the skeleton control parameters in step S6 and the optimal solutions of the hysteresis control parameters in step S7 as output parameters, a component reinforcement constitutive parameter prediction model is obtained. The component reinforcement constitutive parameter prediction model is trained and the prediction effect is evaluated to obtain the improved reinforcement restoring force model with excellent prediction effect.

[0015] S9. Perform elastoplastic analysis on the improved steel reinforcement restoring force model described in step S8.

[0016] A better option, step S1 includes the following steps:

[0017] S101. Collect low-cycle cyclic test data of components from the PEER structural performance database and literature.

[0018] S102. Perform an equivalent transformation of the component loading mode on the low-cycle reciprocating test data of the component to obtain basic characteristic parameters;

[0019] S103. Calculate the basic feature parameters to obtain the calculated feature parameters;

[0020] S104. Extract the hysteresis curve from the PEER structural performance database;

[0021] S105. Extract the skeleton curve from the hysteresis curve;

[0022] S106. By matching the component design feature parameters, the hysteresis curve and the skeleton curve one by one, a digital component test database is built.

[0023] A better option is that the basic characteristic parameters in step S102 include geometric information, concrete information, longitudinal reinforcement information, stirrup information, and axial force information.

[0024] A better option is that the calculated characteristic parameters in step S103 include longitudinal reinforcement ratio, volumetric stirrup ratio, shear span ratio, axial compression coefficient, and bending-shear ratio.

[0025] A better option, step S8 includes the following steps:

[0026] S801. Determine the evaluation index of the constitutive parameter prediction model for the structural reinforcement of the component;

[0027] S802. Use the component design characteristic parameters as input parameters for the component reinforcement constitutive parameter prediction model;

[0028] S803. The optimal solutions of the skeleton control parameters and the optimal solutions of the hysteresis control parameters are used as the output parameters of the component reinforcement constitutive parameter prediction model.

[0029] S804. The gradient boosting regression tree algorithm is adopted as the core intelligent algorithm of the structural steel reinforcement constitutive parameter prediction model. The input parameters and output parameters are randomly divided into training set and test set using the k-fold cross-validation method. The training set is used to train the structural steel reinforcement constitutive parameter prediction model, and the test set is used to evaluate the effect of the structural steel reinforcement constitutive parameter prediction model, so as to obtain the improved steel reinforcement restoring force model with excellent prediction effect.

[0030] A better option is the method for performing elastoplastic analysis on the fiber elements in step S9, which includes the following steps:

[0031] S901. Evaluate the model prediction accuracy and generalization ability of the improved steel bar restoring force model described in step S8. If the improved steel bar restoring force model has good accuracy, proceed to step S902; otherwise, return to step S8.

[0032] S902. Perform component elastic-plastic analysis verification on the automatic elastic-plastic analysis model of the component fiber unit in step S5. If the automatic elastic-plastic analysis model of the component fiber unit is verified as good, proceed to step S903; otherwise, return to step S8.

[0033] S903. Based on machine learning, perform parameter prediction on the improved steel bar restoring force model described in step S8.

[0034] A better option is that the key inflection points of the skeleton curve in step S2 include the yield strength point, the ultimate strength point, and the strength degradation point.

[0035] A better option is that the skeleton control parameters in step S2 include the strength adjustment coefficient, strength hardening coefficient, ductility coefficient, strength degradation coefficient, and residual strength coefficient.

[0036] A better option is that the hysteresis control parameters in step S3 include damage control coefficient, pinch control coefficient, and unloading stiffness control coefficient.

[0037] A better option is that the key target parameters of the skeleton curve in step S6 include the strength adjustment coefficient, the ductility coefficient, and the strength degradation coefficient.

[0038] The present invention has the following advantages and beneficial effects compared with the prior art:

[0039] This invention employs an improved steel reinforcement restoring force model for seismic analysis, which can consider the interaction between different materials and the influence of the macroscopic characteristics of the components on the mechanical properties of the materials. Furthermore, it considers the complex hysteretic characteristics of the components. By embedding the improved steel reinforcement restoring force model into fiber elements, it performs elastoplastic analysis of components in seismic structural resistance, thereby improving the accuracy of elastoplastic calculations while ensuring computational efficiency. Attached Figure Description

[0040] Figure 1 This is a flowchart of the seismic analysis method using an improved steel reinforcement restoring force model according to the present invention;

[0041] Figure 2 This is a schematic diagram of the experimental loading method of the present invention;

[0042] Figure 3 This is a schematic diagram of skeleton curve extraction according to the present invention;

[0043] Figure 4 This is a schematic diagram of the automatic elastoplastic analysis model for the fiber unit of the present invention;

[0044] Figure 5 This is a flowchart of step S6 of the present invention for identifying the optimal solution of the skeleton control parameters;

[0045] Figure 6 A schematic diagram of the minimum value obtained by the three-way search algorithm in step S6 of the present invention;

[0046] Figure 7 This is a flowchart of step S7 of the present invention, which involves solving for the hysteresis control parameter identification.

[0047] Figure 8 This is a scatter plot comparing the prediction results of the SteelML model with the parameter identification results in step S9 of the present invention. Detailed Implementation

[0048] The invention's objective will be further described in detail below with reference to the accompanying drawings and specific embodiments. The embodiments cannot be described in detail here, but the implementation of the invention is not limited to the following embodiments.

[0049] This embodiment takes the establishment of a database, the determination of control parameters for the improved rebar restoring force model, the identification of optimal solutions for control parameters, and the construction and application of a structural member rebar constitutive parameter prediction model as examples. The seismic analysis method using the improved rebar restoring force model includes the following steps:

[0050] S1. Initially collect low-cycle reciprocating test data, perform equivalent transformation of the component loading mode on the low-cycle reciprocating test data to obtain component design characteristic parameters (including basic characteristic parameters and calculated characteristic parameters), then transform and extract the low-cycle reciprocating test data to obtain hysteresis curves and skeleton curves, and build a digital component test database based on the component design characteristic parameters, hysteresis curves, and skeleton curves; Step S1 includes the following steps:

[0051] S101. Collect low-cycle cyclic test data of reinforced concrete members from relevant literature and database information provided by the PEER (Pacific Earthquake Engineering Research) structural performance database.

[0052] S102. The low-cycle cyclic test data of the components undergoes an equivalent transformation of the component loading method to obtain basic characteristic parameters. These parameters include geometric information, concrete information, longitudinal reinforcement information, stirrup information, and axial force information. The component loading methods include cantilever (the component has a fixed support at the bottom, and the lateral force is applied to the cantilever end), double-curvature (the component has a fixed support at the bottom, and the lateral force is applied to a horizontally sliding top support), and double-simply supported (the component is simply supported at both ends, and the lateral force is applied to the middle support). To unify the load and displacement results in the low-cycle cyclic test database of reinforced concrete components, it is necessary to perform an equivalent transformation of the above three lateral loading methods, that is, to convert the component loading method into an equivalent cantilever component loading method, such as... Figure 2 The formula for calculating the conversion relationship is as follows:

[0053] V E =V C =V DC =V DE / 2 (1-1)

[0054] Δ E =Δ C =Δ DC / 2=Δ DE (1-2)

[0055] L E =L C =L DC / 2=L DE (1-3)

[0056] (1) Geometric information includes section height h, section width b, equivalent cantilever length l, and protective layer thickness c;

[0057] (2) Concrete information includes the axial compressive strength f′ of the concrete cylinder. c axial compressive strength f of concrete c , compressive strength f of concrete cube cu ;

[0058] (3) Longitudinal reinforcement information includes the diameter of the corner bars, the diameter of the central bars, the number of central bars in the X direction, the number of central bars in the Y direction, and the yield strength f of the longitudinal reinforcement. y Ultimate strength of longitudinal reinforcement f u Elastic modulus E s ;

[0059] (4) Stirrup information includes stirrup diameter, stirrup type, stirrup spacing s, and stirrup yield strength f. yv Ultimate strength of stirrups f uv ;

[0060] (5) Axial force information includes the design axial compression ratio n d Axial force value P.

[0061] To facilitate subsequent parameter identification of the improved rebar restoring force model and the construction of a constitutive parameter prediction model for structural members, the following formula is used to uniformly convert the concrete strength information in the database into the axial compressive strength f′ of the concrete cylinder. c The conversion coefficients for concrete of different strengths were adjusted based on the correlation coefficients given by CEB-FIP and MC-90.

[0062] f′ c =0.79f cu,k (1-4)

[0063] In the statistics of basic material characteristic parameters in the PEER structural performance database, the units such as N, kN, mm, m, in, and lb are uniformly converted using N and mm.

[0064] S103. Calculate the basic characteristic parameters to obtain the calculated characteristic parameters; the calculated characteristic parameters include longitudinal reinforcement ratio, volumetric stirrup ratio, shear span ratio, axial compression coefficient, and bending-shear ratio.

[0065] (1) The longitudinal reinforcement ratio ρ is the ratio of the reinforcement area of ​​the entire cross section of the RC column member to the cross section area of ​​the RC column. Since the collected RC column tests are all symmetrically reinforced, the single-sided reinforcement ratio of each member is half of the longitudinal reinforcement ratio.

[0066] ρ=A s / A (1-5)

[0067] In the formula, ρ is the longitudinal reinforcement ratio, and A s Let A be the total reinforcement area of ​​the cross section, and let A be the cross-sectional area of ​​the member.

[0068] (2) Volumetric stirrup ratio ρ v The ratio of the volume of the stirrup reinforcement to the volume of the core concrete represents the magnitude of the confinement effect of the stirrup on the core concrete.

[0069]

[0070] In the formula, ρ v Let n1 and n2 be the number of stirrup legs in the X and Y directions, respectively, and A be the stirrup volume ratio. s1 and A s2 Let l1 and l2 be the cross-sectional areas of the single-leg stirrups in the X and Y directions, respectively, and let A be the lengths of the single-leg stirrups in the X and Y directions. cor s represents the area of ​​the concrete in the core area of ​​the component, and s represents the spacing of the stirrups.

[0071] (3) The equivalent cantilever height L is obtained by calculating the shear span ratio λ using equation (1-3). E The ratio of the effective height h0 of the cross section is obtained.

[0072] λ=L E / h0 (1-7)

[0073] In the formula, λ is the shear span ratio, and L E h0 is the equivalent cantilever height, and h0 is the effective height of the cross section.

[0074] (4) The axial compression coefficient n is the ratio of the test axial compression of the member to the product of the total cross-sectional area of ​​the member and the standard value of the axial compressive strength of the concrete. As the test axial compression coefficient increases, the bending capacity of the member first increases and then decreases.

[0075]

[0076] In the formula, n is the axial pressure coefficient, P is the experimental axial pressure value, and A c f is the concrete area of ​​the component. ck This is the standard value for the axial compressive strength of concrete.

[0077] (5) The bending-shear ratio m reflects the difference between the bending capacity and the shear capacity of the member. For cantilever members in the RC column test database, it can be equivalent to the ratio of the bending capacity of the section to the product of the shear capacity of the section and the equivalent cantilever height.

[0078]

[0079] In the formula, m is the bending-shear ratio, and M u V represents the flexural capacity of the component. u L represents the shear capacity of the component. E This is the equivalent cantilever height.

[0080] S104. Extract the hysteresis curve from the low-cycle reciprocating test data; and convert the force-displacement curve and moment-rotation curve included in the low-cycle reciprocating test data, as well as the units such as N, kN, m, and mm involved, into force-displacement curves in kN and mm units.

[0081] S105. The skeleton curve is obtained by transforming the hysteresis curve. The skeleton curve of the component during the low-cycle reciprocating loading process is obtained by connecting the loading segment of the first cycle of the hysteresis curve and the displacement peak point of each subsequent loading stage. This skeleton curve is an important reference for studying the mechanical properties and deformation characteristics of the component.

[0082] S106. A digital component test database was established by matching the component design characteristic parameters, hysteresis curves, and skeleton curves one by one. A digital component test database of 140 RC (Reinforced Concrete) column test data was established. In this database, the cross-sectional shapes of the components are square and rectangular, and the reinforcement is symmetrical.

[0083] S2 and S1 have key inflection points in their skeleton curves. The stress and strain values ​​at these key inflection points are transformed into dimensionless values ​​to obtain the skeleton control parameters of the improved rebar restoring force model.

[0084] Key inflection points include the yield strength point, ultimate strength point, and strength degradation point. Assuming the skeleton curve of the rebar restoring force model is symmetrical about the origin, to reduce the skeleton control parameters of the rebar restoring force model, the yield strength point, ultimate strength point, and strength degradation point in the skeleton curve are sequentially dimensionless. The stress and strain values ​​at each key inflection point are converted into five dimensionless skeleton control parameters, including the strength adjustment coefficient, strength hardening coefficient, ductility coefficient, strength degradation coefficient, and residual strength coefficient.

[0085] The yield strength point (e1, s1) will be converted into a strength adjustment coefficient by combining the yield strength and initial elastic modulus of the steel reinforcement according to equations (3-1) and (3-2). Definition:

[0086]

[0087] e1 = s1 / E0 (2-2)

[0088] Among them, f y Let E be the yield strength of the steel reinforcement (MPa), and E0 be the initial elastic modulus of the steel reinforcement (2.0 × 10⁻⁶). 5 MPa), This is the adjustment coefficient for the strength of the reinforcing steel.

[0089] To reasonably describe the physical relationship between the ultimate strength point and the yield strength point, two dimensionless parameters, the ductility coefficient μ and the strength hardening coefficient α, are introduced. h Its definition is shown in equations (3-3) and (3-4):

[0090] μ=ε u / ε y (2-3)

[0091] α h =k h / E0 (2-4)

[0092] Where, ε y ε is the yield strain of the steel reinforcement.u Let μ be the ultimate strain of the steel reinforcement, E0 be the initial elastic modulus of the steel reinforcement, and k be the ductility coefficient. h Let α be the slope of the hardened section of the reinforcing bar. h This is the strength hardening coefficient.

[0093] The ultimate strength point (e2, s2) is converted into the strength hardening coefficient α according to equations (3-5) and (3-6). h And ductility coefficient μ:

[0094] e2=e1·μ (2-5)

[0095] s2=s1+α h ·E0·s1·(μ-1) (2-6)

[0096] Where e1 is the strain at the yield strength point of the steel reinforcement, s1 is the stress at the yield strength point of the steel reinforcement, e2 is the strain at the ultimate strength point of the steel reinforcement, s2 is the stress at the ultimate strength point of the steel reinforcement, E0 is the initial elastic modulus of the steel reinforcement, μ is the ductility coefficient, and α h This is the strength hardening coefficient.

[0097] To reasonably describe the physical relationship between the strength degradation point and the ultimate strength point when steel reinforcement undergoes strength degradation, a dimensionless parameter, the strength degradation coefficient α, needs to be introduced into the steel reinforcement restoring force model. s The residual strength coefficient R is defined as shown in equations (3-7) and (3-8):

[0098] Rε rs / ε u (2-7)

[0099] α s =-k s / E0 (2-8)

[0100] Where, ε u ε is the point stress representing the ultimate strength of the reinforcing steel. rs Let R be the stress at the point of strength degradation of the steel reinforcement, E0 be the residual strength coefficient, and k be the initial elastic modulus of the steel reinforcement. s Let α be the slope of the degenerate segment of the reinforcing bar. s This is the strength degradation coefficient.

[0101] The ultimate strength point (e3, s3) will be combined with the yield strength point and converted into the strength degradation coefficient α according to equations (2-9) and (2-10). s and residual strength coefficient R:

[0102] s3=s2·R (2-9)

[0103] e3=e2+·s2·(1-R) / (α d ·E0) (2-10)

[0104] Where s2 is the ultimate strength stress of the steel reinforcement, s3 is the strength degradation stress of the steel reinforcement, R is the residual strength coefficient, e2 is the ultimate strength strain of the steel reinforcement, e3 is the strength degradation strain of the steel reinforcement, E0 is the initial elastic modulus of the steel reinforcement, and α s This is the strength degradation coefficient.

[0105] S3. Using the hysteresis curves from step S1, perform single-factor analysis to obtain hysteresis control parameters that characterize the pinching effect and cyclic degradation characteristics of the component. These hysteresis control parameters include the damage control coefficient, pinching control coefficient, and unloading stiffness control coefficient. These hysteresis control parameters are used as the hysteresis rules for improving the rebar restoring force model. The hysteresis control parameters include the damage control coefficient d and the pinching control coefficient p. ch And the unloading stiffness control coefficient β, the selection method of each coefficient is explained in detail below.

[0106] The hysteretic model defines its hysteresis rules using five parameters: $damage1, $damage2, $pinchX, $pinchY, and $beta. $damage1 is the damage coefficient corresponding to the ductility change during material loading; $damage2 is the damage coefficient related to material energy dissipation during loading; $pinchX and $pinchY are the pinching coefficients controlling the loading segment of the hysteresis curve in the material restoring force model; and $beta is the unloading stiffness degradation coefficient related to the ductility change during loading.

[0107] In order to accurately analyze the influence of each hysteretic parameter in the rebar restoring force model, the hysteretic control parameters of the rebar restoring force model will be divided into three groups for single-factor analysis: damage control parameters, pinching control parameters, and unloading stiffness control parameters.

[0108] (1) Damage control parameter d: As damage1 increases, the strength and stiffness of the component significantly degrade when loaded to the 50mm displacement level. However, before the component reaches its peak strength, this damage coefficient has no significant effect on the hysteresis curve of the component. Simultaneously, the energy dissipation capacity of the component decreases with increasing ductile damage coefficient. Compared to the damage1 coefficient, the change in the damage2 coefficient has lower sensitivity to the hysteresis response of the component and the stress-strain relationship of the fiber, and its corresponding component damage and skeleton curve strength degradation coefficient α... s The residual strength coefficient R is coupled with the fiber element, which hinders the identification of subsequent damage control parameters. To ensure that the fiber element accurately describes the damage of the component under cyclic loading, only $damage1 is used as the damage control parameter for the rebar restoring force model, and it is represented by the damage coefficient d.

[0109] (2) Pinch control parameter p ch The loading segment path of the restoring force model during hysteretic loading is defined using the parameters $pinchX and $pinchY, thereby describing the hysteretic shape of the steel reinforcement material in RC columns under different failure modes. Variations in the values ​​of $pinchX and $pinchY will cause the hysteretic characteristics of the member to exhibit either a full or pinched hysteretic shape. Since the evaluation index for hysteretic simulation effectiveness in member elastoplastic analysis generally uses the energy dissipation area of ​​the hysteretic loop, there will be many combinations of $pinchX and $pinchY coefficients corresponding to the same hysteretic energy dissipation area in the Hysteretic model. This many-to-one mapping characteristic is not conducive to the subsequent identification of the pinching coefficient parameter in the restoring force model. To solve the above problem, the constraint $pinchX + $pinchY = 1 is introduced, and the pinching coefficient p is used to determine the hysteretic shape of the RC column under different failure modes. ch This represents the pinching control coefficient of the rebar restoring force model, based on the pinching coefficient p. ch The value of is changed, the loading path of the steel reinforcement restoring force model is adjusted, and the pinching coefficient p is adjusted. ch The conversion relationships with $pinchX and $pinchY are shown in equations (3-1) and (3-2):

[0110] $pinchX = p ch (3-1)

[0111] $pinchY = 1 - p ch (3-2)

[0112] When p ch When p = 0.5, the hysteresis rule of the rebar restoring force model is peak-oriented; when p ch As p approaches 0, the hysteresis shape of the rebar restoring force model becomes more complete; when p ch When the value approaches 1, the steel reinforcement restoring force model will exhibit pinching phenomenon.

[0113] (3) Unloading stiffness control parameter β: As $beta increases, the unloading stiffness of the steel reinforcement fibers degrades more significantly, which in turn causes the unloading stiffness in the hysteresis curve of the member to degrade and affects the hysteresis energy dissipation area of ​​the member. The $beta coefficient has a clear physical meaning in the unloading stiffness control of the member and can be used as the unloading stiffness control parameter β of the steel reinforcement restoring force model.

[0114] S4. Based on the skeleton control parameters of step S2 and the hysteresis control parameters of step S3, establish an improved steel reinforcement restoring force model.

[0115] S5. Based on the concrete constitutive model and the improved steel reinforcement restoring force model in step S4, establish an automatic elastic-plastic analysis model for the fiber element of the component. If the automatic elastic-plastic analysis model of the fiber element of the component conforms to the structural concept, proceed to step S6; otherwise, return to step S4.

[0116] Concrete02, a concrete constitutive model that can consider both compressive and tensile forces on concrete, is divided into confined concrete constitutive models and plain concrete constitutive models. To reasonably account for the improvement in ductility and strength of concrete caused by stirrups, the concrete surrounded by stirrups and the concrete cover in the cross-section are divided into two types of fiber materials, and the confined concrete constitutive model and the plain concrete constitutive model (without considering the improvement caused by stirrups) are used for simulation respectively.

[0117] The established automatic elastoplastic analysis model for fiber-reinforced concrete members divides the member into a bottom plastic zone and an upper elastoplastic zone, with the length of the bottom plastic zone being half the section height. The reinforced concrete column member is sectioned along the X and Y directions at a scale of 50 mm. For the reinforced concrete column member, its element section is mainly divided into three types of fibers: core concrete fibers, cover concrete fibers, and reinforcing steel fibers. Their stress-strain relationships are defined according to the selected constitutive models for confined concrete, plain concrete, and improved reinforcing steel restoring force, respectively.

[0118] A program for elastoplastic analysis of reinforced concrete columns was developed using OpenSeesPy, enabling fiber element modeling, elastoplastic analysis, and data visualization of the components.

[0119] S6. Determine the key target parameters of the skeleton curve in step S1. Based on the target error function of the skeleton control parameters in step S2, and based on the improved steel rebar restoring force model in step S4, use the three-way search algorithm to identify the optimal solution of the skeleton control parameters of the improved steel rebar restoring force model in step S4, and obtain the optimal solution of the skeleton control parameters.

[0120] Key target parameters for the skeleton curve include the strength adjustment coefficient. Ductility coefficient μ and strength degradation coefficient α s The target error functions for the skeleton control parameters are the errors in the peak bearing capacity, peak point displacement, and energy dissipation area of ​​the descending segment of the skeleton curve.

[0121] The skeleton curve of the improved rebar restoring force model proposed in this embodiment is adjusted by a strength adjustment coefficient. Strength hardening coefficient α h Ductility coefficient μ, strength degradation coefficient α s The three-segment skeleton curve is defined using five parameters, including the residual strength coefficient R. To avoid plastic localization, the strength hardening coefficient α is... hThe value is set to 0.03; since the residual strength coefficient R has a relatively small impact on the hysteretic response of the component, the residual strength coefficient R is set to 0.2. The strength adjustment coefficients for the other three parameters are... Ductility coefficient μ and strength degradation coefficient α s These are the key target parameters for the skeleton curve.

[0122] Based on the key target parameters of the three skeleton curves, the target error function for the skeleton control parameters is determined as follows:

[0123]

[0124] Among them, F pos_t F neg_ F′ represents the positive peak bearing capacity and negative peak bearing capacity in the component test results. pos_s F′ neg_s The positive and negative bearing capacities in the component simulation results correspond to the peak displacement of its test results. The objective function is the intensity adjustment coefficient.

[0125]

[0126] Among them, D pos_t D neg_t D represents the displacement values ​​corresponding to the positive and negative peak bearing capacities in the component test results. pos_s D neg_s δ represents the displacement values ​​corresponding to the positive and negative peak bearing capacities in the component simulation results. μ The objective function is the ductility coefficient.

[0127]

[0128] Among them, E pos_down_t E neg_down_t E represents the area corresponding to the descending segments of the positive and negative skeleton curves in the component test results. pos_down_s E neg_down_s This refers to the area corresponding to the descending segments of the positive and negative skeleton curves in the component simulation results. The objective function is the intensity degradation coefficient.

[0129] As the skeleton control parameters approach the optimal solution, their objective function value approaches 0. The optimization identification process of the skeleton control parameters involves finding the maximum and minimum values ​​of a unimodal function, and a three-way search algorithm is used for skeleton parameter identification. Figure 5 To find the minimum value of a known interval [L, R], the interval can be divided into three equal parts based on its length to obtain the midpoint L. mid With R mid By comparing L midWith R mid The corresponding function values ​​are used to update the boundary values ​​of the solution interval; this process is repeated iteratively until the interval length or computational accuracy meets the solution requirements; where L, R, and L... mid and R mid represent Figure 7 The values ​​of the horizontal axis of the curve, and δ(L), δ(R), δ(L) mid ) and δ(R mid ) then represents Figure 7 The values ​​of the vertical axis of the curve are in one-to-one correspondence with each other. Figure 6 is a schematic diagram of the three-way search algorithm to find the minimum value. In the first three-way search, δ(L) mid_1 )<f(R mid_1 The solution interval is updated to [L, R]. mid_1 During the second three-way search, δ(L) mid_2 )>f(R mid_2 The solution interval is updated to [L]. mid_2 ,R mid_1 In the identification of skeleton control parameters, when the length of the interval solved by the ternary search is less than the allowable error tol of the parameter or the maximum value of the error objective function corresponding to the interval boundary value is less than 1%, the current iterative solution will be stopped, and the midpoint of the current solution interval is the optimal solution of the skeleton control parameters.

[0130] S7. Determine the key target parameters of the hysteresis curve in step S1. Based on the target error function of the hysteresis control parameters in step S3, and based on the improved steel reinforcement restoring force model in step S4, use the differential evolution algorithm to identify the optimal solution of the hysteresis control parameters of the improved steel reinforcement restoring force model in step S4, and obtain the optimal solution of the hysteresis control parameters.

[0131] The key target parameter of the hysteresis curve is the pinch factor p. ch The target error function of the hysteresis control parameter is the non-overlapping area of ​​the hysteresis loop of the component, along with the unloading stiffness degradation coefficient β.

[0132] (1) The improved steel reinforcement restoring force model selected in this embodiment is mainly based on the pinching coefficient p. ch The hysteretic energy dissipation of the component is simulated by adjusting the unloading stiffness degradation coefficient β. The non-overlapping area of ​​the component's hysteresis loop is chosen as the pinching coefficient p. ch The target parameter identified by the unloading stiffness degradation coefficient β, and the error function related to the non-overlapping area of ​​the component hysteresis loop are calculated by equations (6-1) and (6-2):

[0133]

[0134]

[0135] Since the process of solving the error function of the non-overlapping area of ​​the hysteresis loop of the component is a multi-parameter optimization process, the differential evolution algorithm is used to solve the hysteresis control parameters of the improved steel reinforcement restoring force model.

[0136] (2) Automated solution of hysteretic control parameters for the improved steel reinforcement restoring force model based on differential evolution algorithm, such as... Figure 7 As shown, the solution to its optimal parameters mainly consists of four steps: initializing the population, mutation, crossover, and selection. The optimal parameters are determined based on the corresponding fitness function and the maximum number of generations G. max Determine the optimal combination of parameters for the solution:

[0137] ① Initialize the population: Within the initially defined parameter range, randomly generate a certain number of individuals to form an initial population. The larger the population size N, the lower the algorithm's efficiency; the smaller N is, the more likely the algorithm is to get trapped in local optima. Typically, N is 5-10 times the vector dimension. For a two-dimensional vector, let N = 20, generating 20 random individuals (x1, x2, ..., x...). 20 The fitness of the initial population is calculated based on the fitness function. For parameter identification, the reciprocal of the pinch-down coefficient target error function is used as the fitness function.

[0138]

[0139] ② Mutation: For each individual in the population, 3 individuals (xi, xi, xi) are randomly selected from the other 19 individuals. r1 ,x r2 ,x r3 Differential mutation is performed, and the degree of mutation is determined according to the scaling factor F (0.5 in this chapter) to obtain the mutant population (v1, v2, ..., v). 20 The difference variation is shown in equation (6-4):

[0140] v i =x r1 +F·(x r2 -x r3 (6-4)

[0141] ③ Crossover: Through crossover operation, individuals in the original population undergo feature transformation with their corresponding mutated individuals. During the process, each original individual randomly retains one-dimensional information, and the remaining information is replaced according to the crossover probability CR (0.5 in this embodiment), that is, information is replaced with a 50% probability, thereby obtaining the crossover population (c1, c2, ..., c...). 20 ).

[0142] ④ Selection: Based on the principle of survival of the fittest, select the x-th elements of the original population in sequence. i c of cross-population iSelection is performed, that is, the number of individuals s in the offspring population is determined based on the size of the fitness function. i This is the process of biological evolution.

[0143] ⑤ Calculation Termination: When the fitness of the best individual in the population is greater than the fitness limit of 100, i.e. When the error value is less than 0.01, or the number of evolutionary generations reaches the maximum number of evolutionary generations G. max The calculation can be terminated when the optimal individual in the population is reached, which is the optimal solution for the hysteresis control parameters.

[0144] S8. Using the component design feature parameters from step S1 as input parameters, and the optimal solutions of the skeleton control parameters from step S6 and the optimal solutions of the hysteresis control parameters from step S7 as output parameters, a constitutive model of component steel bar based on machine learning (SteelML) is obtained. This model is then trained and its prediction performance is evaluated to obtain an improved steel bar restoring force model with excellent prediction results. Step S8 includes the following steps:

[0145] S801. Determine the evaluation index of the constitutive parameter prediction model for structural members; the evaluation index includes the coefficient of determination (R2), mean absolute error (MAE), root mean square error (RMSE), root mean square logarithmic error (RMSLE), and mean absolute percentage error (MAPE).

[0146] S802. The component design characteristic parameters are used as input parameters for the component reinforcement constitutive parameter prediction model; these input parameters include the axial compressive strength f′ of the concrete cylinder. c Longitudinal reinforcement ratio ρ, volumetric stirrup ratio ρ v Shear span ratio λ, axial compressive coefficient n, and bending-shear ratio m;

[0147] S803. The optimal solutions of the skeleton control parameters and the optimal solutions of the hysteretic control parameters are used as the output parameters of the structural reinforcement constitutive parameter prediction model; these output parameters include the strength adjustment coefficients of the skeleton control parameters in the improved reinforcement restoring force model. Ductility coefficient μ, strength degradation coefficient α s Hysteresis control parameter pinch coefficient p ch and unloading stiffness degradation coefficient β;

[0148] S804. Gradient Boost Regression Tree (GBRT) algorithm is adopted as the core intelligent algorithm for predicting the constitutive parameters of steel reinforcement in structural members. The k-fold cross-validation method is used to randomly divide all input and output parameters into training and test sets. The training set is used to train the model for predicting the constitutive parameters of steel reinforcement in structural members, and the test set is used to evaluate the effect of the model. This results in an improved steel reinforcement restoring force model with excellent prediction performance.

[0149] The prediction performance of the GBRT algorithm model depends on the training sample dataset and the selection of model hyperparameters. To build a reliable SteelML model, key steps such as sample dataset partitioning and data preprocessing need to be completed sequentially in the model design and training.

[0150] (1) Data set partitioning: The dataset is divided into training set and test set. 85% of the dataset (i.e., the training set) is used to train and build the constitutive parameter prediction model of structural steel reinforcement. The remaining 15% of the dataset (i.e., the test set) is used to evaluate the prediction effect of the GBRT algorithm model.

[0151] To ensure the test set is sufficiently representative of the components in the digital component test database, stratified random sampling was used to sample components in the test set exhibiting bending, bending-shear, and shear failure modes at a ratio of 4:2:1, taking into account the proportions of components with the three failure modes in the database. The test set contained 21 RC column components, of which 12 failed in bending, 6 failed in bending-shear, and 3 failed in shear.

[0152] (2) Data Preprocessing: Data normalization is selected for preprocessing the dataset, and feature interval scaling is performed based on the maximum absolute value of the data features. This limits the data distribution range to [-1, 1], and the transformation formula is shown in equation (7-1).

[0153]

[0154] Where, |x| max The maximum absolute value of a feature in the dataset.

[0155] Based on the determined prediction model evaluation indices, the model evaluation indices for predicting 21 components in the test set are shown in Table 1. Since the results of the strength degradation coefficient and unloading stiffness degradation coefficient contain 0 values ​​or near-0 values, RMSLE and MAPE are not suitable for analysis. Therefore, analysis is mainly conducted using RMSLE and MAPE. 2 The model was evaluated using three metrics: strength adjustment factor (MAE), ductility coefficient (RMSE), and unloading stiffness coefficient (RMSE). The SteelML model demonstrated high simulation accuracy for the strength adjustment factor, ductility coefficient, and unloading stiffness coefficient.2 It can reach around 0.9, the strength degradation coefficient R 2 The R value is 0.733, representing the unloading stiffness degradation coefficient. 2 The value was 0.799, and the MAE and RMSE of each model were at a low level, indicating that the SteelML model has sufficient generalization ability on the test set and can accurately describe the nonlinear topological relationship between the component design characteristic parameters of the components in the training set and the control parameters of the improved steel reinforcement restoring force model. The prediction results of the control parameters of the improved steel reinforcement restoring force model of the SteelML model have high reliability.

[0156] Table 1 Evaluation metrics for the SteelML model test set

[0157]

[0158] To visually demonstrate the prediction accuracy of the SteelML model on the test set samples, such as Figure 8 As shown, using the control parameter identification results of the improved rebar restoring force model in the digital component test database as the x-axis and the prediction results of the SteelML model as the y-axis, scatter plots comparing the predictions of five machine learning models were drawn. The circular dots represent the prediction results of the SteelML model for components divided into the training set, the square dots represent the prediction results of the SteelML model for components divided into the test set, and the solid line in the middle is a function of y = x. When the scatter points are concentrated near the solid line, it indicates that the prediction accuracy of the SteelML model is high, and the prediction results are consistent with the parameter identification results.

[0159] S9. Perform elastoplastic analysis on the improved reinforcing steel restoring force model from step S8; the method for performing elastoplastic analysis on the fiber elements in step S9 includes the following steps:

[0160] S901. Evaluate the prediction progress and generalization ability of the improved steel bar restoring force model in step S8. If the improved steel bar restoring force model has good accuracy, proceed to step S902; otherwise, return to step S8.

[0161] S902. Perform component elastic-plastic analysis verification on the automatic elastic-plastic analysis model of component fiber element in step S5. If the improved steel bar restoring force model is verified as good, proceed to step S903; otherwise, return to step S8.

[0162] S903. Based on machine learning, perform parameter prediction on the improved steel bar restoring force model of step S8.

[0163] To verify the effectiveness of the SteelML model in simulating the response of RC columns under cyclic loads in the elastoplastic analysis of RC columns, elastoplastic analysis was performed on RC column members in the test set using fiber elements with different improved steel reinforcement restoring force models. Since the members in the test set were not involved in the construction of the SteelML model, the generalization ability of the SteelML model can be fully verified, and it is representative of RC column members in practical applications. The elastoplastic analysis results of 9 typical members were selected for comparative analysis, including 3 RC column members each of bending failure, bending-shear failure and shear failure.

[0164] As shown in Table 2, elastoplastic analysis was conducted on nine RC column members using the commonly used Steel01 and Steel02 models, the SteelML model built based on machine learning, and parameter results identified from experimental data. The SteelML model showed an average fitting error of approximately 10% for the peak bearing capacity, cumulative energy dissipation area, and hysteretic energy dissipation capacity of the members in the elastoplastic analysis. This significantly improved the fitting accuracy compared to the commonly used Steel01 and Steel02 models, with average fitting accuracies of 11.60% and 17.84% for peak bearing capacity and cumulative energy dissipation area, respectively. Furthermore, the commonly used improved steel reinforcement restoring force model performed poorly in fitting the hysteretic energy dissipation capacity of the members, with an average error of approximately 40%. The fitting accuracy of the SteelML model was 28.47% higher than that of the commonly used improved steel reinforcement restoring force model. Meanwhile, the accuracy of the elastoplastic analysis model of the SteelML model is basically consistent with the simulation accuracy of the parameter identification results based on experimental data. This indicates that the SteelML model can replace the cumbersome parameter identification steps and accurately predict the control parameters of the improved steel reinforcement restoring force model of RC column members through the powerful generalization ability of machine learning models, effectively improving the elastoplastic analysis simulation accuracy of fiber elements.

[0165] Table 2 Comparison of fiber element fitting errors using different improved steel reinforcement restoring force models

[0166]

[0167]

[0168] The above-described specific embodiments are preferred embodiments of the present invention and are not intended to limit the present invention. Any other changes or equivalent substitutions made without departing from the technical solution of the present invention are included within the protection scope of the present invention.

Claims

1. A seismic analysis method employing an improved steel reinforcement restoring force model, characterized in that, Includes the following steps: S1. Collect low-cycle reciprocating test data, perform equivalent transformation of the component loading mode on the low-cycle reciprocating test data to obtain component design characteristic parameters, then transform and extract the PEER structural performance database to obtain hysteresis curves and skeleton curves, and build a digital component test database based on the component design characteristic parameters, the hysteresis curves and the skeleton curves. S2. Perform dimensionless transformation on the skeleton curve described in step S1 to obtain the skeleton control parameters; S3. Perform single-factor analysis based on the hysteresis curve described in step S1 to obtain hysteresis control parameters, and use the hysteresis control parameters as the hysteresis rules for improving the steel reinforcement restoring force model. S4. Based on the skeleton control parameters in step S2 and the hysteresis control parameters in step S3, establish the improved steel reinforcement restoring force model; S5. Based on the concrete constitutive model and the improved steel reinforcement restoring force model described in step S4, establish an automatic elastoplastic analysis model for the fiber elements of the component; wherein, establishing the automatic elastoplastic analysis model for the fiber elements of the component includes the following steps: S51. Divide the component into a bottom plastic hinge region and an upper elastoplastic region; S52. Perform fiber mesh subdivision on the cross section of the component to distinguish the core area concrete fibers, protective layer concrete fibers and steel reinforcement fibers; assign a constrained concrete constitutive model to the core area concrete fibers, assign a plain concrete constitutive model to the protective layer concrete fibers, and assign the improved steel reinforcement restoring force model established in step S4 to the steel reinforcement fibers. After establishing the automatic elastoplastic analysis model of the fiber unit of the component, proceed to step S6; S6. Determine the key target parameters of the skeleton curve in step S1. Based on the target error function of the skeleton control parameters in step S2, and based on the improved steel rebar restoring force model in step S4, use the three-way search algorithm to identify the optimal solution of the skeleton control parameters of the improved steel rebar restoring force model in step S4, and obtain the optimal solution of the skeleton control parameters. S7. Determine the key target parameters of the hysteresis curve in step S1. Based on the target error function of the hysteresis control parameters in step S3, and based on the improved steel reinforcement restoring force model in step S4, use the differential evolution algorithm to identify the optimal solution of the hysteresis control parameters of the improved steel reinforcement restoring force model in step S4, and obtain the optimal solution of the hysteresis control parameters. S8. Using the component design feature parameters in step S1 as input parameters, and the optimal solutions of the skeleton control parameters in step S6 and the optimal solutions of the hysteresis control parameters in step S7 as output parameters, a component reinforcement constitutive parameter prediction model is obtained. The component reinforcement constitutive parameter prediction model is trained and the prediction effect is evaluated to obtain the improved reinforcement restoring force model with excellent prediction effect. S9. Perform elastoplastic analysis on the improved steel reinforcement restoring force model described in step S8.

2. The seismic analysis method using the improved steel reinforcement restoring force model according to claim 1, characterized in that, Step S1 includes the following steps: S101. Collect low-cycle cyclic test data of components from the PEER structural performance database and literature. S102. Perform an equivalent transformation of the component loading mode on the low-cycle reciprocating test data of the component to obtain basic characteristic parameters; S103. Calculate the basic feature parameters to obtain the calculated feature parameters; S104. Extract the hysteresis curve from the PEER structural performance database; S105. Extract the skeleton curve from the hysteresis curve; S106. By matching the component design feature parameters, the hysteresis curve and the skeleton curve one by one, a digital component test database is built. The basic characteristic parameters in step S102 include geometric information, concrete information, longitudinal reinforcement information, stirrup information, and axial force information.

3. The seismic analysis method using the improved steel reinforcement restoring force model according to claim 2, characterized in that, The calculated characteristic parameters in step S103 include longitudinal reinforcement ratio, volumetric stirrup ratio, shear span ratio, axial compressive strength coefficient, and bending-shear ratio.

4. The seismic analysis method using the improved steel reinforcement restoring force model according to claim 1, characterized in that, Step S8 includes the following steps: S801. Determine the evaluation index of the constitutive parameter prediction model for the structural reinforcement of the component; S802. Use the component design characteristic parameters as input parameters for the component reinforcement constitutive parameter prediction model; S803. The optimal solutions of the skeleton control parameters and the optimal solutions of the hysteresis control parameters are used as the output parameters of the component reinforcement constitutive parameter prediction model. S804. The gradient boosting regression tree algorithm is adopted as the core intelligent algorithm of the structural steel reinforcement constitutive parameter prediction model. The input parameters and output parameters are randomly divided into training set and test set using the k-fold cross-validation method. The training set is used to train the structural steel reinforcement constitutive parameter prediction model, and the test set is used to evaluate the effect of the structural steel reinforcement constitutive parameter prediction model, so as to obtain the improved steel reinforcement restoring force model with excellent prediction effect.

5. The seismic analysis method using the improved steel reinforcement restoring force model according to claim 1, characterized in that, The method for performing elastoplastic analysis on the fiber unit in step S9 includes the following steps: S901. Evaluate the model prediction accuracy and generalization ability of the improved steel bar restoring force model described in step S8. If the improved steel bar restoring force model has good accuracy, proceed to step S902; otherwise, return to step S8. S902. Perform component elastic-plastic analysis verification on the automatic elastic-plastic analysis model of the component fiber unit in step S5. If the automatic elastic-plastic analysis model of the component fiber unit is verified as good, proceed to step S903; otherwise, return to step S8. S903. Based on machine learning, perform parameter prediction on the improved steel bar restoring force model described in step S8.

6. The seismic analysis method using the improved steel reinforcement restoring force model according to claim 1, characterized in that, The key inflection points of the skeleton curve in step S2 include the yield strength point, the ultimate strength point, and the strength degradation point.

7. The seismic analysis method using the improved steel reinforcement restoring force model according to claim 1, characterized in that, The skeleton control parameters mentioned in step S2 include strength adjustment coefficient, strength hardening coefficient, ductility coefficient, strength degradation coefficient, and residual strength coefficient.

8. The seismic analysis method using the improved steel reinforcement restoring force model according to claim 1, characterized in that, The hysteresis control parameters in step S3 include damage control coefficient, pinch control coefficient, and unloading stiffness control coefficient.

9. The seismic analysis method using the improved steel reinforcement restoring force model according to claim 1, characterized in that, The key target parameters of the skeleton curve in step S6 include the strength adjustment coefficient, ductility coefficient, and strength degradation coefficient.

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