CN118504093A - Suspended dome force finding method and system based on machine learning - Google Patents
Suspended dome force finding method and system based on machine learning Download PDFInfo
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Abstract
The invention discloses a machine learning-based suspended dome force finding method and system, wherein the method comprises the steps of determining an initial stress boundary range of a cable rod unit and generating an initial stress data set in the range; establishing a finite element model of the suspended dome structure, applying an initial stress data set to a corresponding cable rod unit, and performing finite element calculation to obtain key node displacement and cable rod unit internal force of the suspended dome structure; carrying out normalization processing on the displacement of the key nodes and the internal force of the cable units, and training a neural network to obtain a self-stress prediction neural network model of the suspended dome; inputting zero displacement into a self-stress prediction neural network model of the suspended dome to predict the self-stress state of the suspended dome; and constructing a finite element model of the prestress equilibrium state size, taking the self-stress state as a design value, and obtaining the initial strain by using an inverse iteration method to finish the force finding of the suspended dome. The invention simplifies the force finding process, improves the prediction precision and reduces the calculation cost.
Description
Technical Field
The invention relates to the technical field of building structures, in particular to a machine learning-based suspended dome force finding method and system.
Background
The suspended dome is a classical space structure system, and the suspended dome structure fully exerts the advantages of both the single-layer spherical net shell and the cable dome structure and overcomes the defects of the single-layer spherical net shell and the cable dome structure. On one hand, the overall stability of the single-layer spherical reticulated shell structure is improved, and on the other hand, compared with a cable dome structure, the suspended dome structure still has initial rigidity when no prestress exists, so that the design, construction forming and node structure are greatly simplified. At the same time, the two structural systems act on the support to cancel each other, so the suspended dome structure is a self-balancing space structural system.
In practical design and analysis, the determination of the initial prestress of the suspended dome structure is of great importance. The traditional force finding method of the suspended dome structure comprises a singular value decomposition method, a tension compensation method (an inverse iteration method), an elastic support method and the like. The traditional force finding method needs a large amount of calculation resources, such as complex mathematical calculation by a singular value decomposition method, an iteration process is tedious when the inverse iteration method is solved, and the elastic support method is simple in principle but also needs finite element calculation. Therefore, how to reduce the calculation cost of the force finding analysis of the suspended dome structure on the premise of ensuring the precision is a problem worthy of research.
Disclosure of Invention
The technical problems to be solved by the invention are as follows: the method and the system for finding the forces of the suspended dome based on the machine learning combine the advantages of finite element analysis and neural network in nonlinear data simulation and prediction, can reduce the complexity of the force finding process, and improve the force finding efficiency and accuracy.
In order to solve the technical problems, the invention provides a machine learning-based suspended dome force finding method, which comprises the following steps:
S1, determining an initial stress boundary range of the cable pole unit, and generating an initial stress data set in the range through a random function.
S2, establishing a finite element model of the suspended dome structure, applying an initial stress data set to a corresponding cable rod unit, and performing finite element calculation to obtain key node displacement and cable rod unit internal force of the suspended dome structure.
And S3, respectively carrying out normalization processing on the displacement of the key node and the internal force of the cable pole unit, training a neural network by using normalized data to obtain a self-stress prediction neural network model of the suspended dome, and further obtaining a prediction result and evaluating the model.
S4, inputting zero displacement into a self-stress prediction neural network model of the suspended dome, and predicting the self-stress state of the suspended dome.
S5, constructing a finite element model of the prestress equilibrium state size, taking the self-stress state in the step S4 as a design value, and obtaining initial strain by using an inverse iteration method to finish the force finding of the string dome.
Further, in step S1, generating the initial stress data set includes the sub-steps of:
S101, reasonably determining the initial tension of the cable and the initial pressure value range of the rod according to the actual demand and engineering experience of the suspended dome structure.
S102, randomly generating a large amount of sample data in a value range through a random function in MATLAB to form an initial stress data set of the suspended dome structure.
Further, in step S2, obtaining the key node displacement and the cable lever unit internal force data set includes the following sub-steps:
S201, establishing a finite element model of the suspended dome by using APDL (ANSYS PARAMETRIC DESIGN Language, ANSYS parameterized design Language), and simulating a cable rod unit by using LINK 180.
S202, applying the initial stress data set obtained in the step S1 to a cable pole unit, and carrying out finite element calculation by utilizing a finite element model of a suspended dome structure to obtain key node displacement and cable pole unit internal force.
Further, in step S3, obtaining a self-stress prediction neural network model of the suspended dome includes the following sub-steps:
s301, combining the key node displacement and the internal force of the cable lever unit, dividing the key node displacement and the internal force of the cable lever unit into a training set and a testing set according to a set proportion, and respectively carrying out normalization processing on the training set and the testing set by using mapminmax functions of MATLAB, wherein the specific formula is as follows:
Where x represents the true value, x' represents the normalized data, and x min and x max represent the minimum and maximum values of the data, respectively.
S302, building a neural network by utilizing a MATLAB environment, training the neural network by utilizing a training set to obtain a network error, continuously adjusting the super parameters until the neural network with the minimum error is obtained, and outputting a self-stress prediction neural network model of the suspended dome at the moment.
Inputting the displacement of the key node into a self-stress prediction neural network model of the suspended dome to obtain a predicted value of each sample corresponding to the displacement of the key node, and further obtaining an evaluation index of the model through calculation; wherein the evaluation index comprises a determination coefficient, a root mean square error, an average absolute error and an average error, and the specific expression is as follows:
Wherein R 2 represents a decision coefficient, SS res represents a sum of squares of residuals, SS tot represents a sum of squares of total, N represents a total number of samples in the dataset, y i represents a true value of an ith sample, y' i represents a predicted value of the ith sample, Representing the average of the true values of the samples, RMSE represents the root mean square error, MSE represents the mean square error, MAE represents the mean absolute error, and MRE represents the mean relative error.
The decision coefficient R 2 ranges from 0 to 1, the closer to 1 represents higher network training accuracy, the remaining index ranges from 0 to positive infinity, and the closer to 0 represents smaller global error.
Further, in step S4, predicting the self-stress state includes:
and determining a displacement control target, namely node displacement is 0, normalizing zero displacement, inputting the zero displacement into a self-stress prediction neural network model of the suspended dome to obtain normalized self-stress, and carrying out inverse normalization on the normalized self-stress to obtain the self-stress state of the predicted suspended dome structure.
Further, in step S5, obtaining the initial strain includes the following:
S501, taking the geometric dimension of the suspended dome on the design blueprint as the dimension of the prestress equilibrium state (the dimension at the moment is also regarded as the approximate loft state dimension calculated for the first time), and establishing a finite element model of the prestress equilibrium state dimension by utilizing the dimension.
S502, applying prestress to a finite element model with the prestress equilibrium state size, namely applying initial strain to the cable rod unit, and estimating a first initial strain value by using the self-stress state obtained in the step S4 as a prestress design value, wherein a specific formula is as follows:
ε＝σ/E
Wherein epsilon represents initial strain, sigma represents prestress, E represents elastic modulus;
and carrying out static analysis on the suspended dome structure in ANSYS based on the initial strain to obtain an approximate prestress balance state.
S503, reversely increasing the difference between the approximate prestress equilibrium state size and the prestress equilibrium state size to the node coordinates of the finite element model of the prestress equilibrium state size to obtain an approximate lofting state and re-modeling, calculating the difference between the prestress design value and the internal force of the cable rod to update the initial strain, wherein the expression of the initial strain update is as follows:
εi(k+1)＝[Pi+ΔFi(k)]/(EiAi)
Wherein, P i represents the tension design value of the ith group of cable rods, deltaF i (k) represents the difference value between the prestress design value of the ith group of cable rods and the actual internal force after the calculation of the kth cycle, E i represents the elastic modulus of the ith group of cable rods, A i represents the sectional area of the ith group of cable rods, epsilon i (k+1) represents the initial strain value which the ith group of cable rods should exert during the calculation of the kth+1 cycle, and i=1, 2, … and n.
S504, pre-stressing the finite element model with the pre-stressing equilibrium state size again by utilizing the updated initial strain, repeating the steps S502-S503 for cyclic iteration until the difference value between the approximate pre-stressing equilibrium state size and the pre-stressing equilibrium state size is within 5mm and the error between the pre-stressing design value and the internal force of the cable rod is within 10%, and stopping iteration; the approximate prestress equilibrium state is the prestress equilibrium state, the approximate lofting state is the required lofting state, and the initial strain is the initial strain applied to the cable rod unit.
Furthermore, the invention also provides a machine learning-based suspended dome force finding system, which comprises:
And the initial stress data set module acquisition module is used for empirically determining the initial stress boundary range of the cable rod unit and generating an initial stress data set in the range through a random function of MATLAB.
And the key node displacement and cable pole unit internal force acquisition module is used for establishing a finite element model of the suspended dome structure, applying the initial stress data set to the corresponding cable pole unit, and carrying out finite element calculation to obtain the key node displacement and cable pole unit internal force of the suspended dome structure.
The prediction result acquisition module is used for respectively carrying out normalization processing on the key node displacement and the internal force of the cable pole unit, training the neural network by utilizing the normalized data to obtain a self-stress prediction neural network model of the string dome, further obtaining a prediction result and evaluating the model.
And the self-stress state prediction module is used for inputting zero displacement into the self-stress prediction neural network model of the suspended dome to predict the self-stress state of the suspended dome.
The initial strain acquisition module is used for constructing a finite element model of the prestress equilibrium state size, taking the self-stress state as a design value, and obtaining the initial strain by using an inverse iteration method to finish the force finding of the string dome.
Furthermore, the invention also provides electronic equipment, which comprises a memory, a processor and a computer program stored on the memory and capable of running on the processor, wherein the processor realizes the steps of the machine learning-based suspended dome force finding method when executing the computer program.
Further, the invention also provides a computer readable storage medium, wherein the computer readable storage medium stores a computer program, and the computer program is executed by a processor to execute the machine learning-based suspended dome force finding method.
Compared with the prior art, the technical scheme provided by the invention has the following technical effects:
(1) The invention overcomes the defect of complicated calculation of the traditional force finding method of the suspended dome structure and reduces the complexity of the force finding process.
(2) The invention directly establishes the association between the input quantity and the target quantity in a data driving mode, has the advantages of no iteration and high calculation speed, and has good prediction precision due to the strong nonlinear fitting capability of the machine learning model. Therefore, on the premise of ensuring the precision, the machine learning method can greatly reduce the calculation cost of the force finding analysis of the suspended dome structure.
Drawings
FIG. 1 is a flow chart of an overall implementation of the present invention.
Fig. 2 is a schematic diagram of a central stadium dome in a city in accordance with an embodiment of the present invention.
Fig. 3 is a schematic topology diagram of a radial basis function neural network in an embodiment of the invention.
FIG. 4 shows absolute relative errors of the radial basis function neural network prediction result and the conventional force finding method in the embodiment of the present invention.
FIG. 5 is a graph comparing predicted values of a neural network and verified values of finite element modeling of self-stress in an embodiment of the present invention.
Fig. 6 is a displacement cloud for finite element simulation verification in an embodiment of the present invention.
Detailed Description
The invention is further described below with reference to the accompanying drawings. The following examples are only for more clearly illustrating the technical aspects of the present invention, and are not intended to limit the scope of the present invention.
In order to achieve the above objective, the present invention provides a machine learning-based force finding method for a suspended dome, as shown in fig. 1, which specifically comprises the following steps:
s1, determining an initial stress boundary range of a cable pole unit according to experience, and generating an initial stress data set in the range through a random function of MATLAB, wherein the initial stress data set comprises the following specific contents:
S101, reasonably determining the initial tension of the cable and the initial pressure value range of the rod according to the actual demand and engineering experience of the suspended dome structure.
S102, randomly generating a large amount of sample data in a value range through a random function in MATLAB to form an initial stress data set of the suspended dome structure.
In this embodiment, a central stadium dome model of an austenite city is selected, as shown in fig. 2, where (a) of fig. 2 is an isometric view, (b) of fig. 2 is an isometric view of a lower cable structure, (c) of fig. 2 is a plan view, and (d) of fig. 2 is a plan view of a lower cable structure. The structural cable system is divided into 9 groups of units, namely three groups of stay bars (CG 01, CG02 and CG 03), three groups of endless cables (HS 01, HS02 and HS 03) and three groups of inclined cables (XS 01, XS02 and XS 03).
The range of values for the cable tension and the rod pressure are shown in table 1.
TABLE 1 initial prestress Range
| Cable pole class | Minimum value/kN | Maximum value/kN |
| HS01～03,XS01～03 | 500 | 3000 |
| CG01～03 | -500 | 0 |
The initial prestress of 9 groups of cable rods is 10000 groups.
S2, establishing a finite element model of the suspended dome structure, applying an initial stress data set to a corresponding cable rod unit, and performing finite element calculation to obtain key node displacement and cable rod unit internal force of the suspended dome structure, wherein the specific contents are as follows:
S201, establishing a finite element model of the suspended dome by using APDL (ANSYS PARAMETRIC DESIGN Language, ANSYS parameterized design Language), and simulating a cable rod unit by using LINK 180.
S202, applying the initial stress data set obtained in the step S1 to a cable pole unit, and carrying out finite element calculation by utilizing a finite element model of a suspended dome structure in combination with the dead weight of the structure to obtain key node displacement of 10000 groups of stay pole vertexes and internal force of the cable pole unit.
S3, respectively carrying out normalization processing on the displacement of the key node and the internal force of the cable pole unit, training a radial basis function neural network by using normalized data to obtain a self-stress prediction neural network model of the string dome, further obtaining a prediction result and evaluating the model, wherein the specific contents are as follows:
S301, combining the key node displacement and the internal force of the cable lever unit, and according to 7:3 is divided into a training set and a testing set, wherein the training set and the testing set are respectively normalized by using mapminmax functions of MATLAB, and the specific formula is as follows:
Where x represents the true value, x' represents the normalized data, and x min and x max represent the minimum and maximum values of the data, respectively.
S302, constructing a radial basis function neural network by utilizing a MATLAB environment, wherein the topological structure of the network is shown in figure 3, W is a weight, and b is a bias. The radial basis function neural network core code is as follows:
net＝newrbe(P,T,spread)
Wherein net represents a radial basis function neural network and returns in the form of a network object; p is an r×q matrix consisting of Q R element input vectors; t is an SxQ matrix consisting of Q S element target class vectors; the spread represents the spread of the radial basis functions.
And training the radial basis function neural network by using the training set to obtain a network error, and continuously adjusting the super parameters until the radial basis function neural network with the minimum error is obtained, wherein the output is a self-stress prediction neural network model of the suspended dome.
The first training time, the set spin is 1.0, the larger the spin, the smoother the function approximation, but too much spreading can lead to numerical problems, and the training results are shown in Table 2.
TABLE 2 super parameters and evaluation index of radial basis function neural network
As can be seen from table 2, when the value of the spread is 0.1 or 0.5, the error of the test set and the error of the training set differ greatly, which indicates that the neural network is over-fitted; when the value of the spread is 1, 5, 10 or 100, the error change is not large, so that the radial basis function neural network trained by the value of the spread is selected for searching force.
The training set is input into the radial basis function neural network during training, the radial basis function neural network is adjusted in time according to the error of the radial basis function neural network, and the test set has no influence on training, so that independent measurement of network performance can be provided during and after training.
Inputting the displacement of the key node into a self-stress prediction neural network model of the suspended dome to obtain a predicted value of each sample corresponding to the displacement of the key node, and further obtaining an evaluation index of the model through calculation; wherein the evaluation index comprises a determination coefficient, a root mean square error, an average absolute error and an average error, and the specific expression is as follows:
Wherein R 2 represents a decision coefficient, SS res represents a sum of squares of residuals, SS tot represents a sum of squares of total, N represents a total number of samples in the dataset, y i represents a true value of an ith sample, y i' represents a predicted value of the ith sample, Representing the average of the true values of the samples, RMSE represents the root mean square error, MSE represents the mean square error, MAE represents the mean absolute error, and MRE represents the mean relative error.
The decision coefficient R 2 ranges from 0 to 1, the closer to 1 represents higher network training accuracy, the remaining index ranges from 0 to positive infinity, and the closer to 0 represents smaller global error.
S4, inputting zero displacement into a self-stress prediction neural network model of the suspended dome, and predicting the self-stress state of the suspended dome, wherein the specific contents are as follows:
and determining a displacement control target, namely node displacement is 0, normalizing zero displacement, inputting the zero displacement into a self-stress prediction neural network model of the suspended dome to obtain normalized self-stress, and carrying out inverse normalization on the normalized self-stress to obtain the self-stress state of the predicted suspended dome structure.
Comparing the predicted value with the calculated value of the elastic support method, as shown in table 3, the absolute relative error is shown in fig. 4, and the predicted value of the self-stress has higher precision.
Table 3 comparison of neural network predictors and elastic support method calculations
| Cell type | Self stress prediction value/N | Calculated value/N by elastic support method | Ratio of | Average ratio of | Absolute relative error |
| CG01 | -178482.3 | -164785.1018 | 1.0831 | 1.1014 | -1.6897％ |
| CG02 | -67056.8 | -60071.86875 | 1.1163 | 1.1014 | 1.3306％ |
| CG03 | -39169.6 | -34684.59762 | 1.1293 | 1.1014 | 2.4693％ |
| XS01 | 381788.0 | 355054.6078 | 1.0753 | 1.1014 | -2.4300％ |
| XS02 | 145837.4 | 133562.0619 | 1.0919 | 1.1014 | -0.8715％ |
| XS03 | 86062.1 | 76445.68374 | 1.1258 | 1.1014 | 2.1648％ |
| HS01 | 1897015.6 | 1763780.121 | 1.0755 | 1.1014 | -2.4065％ |
| HS02 | 732354.3 | 665735.9936 | 1.1001 | 1.1014 | -0.1233％ |
| HS03 | 211349.9 | 189466.7323 | 1.1155 | 1.1014 | 1.2618％ |
S5, constructing a finite element model of the prestress equilibrium state size, and obtaining initial strain by using the self-stress state in the step S4 as a design value and using an inverse iteration method to finish the force finding of the string dome, wherein the specific contents are as follows:
S501, taking the geometric dimension of the suspended dome on the design blueprint as the dimension of the prestress equilibrium state (the dimension at the moment is also regarded as the approximate loft state dimension calculated for the first time), and establishing a finite element model of the prestress equilibrium state dimension by utilizing the dimension.
S502, applying prestress to a finite element model with the prestress equilibrium state size, namely applying initial strain to the cable rod unit, and estimating a first initial strain value by using the self-stress state obtained in the step S4 as a prestress design value, wherein a specific formula is as follows:
ε＝σ/E
Wherein epsilon represents initial strain, sigma represents prestress, E represents elastic modulus;
and carrying out static analysis on the suspended dome structure in ANSYS based on the initial strain to obtain an approximate prestress balance state.
S503, reversely increasing the difference between the approximate prestress equilibrium state size and the prestress equilibrium state size to the node coordinates of the finite element model of the prestress equilibrium state size to obtain an approximate lofting state and re-modeling, calculating the difference between the prestress design value and the internal force of the cable rod to update the initial strain, wherein the expression of the initial strain update is as follows:
εi(k+1)＝[Pi+ΔFi(k)]/(EiAi)
Wherein, P i represents the tension design value of the ith group of cable rods, deltaF i (k) represents the difference value between the prestress design value of the ith group of cable rods and the actual internal force after the calculation of the kth cycle, E i represents the elastic modulus of the ith group of cable rods, A i represents the sectional area of the ith group of cable rods, epsilon i (k+1) represents the initial strain value which the ith group of cable rods should exert during the calculation of the kth+1 cycle, and i=1, 2, … and n.
S504, pre-stressing the finite element model with the pre-stressing equilibrium state size again by utilizing the updated initial strain, repeating the steps S502-S503 for cyclic iteration until the difference value between the approximate pre-stressing equilibrium state size and the pre-stressing equilibrium state size is within 5mm and the error between the pre-stressing design value and the internal force of the cable rod is within 10%, and stopping iteration; the approximate prestress equilibrium state is the prestress equilibrium state, the approximate lofting state is the required lofting state, and the initial strain is the initial strain applied to the cable rod unit.
The primary strain calculation results are shown in table 4; then verifying the primary strain back generation model, and calculating to obtain the approach predicted value of the internal force of the cable pole, as shown in figure 5; and outputting a structural displacement cloud picture, wherein the displacement is close to zero, as shown in fig. 6 (the unit is meter, MX refers to the position where the displacement maximum value is located, and MN refers to the position where the displacement minimum value is located), so that the correctness of the method provided by the invention is verified.
TABLE 4 initial strain calculation results
| Cell type | Initial strain |
| CG01 | -9.58E-05 |
| CG02 | -4.48E-05 |
| CG03 | -2.91E-05 |
| XS01 | 3.27E-04 |
| XS02 | 2.99E-04 |
| XS03 | 2.66E-04 |
| HS01 | 1.28E-03 |
| HS02 | 1.22E-03 |
| HS03 | 1.03E-03 |
The embodiment of the invention also provides a suspended dome force finding system based on machine learning, which comprises an initial stress data set module acquisition module, a key node displacement and cable rod unit internal force acquisition module, a prediction result acquisition module, a self-stress state prediction module, an initial strain acquisition module and a computer program capable of running on a processor. It should be noted that each module in the above system corresponds to a specific step of the method provided by the embodiment of the present invention, and has a corresponding functional module and beneficial effect of executing the method. Technical details not described in detail in this embodiment may be found in the methods provided in the embodiments of the present invention.
The embodiment of the invention also provides an electronic device which comprises a memory, a processor and a computer program stored on the memory and capable of running on the processor. It should be noted that, when executing the computer program, the processor corresponds to the specific steps of the method provided by the embodiment of the present invention, and has the corresponding functional modules and beneficial effects of the execution method. Technical details not described in detail in this embodiment may be found in the methods provided in the embodiments of the present invention.
The embodiment of the invention also provides a computer readable storage medium, and the computer readable storage medium stores a computer program. It should be noted that, when the computer program is executed by the processor, the specific steps of the method provided by the embodiment of the present invention are corresponding to the functional modules and beneficial effects of the execution method. Technical details not described in detail in this embodiment may be found in the methods provided in the embodiments of the present invention.
The foregoing is merely a preferred embodiment of the present invention, and it should be noted that modifications and variations could be made by those skilled in the art without departing from the technical principles of the present invention, and such modifications and variations should also be regarded as being within the scope of the invention.
Claims (9)
1. A machine learning-based suspended dome force finding method, comprising:
s1, determining an initial stress boundary range of a cable pole unit, and generating an initial stress data set in the range through a random function;
s2, establishing a finite element model of the suspended dome structure, applying an initial stress data set to a corresponding cable rod unit, and performing finite element calculation to obtain key node displacement and cable rod unit internal force of the suspended dome structure;
S3, training a neural network by using the normalized key node displacement and the internal force of the cable rod unit to obtain a self-stress prediction neural network model of the suspended dome, and further obtaining a prediction result and evaluating the model;
S4, inputting zero displacement into a self-stress prediction neural network model of the suspended dome, and predicting the self-stress state of the suspended dome;
S5, constructing a finite element model of the prestress equilibrium state size, taking the self-stress state in the step S4 as a design value, and obtaining initial strain by using an inverse iteration method to finish the force finding of the string dome.
2. The machine learning based suspended dome force finding method of claim 1, wherein in step S1, generating the initial stress data set comprises the sub-steps of:
s101, determining the primary tension of a cable and the primary pressure value range of a rod according to the actual requirement of a suspended dome structure and engineering experience;
S102, randomly generating a large amount of sample data in a value range through a random function in MATLAB to form an initial stress data set of the suspended dome structure.
3. The machine learning based suspended dome force finding method of claim 1, wherein in step S2, obtaining the key node displacement and in-cable-unit force dataset comprises the sub-steps of:
S201, establishing a finite element model of the string dome by using an ANSYS parameterized design language, and simulating a cable rod unit by using a LINK 180;
S202, applying the initial stress data set obtained in the step S1 to a cable pole unit, and carrying out finite element calculation by utilizing a finite element model of a suspended dome structure to obtain key node displacement and cable pole unit internal force.
4. The machine learning based suspended dome force finding method of claim 1, wherein in step S3, obtaining a self-stress predictive neural network model of the suspended dome comprises the sub-steps of:
s301, combining the key node displacement and the internal force of the cable lever unit, dividing the key node displacement and the internal force of the cable lever unit into a training set and a testing set according to a set proportion, and respectively carrying out normalization processing on the training set and the testing set by using mapminmax functions of MATLAB, wherein the specific formula is as follows:
Wherein x represents a true value, x' represents normalized data, and x min and x max represent a minimum value and a maximum value of the data, respectively;
S302, building a neural network by utilizing a MATLAB environment, training the neural network by utilizing a training set to obtain a network error, continuously adjusting super parameters until a neural network with the minimum error is obtained, and outputting a self-stress prediction neural network model of the suspended dome at the moment;
Inputting the displacement of the key node into a self-stress prediction neural network model of the suspended dome to obtain a predicted value of each sample corresponding to the displacement of the key node, and obtaining an evaluation index of the model through calculation; wherein the evaluation index comprises a determination coefficient, a root mean square error, an average absolute error and an average error, and the specific expression is as follows:
Wherein R 2 represents a decision coefficient, SS res represents a sum of squares of residuals, SS tot represents a sum of squares of total, N represents a total number of samples in the dataset, y i represents a true value of an ith sample, y i' represents a predicted value of the ith sample, Representing the average of the true values of the samples, RMSE represents the root mean square error, MSE represents the mean square error, MAE represents the mean absolute error, and MRE represents the mean relative error.
5. The machine learning based suspended dome force finding method of claim 1, wherein in step S4, predicting the self-stress state comprises:
and determining a displacement control target, namely node displacement is 0, normalizing zero displacement, inputting the zero displacement into a self-stress prediction neural network model of the suspended dome to obtain normalized self-stress, and carrying out inverse normalization on the normalized self-stress to obtain the self-stress state of the predicted suspended dome structure.
6. The machine learning based suspended dome force finding method of claim 1, wherein in step S5, obtaining the initial strain comprises:
S501, taking the geometric dimension of a suspended dome on a design drawing as the dimension of a prestress equilibrium state, and establishing a finite element model of the prestress equilibrium state dimension by utilizing the dimension;
S502, applying prestress to a finite element model with the prestress equilibrium state size, namely applying initial strain to the cable rod unit, and obtaining a first initial strain value by using the self-stress state obtained in the step S4 as a prestress design value, wherein the specific formula is as follows:
εσ/E
Wherein epsilon represents initial strain, sigma represents prestress, E represents elastic modulus;
Carrying out static analysis on the suspended dome structure in ANSYS based on the initial strain to obtain a theoretical prestress equilibrium state;
S503, reversely increasing the difference between the theoretical prestress equilibrium state size and the prestress equilibrium state size to the node coordinates of the finite element model of the prestress equilibrium state size to obtain a theoretical lofting state and re-modeling, calculating the difference between the prestress design value and the internal force of the cable rod to update the primary strain, wherein the expression of the primary strain update is as follows:
εi(k+1)＝[Pi+ΔFi(k)]/(EiAi)
Wherein P i represents a tension design value of the ith group of cable rods, deltaF i (k) represents a difference value between a prestress design value of the ith group of cable rods and an actual internal force after calculation of the kth cycle, E i represents an elastic modulus of the ith group of cable rods, A i represents a cross-sectional area of the ith group of cable rods, epsilon i (k+1) represents a primary strain value to be applied by the ith group of cable rods during calculation of the kth+1 cycle, and i=1, 2, … and n;
S504, pre-stressing the finite element model with the pre-stressing equilibrium state size again by utilizing the updated initial strain, repeating the steps S502-S503 for cyclic iteration until the difference value between the theoretical pre-stressing equilibrium state size and the pre-stressing equilibrium state size is within 5mm and the error between the pre-stressing design value and the internal force of the cable rod is within 10%, and stopping iteration; the theoretical prestress equilibrium state is the prestress equilibrium state, the theoretical lofting state is the required lofting state, and the initial strain is the initial strain applied to the cable rod unit.
7. A system for applying the machine learning based suspended dome force finding method of claim 1, comprising:
The initial stress data set module acquisition module is used for empirically determining the initial stress boundary range of the cable rod unit and generating an initial stress data set in the range through a random function of MATLAB;
The key node displacement and cable pole unit internal force acquisition module is used for establishing a finite element model of the suspended dome structure, applying an initial stress data set to a corresponding cable pole unit, and carrying out finite element calculation to obtain the key node displacement and cable pole unit internal force of the suspended dome structure;
The prediction result acquisition module is used for respectively carrying out normalization processing on the key node displacement and the internal force of the cable pole unit, training the neural network by utilizing the normalized data to obtain a self-stress prediction neural network model of the string dome, further obtaining a prediction result and evaluating the model;
The self-stress state prediction module is used for inputting zero displacement into a self-stress prediction neural network model of the suspended dome to predict the self-stress state of the suspended dome;
The initial strain acquisition module is used for constructing a finite element model of the prestress equilibrium state size, taking the self-stress state as a design value, and obtaining the initial strain by using an inverse iteration method to finish the force finding of the string dome.
8. An electronic device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, characterized in that the processor implements the steps of the machine learning based dome force finding method of any one of claims 1 to 6 when the computer program is executed.
9. A computer-readable storage medium storing a computer program, characterized in that the computer program, when executed by a processor, performs the machine learning based suspended dome force finding method of any one of claims 1 to 6.
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