CN115659813A - Seismic analysis method adopting improved steel bar restoring force model - Google Patents
Seismic analysis method adopting improved steel bar restoring force model Download PDFInfo
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Abstract
The invention discloses an earthquake-resistant analysis method adopting an improved steel bar restoring force model, which is based on a built digital component test database, takes the improved steel bar restoring force model and a concrete constitutive model which can consider the tension characteristic as material constitutive, adopts a fiber unit based on a rigidity method to build an automatic elastoplasticity analysis model of the component fiber unit, performs optimal solution identification of control parameters, and builds a component steel bar constitutive parameter prediction model which takes component design characteristic parameters as input and takes the improved steel bar restoring force model control parameters as output and trains the model. The invention can consider the interaction among different materials and the influence of the macroscopic characteristics of the component on the mechanical property of the material, further consider the complex hysteresis characteristic of the component, and improve the elastic-plastic calculation precision and simultaneously ensure the calculation efficiency by embedding the improved steel bar restoring force model into the fiber unit to perform the elastic-plastic analysis of the component in the structural earthquake resistance.
Description
Technical Field
The invention relates to the technical field of structural seismic analysis and numerical simulation, in particular to a seismic analysis method adopting an improved steel bar restoring force model.
Background
At present, a structural seismic analysis work is mainly to establish a fine finite element model for a structure and carry out accurate and efficient elastoplasticity analysis, and a seismic design method which tends to be perfect is gradually formed at home and abroad. Among them, the earthquake-resistant design method based on performance is more and more favored by scholars and engineers as a mainstream of the earthquake-resistant analysis method.
The implementation of structural seismic performance design relies on reliable elasto-plastic analysis methods. The selection of the unit constitutive model is a key ring in the finite element elastic-plastic model building process, and the quality of the unit constitutive model directly influences the accuracy of numerical analysis. At present, the mainstream unit constitutive model at home and abroad comprises a fiber unit and a concentrated plastic hinge unit. Compared with a centralized plastic hinge unit, the fiber unit allows plasticity to develop at any position in the unit, and is widely applied to simulation of elastic-plastic response of beam-column members. The fiber unit simulates the elastic-plastic response of the reinforced concrete member under the reciprocating load through the assumption of a flat section and the uniaxial constitutive relation of the steel bar and the concrete, but the complex hysteresis characteristics caused by the interaction between materials, such as shearing effect, bonding slippage and the like, are difficult to describe, so that the mechanical property of a finite element model using the fiber unit cannot be accurately evaluated. Although many scholars consider the adhesion slip effect by adding adhesion slip units or correcting a steel bar restoring force model, the problems of low calculation efficiency or complicated definition of model parameter correction and the like still exist.
In conclusion, the fiber unit is mostly adopted to simulate the elastic-plastic response of the reinforced concrete member under the action of the reciprocating load. In order to overcome the defects that a classical fiber model cannot accurately simulate interaction between materials such as a shearing effect and a bonding slippage effect due to the fact that a uniaxial tension-compression mechanism is adopted, calculation precision is further improved, calculation efficiency is considered, a more efficient and accurate method needs to be adopted to correct a steel bar restoring force model based on component test data so as to effectively improve simulation precision of a fiber unit, and then interaction between different materials and influence of component macroscopic characteristics on mechanical properties of the materials are considered.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides an earthquake-resistant analysis method adopting an improved steel bar restoring force model.
The purpose of the invention is realized by the following technical scheme: the earthquake resistance analysis method adopting the improved steel bar restoring force model comprises the following steps:
s1, collecting low-cycle reciprocating test data, performing equivalent conversion of a component loading mode on the low-cycle reciprocating test data to obtain component design characteristic parameters, converting and extracting a PEER structural performance database to obtain a hysteresis curve and a skeleton curve, and building a digital component test database according to the component design characteristic parameters, the hysteresis curve and the skeleton curve;
s2, carrying out dimensionless conversion according to the skeleton curve in the step S1 to obtain skeleton control parameters;
s3, performing single-factor analysis according to the hysteresis curve in the step S1 to obtain a hysteresis control parameter, and taking the hysteresis control parameter as a hysteresis rule of an improved steel bar restoring force model;
s4, establishing an improved steel bar restoring force model according to the skeleton control parameters in the step S2 and the hysteresis control parameters in the step S3;
s5, establishing an automatic elastic-plastic analysis model of the member fiber unit according to the concrete constitutive model and the improved steel bar restoring force model in the step S4, executing the step S6 if the automatic elastic-plastic analysis model of the member fiber unit conforms to the structural concept, and otherwise, returning to the step S4;
s6, determining key target parameters of the skeleton curve in the step S1, and identifying optimal solutions of skeleton control parameters of the improved steel bar restoring force model in the step S4 by utilizing a trisection search algorithm on the basis of a target error function of the skeleton control parameters in the step S2 to obtain optimal solutions of the skeleton control parameters;
s7, determining key target parameters of the hysteresis curve in the step S1, and carrying out optimal solution identification on the hysteresis control parameters of the improved steel bar restoring force model in the step S4 by using a differential evolution algorithm based on the improved steel bar restoring force model by taking the target error function of the hysteresis control parameters in the step S3 as a basis to obtain the optimal solution of the hysteresis control parameters;
s8, obtaining a component steel bar constitutive parameter prediction model by taking the component design characteristic parameters in the step S1 as input parameters and the optimal framework control parameter solution in the step S6 and the optimal hysteresis control parameter solution in the step S7 as output parameters, and training and estimating the prediction effect of the component steel bar constitutive parameter prediction model to obtain the improved steel bar restoring force model with excellent prediction effect;
and S9, performing component elastic-plastic analysis on the improved steel bar restoring force model in the step S8.
Preferably, step S1 includes the following steps:
s101, collecting low-cycle reciprocating test data of the component from a PEER structural performance database and literature data;
s102, performing equivalent conversion of a component loading mode on the component low-cycle reciprocating test data to obtain basic characteristic parameters;
s103, calculating the basic characteristic parameters to obtain calculated characteristic parameters;
s104, extracting from the PEER structure performance database to obtain a hysteresis curve;
s105, extracting through the hysteresis curve to obtain a skeleton curve;
and S106, establishing a digital component test database by matching the component design characteristic parameters, the hysteresis curves and the skeleton curves one by one.
Preferably, the basic characteristic parameters in step S102 include geometric information, concrete information, longitudinal bar information, stirrup information, and axial force information.
Preferably, the characteristic parameters calculated in step S103 include longitudinal bar reinforcement ratio, volume reinforcement ratio, shear span ratio, axial pressure coefficient and bending shear ratio.
Preferably, step S8 includes the following steps:
s801, determining an evaluation index of the component steel bar constitutive parameter prediction model;
s802, taking the component design characteristic parameters as input parameters of the component steel bar constitutive parameter prediction model;
s803, taking the optimal solution of the skeleton control parameters and the optimal solution of the hysteresis control parameters as output parameters of the constitutive parameter prediction model of the member steel bar;
s804, a gradient lifting regression tree algorithm is adopted as a core intelligent algorithm of the component steel bar constitutive parameter prediction model, the input parameters and the output parameters are randomly divided into a training set and a testing set by adopting a k-fold cross verification method, the data training of the component steel bar constitutive parameter prediction model is carried out by adopting the training set, the effect evaluation of the component steel bar constitutive parameter prediction model is carried out by adopting the testing set, and the improved steel bar restoring force model with excellent prediction effect is obtained.
Preferably, the method for performing elastic-plastic analysis on the component by the fiber unit in step S9 includes the following steps:
s901, carrying out model prediction precision and generalization capability evaluation on the improved steel bar restoring force model in the step S8, if the improved steel bar restoring force model is good in precision, executing the step S902, otherwise, returning to the step S8;
s902, performing component elastoplasticity analysis verification on the component fiber unit automatic elastoplasticity analysis model in the step S5, executing the step S903 if the component fiber unit automatic elastoplasticity analysis model is verified well, otherwise, returning to the step S8;
and S903, performing parameter prediction on the improved steel bar restoring force model in the step S8 based on machine learning.
Preferably, the key turning points of the skeleton curve in step S2 include yield strength points, ultimate strength points, and strength degradation points.
Preferably, the skeleton control parameters in step S2 include a strength adjustment coefficient, a strength hardening coefficient, a ductility coefficient, a strength degradation coefficient, and a residual strength coefficient.
Preferably, the hysteresis control parameter in step S3 includes a damage control coefficient, a pinch control coefficient, and an unload stiffness control coefficient.
Preferably, the key target parameters of the skeleton curve in step S6 include an intensity adjustment coefficient, a ductility coefficient, and an intensity degradation coefficient.
Compared with the prior art, the invention has the following advantages and beneficial effects:
the invention adopts the earthquake-resistant analysis method of the improved steel bar restoring force model, can consider the interaction among different materials and the influence of the macroscopic characteristics of the component on the mechanical property of the material, further consider the complex hysteresis characteristic of the component, and carry out the elastic-plastic analysis of the component in the structural earthquake resistance by embedding the improved steel bar restoring force model in the fiber unit, thereby improving the elastic-plastic calculation precision and simultaneously ensuring the calculation efficiency.
Drawings
FIG. 1 is a flow chart of a seismic analysis method of the present invention using an improved steel bar restoring force model;
FIG. 2 is a schematic diagram of the experimental loading mode of the present invention;
FIG. 3 is a schematic diagram of skeleton curve extraction according to the present invention;
FIG. 4 is a schematic view of an automatic elasto-plastic analysis model of a component fiber unit of the present invention;
FIG. 5 is a flowchart of the step S6 of solving the optimal solution identification of the skeleton control parameters according to the present invention;
FIG. 6 is a schematic diagram of the minimum value calculated by the trisection search algorithm in step S6 according to the present invention;
FIG. 7 is a flowchart illustrating the identification of the hysteresis control parameter in step S7 according to the present invention;
fig. 8 is a scatter diagram comparing the predicted result of the SteelML model and the parameter identification result in step S9.
Detailed Description
The objects of the present invention will be described in further detail with reference to the drawings and specific examples, which are not repeated herein, but the embodiments of the present invention are not limited to the following examples.
The embodiment takes the establishment of a database, the determination of control parameters of an improved steel bar restoring force model, the identification of an optimal solution of the control parameters, and the establishment and application of a component steel bar constitutive parameter prediction model as examples. The earthquake resistance analysis method adopting the improved steel bar restoring force model comprises the following steps:
s1, preliminarily collecting low-cycle reciprocating test data, performing equivalent conversion of a component loading mode on the low-cycle reciprocating test data to obtain component design characteristic parameters (including basic characteristic parameters and calculation characteristic parameters), converting and extracting the low-cycle reciprocating test data to obtain a hysteresis curve and a skeleton curve, and building a digital component test database according to the component design characteristic parameters, the hysteresis curve and the skeleton curve; the step S1 includes the steps of:
s101, collecting low-cycle reciprocating test data of the reinforced concrete member from literature data related to the reinforced concrete member test and database information provided by a Peer (Pacific Earth Engineering Research) structural performance database;
s102, carrying out equivalent conversion of a component loading mode on the component low-cycle reciprocating test data to obtain basic characteristic parameters; the basic characteristic parameters comprise geometric information, concrete information, longitudinal bar information, stirrup information and axial force information; the component loading mode includes cantilever type (the component bottom is equipped with fixing support, and the lateral force is applyed in the cantilever end), double curvature formula (the component bottom is equipped with fixing support, and the lateral force is applyed in top support department that can horizontal slip), two simple support formulas (the component both ends are simply supported, and the lateral force is applyed in middle part support). In order to unify the load and displacement results of the reinforced concrete member low-cycle reciprocating test database, the three lateral loading modes need to be equivalently converted, namely, the member loading mode is converted into equivalent cantilever member loading, as shown in fig. 2. The conversion relation is calculated as follows:
V E ＝V C ＝V DC ＝V DE /2 (1-1)
Δ E ＝Δ C ＝Δ DC /2＝Δ DE (1-2)
L E ＝L C ＝L DC /2＝L DE (1-3)
(1) The geometric information comprises a section height h, a section width b, an equivalent cantilever length l and a protective layer thickness c;
(2) The concrete information comprises the compressive strength f of the axis of the concrete cylinder' c Compressive strength f of concrete axle center c Concrete cube compressive strength f cu ；
(3) The longitudinal bar information comprises the diameter of the angle bar, the diameter of the middle steel bar, the number of the middle steel bars in the X direction, the number of the middle steel bars in the Y direction and the yield strength f of the longitudinal bar y Ultimate strength of longitudinal bar f u Elastic modulus E s ；
(4) The stirrup information comprises the diameter of the stirrup, the form of the stirrup, the distance s between the stirrups and the yield strength f of the stirrup yv Ultimate strength f of stirrup uv ；
(5) The axial force information includes a design axial compression ratio n d And an axial force value P.
In order to facilitate parameter identification of subsequent improved steel bar restoring force model and construction of component steel bar constitutive parameter prediction model, concrete strength information in a database is uniformly converted into concrete cylinder axis compressive strength f 'by adopting the following formula' c And adjusting the conversion coefficient of the concrete with different strengths according to the correlation coefficient given by CEB-FIP and MC-90:
f′ c ＝0.79f cu,k (1-4)
in units of N, kN, mm, m, in, lb and the like related in the statistics of the basic characteristic parameters of the materials of the PEER structure performance database, the database uniformly adopts N and mm for conversion.
S103, calculating the basic characteristic parameters to obtain calculated characteristic parameters; the characteristic parameters comprise longitudinal bar reinforcement ratio, volume reinforcement ratio, shear span ratio, axial pressure coefficient and bending shear ratio.
(1) The longitudinal reinforcement ratio rho is the ratio of the reinforcement area of the full section of the RC column component to the section area of the RC column, and the collected RC column tests are symmetrical reinforcement, so that the reinforcement ratio of the single-side reinforcement of each component is half of the reinforcement ratio of the longitudinal reinforcement.
ρ＝A s /A (1-5)
Where ρ is the longitudinal reinforcement ratio, A s The area of the reinforcing bar is the whole section area, and A is the section area of the component.
(2) Volume hooping ratio rho of hooped reinforcement v The volume of the reinforcement of the stirrup is compared with the volume of the concrete in the core area, and the size of the restraint effect of the stirrup on the core concrete is represented.
In the formula, ρ v For the volume of the stirrup, n 1 And n 2 The number of limbs of the stirrup in the X-and Y-directions, A s1 And A s2 Is the cross-sectional area of the X-direction and Y-direction single limb stirrups 1 And l 2 The length of the X-and Y-directional single limb stirrup, A cor The area of the concrete in the core area of the member is s, and the distance between stirrups is s.
(3) Equivalent cantilever height L calculated by the formula (1-3) of the shear-span ratio lambda E And effective height h of the cross section 0 The ratio of (a) to (b) is obtained.
λ＝L E /h 0 (1-7)
Wherein λ is the shear-span ratio, L E To an equivalent cantilever height, h 0 Is the effective height of the cross section.
(4) The axial pressure coefficient n is the ratio of the tested axial pressure of the member to the product of the full section area of the member and the axial compression strength standard value of the concrete. As the tested axial pressure coefficient increases, the bending resistance bearing capacity of the component increases firstly and then decreases.
Wherein n is the axial pressure coefficient, P is the axial pressure value of the test, A c Is the concrete area of the member, f ck Is the standard value of the compressive strength of the axle center of the concrete.
(5) The bending shear ratio m reflects the difference between the bending resistance bearing capacity and the shearing resistance bearing capacity of the component, and can be equivalent to the ratio of the bending resistance bearing capacity of the section to the product of the shearing resistance bearing capacity of the section and the equivalent cantilever height for the cantilever component in the RC column test database.
Wherein M is the bending shear ratio, M u Is the bending resistance bearing capacity of the member, V u Is the shear-resisting bearing capacity of the component, L E Equivalent cantilever height.
S104, extracting from the low cycle reciprocating test data to obtain a hysteresis curve; and uniformly converting a force-displacement curve and a bending moment-corner curve included in the low-cycle reciprocating test data and related units of N, kN, m, mm and the like into a force-displacement curve taking kN and mm as units.
S105, converting through a hysteresis curve to obtain a skeleton curve; a skeleton curve of the component in the low-cycle reciprocating loading process is obtained by a connecting line of a first-circle hysteretic loading section of a hysteretic curve and a displacement peak point of each subsequent level of loading, and the skeleton curve is an important reference for researching the mechanical property and the deformation characteristic of the component.
And S106, matching the component design characteristic parameters, the hysteresis curves and the skeleton curves one by one, and thus building a digital component test database. A digital component test database of 140 RC (reinforced Concrete) column test data is built, in the database, the cross section of a component is square or rectangular, and the reinforcing bars are symmetrically arranged.
S2, setting a key turning point on the skeleton curve in the step S1, and carrying out dimensionless conversion on the stress value and the strain value of the key turning point to obtain skeleton control parameters of an improved steel bar restoring force model;
key turning points include yield strength points, ultimate strength points, and strength degradation points. Assuming that the framework curve of the steel bar restoring force model is in an origin point symmetry type, so as to reduce framework control parameters of the steel bar restoring force model, sequentially carrying out dimensionless processing on a yield strength point, an ultimate strength point and a strength degradation point in the framework curve, converting the definitions of the stress value and the strain value of each key turning point into 5 dimensionless framework control parameters, wherein the framework control parameters comprise a strength adjustment coefficient, a strength hardening coefficient, a ductility coefficient, a strength degradation coefficient and a residual strength coefficient.
Yield strength point (e) 1 ,s 1 ) The yield strength and initial modulus of elasticity of the bonded steel bar are converted into strength adjustment coefficients according to the formulas (3-1) and (3-2)
Definition of (1):
e 1 ＝s 1 /E 0 (2-2)
wherein, f y Is the yield strength (MPa), E, of the steel bar 0 Is the initial modulus of elasticity (2.0X 10) of the steel bar 5 MPa)，
The coefficient is adjusted for the strength of the steel bar.
In order to reasonably describe the physical relationship between the ultimate strength point and the yield strength point, two dimensionless parameters, namely a ductility coefficient mu and a strength hardening coefficient alpha, are introduced h The definitions of which are shown in formula (3-3) and formula (3-4):
μ＝ε u /ε y (2-3)
α h ＝k h /E 0 (2-4)
wherein epsilon y Is the yield strain of the steel bar,. Epsilon u Is the ultimate strain of the steel bar, mu is the ductility factor, E 0 Is the initial modulus of elasticity, k, of the steel bar h Slope of the hardened section of the bar, alpha h Is the strength hardening factor.
Ultimate Strength Point (e) 2 ,s 2 ) Conversion into the strength hardening factor alpha according to the formulae (3-5) and (3-6) h And ductility factor μ:
e 2 ＝e 1 ·μ (2-5)
s 2 ＝s 1 +α h ·E 0 ·s 1 ·(μ-1) (2-6)
wherein e is 1 Is the yield point strain of the steel bar, s 1 Stress at yield strength point of steel bar, e 2 Is the ultimate strength point strain of the steel bar, s 2 Stress at the ultimate strength point of the steel bar, E 0 Is the initial modulus of elasticity of the steel bar, mu is the ductility factor, alpha h Is the strength hardening factor.
In order to reasonably describe the physical relationship between the strength degradation point and the ultimate strength point when the strength degradation occurs to the steel bar, a dimensionless parameter strength degradation coefficient alpha needs to be introduced into a steel bar restoring force model s And a residual intensity coefficient R defined as shown in the formulae (3-7) and (3-8):
Rε rs /ε u (2-7)
α s ＝-k s /E 0 (2-8)
wherein epsilon u Is the ultimate strength point stress of the steel bar, epsilon rs Is the stress at the point of strength degradation of the steel bar, R is the coefficient of residual strength, E 0 Is the initial modulus of elasticity, k, of the steel bar s Is the slope of the degenerate section of the reinforcing bar, alpha s Is the intensity degradation factor.
Ultimate strength point (e) 3 ,s 3 ) The combined yield strength point is converted into a strength degradation coefficient alpha according to the expressions (2-9) and (2-10) s And residual intensity coefficient R:
s 3 ＝s 2 ·R (2-9)
e 3 ＝e 2 +·s 2 ·(1-R)/(α d ·E 0 ) (2-10)
wherein s is 2 Stress at the ultimate strength point of the steel bar, s 3 Is the stress at the point of strength degradation of the steel bar, R is the coefficient of residual strength, e 2 Strain at the ultimate strength point of the steel bar, e 3 Strain at the point of strength degradation of the reinforcing bar, E 0 Is the initial modulus of elasticity, alpha, of the steel bar s Is the intensity degradation factor.
S3, performing single factor analysis through the hysteresis curve in the step S1 to obtain hysteresis control parameters capable of representing the pinching effect and the cycle degradation characteristic of the component; the hysteresis control parameters comprise a damage control coefficient, a pinch control coefficient and an unloading rigidity control coefficient; and taking the hysteresis control parameter as a hysteresis rule of the improved steel bar restoring force model. The hysteresis control parameters comprise a damage control coefficient d and a pinch control coefficient p ch And unloading the stiffness control coefficients beta, the selection method of each coefficient being specifically described below.
The hysteric model (hysteresis model) defines its hysteresis rule by five parameters, $ damage1, $ damage2, $ pinchX, $ pinchY, and $ beta. Wherein, the Damage1 is a damage coefficient corresponding to ductility change in the material loading process; damage2 is a damage coefficient related to material energy consumption in the material loading process; pinchX and pinchY are pinching coefficients of a loading section of a hysteresis curve in the control material restoring force model; and $ beta is the unloading rigidity degradation coefficient related to the ductility change of the material in the loading process of the material.
In order to accurately analyze the influence of each hysteretic parameter in the steel bar restoring force model, the hysteretic control parameters of the steel bar restoring force model are divided into three groups of damage control parameters, pinching control parameters and unloading rigidity control parameters to carry out single-factor analysis.
(1) And a damage control parameter d: with increasing $ damage1, there was a significant degradation in strength and stiffness of the member when loaded to the 50mm displacement stage, while the damage factor had no significant effect on the hysteretic curve of the member until it reached peak strength; meanwhile, the energy consumption capability of the component is reduced along with the increase of the ductility damage coefficient. Compared with the damage1 coefficient, the damage2 coefficient change has lower sensitivity to the influence of the hysteretic response of the component and the stress-strain relationship of the fiber, and the corresponding component damage and strength degradation coefficient alpha in the skeleton curve s And the residual intensity coefficient RIn the coupling relationship, the correlation characteristic is not favorable for the parameter identification of the subsequent damage control coefficient. In order to accurately describe the damage of the component under the action of reciprocating load, only $ damage1 is used as a damage control parameter of a steel bar restoring force model and is represented by a damage coefficient d.
(2) Pinch control parameter p ch : and (3) defining a loading section path of the restoring force model in the hysteretic loading process through two parameters of $ pinchX and $ pinchY, and further describing the hysteretic shape of the steel bar material of the RC column under different failure modes. The change of the values of pinchX and pinchY can make the hysteretic characteristic of the component show a full or pinch hysteretic shape. Because the evaluation index of the hysteresis simulation effect in the component elastoplasticity analysis generally adopts the energy consumption area of the hysteresis loop, a large number of combinations of coefficients $ pinchX and $ pinchY in the Hysteretic model correspond to the same hysteresis energy consumption area, and the multi-to-one mapping relation characteristic is not beneficial to parameter identification of the pinch coefficient of the subsequent restoring force model. To solve the above problem, a limiting condition $ pinchX + $ pinchY =1 is introduced by a pinching coefficient p ch Pinch control coefficient representing model of restoring force of reinforcing bar based on pinch coefficient p ch The value change of the model, the loading path of the model of the restoring force of the steel bar and the pinch coefficient p ch The transformation relationships with $ pinchX and $ pinchY are shown in formulas (3-1) and (3-2):
$pinchX＝p ch (3-1)
$pinchY＝1-p ch (3-2)
when p is ch When the model is not less than 0.5, the hysteresis rule of the steel bar restoring force model is a peak value pointing type; when p is ch When the model approaches to 0, the hysteretic shape of the steel bar restoring force model is more full; when p is ch Approaching 1, the steel bar restoring force model may exhibit a pinch phenomenon.
(3) Unloading rigidity control parameter beta: with the increase of $ beta, the unloading rigidity of the reinforcing steel bar fiber is obviously degraded, and meanwhile, the unloading rigidity in the hysteretic curve of the component is also degraded and affects the hysteretic energy consumption area of the component. The beta coefficient has definite physical significance in unloading rigidity control of the member and can be used as an unloading rigidity control parameter beta of a steel bar restoring force model.
And S4, establishing an improved steel bar restoring force model according to the skeleton control parameters in the step S2 and the hysteretic control parameters in the step S3.
And S5, establishing an automatic component fiber unit elastic-plastic analysis model according to the concrete constitutive model and the improved steel bar restoring force model in the step S4, executing the step S6 if the automatic component fiber unit elastic-plastic analysis model conforms to the structural concept, and otherwise, returning to the step S4.
Concrete infrastructure Concret 02 capable of considering tension characteristics is a Concrete infrastructure model capable of simultaneously considering Concrete compression and tension effects and is divided into a confined Concrete infrastructure and a plain Concrete infrastructure. In order to reasonably consider the improvement of the stirrup on the ductility and the strength of concrete, the concrete surrounded by the stirrup in the cross section and the concrete of the protective layer are divided into two fiber materials, and a constrained concrete structure and a plain concrete structure (without considering the improvement of the stirrup) are respectively adopted for simulation.
The component is divided into a bottom plastic interval and an upper elastic-plastic interval by the established component fiber unit automatic elastic-plastic analysis model, and the length of the bottom plastic interval is half of the height of a section. And (4) splitting the section of the reinforced concrete column member along the X direction and the Y direction, wherein the splitting dimension is 50mm. For the reinforced concrete column member, the unit section is mainly divided into three types of fibers: and the stress-strain relation of the core area concrete fiber, the protective layer concrete fiber and the reinforcing steel bar fiber is defined according to the selected constraint concrete constitutive model, the plain concrete constitutive model and the improved reinforcing steel bar restoring force model.
And writing an elastic-plastic analysis program of the reinforced concrete column through OpenSeesPy to realize component fiber unit modeling, elastic-plastic analysis and data visualization.
And S6, determining key target parameters of the skeleton curve in the step S1, based on the target error function of the skeleton control parameters in the step S2, and based on the improved steel bar restoring force model in the step S4, performing optimal solution identification on the skeleton control parameters of the improved steel bar restoring force model in the step S4 by utilizing a three-component search algorithm to obtain an optimal solution of the skeleton control parameters.
Key target parameters of the skeleton curve include intensity adjustment coefficients
Coefficient of ductility mu and coefficient of strength degradation alpha s . The target error functions of the framework control parameters are respectively the peak bearing capacity of the component, the peak point displacement and the error of the energy consumption area of the descending section of the framework curve.
The coefficient of adjustment of the pass-through strength of the skeleton curve of the model for improving the restoring force of the steel bars provided in the embodiment
Coefficient of strength hardening alpha h Ductility coefficient mu, strength deterioration coefficient alpha s And defining a three-fold skeleton curve by using five parameters of the residual intensity coefficient R. To avoid plastic localization, the strength hardening factor alpha is set h Taking the value as 0.03; since the influence of the residual intensity coefficient R on the hysteresis response of the member is small, the residual intensity coefficient R is taken to be 0.2. Intensity adjustment coefficients of the other three parameters
Coefficient of ductility mu and coefficient of strength degradation alpha s Is a key target parameter of the skeleton curve.
Determining a skeleton control parameter target error function according to the key target parameters of the three skeleton curves as follows:
wherein, F pos_t 、F neg_ The peak bearing capacity is positive peak bearing capacity and negative peak bearing capacity in the component test result; f' pos_s 、F′ neg_s Positive bearing capacity and negative bearing capacity corresponding to the displacement of the test result peak point in the member simulation result;
the coefficient objective function is adjusted for intensity.
Wherein D is pos_t 、D neg_t Displacement values corresponding to the positive peak bearing capacity and the negative peak bearing capacity in the component test result are obtained; d pos_s 、D neg_s Displacement values corresponding to positive peak bearing capacity and negative peak bearing capacity in the component simulation result; delta μ Is the ductility factor objective function.
Wherein, E pos_down_t 、E neg_down_t The areas corresponding to a descending section of a positive skeleton curve and a descending section of a negative skeleton curve in the component test result are obtained; e pos_down_s 、E neg_down_s Areas corresponding to a descending section of a positive skeleton curve and a descending section of a negative skeleton curve in a member simulation result;
is an intensity degradation coefficient objective function.
When the skeleton control parameter is closer to the optimal solution, the objective function value of the skeleton control parameter approaches to 0, the optimal identification process of the skeleton control parameter is the most valued solution of the unimodal function, and the three-thirds search algorithm is adopted for identifying the skeleton parameter. As shown in fig. 5, for known L, R]Solving the minimum value of the interval, and dividing the interval into three equal parts according to the length of the interval to obtain an intermediate point L mid And R mid By comparison of L mid And R mid Updating the boundary value of the solving interval according to the size of the corresponding function value; sequentially carrying out iterative solution until the interval length or the calculation precision meets the requirement of the solution condition; wherein, L, R, L mid And R mid Values representing the abscissa of the graph of FIG. 7, and δ (L), δ (R), δ (L) mid ) And delta (R) mid ) Then represent the values of the ordinate of the graph of figure 7, with one-to-one correspondence. FIG. 6 is a diagram of the trisection search algorithm for minimumGraph of values, delta (L) at first three-component lookup mid_1 )＜f(R mid_1 ) And the solution interval is updated to [ L, R ] mid_1 ](ii) a Second three point lookup time delta (L) mid_2 )＞f(R mid_2 ) The solution interval is updated to [ L ] mid_2 ,R mid_1 ]. In the identification of the framework control parameters, when the interval length of the trisection search solution is smaller than the allowable error tol of the parameters or the maximum value in the error objective function values corresponding to the interval boundary values is smaller than 1%, the current iteration solution is stopped, and the midpoint of the current solution interval is the optimal solution of the framework control parameters.
And S7, determining key target parameters of the hysteresis curve in the step S1, based on the target error function of the hysteresis control parameters in the step S3, based on the improved steel bar restoring force model in the step S4, and performing optimal solution identification on the hysteresis control parameters of the improved steel bar restoring force model in the step S4 by using a differential evolution algorithm to obtain an optimal solution of the hysteresis control parameters.
The key target parameter of the hysteresis curve is the pinching coefficient p ch And unloading the stiffness degradation coefficient beta, wherein the target error function of the hysteresis control parameter is the non-overlapping area of the hysteresis loop of the member.
(1) The improved steel bar restoring force model selected in the embodiment is mainly formed by a pinching coefficient p ch And adjusting the unloading rigidity degradation coefficient beta to simulate hysteretic energy consumption of the component. Selecting the non-overlapping area of the hysteresis loop of the member as the pinch factor p ch And a target parameter identified by the unloading rigidity degradation coefficient beta, and calculating an error function related to the non-overlapping area of the hysteresis loop of the member by the following equations (6-1) and (6-2):
because the solving process of the error function of the non-overlapping area of the hysteresis loop of the member is a multi-parameter optimizing process, the solution of the hysteresis control parameter of the improved steel bar restoring force model is carried out by adopting a differential evolution algorithm.
(2) The automatic solution of the hysteresis control parameters of the improved steel bar restoring force model based on the differential evolution algorithm is shown in figure 7, the optimal parameter solution mainly comprises the steps of initializing population, carrying out variation, crossing and selecting 4 operation steps, and the optimal parameter solution is carried out according to the corresponding fitness function and the maximum evolution algebra G max Determining the optimal parameter combination of the solution:
(1) initializing a population: and randomly generating a certain number of individuals to form an initialized population within the initially determined parameter value range. Wherein, when the size N of the population is larger, the solving efficiency of the algorithm is lower, when N is smaller, the solving of the algorithm is easy to fall into the local optimum, the value of N is usually 5-10 times of the vector dimension, and for a two-dimensional vector, N20 is made to generate 20 random individuals (x) 1 ,x 2 ,…,x 20 ) (ii) a And calculating the fitness of the initial population according to the fitness function. And aiming at parameter identification, adopting the reciprocal of a pinching coefficient target error function as a fitness function.
(2) And (3) mutation: for each individual in the population, 3 individuals were randomly selected among the other 19 individuals (x) r1 ,x r2 ,x r3 ) Carrying out differential variation, determining the variation degree according to a scaling factor F (the value of the chapter is 0.5), and obtaining a variation population (v) 1 ,v 2 ,…,v 20 ) The difference variation is shown in formula (6-4):
v i ＝x r1 +F·(x r2 -x r3 ) (6-4)
(3) and crossing: performing feature transformation on the individuals in the original population and the corresponding variant individuals through cross operation, wherein each original individual randomly retains one-dimensional information, and the rest of the information is replaced according to a cross probability CR (the value in the embodiment is 0.5), namely, according to a 50% probability, so as to obtain a cross population (c) 1 ,c 2 ,…,c 20 )。
(4) And selecting: according to the principle of superior and inferior elimination, sequentially carrying out treatment on x of the original population i And c of cross population i Selection is carried out, namely the individuals s of the filial generation population are determined according to the size of the fitness function i And realizing the process of biological evolution.
(5) And calculating termination: when the fitness of the best individual in the population is greater than the fitness limit of 100, i.e., when the fitness of the best individual in the population is greater than the fitness limit
When the error value of (2) is less than 0.01, or the evolution algebra reaches the maximum evolution algebra G max And stopping calculation, wherein the optimal individual in the population is the optimal solution of the hysteresis control parameter.
S8, taking the Component design characteristic parameters in the step S1 as input parameters, taking the optimal solution of the framework control parameters in the step S6 and the optimal solution of the hysteresis control parameters in the step S7 as output parameters, and obtaining a Component Steel Bar Constitutive parameter prediction Model (structural Model of Component Steel Bar Based on Machine Learning, steelML), and carrying out training and prediction effect evaluation on the Component Steel Bar Constitutive parameter prediction Model to obtain an improved Steel Bar restoring force Model with excellent prediction effect; step S8 includes the steps of:
s801, determining an evaluation index of a component steel bar constitutive parameter prediction model; the evaluation index comprises a decision coefficient (R2), a Mean Absolute Error (MAE), a Root Mean Square Error (RMSE), a Root Mean Square Logarithmic Error (RMSLE) and a Mean Absolute Percentage Error (MAPE);
s802, taking the component design characteristic parameters as input parameters of a component steel bar constitutive parameter prediction model; the input parameters comprise the axial compressive strength f 'of the concrete cylinder' c Longitudinal reinforcement ratio rho and volume reinforcement ratio rho v A shear span ratio lambda, an axial pressure coefficient n and a bending shear ratio m;
s803, taking the optimal solution of the framework control parameter and the optimal solution of the hysteresis control parameter as output parameters of the constitutive parameter prediction model of the member steel bar; the output parameters comprise strength adjustment coefficients of control parameters of the framework of the model with the improved steel bar restoring force
Coefficient of ductility mu and coefficient of strength degradation alpha s Hysteresis control parameter pinch coefficient p ch And an unload stiffness degradation coefficient β;
s804, a Gradient Boosting Regression Tree (GBRT) algorithm is adopted as a core intelligent algorithm of the component steel bar constitutive parameter prediction model, all input parameters and output parameters are randomly divided into a training set and a test set by adopting a k-fold cross validation method, data training of the component steel bar constitutive parameter prediction model is carried out by adopting the training set, effect evaluation of the component steel bar constitutive parameter prediction model is carried out by adopting the test set, and an improved steel bar restoring force model with excellent prediction effect is obtained.
The prediction effect of the GBRT algorithm model depends on the trained sample data set and the hyper-parameter selection of the model, and in order to build a reliable SteelML model, the key steps of sample data set division, data preprocessing and the like need to be completed in sequence in model design and training.
(1) And data set division: the data set is divided into a training set and a testing set, 85% of the data set (namely the training set) is used for training and building the component steel reinforcement constitutive parameter prediction model, and the prediction effect of the GBRT algorithm model is evaluated through the rest 15% of the data set (namely the testing set).
In order to ensure that the testing set has enough representativeness to the members in the digital member test database, the members in the bending, bending and shearing failure modes in the testing set are sampled in a layered random sampling mode according to the proportion of 4. The RC column members in the test set have 21 members, wherein 12 bending failure members, 6 bending shear failure members and 3 shearing failure members are adopted.
(2) And data preprocessing: and selecting a data normalization mode to preprocess the data set, and zooming the characteristic interval according to the maximum absolute value of the data characteristic. The distribution range of the data is limited to [ -1,1], and the conversion formula is shown as the formula (7-1):
wherein | x | n | max The characteristic maximum absolute value of the data set.
In combination with the determined evaluation indexes of the prediction model, the model evaluation indexes of the prediction model when predicting 21 components in the test set are shown in table 1. Since the results in the strength degradation coefficient and the unload stiffness degradation coefficient have a value of 0 or approximately 0, it is not suitable to use RMSLE and MAPE for analysis, mainly by R 2 And performing model evaluation on three indexes including MAE and RMSE. The SteelML model has higher simulation precision on strength adjustment coefficient, ductility coefficient and unloading rigidity coefficient, R 2 Can reach about 0.9, and the R of the strength degradation coefficient 2 0.733, R of the unload stiffness degradation coefficient 2 The prediction result is 0.799, and the MAE and the RMSE of each model are at lower levels, which shows that the SteelML model has enough generalization capability in a test set, can accurately describe the nonlinear topological relation between the component design characteristic parameters of the components in the training set and the control parameters of the improved steel bar restoring force model, and has higher reliability.
TABLE 1 SteelML model test set assessment index
In order to visually show the prediction accuracy of the SteelML model on the test set sample, as shown in fig. 8, the control parameter identification result of the improved steel bar restoring force model in the digital component test database is used as an abscissa, and the prediction result of the SteelML model is used as an ordinate, and prediction comparison scatter diagrams of five machine learning models are respectively drawn. The circular points represent component prediction results of the SteelML model divided into the training set, the square points represent component prediction results of the SteelML model divided into the testing set, the solid line in the middle is a function with y = x, and when scattered points are distributed around the solid line in a concentrated mode, the SteelML model is high in prediction accuracy, and the prediction results are consistent with the parameter identification results.
S9, performing component elastic-plastic analysis on the improved steel bar restoring force model in the step S8; the method for analyzing the elasticity and the plasticity of the component by the fiber unit in the step S9 comprises the following steps:
s901, carrying out model prediction progress and generalization capability evaluation on the improved steel bar restoring force model in the step S8, if the improved steel bar restoring force model is good in precision, executing the step S902, and if not, returning to the step S8;
s902, performing component elastic-plastic analysis verification on the component fiber unit automatic elastic-plastic analysis model in the step S5, if the improved steel bar restoring force model is verified well, executing the step S903, otherwise, returning to the step S8;
and S903, performing parameter prediction on the improved steel bar restoring force model in the step S8 based on machine learning.
In order to verify the effectiveness of the response of the components under the action of the simulated reciprocating load in the elastic-plastic analysis of the SteelML model, fiber units of different improved reinforcing steel bar restoring force models are respectively adopted to carry out the elastic-plastic analysis on the RC column components in the test set, and the components in the test set do not participate in the construction of the SteelML model, so that the generalization capability of the SteelML model can be fully verified, the RC column components in practical application have representative significance, the elastic-plastic analysis results of 9 typical components are selected to carry out comparative analysis, and 3 RC column components including bending damage, bending shear damage and shearing damage are respectively selected.
As shown in table 2, the common Steel01 and Steel02 models, the Steel ml model constructed based on machine learning, and the parameter result identified based on test data are respectively adopted for the 9 RC column members to perform elastoplasticity analysis, the average fitting error of the Steel ml model to the peak bearing capacity, the accumulated energy consumption area and the hysteretic energy consumption capacity of the members in the elastoplasticity analysis is about 10%, the fitting accuracy is significantly improved compared with the common Steel01 and Steel02 models, and the average fitting accuracy to the peak bearing capacity and the accumulated energy consumption area is respectively improved by 11.60% and 17.84%; and the fitting effect of the common improved steel bar restoring force model on the hysteretic energy consumption capability of the component is poor, the average error is about 40%, and the fitting precision of the SteelML model is improved by 28.47% on the basis of the common improved steel bar restoring force model. Meanwhile, the precision of the elastic-plastic analysis model of the SteelML model is basically consistent with the simulation precision of the parameter identification result based on the test data, which shows that the SteelML model can replace the fussy parameter identification step, and the control parameters of the improved steel bar restoring force model of the RC column member are accurately predicted through the powerful generalization capability of the machine learning model, so that the elastic-plastic analysis simulation precision of the fiber unit is effectively improved.
TABLE 2 fibre unit fitting error contrast using different improved model of the restoring force of the reinforcement
The above detailed description is a preferred embodiment of the present invention, and is not intended to limit the present invention, and any other modifications or equivalent substitutions that do not depart from the spirit of the present invention are intended to be included within the scope of the present invention.
Claims (10)
1. The seismic analysis method adopting the improved steel bar restoring force model is characterized by comprising the following steps of:
s1, collecting low-cycle reciprocating test data, performing equivalent conversion of a component loading mode on the low-cycle reciprocating test data to obtain component design characteristic parameters, converting and extracting a PEER structural performance database to obtain a hysteresis curve and a skeleton curve, and building a digital component test database according to the component design characteristic parameters, the hysteresis curve and the skeleton curve;
s2, carrying out dimensionless transformation according to the skeleton curve in the step S1 to obtain skeleton control parameters;
s3, performing single factor analysis according to the hysteresis curve in the step S1 to obtain a hysteresis control parameter, and taking the hysteresis control parameter as a hysteresis rule of an improved steel bar restoring force model;
s4, establishing an improved steel bar restoring force model according to the skeleton control parameters in the step S2 and the hysteresis control parameters in the step S3;
s5, establishing an automatic elastic-plastic analysis model of the member fiber unit according to the concrete constitutive model and the improved steel bar restoring force model in the step S4, executing the step S6 if the automatic elastic-plastic analysis model of the member fiber unit conforms to the structural concept, and otherwise, returning to the step S4;
s6, determining key target parameters of the framework curve in the step S1, and based on the target error function of the framework control parameters in the step S2 and the improved steel bar restoring force model in the step S4, performing framework control parameter optimal solution identification on the improved steel bar restoring force model in the step S4 by utilizing a trisection search algorithm to obtain a framework control parameter optimal solution;
s7, determining key target parameters of the hysteresis curve in the step S1, and based on the target error function of the hysteresis control parameters in the step S3, performing optimal solution identification on the hysteresis control parameters of the improved steel bar restoring force model in the step S4 by using a differential evolution algorithm on the basis of the improved steel bar restoring force model in the step S4 to obtain an optimal solution of the hysteresis control parameters;
s8, obtaining a component steel bar constitutive parameter prediction model by taking the component design characteristic parameters in the step S1 as input parameters and the optimal framework control parameter solution in the step S6 and the optimal hysteresis control parameter solution in the step S7 as output parameters, and training and estimating the prediction effect of the component steel bar constitutive parameter prediction model to obtain the improved steel bar restoring force model with excellent prediction effect;
and S9, performing component elastic-plastic analysis on the improved steel bar restoring force model in the step S8.
2. An earthquake resistance analysis method using an improved reinforcing steel restoring force model according to claim 1, wherein the step S1 comprises the steps of:
s101, collecting low-cycle reciprocating test data of the component from a PEER structure performance database and literature data;
s102, performing equivalent conversion of a component loading mode on the component low-cycle reciprocating test data to obtain basic characteristic parameters;
s103, calculating the basic characteristic parameters to obtain calculated characteristic parameters;
s104, extracting from the PEER structure performance database to obtain a hysteresis curve;
s105, extracting through the hysteresis curve to obtain a skeleton curve;
and S106, establishing a digital component test database by matching the component design characteristic parameters, the hysteresis curve and the skeleton curve one by one.
3. An earthquake-proof analysis method using an improved steel restoring force model according to claim 2, wherein the basic characteristic parameters in step S102 include geometric information, concrete information, longitudinal bar information, stirrup information and axial force information.
4. An earthquake-proof analysis method using an improved steel bar restoring force model according to claim 2, wherein the calculated characteristic parameters in the step S103 include longitudinal bar reinforcement ratio, volume reinforcement ratio, shear span ratio, axial pressure coefficient and bending shear ratio.
5. An earthquake resistance analysis method using an improved reinforcing steel restoring force model according to claim 1, wherein the step S8 comprises the steps of:
s801, determining an evaluation index of the component steel bar constitutive parameter prediction model;
s802, taking the component design characteristic parameters as input parameters of the component steel bar constitutive parameter prediction model;
s803, taking the optimal solution of the skeleton control parameters and the optimal solution of the hysteresis control parameters as output parameters of the constitutive parameter prediction model of the member steel bar;
s804, a gradient lifting regression tree algorithm is adopted as a core intelligent algorithm of the component steel bar constitutive parameter prediction model, the input parameters and the output parameters are randomly divided into a training set and a testing set by adopting a k-fold cross verification method, the data training of the component steel bar constitutive parameter prediction model is carried out by adopting the training set, the effect evaluation of the component steel bar constitutive parameter prediction model is carried out by adopting the testing set, and the improved steel bar restoring force model with excellent prediction effect is obtained.
6. An earthquake resistance analysis method using an improved steel bar restoring force model according to claim 1, wherein the fiber unit component elastoplasticity analysis method of step S9 comprises the steps of:
s901, carrying out model prediction precision and generalization capability evaluation on the improved steel bar restoring force model in the step S8, if the improved steel bar restoring force model is good in precision, executing the step S902, otherwise, returning to the step S8;
s902, performing component elastoplasticity analysis verification on the component fiber unit automatic elastoplasticity analysis model in the step S5, executing the step S903 if the component fiber unit automatic elastoplasticity analysis model is verified well, otherwise, returning to the step S8;
and S903, performing parameter prediction on the improved steel bar restoring force model in the step S8 based on machine learning.
7. An earthquake-proof analysis method using an improved steel restoring force model according to claim 1, wherein the key turning points of the framework curve in step S2 comprise yield strength points, ultimate strength points and strength degradation points.
8. An earthquake-proof analysis method using an improved steel bar restoring force model according to claim 1, wherein the framework control parameters in step S2 include a strength adjustment coefficient, a strength hardening coefficient, a ductility coefficient, a strength degradation coefficient and a residual strength coefficient.
9. An earthquake-proof analysis method using an improved reinforcing steel restoring force model according to claim 1, wherein the hysteresis control parameters in step S3 include a damage control coefficient, a pinch control coefficient and an unload stiffness control coefficient.
10. A method for earthquake analysis using an improved steel restoring force model according to claim 1, wherein the key target parameters of the skeleton curve in step S6 include a strength adjustment coefficient, a ductility coefficient and a strength degradation coefficient.
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