A finite element model size optimization method for road dynamic deflection basin calculation

Abstract

The present invention discloses a finite element model size optimization method for calculating a road dynamic deflection basin, comprising the following steps: S1: constructing a finite element model #imgabs0# for calculating a road dynamic deflection basin; S2: simulating and obtaining the ith dynamic deflection basin #imgabs1# and the ith deflection time domain curve #imgabs2#; S3: calculating the difference #imgabs3# between the deflection basin and the time domain curve; S4: enlarging the model size to #imgabs4#, simulating and obtaining the i+1th dynamic deflection basin #imgabs5# and the i+1th deflection time domain curve #imgabs6#; S5: calculating the deflection basin difference #imgabs7# and the deflection time domain curve difference #imgabs8#; S6: repeating steps S1 to S5 until the model optimization standard is met. The present invention discloses a finite element model size optimization method for calculating a road dynamic deflection basin, which can provide a standardized method for optimizing the size of a finite element model used for simulating a road dynamic deflection basin.

Description

Technical Field

[0001] The invention relates to a finite element model size optimization method for calculating a road dynamic deflection basin, and belongs to the field of road engineering. Background Art

[0002] For pavement structures, the longitudinal length is approximately infinite, the transverse length is composed of several lanes, and the width can reach tens of meters. In finite element simulation, it is impossible to model according to the actual length and width of the road structure, and the longitudinal and transverse dimensions of the model must be limited. The size of the finite element model has a great influence on the simulation deflection results. If the model size is too small, the boundary conditions will significantly affect the simulation deflection results. However, a larger model size means a longer simulation time. In order to achieve a balance between simulation accuracy and efficiency, it is necessary to determine the optimal size of the finite element model.

[0003] The current finite element modeling methods for deflection basins are mostly based on traditional falling weight deflectometers (FWDs), and the applied load is a dynamic load at a fixed point. When finite element simulation of road deflection under continuous moving loading of high-speed deflectometers is performed, there is a lack of effective finite element model size optimization methods. The size selection of road finite element models is often arbitrary, and the correlation between the deflection basin and the deflection time domain curve has not been applied in model size optimization. Summary of the invention

[0004] Purpose of the invention: In view of the above technical problems, the present invention proposes a finite element model size optimization method for road dynamic deflection basin calculation, providing a standardized method for optimizing the finite element model size used for road dynamic deflection basin simulation.

[0005] In order to achieve the above technical objectives, the present invention adopts the following technical solutions:

[0006] A finite element model size optimization method for road dynamic deflection basin calculation includes the following steps:

[0007] S1: Constructing a finite element model for calculating the dynamic deflection basin of a road i ;

[0008] S11: The finite element model initially constructed for calculating the dynamic deflection basin of the road is denoted as M1, and the subsequent models are denoted as M2, M3, ...;

[0009] The constructed models M i (i=1,2,3……) all meet the following requirements: the road model is divided into multiple layers from top to bottom, elastic material or viscoelastic material is selected for each layer of the road model, and the density, Poisson's ratio and damping ratio of each layer of the road model are set;

[0010] S12: When modeling, the elastic material is set to a modulus, and the viscoelastic material is set to a Prony series to characterize its modulus characteristics. The bonding state between each layer is set to be completely bonded or with a certain amount of sliding. When the bonding state between each layer is set to have a certain amount of sliding, the friction coefficient is used to characterize it.

[0011] S13: During modeling, the vehicle load is applied to the upper surface of the finite element model, and the load area is set as a rectangle;

[0012] S14: During simulation, the rectangular load area moves in a straight line along the longitudinal symmetry axis of the upper surface of the finite element model at a specified speed. During the moving process, the rectangular load area always maintains a left-right symmetric state with respect to the longitudinal symmetry axis of the upper surface of the finite element model. The side surfaces and bottom surfaces of the finite element model are set to a fully constrained state, and no constraints are set on the upper surface of the finite element model. The thickness of each layer of the road finite element model is set according to the actual situation.

[0013] S2: Simulate and obtain the i-th dynamic bending basin d i (x) and the i-th deflection time domain curve d i ′(t);

[0014] S3: Calculate the difference dd′ between the bending basin and the time domain curve i,diff ;

[0015] S4: Enlarge the model size to M i+1 , simulate and obtain the i+1th dynamic bending basin d i+i (x) and the i+1th deflection time domain curve d i+1 ′(t);

[0016] S5: The i-th dynamic deflection basin d obtained in step S2 i (x) and the (i+1)th dynamic deflection basin d obtained in step S4 i+i (x) Calculate the deflection basin difference d i,i+1,diff ; The i-th deflection time domain curve d obtained by step S2 i ′(t) and the i+1th deflection time domain curve d obtained in step S4 i+1 ′(t) Calculate the difference d′ of the deflection time domain curve i,i+1,diff ;

[0017] S6: Repeat steps S1 to S5 until the model optimization criterion is met, wherein the model optimization criterion is:

[0018] If the difference between the bending basin and the time domain curve dd′ i,diff , bending basin difference d i,i+1,diff The difference d′ between the time domain curve of deflection i,i+1,diff The value satisfies formula (1), then M i The size of the model is the optimized size of the established road finite element model;

[0019] If formula (1) is not satisfied, construct M i+1 Model, repeat the above steps S2 to S6,

[0020]

[0021] Furthermore, in step S1:

[0022] The road model materials of each layer include asphalt mixture, cement concrete, cement stabilized crushed stone, graded crushed stone and soil, wherein the asphalt mixture material is set to be elastic or viscoelastic;

[0023] Cement concrete, cement-stabilized crushed stone, graded crushed stone, and earth materials were set to elastic;

[0024] The applied loads include vertical loads, horizontal longitudinal loads and horizontal lateral loads.

[0025] Furthermore, the i-th dynamic bending sink d in step S2 i (x) is obtained as follows: For model M i At a certain moment in the simulation, the origin is set at the center of the rectangular load area, the forward direction of the rectangular load area is set as the positive direction of the x-axis, the vertical downward direction of the model is set as the positive direction of the d-axis, and a plane rectangular coordinate system is constructed. When the center point of the rectangular load area coincides with the center point of the upper surface of the model, the i-th dynamic deflection basin d i (x) is composed of all points on the upper surface of the model that satisfy the condition “d ≥ 0”. The left and right limits of the bending basin are denoted by x i,1 (x i,1 <0) and x i,2 (x i,2 >0), where d i (x i,1 )=0 and d i (x i,2 )=0.

[0026] Furthermore, the i-th deflection time domain curve d in step S2 i ′(t) is obtained as follows: For model M i , select the center point of the upper surface of the finite element model, set the vertical downward direction of the model as the positive direction of the d′ axis, set t = 0 as the starting time when the deflection d′ at the center point meets the condition of “d′ ≥ 0”, and set t = t i,max is the last moment when the deflection d′ at the center point satisfies the condition “d′≥0”, where d i ′(0)=0,d i ′(t i,max )=0.

[0027] Furthermore, the difference dd′ between the bending basin and the time domain curve in step S3 i,diff The calculation method is as follows: For a road section with the same structural composition and material parameters, when the load forward speed is v, the i-th dynamic deflection basin d at each point on the road surface i (x) should be equal to Substitute the i-th deflection time domain curve d as the independent variable i ′(t) The difference between the bending basin and the time domain curve dd′ is defined by formula (2): i,diff Indicator, representing d′ at each point on the road surface i (x) and The difference between

[0028]

[0029] Further, step S4 is as follows: the road finite element model M constructed in step S1 is converted into i The length and width of the model are enlarged to 1.2 times of the original, and the thickness of each layer of the model is kept unchanged. The enlarged model is recorded as M i+1 , the load setting remains unchanged, according to the i-th dynamic deflection basin d in step S2 i The calculation method of (x) is based on M i+1 Model, calculate the i+1th dynamic bending basin d i+i (x) and the i+1th deflection time domain curve d i+1 ′(t).

[0030] Further, in step S5,

[0031] The deflection basin difference d is calculated by formula (3): i,i+1,diff ;

[0032] The difference d′ of the deflection time domain curve is calculated by formula (4): i,i+1,diff ;

[0033] Deflection basin difference d i,i+1,diff The smaller the value, the more i The dynamic bending basin d obtained by model simulation i (x) and based on M i+1 The i+1th dynamic bending basin d obtained by model simulation i+1 The smaller the difference between (x);

[0034] Deflection time domain curve difference d′ i,i+1,diff The smaller the value, the more i The i-th deflection time domain curve d obtained by model simulation i ′(t) and based on M i+1 The i+1th deflection time domain curve d obtained by model simulation i+1The smaller the difference between ′(t);

[0035]

[0036]

[0037] Beneficial effects:

[0038] The finite element model size optimization method for calculating road dynamic deflection basin of the present invention has the following advantages:

[0039] The present invention sets finite element models of different sizes, considers the correlation between the deflection basin and the deflection time domain curve, and creatively proposes the difference dd′ between the deflection basin and the time domain curve. i,diff , bending basin difference d i,i+1,diff The difference d′ between the time domain curve of deflection i,i+1,diff Three indicators are used to select the most appropriate model size while ensuring simulation accuracy to improve simulation efficiency.

[0040] The present invention proposes a finite element model size optimization method for road dynamic deflection basin calculation, which can provide a standardized method for finite element model size optimization used for road dynamic deflection basin simulation. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 This is a top view schematic diagram of the constructed road finite element model. DETAILED DESCRIPTION

[0042] The present invention is further described below in conjunction with the accompanying drawings. It should be understood that these embodiments are only used to illustrate the present invention and are not used to limit the scope of the present invention. After reading the present invention, various equivalent forms of modifications to the present invention by those skilled in the art all fall within the scope defined by the claims attached to this application.

[0043] The method of the present invention is divided into the following 6 steps:

[0044] S1: Constructing a finite element model for calculating the dynamic deflection basin of a road i ;

[0045] S2: Simulate and obtain the i-th dynamic deflection basin d1(x) and the i-th deflection time domain curve d1′(t);

[0046] S3: Calculate the difference dd′ between the bending basin and the time domain curve i,diff ;

[0047] S4: Enlarge the model size to M i+1 , simulate and obtain the i+1th dynamic bending basin d i+i (x) and the i+1th deflection time domain curve d i+1 ′(t);

[0048] S5: The i-th dynamic deflection basin d obtained in step S2 i (x) and the (i+1)th dynamic deflection basin d obtained in step S4 i+i (x) Calculate the deflection basin difference d i,i+1,diff ; The i-th deflection time domain curve d obtained by step S2 i ′(t) and the i+1th deflection time domain curve d obtained in step S4 i+1 ′(t) Calculate the difference d′ of the deflection time domain curve i,i+1,diff ;

[0049] S6: Repeat steps S1 to S5 until the model optimization criteria are met. The model optimization criteria are:

[0050] If the difference between the bending basin and the time domain curve dd′ i,diff , bending basin difference d i,i+1,diff The difference d′ between the time domain curve of deflection i,i+1,diff The value satisfies formula (1), then M i The size of the model is the optimized size of the established road finite element model;

[0051] If formula (1) is not satisfied, construct M i+1 Model, repeat the above steps S2 to S6,

[0052]

[0053] The details of step S1 are as follows: the finite element model initially constructed for calculating the dynamic deflection basin of the road is denoted as M1, and the subsequent models are denoted as M2, M3, ... in sequence. i (i=1,2,3……) all meet the following requirements: the road model is divided into multiple layers from top to bottom, and each layer of the road model can select elastic material or viscoelastic material, and set the density, Poisson's ratio and damping ratio of each layer of the road model. Generally, the materials of each layer of the road model include asphalt mixture, cement concrete, cement stabilized gravel, graded gravel, soil, etc.

[0054] Asphalt mixture materials can be set to elastic or viscoelastic, and cement concrete, cement stabilized gravel, graded gravel, soil and other materials can be set to elastic.

[0055] When modeling, the elastic material can set the modulus, and the viscoelastic material can set the Prony series to characterize its modulus characteristics. The bonding state between the layers can be set to complete bonding, or there is a certain amount of sliding, which is characterized by the friction coefficient.

[0056] During modeling, the vehicle load is applied to the upper surface of the finite element model, and the load area is set to a rectangle. The applied loads include vertical loads, horizontal longitudinal loads, and horizontal lateral loads. In the simulation, the rectangular load area moves in a straight line along the longitudinal symmetry axis of the upper surface of the road finite element model at a specified speed. During the moving process, the rectangular load area always maintains a left-right symmetric state with respect to the longitudinal symmetry axis of the upper surface of the road finite element model. The side surfaces and bottom surface of the road finite element model are set to a fully constrained state, and no constraints are set on the upper surface of the road finite element model. The thickness of each layer of the road finite element model is set according to actual conditions. See the top view schematic diagram of the constructed road finite element model. Figure 1 shown.

[0057] The i-th dynamic bending sink d in step S2 i (x) is obtained as follows: For model M i At a certain moment in the simulation, the origin is set at the center of the rectangular load area. The forward direction of the rectangular load area is set as the positive direction of the x-axis, and the vertical downward direction of the model is set as the positive direction of the d-axis to construct a plane rectangular coordinate system. When the center point of the rectangular load area coincides with the center point of the upper surface of the model, the dynamic deflection basin d is obtained. i (x) is composed of all points on the model surface that satisfy the condition "d ≥ 0". The left and right limits of the deflection basin are denoted by x i,1 (x i,1 <0) and x i,2 (x i,2 >0), where d i (x i,1 )=0 and d i (x i,2 )=0.

[0058] The i-th deflection time domain curve d in step S2 i ′(t) is obtained as follows: For model M i , select the center point of the upper surface of the finite element model, and set the vertical downward direction of the model as the positive direction of the d′ axis. Set t = 0 as the starting time when the deflection d′ at the center point meets the condition of “d′ ≥ 0”, and set t = t i,max is the last moment when the deflection d′ at the center point satisfies the condition “d′≥0”, where d i ′(0)=0,d i ′(t i,max )=0.

[0059] The difference dd′ between the bending basin and the time domain curve in step S3 i,diff The calculation method is as follows: For a road section with the same structural composition and material parameters, when the load forward speed is v, the i-th dynamic deflection basin at each point on the road surface takes the value d i (x) should be equal to Substitute the i-th deflection time domain curve d as the independent variable i ′(t) In finite element simulation, due to the influence of model boundary conditions, mesh division and other factors, d i (x) and There will be a difference between them. The greater the difference between the two, the worse the accuracy of the simulation results. Therefore, for a suitable finite element model, d i (x) and It should be very close. Define dd′ by formula (1) i,diff Indicator, characterization i (x) and The difference between.

[0060]

[0061] The details of step S4 are as follows: the road finite element model M constructed in step S1 is i The length and width of the model are kept 1.2 times the original size, and the thickness of each layer of the model is kept unchanged. The enlarged model is recorded as M i+1 The load setting remains unchanged, and according to the method in step S2, based on M i+1 Model, calculation of dynamic deflection basin d i+i (x) and the deflection time domain curve d i+1 ′(t).

[0062] The deflection basin difference d in step S5 i,i+1,diff The difference d′ between the time domain curve of deflection i,i+1,diff The calculation method of is as follows: Formula (2) is the bending basin difference d i,i+1,diff The calculation method of formula (3) is the difference d′ of the deflection time domain curve i,i+1,diff The calculation method of .

[0063] d i,i+1,diff The smaller the value, the more i Dynamic bending basin d obtained by model simulation i (x) and based on M i+1 Dynamic bending basin d obtained by model simulation i+1 The smaller the difference between (x).

[0064] d′ i,i+1,diff The smaller the value, the more i The deflection time domain curve d obtained by model simulation i ′(t) and based on M i+1 The deflection time domain curve d obtained by model simulation i+1 The smaller the difference between ′(t).

[0065]

[0066]

[0067] Example:

[0068] The following are some representative embodiments of the present invention.

[0069] Embodiment 1:

[0070] The dimensions of the finite element model constructed for calculating the dynamic deflection basin of the road are shown in Table 1. The model is divided into three layers from top to bottom: asphalt mixture surface layer, cement stabilized gravel base layer, and soil roadbed. The asphalt mixture surface layer is set to viscoelastic, the cement stabilized gravel base layer and the soil roadbed are set to elastic, and the bonding state between each layer of the road model is set to fully bonded.

[0071] Model Name <![CDATA[M1]]> <![CDATA[M2]]> <![CDATA[M3]]> <![CDATA[M4]]> <![CDATA[M5]]> Length(m) 7.00 8.40 10.08 12.10 14.52 Width(m) 3.00 3.60 4.32 5.18 6.22

[0072] Table 1

[0073] The thickness and material parameter settings of each layer of the road model are shown in Table 2. The load area is set as a rectangle with a length of 180 mm and a width of 150 mm. The vertical load is 707 kPa, the horizontal longitudinal load is 200 kPa, and the horizontal transverse load is 170 kPa.

[0074]

[0075] Viscoelastic modulus of asphalt mixture surface layer characterized by Prony series

[0076] k 1 2 3 4 5 6 7 8 ∞ <![CDATA[ρ k ]]> <![CDATA[2×10 -6 ]]> <![CDATA[2×10 -5 ]]> <![CDATA[2×10 -4 ]]> <![CDATA[2×10 -3 ]]> <![CDATA[2×10 -2 ]]> <![CDATA[2×10 -1 ]]> 2 20 ∞ <![CDATA[E k (MPa)]]> 4328.06 5791.82 7181.28 6264.2 5261.67 2487.68 1016 298.19 101.49

[0077] Table 2

[0078] The difference dd′ between the deflection basin and the time domain curve corresponding to the finite element model of roads with different sizes i，diff Value, bending basin difference d i，i+1，diff The difference between the deflection time domain curve d′ i，i+1，diff The values ​​are shown in Table 3.

[0079] <![CDATA[d-d′ 1，diff ]]> <![CDATA[d-d′ 2，diff ]]> <![CDATA[d-d′ 3，diff ]]> <![CDATA[d-d′ 4，diff ]]> 8.62％ 6.84％ 5.23％ 4.66％ <![CDATA[d 1，2，diff ]]> <![CDATA[d 2，3，diff ]]> <![CDATA[d 3，4，diff ]]> <![CDATA[d 4，5，diff ]]> 15.62％ 10.94％ 7.65％ 4.21％ <![CDATA[d′ 1，2，diff ]]> <![CDATA[d′ 2，3，diff ]]> <![CDATA[d′ 3，4，diff ]]> <![CDATA[d′ 4，5，diff ]]> 14.62％ 10.75％ 7.37％ 4.97％

[0080] Table 3

[0081] For model M4, the corresponding difference between the bending basin of model M4 and the time domain curve dd′ 4，diff , Model M4 bending basin difference d 4，5，diff The difference d′ between the deflection time domain curve of model M4 4，5，diff The values ​​are all less than 5%, which meets the requirement of formula (4). Therefore, in this embodiment, model M4 is selected as the road finite element model with the preferred size.

Claims

1. A finite element model size optimization method for road dynamic deflection basin calculation, characterized in that: This method consists of the following 6 steps: S1: Constructing a finite element model for calculating the dynamic deflection basin of a road i ; S11: The finite element model initially constructed for calculating the dynamic deflection basin of the road is denoted as M1, and the subsequent models are denoted as M2, M3, ...; The constructed models M i , i=1,2,3……all meet the following requirements: the road model is divided into multiple layers from top to bottom, each layer of the road model selects elastic material or viscoelastic material, and sets the density, Poisson's ratio and damping ratio of each layer of the road model; S12: When modeling, the elastic material is set to a modulus, and the viscoelastic material is set to a Prony series to characterize its modulus characteristics. The bonding state between each layer is set to be completely bonded or with a certain amount of sliding. When the bonding state between each layer is set to have a certain amount of sliding, the friction coefficient is used to characterize it. S13: During modeling, the vehicle load is applied to the upper surface of the finite element model, and the load area is set as a rectangle; S14: During simulation, the rectangular load area moves in a straight line along the longitudinal symmetry axis of the upper surface of the finite element model at a specified speed. During the moving process, the rectangular load area always maintains a left-right symmetric state with respect to the longitudinal symmetry axis of the upper surface of the finite element model. The side surfaces and bottom surfaces of the finite element model are set to a fully constrained state, and no constraints are set on the upper surface of the finite element model. The thickness of each layer of the road finite element model is set according to the actual situation. S2: Simulate and obtain the i-th dynamic bending basin d i (x) and the i-th deflection time domain curve d i ′(t); S3: Calculate the difference dd′ between the bending basin and the time domain curve i,diff ; S4: Enlarge the model size to M i+1 , simulate and obtain the i+1th dynamic bending basin d i+i (x) and the i+1th deflection time domain curve d i+1 ′(t); S5: The i-th dynamic deflection basin d obtained in step S2 i (x) and the (i+1)th dynamic deflection basin d obtained in step S4 i+i (x) Calculate the deflection basin difference d i,i+1,diff ; The i-th deflection time domain curve d obtained by step S2 i ′(t) and the i+1th deflection time domain curve d obtained in step S4 i+1 ′(t) Calculate the difference d′ of the deflection time domain curve i,i+1,diff ; S6: Repeat steps S1 to S5 until the model optimization criterion is met, wherein the model optimization criterion is: If the difference between the bending basin and the time domain curve dd′ i,diff , bending basin difference d i,i+1,diff The difference d′ between the time domain curve of deflection i,i+1,diff The value satisfies formula (1), then M i The size of the model is the optimized size of the established road finite element model; If formula (1) is not satisfied, construct M i+1 Model, repeat the above steps S2 to S6, 2. The finite element model size optimization method for road dynamic deflection basin calculation according to claim 1, characterized in that: In step S1: The road model materials of each layer include asphalt mixture, cement concrete, cement stabilized crushed stone, graded crushed stone and soil, wherein the asphalt mixture material is set to be elastic or viscoelastic; Cement concrete, cement-stabilized crushed stone, graded crushed stone, and earth materials were set to elastic; The applied loads include vertical loads, horizontal longitudinal loads and horizontal lateral loads.

3. The finite element model size optimization method for road dynamic deflection basin calculation according to claim 1, characterized in that: The i-th dynamic bending sink d in step S2 i (x) is obtained as follows: For model M i At a certain moment in the simulation, the origin is set at the center of the rectangular load area, the forward direction of the rectangular load area is set as the positive direction of the x-axis, the vertical downward direction of the model is set as the positive direction of the d-axis, and a plane rectangular coordinate system is constructed. When the center point of the rectangular load area coincides with the center point of the upper surface of the model, the i-th dynamic deflection basin d i (x) is composed of all points on the upper surface of the model that satisfy the condition "d ≥ 0". The left and right limits of the bending basin are denoted by x i,1 and x i,2 , where x i,1 <0,x i,2 >0, where d i (x i,1 )=0 and d i (x i,2 )=0.

4. The finite element model size optimization method for road dynamic deflection basin calculation according to claim 1, characterized in that: The i-th deflection time domain curve d in step S2 i ′(t) is obtained as follows: For model M i , select the center point of the upper surface of the finite element model, set the vertical downward direction of the model as the positive direction of the d′ axis, set t = 0 as the starting time when the deflection d′ at the center point meets the "d′ ≥ 0" condition, and set t = t i,max is the last moment when the deflection d′ at the center point satisfies the condition "d′≥0", where d i ′(0)=0,d i ′(t i,max )=0.

5. The finite element model size optimization method for road dynamic deflection basin calculation according to claim 1, characterized in that: The difference dd′ between the bending basin and the time domain curve in step S3 i,diff The calculation method is as follows: For a road section with the same structural composition and material parameters, when the load forward speed is v, the i-th dynamic deflection basin d at each point on the road surface i (x) should be equal to Substitute the i-th deflection time domain curve d as the independent variable i ′(t) The difference between the bending basin and the time domain curve dd′ is defined by formula (2): i,diff Indicator, representing d′ at each point on the road surface i (x) and The difference between 6. The finite element model size optimization method for road dynamic deflection basin calculation according to claim 3, characterized in that: Step S4 is as follows: the road finite element model M constructed in step S1 is converted into i The length and width of the model are enlarged to 1.2 times of the original, and the thickness of each layer of the model is kept unchanged. The enlarged model is recorded as M i+1 , the load setting remains unchanged, according to the i-th dynamic deflection basin d in step S2 i The calculation method of (x) is based on M i+1 Model, calculate the i+1th dynamic bending basin d i+i (x) and the i+1th deflection time domain curve d i+1 ′(t).

7. The finite element model size optimization method for road dynamic deflection basin calculation according to claim 1, characterized in that: In step S5, The deflection basin difference d is calculated by formula (3): i,i+1,diff ; The difference d′ of the deflection time domain curve is calculated by formula (4): i,i+1,diff ; Deflection basin difference d i,i+1,diff The smaller the value, the more i The dynamic bending basin d obtained by model simulation i (x) and based on M i+1 The i+1th dynamic bending basin d obtained by model simulation i+1 The smaller the difference between (x); Deflection time domain curve difference d′ i,i+1,diff The smaller the value, the more i The i-th deflection time domain curve d obtained by model simulation i ′(t) and based on M i+1 The i+1th deflection time domain curve d obtained by model simulation i+1 The smaller the difference between ′(t);

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