A Data- and Mechanics-Driven Method for Calculating the Seismic Response of Reinforced Concrete Frame Structures

Abstract

This invention provides a data- and mechanics-driven method for calculating the seismic response of concrete frame structures, relating to the field of civil engineering structural analysis technology. By constructing a heterogeneous graph neural network model and training it based on real engineering data, a fundamental period prediction model is obtained. For the concrete frame structure to be calculated, a multi-degree-of-freedom mechanical model containing undetermined equivalent shear stiffness is constructed. The predicted fundamental period of the concrete frame structure is obtained through the fundamental period prediction model. The undetermined equivalent shear stiffness is calculated from the predicted fundamental period, thus obtaining a definite equivalent multi-degree-of-freedom mechanical model. This model is then solved to obtain the inter-story drift of each floor. The maximum inter-story drift angle is extracted as an evaluation index of the structure's seismic performance. This invention solves the problems of low efficiency and low reliability in existing seismic response calculations for concrete frame structures. This invention is applicable to the seismic response calculation of concrete frame structures.

Description

Technical Field

[0001] This invention relates to the field of civil engineering structural analysis technology, and in particular to a method for calculating the seismic response of concrete frame structures driven by a combination of data and mechanics. Background Technology

[0002] Seismic response calculation of reinforced concrete frame structures is crucial for structural design and optimization. This calculation primarily relies on two types of methods: purely mechanical methods and purely data-driven methods.

[0003] Purely mechanical methods: Engineers use modal response spectrum analysis or time history analysis to calculate seismic response, which requires an accurate structural mechanics model. This typically involves: creating a refined truss or shell element model using finite element software (such as SAP2000 or ETABS); solving for eigenvalues ​​based on the stiffness and mass distribution of beam-column joints to obtain the natural period and mode shape; and then calculating inter-story displacement and seismic action. For multi-story regular frames, complete modeling requires a large number of geometric parameters, and modal and time history analyses are time-consuming, especially when parameters need to be repeatedly adjusted during the design phase, resulting in low efficiency.

[0004] Purely data-driven methods: These methods use artificial neural networks (ANNs) or convolutional neural networks (CNNs) to directly predict inter-story drift angles or base shear forces. However, they cannot guarantee that the predictions conform to the laws of conservation of mechanics or the principles of dynamics. For example, the predicted period may contradict the actual stiffness and mass distribution, leading to unreliable subsequent response calculations.

[0005] In conclusion, how to combine mechanical methods with purely data-driven methods to make the seismic response calculation of concrete frame structures more efficient and reliable has become an urgent problem to be solved. Summary of the Invention

[0006] The technical problem solved by this invention: This invention provides a data- and mechanics-driven method for calculating the seismic response of concrete frame structures, which solves the problems of low efficiency and low reliability in existing seismic response calculations for concrete frame structures.

[0007] The technical solution adopted by this invention to solve the above-mentioned technical problems is: a data- and mechanics-driven method for calculating the seismic response of a concrete frame structure, wherein the concrete frame structure is a multi-story regular concrete frame structure, and the method includes the following steps:

[0008] S1. Based on the statistical regularities and standard limits of real engineering data, a set of concrete frame structure parameters is generated. The parameters are then analyzed using structural analysis software to obtain a compliant set of concrete frame structure parameters and the corresponding basic structural period, forming a dataset. The set of concrete frame structure parameters includes beam node parameters, column node parameters, and floor slab node parameters.

[0009] S2. Construct a heterogeneous graph neural network model. Take the set of concrete frame structure parameters in the dataset as input and the basic period of the structure as output. Train the heterogeneous graph neural network model to obtain a prediction model of the basic period of the structure. The heterogeneous graph neural network model represents the heterogeneous topology of the frame structure with three types of heterogeneous nodes, namely beams, columns and floor slabs and their connection relationships. Store the node features in the nodes and the edges only represent the connection relationships between the nodes.

[0010] S3. For the concrete frame structure to be calculated, construct a multi-degree-of-freedom mechanical model with undetermined equivalent shear stiffness, including: based on Timoshenko beam theory, the concrete frame structure is equivalent to a vertical cantilever beam with uniform cross section; based on the principle of virtual work and the unit load method, the total flexibility matrix of the concrete frame structure is decoupled into a linear superposition of bending flexibility matrix and shear flexibility matrix.

[0011] S4. Using the predicted fundamental period of the concrete frame structure to be calculated as the benchmark, construct the solution formula for the undetermined equivalent shear stiffness based on the fundamental period prediction model of the structure, and solve the undetermined equivalent shear stiffness to obtain a definite equivalent multi-degree-of-freedom mechanical model.

[0012] S5. For the determined equivalent multi-degree-of-freedom mechanical model, solve the generalized eigenvalue complete solution corresponding to the equation of motion, extract the first n natural vibration periods and mode shapes, use the mode decomposition response spectrum method to calculate the seismic response of each order, and obtain the inter-story displacement of each floor by combining the square root of each order response. Extract the maximum inter-story displacement angle as the evaluation index of the seismic performance of the structure.

[0013] Furthermore, in S1, based on the statistical regularities and standard limits of real engineering data, a set of parameters for concrete frame structures is generated, and weighted random sampling is adopted.

[0014] Furthermore, in S1, the beam node parameters include length, direction, relative coordinates, and cross-sectional dimensions; the column node parameters include length, direction, relative coordinates, and cross-sectional dimensions; and the floor slab node parameters include floor slab area and relative coordinates.

[0015] Furthermore, in S2, the structural fundamental period prediction model is also used to extract global features from the set of parameters of the concrete frame structure, which include the total dimensions, story height, total number of stories, PGA, and total equivalent mass of the concrete frame structure.

[0016] Furthermore, in S3, the overall flexibility matrix of the concrete frame structure is decoupled into a linear superposition of the bending flexibility matrix and the shear flexibility matrix, specifically as follows: ,in, Represents the overall compliance matrix. Represents the bending compliance matrix. Represents the shear compliance matrix. It represents the equivalent shear stiffness.

[0017] Furthermore, in S4, the formula for solving the undetermined equivalent shear stiffness is: ;in, Represents the largest eigenvalue of the matrix. Represents the symmetric bending compliance matrix. Represents the symmetric unit shear compliance matrix. Indicates the basic period of the forecast. Indicates the equivalent shear stiffness. It represents pi (π).

[0018] Furthermore, in S4, the Newton-Raphson method with analytical derivatives is used to iteratively find the root of the undetermined equivalent shear stiffness to obtain the optimal solution of the undetermined equivalent shear stiffness, which is then used as the solution of the undetermined equivalent shear stiffness.

[0019] Furthermore, S5 also includes the introduction of a period reduction factor to reduce the natural vibration period, in order to reflect the contribution of non-structural components to stiffness.

[0020] Furthermore, S5 also includes the introduction of a shear-weight ratio verification mechanism to verify whether the seismic shear force of each floor meets the minimum shear-weight ratio requirement. For floors that do not meet the requirement, the shear force and inter-story displacement are adjusted by the same ratio.

[0021] Furthermore, the formula for calculating the maximum inter-story drift angle is: ,in, Indicates the maximum inter-story drift angle. Indicates the first Inter-floor displacement after floor adjustment Indicates the first The floor height.

[0022] The beneficial effects of this invention are as follows: This invention provides a data- and mechanics-driven method for calculating the seismic response of reinforced concrete frame structures. By constructing a heterogeneous graph neural network model and training it based on real engineering data, a fundamental period prediction model of the structure is obtained. For the reinforced concrete frame structure to be calculated, a multi-degree-of-freedom mechanical model containing undetermined equivalent shear stiffness is constructed. The predicted fundamental period of the reinforced concrete frame structure is obtained through the fundamental period prediction model. The undetermined equivalent shear stiffness is calculated from the predicted fundamental period, thus obtaining a definite equivalent multi-degree-of-freedom mechanical model. This model is then solved to obtain the inter-story drift of each floor. The maximum inter-story drift angle is extracted as an evaluation index of the structure's seismic performance. This solves the problems of low efficiency and low reliability in existing seismic response calculations for reinforced concrete frame structures. Compared with existing technologies, this invention rapidly predicts the fundamental period of the structure through a data-driven heterogeneous graph neural network model, avoiding the time-consuming process of detailed modeling and complex modal analysis in purely mechanical methods. By combining the data prediction results with the equivalent multi-degree-of-freedom mechanical model, the reliability of the seismic response calculation is ensured. Attached Figure Description

[0023] Figure 1 This is a flowchart illustrating a data- and mechanics-driven method for calculating the seismic response of a concrete frame structure, as provided by the present invention.

[0024] Figure 2 This is a fundamental periodicity distribution diagram of the sampling data in the X-direction of a data- and mechanics-driven method for calculating the seismic response of a concrete frame structure, provided by this invention.

[0025] Figure 3 This is a fundamental periodicity distribution diagram in the Y direction of the sampled data in a data- and mechanics-driven seismic response calculation method for concrete frame structures provided by this invention.

[0026] Figure 4 This is a diagram showing the X-direction prediction results of a data- and mechanics-driven method for calculating the seismic response of a concrete frame structure, as provided by this invention.

[0027] Figure 5 This is an X-direction error analysis diagram of a data- and mechanics-driven method for calculating the seismic response of a concrete frame structure, provided by this invention.

[0028] Figure 6 This is a Y-direction prediction result diagram of a data- and mechanics-driven method for calculating the seismic response of a concrete frame structure provided by this invention.

[0029] Figure 7 This is a Y-direction error analysis diagram of a data- and mechanics-driven method for calculating the seismic response of a concrete frame structure, as provided by this invention. Detailed Implementation

[0030] This invention addresses the problems of low efficiency and low reliability in existing seismic response calculations for reinforced concrete frame structures by providing a data- and mechanics-driven method for calculating the seismic response of such structures. The reinforced concrete frame structure is a multi-story regular reinforced concrete frame structure. The method, as follows... Figure 1 As shown, it includes the following steps:

[0031] S1. Based on the statistical regularities and standard limits of real engineering data, a set of concrete frame structure parameters is generated. The parameters are then analyzed using structural analysis software to obtain a compliant set of concrete frame structure parameters and the corresponding basic structural period, forming a dataset. The set of concrete frame structure parameters includes beam node parameters, column node parameters, and floor slab node parameters.

[0032] Specifically, based on the statistical regularities and standard limits of real engineering data, a set of parameters for the concrete frame structure is generated, using weighted random sampling. Beam node parameters include length, direction, relative coordinates, and cross-sectional dimensions; column node parameters include length, direction, relative coordinates, and cross-sectional dimensions; and floor slab node parameters include floor area and relative coordinates.

[0033] The data sampling parameters are as follows: the sampling range for seismic acceleration is [0.05g, 0.3g], the sampling range for site characteristic period is [0.2s, 0.45s], the sampling range for number of floors is 2 to 7, the sampling range for floor height is 3000 to 5000mm (step size 100mm), the sampling range for column cross-section is 300 to 1200mm (step size 50mm), and the sampling range for beam width is 300 to 450mm (step size 50mm).

[0034] After the generated data is organized into a standardized JSON data format, it is automatically modeled in batches using the PKPM official interface. The modeling process involves analysis, calculation, and extraction of the corresponding basic structural periods, which are then integrated into the JSON data. For example, if 30,000 data points are generated using the above automated method and pass structural compliance verification, the basic period distribution in the X direction would be as follows: Figure 2 As shown, the mean is 0.402s and the median is 0.376s; the fundamental period distribution in the Y direction is as follows. Figure 3 As shown, the mean is 0.401s and the median is 0.374s.

[0035] S2. Construct a heterogeneous graph neural network model. Using the set of concrete frame structure parameters in the dataset as input and the basic period of the structure as output, train the heterogeneous graph neural network model to obtain a prediction model of the basic period of the structure.

[0036] Specifically, the heterogeneous graph neural network model represents the heterogeneous topology of the frame structure using three types of heterogeneous nodes—beams, columns, and floor slabs—and their connections. Node features are stored within the nodes, while edges only represent the connections between nodes. The structural fundamental period prediction model is also used to extract global features from the set of parameters of the concrete frame structure. These global features include the total dimensions, story height, total number of stories, PGA, and total equivalent mass of the concrete frame structure.

[0037] S3. For the concrete frame structure to be calculated, construct a multi-degree-of-freedom mechanical model with undetermined equivalent shear stiffness, including: based on Timoshenko beam theory, the concrete frame structure is equivalent to a vertical cantilever beam with uniform cross section; based on the principle of virtual work and the unit load method, the total flexibility matrix of the concrete frame structure is decoupled into a linear superposition of bending flexibility matrix and shear flexibility matrix.

[0038] Specifically, the overall flexibility matrix of the concrete frame structure is decoupled into a linear superposition of the bending flexibility matrix and the shear flexibility matrix, as follows: ,in, Represents the overall compliance matrix. Represents the bending compliance matrix. Represents the shear compliance matrix. It represents the equivalent shear stiffness.

[0039] S4. Using the predicted fundamental period of the concrete frame structure to be calculated as the benchmark, the formula for solving the undetermined equivalent shear stiffness of the components is obtained by solving the undetermined equivalent shear stiffness, thereby obtaining a definite equivalent multi-degree-of-freedom mechanical model.

[0040] Specifically, the formula for solving the undetermined equivalent shear stiffness is as follows: ;in, Represents the largest eigenvalue of the matrix. Represents the symmetric bending compliance matrix. Represents the symmetric unit shear compliance matrix. Indicates the basic period of the forecast. Indicates the equivalent shear stiffness. Let pi represent the mathematical constant π. The undetermined equivalent shear stiffness is solved using the Newton-Raphson method with analytical derivatives through iterative root finding to obtain the optimal solution for the undetermined equivalent shear stiffness, which is then taken as the solution for the undetermined equivalent shear stiffness.

[0041] S5. For the determined equivalent multi-degree-of-freedom mechanical model, solve the generalized eigenvalue complete solution corresponding to the equation of motion, extract the first n natural vibration periods and mode shapes, use the mode decomposition response spectrum method to calculate the seismic response of each order, and obtain the inter-story displacement of each floor by combining the square root of each order response. Extract the maximum inter-story displacement angle as the evaluation index of the seismic performance of the structure.

[0042] Specifically, in S5, a period reduction factor can be introduced to reduce the natural vibration period, reflecting the contribution of non-structural components to stiffness; a shear-weight ratio verification mechanism is introduced to verify whether the seismic shear force of each floor meets the minimum shear-weight ratio requirement. For floors that do not meet the requirement, the shear force and inter-story drift are adjusted by the same proportion. The formula for calculating the maximum inter-story drift angle is: ,in, Indicates the maximum inter-story drift angle. Indicates the first Inter-floor displacement after floor adjustment Indicates the first The floor height.

[0043] The seismic response calculation method for reinforced concrete frame structures driven by a combination of data and mechanics provided in this invention is referred to as the hybrid-driven method. The hybrid-driven method was tested using 500 data sets. The X-direction prediction results of the hybrid-driven method are as follows: Figure 4 As shown, the X-direction error analysis of the hybrid driving method is as follows: Figure 5 As shown, the Y-direction prediction results of the hybrid driving method are as follows: Figure 6 As shown, the Y-direction error analysis of the hybrid driving method is as follows: Figure 7 As shown.

[0044] A detailed comparison between the hybrid-driven method and the conventional data-driven method is shown in Table 1. Analysis of Table 1 shows that although the average error of the hybrid-driven method is 5.01% higher than that of the conventional data-driven model, its standard deviation is 29.74% lower, the maximum error is 49.10% lower, and the pass rate reaches 97.40% (exceeding the 96.30% of the data-driven model), indicating a higher overall pass rate. Simultaneously, the average computation time of the core calculations in the hybrid model is 16.25% lower than that of the data-driven model, making it more efficient. The error of the hybrid-driven method is generally controlled within ±20%, and due to the constraints of the mechanical model, the maximum error is only 45.3%.

[0045] Table 1. Comparison of the present invention with conventional data-driven methods

[0046]

Claims

1. A data- and mechanics-driven method for calculating the seismic response of a concrete frame structure, wherein the concrete frame structure is a multi-story regular concrete frame structure, characterized in that... The method includes the following steps: S1. Based on the statistical regularities and standard limits of real engineering data, a set of concrete frame structure parameters is generated. The parameters are then analyzed using structural analysis software to obtain a compliant set of concrete frame structure parameters and the corresponding basic structural period, forming a dataset. The set of concrete frame structure parameters includes beam node parameters, column node parameters, and floor slab node parameters. S2. Construct a heterogeneous graph neural network model. Take the set of concrete frame structure parameters in the dataset as input and the basic period of the structure as output. Train the heterogeneous graph neural network model to obtain a prediction model of the basic period of the structure. S3. For the concrete frame structure to be calculated, construct a multi-degree-of-freedom mechanical model with undetermined equivalent shear stiffness, including: based on Timoshenko beam theory, the concrete frame structure is equivalent to a vertical cantilever beam with uniform cross section; based on the principle of virtual work and the unit load method, the total flexibility matrix of the concrete frame structure is decoupled into a linear superposition of bending flexibility matrix and shear flexibility matrix. S4. Using the predicted fundamental period of the concrete frame structure to be calculated as the benchmark, construct the solution formula for the undetermined equivalent shear stiffness based on the fundamental period prediction model of the structure, and solve the undetermined equivalent shear stiffness to obtain a definite equivalent multi-degree-of-freedom mechanical model. S5. For the determined equivalent multi-degree-of-freedom mechanical model, solve the generalized eigenvalue complete solution corresponding to the equation of motion, extract the first n natural vibration periods and mode shapes, use the mode decomposition response spectrum method to calculate the seismic response of each order, and obtain the inter-story displacement of each floor by combining the square root of each order response. Extract the maximum inter-story displacement angle as the evaluation index of the seismic performance of the structure.

2. The method for calculating the seismic response of a reinforced concrete frame structure driven by a combination of data and mechanics as described in claim 1, characterized in that, In S1, based on the statistical regularities and standard limits of real engineering data, a set of parameters for concrete frame structures is generated, and weighted random sampling is used.

3. The method for calculating the seismic response of a reinforced concrete frame structure driven by a combination of data and mechanics as described in claim 1, characterized in that, In S1, the beam node parameters include length, direction, relative coordinates, and cross-sectional dimensions; the column node parameters include length, direction, relative coordinates, and cross-sectional dimensions; and the floor slab node parameters include floor slab area and relative coordinates.

4. The method for calculating the seismic response of a reinforced concrete frame structure driven by a combination of data and mechanics as described in claim 1, characterized in that, In S2, the structural fundamental period prediction model is also used to extract global features from the set of parameters of the concrete frame structure. The global features include the total dimensions, story height, total number of stories, PGA, and total equivalent mass of the concrete frame structure.

5. The method for calculating the seismic response of a reinforced concrete frame structure driven by a combination of data and mechanics as described in claim 1, characterized in that, In S3, the overall flexibility matrix of the concrete frame structure is decoupled into a linear superposition of the bending flexibility matrix and the shear flexibility matrix, specifically as follows: ,in, Represents the overall compliance matrix. Represents the bending compliance matrix. Represents the shear compliance matrix. It represents the equivalent shear stiffness.

6. The method for calculating the seismic response of a reinforced concrete frame structure driven by a combination of data and mechanics as described in claim 1, characterized in that, In S4, the formula for solving the undetermined equivalent shear stiffness is: ;in, Represents the largest eigenvalue of the matrix. Represents the symmetric bending compliance matrix. Represents the symmetric unit shear compliance matrix. Indicates the basic period of the forecast. Indicates the equivalent shear stiffness. It represents pi (π).

7. The method for calculating the seismic response of a reinforced concrete frame structure driven by a combination of data and mechanics as described in claim 1, characterized in that, In S4, the Newton-Raphson method with analytical derivatives is used to iteratively find the root of the undetermined equivalent shear stiffness to obtain the optimal solution of the undetermined equivalent shear stiffness, which is then used as the solution of the undetermined equivalent shear stiffness.

8. The method for calculating the seismic response of a reinforced concrete frame structure driven by a combination of data and mechanics as described in claim 1, characterized in that, S5 also includes the introduction of a period reduction factor to reduce the natural vibration period in order to reflect the contribution of non-structural components to stiffness.

9. The method for calculating the seismic response of a reinforced concrete frame structure driven by a combination of data and mechanics as described in claim 8, characterized in that, S5 also includes the introduction of a shear-weight ratio verification mechanism to verify whether the seismic shear force of each floor meets the minimum shear-weight ratio requirement. For floors that do not meet the requirement, the shear force and inter-story displacement are adjusted by the same ratio.

10. The data- and mechanics-driven seismic response calculation method for reinforced concrete frame structures according to claim 9, characterized in that, The formula for calculating the maximum inter-story drift angle is: ,in, Indicates the maximum inter-story drift angle. Indicates the first Inter-floor displacement after floor adjustment Indicates the first The floor height.

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