CN110414066A - Armored concrete damage model approximating method based on genetic algorithm - Google Patents
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Abstract
The invention discloses a kind of armored concrete damage model approximating method based on genetic algorithm, is related to Assessment of Seismic Vulnerability technical field.The present invention adjusts the combining form of model deformation and energy accumulation effect, constructs modified armored concrete damage model according to three kinds of Nonlinear Superposition rules.D is damaged in hysteretic energyCThe middle influence for considering low-cycle fatigue effect, goes out D by Genetic algorithm searchingCOptimal function more accurately calculate lesion development rule of the component in entire loading procedure and with the data Automatic Optimal damage function in PEER database.The model established using the present invention accurately and effectively can carry out lesion assessment to component, compared to the approximating method of traditional damage model, armored concrete damage model approximating method proposed by the present invention based on genetic algorithm improves the accuracy and applicability of model built, overcomes traditional damage model and considers low-cycle fatigue effect insufficient problem.
Description
Technical field
The present invention relates to a kind of armored concrete damage model approximating method based on genetic algorithm, belongs to anti-seismic performance and comments
Estimate technical field.
Background technique
For the degree of injury after the shake of accurate evaluation reinforced concrete structure, need to establish reasonable, effective reinforced concrete
Native damage model, to assess the damage development process of component.It is broken under geological process about reinforced concrete structural element
Bad degree, domestic and foreign scholars have proposed a variety of lesion assessment models, mainly include several class models: the damage mould based on deformation
Type, the damage model based on strength degradation, the damage model based on Stiffness Deterioration, the damage model based on energy and above-mentioned four
The combination of two model of kind model.
Although current armored concrete correction model accurate assessment component damage degree of energy in particular experiment,
There are still defects for the deformation damage and accumulation energy consumption damaged portion combination for being model, in fitting parameter, use mostly
The reciprocal loading experiment data of constant amplitude increment, and low-cycle fatigue effect is considered insufficient.Therefore, armored concrete amendment damage is improved
The accuracy and applicability of model are of great significance to for assessment component damage evolutionary process.
Summary of the invention
In view of the above shortcomings of the prior art, the present invention provides a kind of armored concrete damage model based on genetic algorithm
It is insufficient to solve the problems, such as that traditional damage model considers low-cycle fatigue effect for approximating method.
The present invention uses following technical scheme to solve above-mentioned technical problem:
The present invention provides a kind of armored concrete damage model approximating method based on genetic algorithm, the specific steps are as follows:
Step 1, according to Nonlinear Superposition rule, modified armored concrete damage model: D=D is constructedC+(1-DM)DC,
Wherein, DMFor maximum distortion damage, DCFor hysteretic energy damage, D is the nonlinear combination damage of maximum distortion and hysteretic energy effect
Wound；
Step 2, maximum distortion damages DMRatio for maximum displacement and dull load limit inferior displacement is big according to bearing capacity
Small Nonlinear Cumulative amount: DM=Epl,mo(δM)/Eu,mo,Epl,mo(δM) indicate dull load deflection δMCorresponding plasticity energy consumption
Epl,mo(δM)=Emo(δM)-Eel,mo(δM), Emo(δM)、Eel,mo(δM) respectively indicate dull load deflection δMCorresponding total energy consumption,
Elastic dissipation energy, Eu,moIt indicates dull and loads lower collapse state energy consumption；
Step 3, D is damaged in hysteretic energyCThe middle influence for considering low-cycle fatigue effect, respectively according to different displacement amplitude and
The nonlinear Evolution rule of any loading cycle, D under same displacement amplitudeCOptimal function are as follows: Dc=1- (μF-μF,u)/(1-
μF,u), μFFor peak load ratio, μF,uFor limiting condition peak load ratio.
As further technical solution of the present invention, the Symbolic Regression program in step 3 based on genetic algorithm determines DC's
Optimal 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, ry,mo、ru,mo、μu,moAnd R, wherein n is the loaded cycle period, and r is load width
Spend angle of displacement, ry,moDrift ratio at yielding, r are loaded for dullnessu,moLimiting displacement drift is loaded for dullness, μ is the displacement under CYCLIC LOADING
Ductility ratio, μu,moFor the extreme displacement ductility ratio under dull load, R is plastic deformation ductility factor；
Set goal expression are as follows: μF=f (n, r, ry,mo,ru,mo)、μF=f (n, μ, μu,mo) or μF=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.
As further technical solution of the present invention, basic mathematical operator, trigonometric function and index logarithm operator packet
Include :+, ﹣, ×, ÷, Sin, Cos, Tan, Exp, Log,！, ^ and √.
As further technical solution of the present invention, program is write with matlab, realizes that webpage automatically extracts PEER data
Experiment in library loads data.
As further technical solution of the present invention, experimental data is carried out according to genetic condition to implicit goal expression
Symbolic Regression obtains expression: μF=A1-A2×lg(n+A4), A1=0.957+0.124R2, A2=0.0691+
0.0873R2- 0.344R, A4=1.598.
The invention adopts the above technical scheme compared with prior art, has following technical effect that and is established using the present invention
Model lesion assessment accurately and effectively can be carried out to component, compared to the approximating method of traditional damage model, the present invention is proposed
The armored concrete damage model approximating method based on genetic algorithm improve the accuracy and applicability of model built, overcome
Traditional damage model considers low-cycle fatigue effect insufficient problem.
Detailed description of the invention
Fig. 1 is method implementation flow chart；
Fig. 2 is deformation damage DM parameter schematic diagram；
Fig. 3 is component damage calculation flow chart；
Fig. 4 is certain rectangular reinforced concrete test specimen geometric dimension and arrangement of reinforcement；
Fig. 5 is certain circular cross-section reinforcing bar concrete sample geometric dimension and arrangement of reinforcement；
Fig. 6 is certain rectangular reinforced concrete component dullness loading curve vertex force-displacement curve；
Fig. 7 is each damage model calculated result comparison of certain rectangular reinforced concrete component dullness loading procedure；
Fig. 8 is certain reciprocal loading curve vertex force-displacement curve of circular cross-section reinforcing bar concrete component constant amplitude increment；
Fig. 9 is certain each damage model calculated result pair of the reciprocal loading procedure of circular cross-section reinforcing bar concrete component constant amplitude increment
Than；
Figure 10 is certain reciprocal loading curve vertex force-displacement curve of rectangular reinforced concrete component constant amplitude；
Figure 11 is each damage model calculated result comparison of certain reciprocal loading procedure of rectangular reinforced concrete component constant amplitude.
Specific embodiment
For further instruction technical solution disclosed by the invention, make with reference to the accompanying drawings of the specification with specific embodiment
Detailed elaboration.Those skilled in the art should learn, made under the premise of without prejudice to spirit of that invention preferably and improve
Protection scope of the present invention is each fallen within, the conventional means and conventional techniques for this field are not done in detail in this embodiment
Record and explanation.
Process is embodied in the armored concrete damage model approximating method to be a kind of based on genetic algorithm as shown in Figure 1
Figure.
A kind of armored concrete damage model approximating method based on genetic algorithm of the present invention, the model constructed is with reinforcing bar
Concrete column is research object, according to Nonlinear Superposition rule, constructs modified armored concrete damage model: D=DC+(1-
DM)DC, wherein DMFor maximum distortion damage, DCFor hysteretic energy damage, D is the non-linear of maximum distortion and hysteretic energy effect
Combination damage.According to the deformation of component and energy accumulation Nonlinear Superposition, deformation damage part with the increased non-linear damage of displacement
Wound accumulation, different displacement amplitude and the nonlinear Evolution of identical amplitude difference loading cycle these three Nonlinear Superpositions rule, are adjusted
The combining form of integral mould deformation and energy accumulation effect.Based on damage criterion is answered with maximum distortion efficiency, hysteretic energy effect
Supplemented by, serviceable condition 0, complete faulted condition is 1.
The present invention constructs nonlinear function DM and D with experience, and with the non-linear optimal function of Genetic algorithm searching DC.
As shown in Fig. 2, damaging D in maximum distortionMThe middle size for considering respective carrier power in dull loading curve is non-linear
Accumulation, maximum distortion damage DMFor maximum displacement with the dull ratio for loading limit inferior displacement according to the non-of bearing capacity size
Linear accumulation amount.DM=Epl,mo(δM)/Eu,mo, Epl,mo(δM)=Emo(δM)-Eel,mo(δM), wherein Emo(δM)、Eel,mo(δM) and
Epl,mo(δM) respectively indicate dull load deflection δMCorresponding total energy consumption, elastic dissipation energy and plasticity energy consumption, Eu,moFor under dullness load
Collapse state energy consumption.
D is damaged in hysteretic energyCThe middle influence for considering low-cycle fatigue effect, respectively according to different displacement amplitude and identical bits
The nonlinear Evolution rule for moving any loading cycle under amplitude, goes out D by Genetic algorithm searchingCOptimal function.For determining DC
Symbolic Regression program based on genetic algorithm used by function, the initial function collection of definition are as follows: basic mathematical operator, triangle
Function and index logarithm operator (that is :+, ﹣, ×, ÷, Sin, Cos, Tan, Exp, Log,！, ^ and √).Used variable is
μ、n、r、ry,mo、ru,mo、μ、μu,moAnd R.Wherein, μFFor peak load ratio, n is the loaded cycle period, and r is load amplitude displacement
Angle, ry,moDrift ratio at yielding is loaded for dullness, μ is the displacement Ductility ratio under CYCLIC LOADING, ru,moExtreme displacement is loaded for dullness
Angle, μu,moFor the extreme displacement ductility ratio under dull load, R is plastic deformation ductility factor.Goal expression is set as μF=f
(n,r,ry,mo,ru,mo)、μF=f (n, μ, μu,mo) or μF=f (n, R).Fitness evaluation is average exhausted using original relevance grade index
To error (MAE), the individual of MAE>0.2 is eliminated, only regard MAE<0.01 as program determination operation standard.Journey is write with matlab
Sequence realizes that webpage automatically extracts the load data of the experiment in PEER database, the parameter in Optimal Fitting function, according to existing number
Expression is obtained according to Symbolic Regression: μF=A1-A2×lg(n+A4),A1=0.957+0.124R2, A2=0.0691+
0.0873R2-0.344R,A4=1.598, hysteretic energy damage calculation formula are as follows: Dc=1- (μF-μF,u)/(1-μF,u)。
Damage n hysteretic energy damage model under constant amplitude loading condition being generalized under any loading conditionh,i+1=f
(Ri,nh,i,Ri+1)；μi+1=f (nh,i+1,Ri+1)；DC,i+1=f (μi+1), component is more accurately calculated in entire loading procedure
Lesion development rule.
Entire loading procedure is that unit is divided into n according to every half cyclesh,NLoad events, it is known that adjacent process i and i+1
Plastic displacement than be respectively RiAnd Ri+ 1, it is known that the i-th process equivalent damage degree corresponds to Ri+1The half cycle of fatigue loading amplitude
Number calculates i+1 process half cycle frequency nh,i+1, nh,i+1=f (Ri,nh,i,Ri+1) formula it is as follows:
The peak load ratio μ of i+1 loading procedurei+1Formula it is as follows:
Work as μi+1<μF,uWhen, indicate that the load events rear part of i+1 is destroyed；Otherwise it does not destroy, next load can be entered
The calculating of process.
D is damaged after i-th load eventsc,iSuch as following formula:
μiFor the peak load ratio of the i-th loading procedure.
The present invention adjusts the combining form of model deformation and energy accumulation effect, structure according to three kinds of Nonlinear Superposition rules
Modified armored concrete damage model is made, Fig. 3 indicates the process that component damage is specifically calculated using damage model.It is consumed in hysteresis
D can be damagedCThe middle influence for considering low-cycle fatigue effect, according to loading cycles different under different displacement amplitude and same displacement amplitude
Nonlinear Evolution rule, D is gone out by Genetic algorithm searchingCOptimal function, and it is automatically excellent with the data in PEER database
Change damage function, more accurately calculates lesion development rule of the component in entire loading procedure.The mould established using the present invention
Type accurately and effectively can carry out lesion assessment, compared to the approximating method of traditional damage model, base proposed by the present invention to component
The accuracy and applicability of model built are improved in the armored concrete damage model approximating method of genetic algorithm, overcomes biography
Damage model of uniting considers low-cycle fatigue effect insufficient problem.
Embodiment 1: reinforced column dullness loading procedure lesion assessment
Using certain rectangular reinforced concrete test specimen as lesion assessment object, column cross-section size is 250mm × 250mm, is mixed
Protective soil layer is coagulated with a thickness of 20mm, pillar height 1200mm, effective height 1050mm.Column section is configured with 4D14 longitudinal stress steel
Muscle, corresponding sectional reinforcement rate are 0.99%, and stirrup uses the reinforcing bar of D8, spacing 50mm, and corresponding stirrup ratio is respectively
2.16%.The yield strength for surveying HTRB630 reinforcing bar is 738.34MPa, tensile strength 928.50MPa.Concrete Design is strong
Degree grade is C60, and cube (150mm × 150mm × 150mm) the compression strength average value for surveying concrete is 66.9MPa.Column
Shear span ratio be 5.53, axial compression ratio 0.25, test specimen geometric dimension and arrangement of reinforcement are as shown in Figure 4.
The entire loading procedure of component is divided into according to displacement monotonicity in the force-displacement curve of vertex and the variation of power positive and negative values
Multiple loading procedures, dullness load only one loading procedure, and vertex force-displacement curve is as shown in Figure 6.It is calculated using based on heredity
The damage model of method has carried out lesion assessment, and with Kunnath model, Chai model, Kumar model, Luo Wenwen model, pay
State's model and 6 kinds of the model of Chen Lin classical damage model assessment result comparisons, as shown in fig. 7, being destroyed the damage number of state
Value is respectively 1.028,1.000,1.036,1.000,1.193,1.040 and 1.000, it is known that the damage model based on genetic algorithm
Dull loading specimen fatigue damage result is calculated more acurrate.
Embodiment 2: reinforced column dullness loading procedure lesion assessment
Using certain circular cross-section reinforcing bar concrete sample as lesion assessment object, column cross-section size is the circle that diameter is 305mm
Tee section, thickness of concrete cover 14.5mm, pillar height 1372mm, effective height 1372mm.Column section is configured with 21
Root Grade60 Reinforcement, corresponding sectional reinforcement rate are 0.0204%, and stirrup uses the reinforcing bar of Grade60, and spacing is
19mm, corresponding stirrup ratio are respectively 0.94%.The yield strength for surveying Grade60 reinforcing bar is 448MPa, and tensile strength is
690MPa.Concrete design strength grade is ASTM C599-85, and the cylinder test specimen of actual measurement concrete 150mm × 300mm is anti-
Compressive Strength average value is 29MPa.The shear span ratio of column is 4.5, axial compression ratio 0.094, test specimen geometric dimension and arrangement of reinforcement such as Fig. 5 institute
Show.
In the reciprocal loading experiment of constant amplitude increment, vertex force-displacement curve is as shown in Figure 8.Using based on genetic algorithm
Damage model has carried out lesion assessment, and compares with 6 kinds of classical damage model assessment results, and component undergoes altogether 125 in experiment
A loading procedure is to collapse state.The model calculation pays the calculated result of state's model as shown in figure 9, in 0~60 process
Damage does not meet objective law less than 0.Kumar model pays state's model and Chai model respectively in loading procedure 70,78 and 72
Damage measurement value is more than 1, and the damage measurement value of final collapse state is 3.986,4.671 and 8.706, hence it is evident that deviates experiment knot
Fruit.Kunnath model and Luo Wenwen model are 0.477 and 0.506, far smaller than 1 in final faulted condition damage measurement value, are commented
It is too big to estimate resultant error.The collapse state impairment value that the model of Chen Lin calculates is 1.169, in contrast more smart slightly larger than 1
Really, above-mentioned model is compared, error can receive.The collapse state impairment value that damage model based on genetic algorithm calculates is
0.901, closest to 1.For loading specimen reciprocal for constant amplitude increment, the model of Chen Lin and the damage model based on genetic algorithm
Can be with the damage development process of accurate reactive means, it is larger that remaining MODEL DAMAGE calculates error.
Embodiment 3: the reciprocal loading procedure lesion assessment of reinforced column constant amplitude
With the armored concrete test specimen in embodiment 3, in the reciprocal loading procedure of constant amplitude, vertex force-displacement curve is as schemed
Shown in 10.Lesion assessment has been carried out using the damage model based on genetic algorithm, and with 6 kinds of classical damage model assessment results pair
Than, as shown in figure 11, Chai model, Kumar model, pay four kinds of models of model of state's model and Chen Lin respectively from process 30,96,
It is more than 1 that 6 and 112 processes, which calculate impairment value, and final collapse state damage measurement value reaches 31.270,4.638,44.547 and
4.885, hence it is evident that deviate experimental result.Luo Wenwen model is 0.402, far smaller than 1 in final faulted condition damage measurement value, is commented
It is too big to estimate resultant error.Kunnath model and the collapse state impairment value of the damage model calculating based on genetic algorithm are 1.014
With 1.007, all it is slightly larger than 1, but error can receive, in contrast, the damage model based on genetic algorithm is more accurate.For
The reciprocal loading specimen of constant amplitude, damage model and Kunnath model based on genetic algorithm can be with the damages of accurate reactive means
Hurt evolutionary process, remaining MODEL DAMAGE calculating error is larger, wherein Chai model, Kumar model, the mould for paying state's model and Chen Lin
Type calculated value is too big, and Luo Wenwen model calculation value is too small.
The effect that the present invention is applied to assessment component damage evolutionary process is verified by above three embodiments, can be seen
Out, by further quantitative analysis, the present invention can be applied to damage development process assessments.
Obviously, various changes and modifications can be made to the invention without departing from essence of the invention by those skilled in the art
Mind and range.In this way, if these modifications and changes of the present invention belongs to the range of the claims in the present invention and its equivalent technologies
Within, then the present invention is also intended 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 constructedC+(1-DM)DC, wherein
DMFor maximum distortion damage, DCFor hysteretic energy damage, D is the nonlinear combination damage of maximum distortion and hysteretic energy effect；
Step 2, maximum distortion damages DMFor maximum displacement with the dull ratio for loading limit inferior displacement according to the non-of bearing capacity size
Linear accumulation amount: DM=Epl,mo(δM)/Eu,mo,Epl,mo(δM) indicate dull load deflection δMCorresponding plasticity energy consumption Epl,mo(δM)
=Emo(δM)-Eel,mo(δM), Emo(δM)、Eel,mo(δM) respectively indicate dull load deflection δMCorresponding total energy consumption, elastic dissipation energy,
Eu,moIt indicates dull and loads lower collapse state energy consumption；
Step 3, D is damaged in hysteretic energyCThe 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 amplitudeCOptimal function are as follows: Dc=1- (μF-μF,u)/(1-μF,u),
μFFor peak load ratio, μF,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 DCOptimal 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, ry,mo、ru,mo、μu,moAnd R, wherein n is the loaded cycle period, and r is load amplitude position
Move angle, ry,moDrift ratio at yielding, r are loaded for dullnessu,moLimiting displacement drift is loaded for dullness, μ is the displacement Ductility under CYCLIC LOADING
Than μu,moFor the extreme displacement ductility ratio under dull load, R is plastic deformation ductility factor；
Set goal expression are as follows: μF=f (n, r, ry,mo,ru,mo)、μF=f (n, μ, μu,mo) or μF=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 expressionF=A1-A2×
lg(n+A4), A1=0.957+0.124R2, A2=0.0691+0.0873R2- 0.344R, A4=1.598.
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| CN112883600A (en) * | 2021-01-11 | 2021-06-01 | 西南交通大学 | Construction method of steel pipe concrete member overall and local damage joint evaluation model |
| CN113111416A (en) * | 2021-04-07 | 2021-07-13 | 同济大学 | Data-driven reinforced concrete structure earthquake damage quantitative evaluation method |
| CN113450333A (en) * | 2021-06-30 | 2021-09-28 | 哈尔滨工业大学 | Machine learning-based reinforced concrete column earthquake damage degree evaluation method |
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