CN110414066A - Fitting Method of Reinforced Concrete Damage Model Based on Genetic Algorithm - Google Patents

Abstract

The invention discloses a method for fitting a reinforced concrete damage model based on a genetic algorithm, and relates to the technical field of seismic performance evaluation. According to the three nonlinear superposition rules, the invention adjusts the combined form of model deformation and energy accumulation effect, and constructs a corrected reinforced concrete damage model. Considering the influence of low-cycle fatigue effect in the hysteretic energy dissipation damage D _C , the optimal function of D _C is searched by genetic algorithm, and the data in the PEER database is used to automatically optimize the damage function, so as to more accurately calculate the component during the entire loading process The law of damage development. The model established by the invention can accurately and effectively assess the damage of the components. Compared with the fitting method of the traditional damage model, the method for fitting the reinforced concrete damage model based on the genetic algorithm proposed by the invention improves the accuracy and accuracy of the built model. Applicability overcomes the problem of insufficient consideration of low-cycle fatigue effects in traditional damage models.

Description

Fitting Method of Reinforced Concrete Damage Model Based on Genetic Algorithm

technical field

The invention relates to a method for fitting a reinforced concrete damage model based on a genetic algorithm, and belongs to the technical field of seismic performance evaluation.

Background technique

In order to accurately evaluate the damage degree of reinforced concrete structures after earthquakes, it is necessary to establish a reasonable and effective reinforced concrete damage model to evaluate the damage evolution process of components. Regarding the damage degree of reinforced concrete structural members under earthquake action, scholars at home and abroad have proposed a variety of damage assessment models, mainly including several types of models: damage model based on deformation, damage model based on strength degradation, damage model based on stiffness degradation, Energy-based damage models and pairwise combination models of the above four models.

Although the current reinforced concrete correction model can accurately evaluate the damage degree of components in specific experiments, there are still defects in the combination of deformation damage and cumulative energy dissipation damage in the model. When fitting parameters, most of them use equal amplitude increments. The experimental data is reciprocated, and the effect of low cycle fatigue is not considered enough. Therefore, improving the accuracy and applicability of the modified damage model of reinforced concrete is of great significance for evaluating the damage evolution process of components.

Contents of the invention

In view of the deficiencies in the prior art above, the present invention provides a method for fitting a reinforced concrete damage model based on a genetic algorithm, which solves the problem that the traditional damage model does not take low-cycle fatigue into consideration.

The present invention adopts the following technical solutions for solving the problems of the technologies described above:

The invention provides a method for fitting a reinforced concrete damage model based on a genetic algorithm, and the specific steps are as follows:

Step 1. According to the nonlinear superposition law, construct a modified reinforced concrete damage model: D=D _C +(1-D _M )D _C , where D _M is the maximum deformation damage, D _C is the hysteretic energy dissipation damage, and D is the nonlinear combined damage of maximum deformation and hysteretic energy dissipation effect;

Step 2, the maximum deformation damage D _M is the ratio of the maximum displacement to the limit displacement under monotonic loading according to the nonlinear cumulative amount of the bearing capacity: D _M ＝E _pl,mo (δ _M )/E _u,mo ,E _pl,mo (δ _M ) represents the plastic energy dissipation corresponding to monotonic loading displacement δ _M E _pl,mo (δ _M )＝E _mo (δ _M )-E _el,mo (δ _M ), E _mo (δ _M ), E _{el, mo} (δ _M ) respectively represent the total energy consumption and elastic energy consumption corresponding to the monotonic loading displacement δ _M , and E _u,mo represent the energy consumption in the failure state under monotonic loading;

Step 3, considering the influence of low-cycle fatigue effect in the hysteretic energy dissipation damage D _C , according to the nonlinear evolution law of different displacement amplitudes and arbitrary loading cycles under the same displacement amplitude respectively, the optimal function of D _C is: Dc ＝1-(μ _F -μ _F,u )/(1-μ _F,u ), μ _F is the peak load ratio, and μ _F,u is the limit state peak load ratio.

As a further technical solution of the present invention, in step 3, the sign regression program based on genetic algorithm determines the optimal function of _DC , specifically:

The initial set of functions defined are: basic mathematical operators, trigonometric functions and exponential logarithmic operators;

The variables used are: μ, n, r, ry _,mo , r _u,mo , μ _u,mo and R, where n is the loading cycle period, r is the displacement angle of the loading amplitude, and ry _,mo is the monotonic Loading yield displacement angle, r _u,mo is the limit displacement angle of monotonic loading, μ is the displacement ductility ratio under cyclic loading, μ _u,mo is the ultimate displacement ductility ratio under monotonic loading, R is the ductility coefficient of plastic deformation;

Set the target expression as: μ _F ＝f(n,r,ry _,mo ,r _u,mo ), μ _F ＝f(n,μ,μ _u,mo ) or μ _F ＝f(n,R );

The fitness index is: mean absolute error MAE, eliminate individuals with MAE>0.2;

The standard for program termination is: MAE<0.01.

As a further technical solution of the present invention, basic mathematical operators, trigonometric functions and exponential logarithmic operators include: +, -, ×, ÷, Sin, Cos, Tan, Exp, Log, ! , ^ and √.

As a further technical solution of the present invention, a program is written with matlab to realize automatic extraction of experimental loading data in the PEER database by the webpage.

As a further technical solution of the present invention, for the implicit target expression, according to the genetic condition, the experimental data sign regression is carried out to obtain the specific expression: μ _F =A ₁ -A ₂ ×lg(n+A ₄ ), A ₁ = 0.957+0.124R ² , A ₂ =0.0691+0.0873R ² −0.344R, A ₄ =1.598.

Compared with the prior art, the present invention adopts the above technical scheme and has the following technical effects: the model established by the present invention can accurately and effectively assess the damage of components. Compared with the traditional damage model fitting method, the genetically based The algorithmic reinforced concrete damage model fitting method improves the accuracy and applicability of the built model, and overcomes the problem of insufficient consideration of low-cycle fatigue effects in traditional damage models.

Description of drawings

Fig. 1 is method implementation flowchart;

Figure 2 is a schematic diagram of deformation damage DM parameters;

Figure 3 is a flow chart of component damage calculation;

Fig. 4 is a rectangular cross-section reinforced concrete specimen geometric dimension and reinforcement diagram;

Figure 5 is a circular cross-section reinforced concrete specimen geometric dimensions and reinforcement diagram;

Figure 6 is the force-displacement curve at the vertex of a monotonic loading curve of a reinforced concrete member with a rectangular section;

Figure 7 is a comparison of the calculation results of various damage models in the monotonic loading process of a reinforced concrete member with a rectangular section;

Fig. 8 is the force-displacement curve at the top of the reciprocating loading curve of a circular cross-section reinforced concrete member with equal amplitude increments;

Figure 9 is a comparison of the calculation results of various damage models in the process of equal-amplitude incremental reciprocating loading of a circular cross-section reinforced concrete member;

Figure 10 is a force-displacement curve at the vertex of a rectangular cross-section reinforced concrete member of equal-amplitude reciprocating loading curve;

Fig. 11 is a comparison of the calculation results of various damage models in the process of equal-amplitude reciprocating loading of a reinforced concrete member with a rectangular cross-section.

Detailed ways

In order to further illustrate the technical solutions disclosed in the present invention, a detailed description will be given below in conjunction with the drawings and specific embodiments of the description. Those skilled in the art should know that the optimization and improvement made without departing from the spirit of the present invention fall within the scope of protection of the present invention, and conventional means and conventional techniques in this field are not discussed in this specific embodiment. Detailed records and explanations.

Figure 1 is a specific implementation flow chart of a method for fitting a reinforced concrete damage model based on a genetic algorithm.

The invention is a method for fitting a reinforced concrete damage model based on a genetic algorithm. The constructed model takes a reinforced concrete column as a research object, and constructs a modified reinforced concrete damage model according to the nonlinear superposition rule: D=D _C +(1- D _M )D _C , where D _M is the maximum deformation damage, D _C is the hysteretic energy dissipation damage, and D is the nonlinear combined damage of the maximum deformation and hysteretic energy dissipation effect. According to the three nonlinear superposition rules of deformation and energy accumulation nonlinear superposition of components, nonlinear damage accumulation of deformation damage part with displacement increase, nonlinear evolution of different displacement amplitudes and different loading cycles of the same amplitude, the deformation and the model are adjusted. Combination of energy accumulation effects. The damage index is mainly based on the maximum deformation energy effect, supplemented by the hysteretic energy consumption effect. The intact state is 0, and the complete damage state is 1.

The invention uses experience to construct nonlinear functions DM and D, and uses genetic algorithm to search for the nonlinear optimal function of DC.

As shown in Figure 2, considering the non-linear cumulative law of the corresponding bearing capacity in the monotonic loading curve in the maximum deformation damage D _M , the maximum deformation damage D _M is the ratio of the maximum displacement to the limit displacement under monotonic loading according to the non-linearity of the bearing capacity. linear cumulant. D _M =E _pl,mo (δ _M )/E _u,mo , E _pl,mo (δ _M )=E _mo (δ _M )-E _el,mo (δ _M ), where E _mo (δ _M ), E _el,mo (δ _M ) and E _pl,mo (δ _M ) represent the total energy consumption, elastic energy consumption and plastic energy consumption corresponding to the monotonic loading displacement δ _M , respectively, and E _u,mo is the energy consumption in failure state under monotonic loading .

Considering the effect of low-cycle fatigue in the hysteretic energy-dissipating damage D _C , the optimal function of D _C is searched by genetic algorithm according to the nonlinear evolution law of different displacement amplitudes and any loading period under the same displacement amplitude respectively. The symbolic regression program based on genetic algorithm used to determine the _DC function, the initial function set defined is: basic mathematical operators, trigonometric functions and exponential logarithmic operators (ie: +, -, ×, ÷, Sin, Cos, Tan, Exp, Log, !, ^, and √). The variables employed are μ, n, r, ry _,mo , r _u,mo , μ, μ _u,mo , and R. Among them, μ _F is the peak load ratio, n is the loading cycle period, r is the displacement angle of the loading amplitude, ry _,mo is the yield displacement angle of monotonic loading, μ is the displacement ductility ratio under cyclic loading, r _u,mo is the monotonic loading The ultimate displacement angle, μ _u,mo is the ultimate displacement ductility ratio under monotonic loading, and R is the plastic deformation ductility coefficient. Set the target expression as μ _F = f(n,r,ry _,mo ,r _u,mo ), μ _F =f(n,μ,μ _u,mo ) or μ _F =f(n,R) . The fitness evaluation adopts the mean absolute error (MAE) of the original fitness index, and the individuals with MAE>0.2 are eliminated, and only MAE<0.01 is used as the standard for program termination. Write a program with matlab to automatically extract the experimental loading data in the PEER database from the web page, optimize the parameters in the fitting function, and obtain a specific expression according to the existing data symbol regression: μ _F = A ₁ -A ₂ ×lg(n+A ₄ ), A ₁ ＝0.957+0.124R ² , A ₂ ＝0.0691+0.0873R ² -0.344R, A ₄ ＝1.598, the calculation formula of hysteresis energy consumption damage is: Dc＝1-( _μF - _μF,u )/(1- _μF,u ).

The hysteretic energy dissipation damage model under constant amplitude loading conditions is extended to the damage under arbitrary loading conditions n _h,i+1 ＝f(R _i ,n _h,i ,R _i+1 ); μ _i+1 ＝f(n _h,i+1 ,R _i+1 ); D _C,i+1 ＝f(μ _i+1 ), more accurately calculate the damage development law of the component during the whole loading process.

The whole loading process is divided into n _{h, N} loading events according to the unit of each half cycle. The plastic displacement ratios of the adjacent processes i and i+1 are known to be R _i and R _i +1 respectively, and the i-th process is known to be equivalent to The degree of damage corresponds to the number of half-cycles of the fatigue loading range of R _i+1 , and the number of half-cycles n _h,i+1 of the i+1th process is calculated, n _h,i+1 = f(R _i ,n _h,i ,R _{i +1} ) has the following formula:

The formula of the peak load ratio μ _i+1 of the i+1th loading process is as follows:

When μ _i+1 < μ _F,u , it means that the component is damaged after the i+1th loading event; otherwise, it is not damaged, and the calculation of the next loading process can be entered.

The damage D _c,i after the i-th loading event is as follows:

μ _i is the peak load ratio of the i-th loading process.

According to the three nonlinear superposition laws, the present invention adjusts the combined form of model deformation and energy accumulation effect, and constructs a revised reinforced concrete damage model. Figure 3 shows the process of using the damage model to specifically calculate component damage. Considering the effect of low-cycle fatigue in the hysteretic energy-dissipating damage D _C , according to the nonlinear evolution law of different displacement amplitudes and different loading cycles under the same displacement amplitude, the optimal function of D _C is searched by genetic algorithm, and used The data in the PEER database automatically optimizes the damage function, and more accurately calculates the damage development law of the component during the entire loading process. The model established by the invention can accurately and effectively assess the damage of the components. Compared with the fitting method of the traditional damage model, the method for fitting the reinforced concrete damage model based on the genetic algorithm proposed by the invention improves the accuracy and accuracy of the built model. Applicability overcomes the problem of insufficient consideration of low-cycle fatigue effects in traditional damage models.

Example 1: Damage assessment of reinforced concrete columns during monotonic loading

Taking a reinforced concrete specimen with a rectangular section as the damage assessment object, the column section size is 250mm×250mm, the concrete cover thickness is 20mm, the column height is 1200mm, and the effective height is 1050mm. The column section is configured with 4D14 longitudinal reinforced steel bars, and the corresponding section reinforcement ratio is 0.99%. The stirrups are D8 steel bars with a spacing of 50mm, and the corresponding stirrup ratios are 2.16%. The measured yield strength of HTRB630 steel bar is 738.34MPa, and the tensile strength is 928.50MPa. The design strength grade of the concrete is C60, and the average compressive strength of the measured concrete cube (150mm×150mm×150mm) is 66.9MPa. The shear-span ratio of the column is 5.53, and the axial compression ratio is 0.25. The geometric dimensions and reinforcement of the specimen are shown in Figure 4.

The entire loading process of the component is divided into multiple loading processes according to the displacement monotonicity and positive and negative value changes in the vertex force-displacement curve. There is only one loading process for monotonic loading. The vertex force-displacement curve is shown in Figure 6. The damage model based on genetic algorithm was used for damage assessment, and compared with the evaluation results of six classic damage models, Kunnath model, Chai model, Kumar model, Luo Wenwen model, Fu Guo model and Chen Linzhi model, as shown in Figure 7, the damage The damage values of the states are 1.028, 1.000, 1.036, 1.000, 1.193, 1.040 and 1.000, respectively. It can be seen that the damage model based on the genetic algorithm is more accurate in calculating the fatigue damage results of the monotonically loaded specimens.

Example 2: Damage assessment of reinforced concrete columns during monotonic loading

Taking a reinforced concrete specimen with a circular section as the damage assessment object, the column section size is a circular section with a diameter of 305mm, the thickness of the concrete cover is 14.5mm, the column height is 1372mm, and the effective height is 1372mm. The section of the column is equipped with 21 pieces of Grade 60 longitudinal steel bars, and the corresponding section reinforcement ratio is 0.0204%. The measured yield strength of Grade60 steel bars is 448MPa, and the tensile strength is 690MPa. The design strength grade of concrete is ASTM C599-85, and the average compressive strength of concrete 150mm×300mm cylindrical specimens is 29MPa. The shear-span ratio of the column is 4.5, and the axial compression ratio is 0.094. The geometric dimensions and reinforcement of the specimen are shown in Figure 5.

In the equal-amplitude incremental reciprocating loading experiment, the vertex force-displacement curve is shown in Figure 8. The damage model based on genetic algorithm was used for damage assessment, and compared with the evaluation results of six classical damage models, the components experienced a total of 125 loading processes to the failure state in the experiment. The calculation results of the model are shown in Figure 9. In the process of 0-60, the damage calculated by the Fuguo model is less than 0, which does not conform to the objective law. The damage calculation values of Kumar model, Fuguo model and Chai model exceeded 1 in the loading process 70, 78 and 72 respectively, and the damage calculation values of the final failure state were 3.986, 4.671 and 8.706, which obviously deviated from the experimental results. Kunnath model and Rowan-Wen model damage calculation values in the final damage state are 0.477 and 0.506, which are far less than 1, and the error of the evaluation result is too large. The damaged state damage value calculated by Chen Linzhi's model is 1.169, which is slightly greater than 1, which is relatively accurate. Compared with the above model, the error is acceptable. The damaged state damage value calculated by the genetic algorithm-based damage model is 0.901, which is the closest to 1. For specimens subjected to reciprocating loading with equal amplitude increments, the Chen Linzhi model and the damage model based on genetic algorithm can more accurately reflect the damage evolution process of components, while the damage calculation errors of other models are relatively large.

Example 3: Damage assessment of reinforced concrete columns during constant-amplitude reciprocating loading

The same as the reinforced concrete specimen in Example 3, in the constant-amplitude reciprocating loading process, the vertex force-displacement curve is shown in Figure 10 . The damage model based on genetic algorithm was used for damage assessment, and compared with the evaluation results of six classic damage models, as shown in Figure 11, the four models of Chai model, Kumar model, Fu Guo model and Chen Linzhi model were obtained from process 30 and 96 respectively. , 6, and 112 process calculation damage values exceed 1, and the final damage state damage calculation values reach 31.270, 4.638, 44.547 and 4.885, which obviously deviate from the experimental results. The damage calculation value of the Rowan-Wen model in the final damage state is 0.402, which is far less than 1, and the error of the evaluation result is too large. The damaged state damage values calculated by the Kunnath model and the damage model based on the genetic algorithm are 1.014 and 1.007, both of which are slightly greater than 1, but the error is acceptable. Relatively speaking, the damage model based on the genetic algorithm is more accurate. For specimens with equal amplitude reciprocating loading, the damage model based on the genetic algorithm and the Kunnath model can reflect the damage evolution process of the component more accurately, and the damage calculation errors of other models are relatively large, among which the Chai model, Kumar model, Fu Guo model and Chen Linzhi model calculate If the value is too large, the calculated value of the Rowan-Wen model is too small.

The effect of the present invention applied to assessing the damage evolution process of components is verified through the above three embodiments, and it can be seen that the present invention can be applied to the assessment of damage evolution process through further quantitative analysis.

Obviously, those skilled in the art can make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalent technologies, the present invention also intends to include these modifications and variations.

Claims (5)

1. the armored concrete damage model approximating method based on genetic algorithm, which is characterized in that specific step is as follows:

Step 1, according to Nonlinear Superposition rule, modified armored concrete damage model: D=D is constructed_C+(1-D_M)D_C, wherein D_MFor maximum distortion damage, D_CFor hysteretic energy damage, D is the nonlinear combination damage of maximum distortion and hysteretic energy effect；

Step 2, maximum distortion damages D_MFor maximum displacement with the dull ratio for loading limit inferior displacement according to the non-of bearing capacity size Linear accumulation amount: D_M=E_pl,mo(δ_M)/E_u,mo,E_pl,mo(δ_M) indicate dull load deflection δ_MCorresponding plasticity energy consumption E_pl,mo(δ_M) =E_mo(δ_M)-E_el,mo(δ_M), E_mo(δ_M)、E_el,mo(δ_M) respectively indicate dull load deflection δ_MCorresponding total energy consumption, elastic dissipation energy, E_u,moIt indicates dull and loads lower collapse state energy consumption；

Step 3, D is damaged in hysteretic energy_CThe middle influence for considering low-cycle fatigue effect, respectively according to different displacement amplitude and identical The nonlinear Evolution rule of any loading cycle, D under displacement amplitude_COptimal function are as follows: Dc=1- (μ_F-μ_F,u)/(1-μ_F,u), μ_FFor peak load ratio, μ_F,uFor limiting condition peak load ratio.

2. the armored concrete damage model approximating method according to claim 1 based on genetic algorithm, which is characterized in that Symbolic Regression program in step 3 based on genetic algorithm determines D_COptimal function, specifically:

The initial function collection of definition are as follows: basic mathematical operator, trigonometric function and index logarithm operator；

Used variable are as follows: μ, n, r, r_y,mo、r_u,mo、μ_u,moAnd R, wherein n is the loaded cycle period, and r is load amplitude position Move angle, r_y,moDrift ratio at yielding, r are loaded for dullness_u,moLimiting displacement drift is loaded for dullness, μ is the displacement Ductility under CYCLIC LOADING Than μ_u,moFor the extreme displacement ductility ratio under dull load, R is plastic deformation ductility factor；

Set goal expression are as follows: μ_F=f (n, r, r_y,mo,r_u,mo)、μ_F=f (n, μ, μ_u,mo) or μ_F=f (n, R)；

Fitness index are as follows: mean absolute error MAE eliminates the individual of MAE > 0.2；

Program determination operation standard are as follows: MAE < 0.01.

3. the armored concrete damage model approximating method according to claim 2 based on genetic algorithm, which is characterized in that Basic mathematical operator, trigonometric function and index logarithm operator include :+, ﹣, ×, ÷, Sin, Cos, Tan, Exp, Log,！,^ And √.

4. according to the armored concrete damage model approximating method based on genetic algorithm any in Claims 2 or 3, It is characterized in that, writes program with matlab, realize that webpage automatically extracts the load data of the experiment in PEER database.

5. the armored concrete damage model approximating method according to claim 4 based on genetic algorithm, which is characterized in that Is carried out by experimental data Symbolic Regression, obtains expression: μ according to genetic condition for implicit goal expression_F=A₁-A₂× lg(n+A₄), A₁=0.957+0.124R², A₂=0.0691+0.0873R²- 0.344R, A₄=1.598.