A method for optimizing the design of energy-consuming systems based on earthquake damage probability fitting

Abstract

The present invention discloses an energy dissipation system optimization design method based on earthquake damage probability fitting, which relates to the field of seismic design of bridge engineering. The method of the present invention optimizes the parameters of the energy dissipation system by establishing a seismic performance response surface model of the bridge structure, combining the performance indicators of the energy dissipation system, and adopting optimization algorithms such as NSGA‑Ⅱ. The present method fully considers the randomness of the earthquake process, and comprehensively evaluates the performance of the energy dissipation system through vulnerability analysis and finite element seismic response calculation. Compared with traditional methods, the present method significantly improves the optimization efficiency, while ensuring the accuracy and reliability of the optimization results. The present invention provides a new technical approach for the parameter optimization of the energy dissipation and shock absorption system in bridge engineering, which has important theoretical and practical significance for improving the seismic performance of bridge structures.

Description

Technical Field

[0001] The present invention relates to the field of earthquake-resistant design of bridge engineering, and more specifically to an energy consumption system optimization design method based on earthquake damage probability fitting. Background Art

[0002] In the field of bridge engineering, energy dissipation and shock absorption technology is widely used as an effective earthquake-resistant measure to improve the seismic performance of structures. The energy dissipation system protects bridges from earthquake damage by consuming seismic energy and reducing the response of the structure. However, the design of the energy dissipation system usually involves multiple unknown parameters, such as the stiffness, damping ratio, and layout of the damper, which have a significant impact on the shock absorption effect.

[0003] Traditional energy dissipation system parameter optimization methods usually use enumeration methods, that is, by trying all possible parameter combinations one by one, applying these parameters to the bridge model, and then horizontally comparing the shock absorption effects under different parameter combinations to determine the optimal parameter combination. Although this method is intuitive, it has obvious limitations. First, the number of parameter combinations may be very large, resulting in huge calculations, time-consuming and labor-intensive. Second, the earthquake process itself is random, and a single earthquake waveform cannot fully evaluate the performance of the energy dissipation system. Therefore, multiple earthquake simulations are required, which further increases the amount of calculations.

[0004] To overcome these limitations, researchers introduced the vulnerability analysis method. Vulnerability analysis provides a more comprehensive and systematic evaluation method for the design of energy dissipation systems by evaluating the damage state of the structure under different earthquake intensities. However, vulnerability analysis also requires a large amount of finite element seismic response calculations, combined with the enumeration method to determine the energy dissipation parameters, making the calculation amount of the entire optimization process still very large.

[0005] In this context, how to efficiently and accurately determine the optimal parameters of the energy dissipation system has become a difficulty and challenge in the field of bridge seismic research. Traditional optimization methods have been unable to meet the needs of modern bridge engineering due to their large amount of calculation and low efficiency. Therefore, there is an urgent need for a new optimization analysis method that can significantly improve the efficiency of parameter optimization while ensuring the accuracy of the analysis. Summary of the invention

[0006] In view of this, a method for optimizing the design of energy dissipation systems based on earthquake damage probability fitting is proposed. This method aims to reduce the amount of calculation and improve the efficiency and accuracy of parameter optimization through innovative analysis methods and optimization strategies, thereby providing more scientific and reasonable guidance for the design of energy dissipation systems for bridge projects. This method can effectively solve the problems existing in traditional optimization methods and provide strong technical support for the seismic design of bridges.

[0007] In order to achieve the above object, the present invention adopts the following technical solution:

[0008] An energy consumption system optimization design method based on earthquake damage probability fitting includes the following steps:

[0009] Step 1: Determine the influencing parameters of the shock absorption and energy dissipation system based on the design drawings and on-site parameters; determine the target to be optimized according to the design requirements; use the central composite design method to select the influencing parameters and obtain n groups of design conditions of influencing parameters;

[0010] Step 2: Based on the design drawings and on-site parameters, a full-bridge finite element analysis model of the target bridge with a detailed consideration of the energy consumption system is established, and n groups of bridge models corresponding to n groups of working conditions are set accordingly;

[0011] Step 3: Based on n groups of bridge models, each type of model inputs N seismic waves for nonlinear dynamic time history analysis and calculation, and extracts the seismic response results of t optimization objectives, which are the structural seismic resistance demand D;

[0012] Step 4: construct an exponential relationship between the structural seismic demand D and the site strength index IM, and construct a probability curve of the structural seismic demand D of the response target reaching or exceeding its bearing capacity C;

[0013] Step 5: Repeat steps 3 and 4 to obtain the damage probability of the optimization target corresponding to each damping system parameter;

[0014] Step 6: Based on the response surface model, a quadratic polynomial is selected as the expression of the response surface function, and the structural seismic response surface function is constructed in combination with the target parameters to be optimized;

[0015] Step 7: Evaluate the fitting performance of the response surface model with the determination coefficient and adjustment coefficient; combine the optimization algorithm, conduct multi-objective optimization analysis with the goal of minimizing the response surface function, and obtain the parameters of each device of the optimal energy consumption system.

[0016] Optionally, in step one, the influencing parameters include: the number of each energy dissipation device, the energy dissipation parameter of a single damper, and the damper installation position parameter.

[0017] Optionally, in step one, the targets to be optimized include lateral displacement of the main beam, damage to the pier, foundation response, and damage to the concrete stopper.

[0018] Optionally, in step 2, a full-bridge finite element analysis model is established using the OpenSeesPy nonlinear finite element analysis platform.

[0019] Optionally, in step three, the process of obtaining N seismic waves is: generating N artificial seismic waves in combination with the geological information of the bridge site and the design specifications, or obtaining seismic waves from PEER in combination with the design response spectrum, assuming that a total of N seismic waves are obtained.

[0020] Optionally, in step 4, an exponential relationship between the structural seismic demand D and the site strength index IM is constructed, as shown in the following formula:

[0021] S D =a(IM) b or In(S D )=In(a)+bIn(IM).

[0022] Where: a and b are S D Exponential regression coefficient with IM.

[0023] Optionally, in step 4, based on the probabilistic seismic demand analysis method, a probability curve of the structural seismic demand D of the key response target reaching or exceeding its bearing capacity C is constructed, and its failure probability is shown in the following formula:

[0024]

[0025] S D =a(IM) b or In(S D ) = In(a) + bIn(IM);

[0026] Where N is the number of earthquakes, D i is the peak seismic demand under the ith earthquake motion, COV is the covariance coefficient of the structure or component capacity, a and b are S D The exponential regression coefficient with IM, β C are the logarithmic standard deviations of demand and affordability, respectively. Optionally, in step 7, the coefficient of determination is calculated as follows:

[0027]

[0028] The calculation formula of the adjustment factor is as follows:

[0029]

[0030] Among them, SSE is the residual sum of squares, which represents the sum of squares of the differences between the actual observed values ​​and the model predicted values; SST is the total sum of squares, which represents the sum of squares of the differences between the observed values ​​and the mean of the observed values; n is the number of samples; and p is the number of explanatory variables in the model.

[0031] It can be seen from the above technical solutions that, compared with the prior art, the present invention provides an energy-consuming system optimization design method based on earthquake damage probability fitting. This method achieves rapid and accurate optimization of energy-consuming system parameters by establishing an accurate bridge structure seismic performance response surface model and combining efficient optimization algorithms such as NSGA-Ⅱ. The present invention not only significantly improves the efficiency of parameter optimization and ensures the accuracy and reliability of the optimization results, but also effectively improves the seismic performance of the bridge structure by comprehensively considering the randomness of seismic effects and conducting a comprehensive performance evaluation. In addition, the present method can accurately identify and quantify non-optimal parameters in the energy-consuming system, providing a scientific basis for the seismic design of bridges and greatly improving the safety and stability of bridges. In general, the present invention has important theoretical significance and application value in the field of bridge engineering, has a far-reaching impact on improving the seismic performance of bridge structures and optimizing seismic design, and provides strong technical support for the sustainable development of bridge engineering. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying creative work.

[0033] Figure 1 This is the general layout of the bridge;

[0034] Figure 2(a) is a layout diagram of the first energy consumption system;

[0035] Figure 2(b) is a layout diagram of the second energy consumption system;

[0036] Figure 2(c) is a layout diagram of the third energy consumption system;

[0037] Figure 3 This is the OpenSeesPy finite element model diagram;

[0038] Figure 4 The waveform diagram of the selected earthquake;

[0039] Figure 5 It is the damage probability curve of a single component;

[0040] Figure 6 It is the Pareto front diagram. DETAILED DESCRIPTION

[0041] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0042] Example 1

[0043] Aiming at the difficulty of optimizing the parameters of energy dissipation and shock absorption system in bridge engineering, the present invention proposes an energy dissipation system optimization design method based on earthquake damage probability fitting, the core of which is to construct an efficient parameterized optimization model and iterative calculation mechanism. The method first establishes a response surface model of the seismic performance of the bridge structure, and on this basis, combines optimization algorithms such as NSGA-Ⅱ to perform systematic and automated iterative optimization of the parameters of the energy dissipation and shock absorption system. By continuously updating and adjusting the parameters until the optimal shock absorption performance is achieved, the seismic performance of the bridge structure under various earthquakes is ensured. At the same time, the method also comprehensively considers the randomness of the seismic action and the complexity of the bridge structure, comprehensively evaluates the performance of the energy dissipation system through vulnerability analysis and finite element seismic response calculation, and realizes the precise optimization of the parameters of the energy dissipation system. In addition, the present invention also provides a quantitative analysis method that can accurately identify and quantify non-optimal parameters, provides a scientific basis for the seismic design of bridges, and greatly improves the safety and stability of bridges. In general, the technical solution of the present invention provides an innovative, efficient and accurate solution for the parameter optimization of energy dissipation and shock absorption systems in bridge engineering, which has important theoretical and practical significance.

[0044] The steps are:

[0045] Step 1: Determine the influencing parameters of the shock absorption and energy dissipation system based on the design drawings and on-site parameters; determine the target to be optimized according to the design requirements; use the central composite design method to select the influencing parameters and obtain n groups of design conditions of influencing parameters;

[0046] Step 2: Based on the design drawings and on-site parameters, a full-bridge finite element analysis model of the target bridge with a detailed consideration of the energy consumption system is established, and n groups of bridge models corresponding to n groups of working conditions are set accordingly;

[0047] Step 3: Based on n groups of bridge models, each type of model inputs N seismic waves for nonlinear dynamic time history analysis and calculation, and extracts the seismic response results of t optimization objectives, which are the structural seismic resistance demand D;

[0048] Step 4: construct an exponential relationship between the structural seismic demand D and the site strength index IM, and construct a probability curve of the structural seismic demand D of the response target reaching or exceeding its bearing capacity C;

[0049] Step 5: Repeat steps 3 and 4 to obtain the damage probability of the optimization target corresponding to each damping system parameter;

[0050] Step 6: Based on the response surface model, a quadratic polynomial is selected as the expression of the response surface function, and the structural seismic response surface function is constructed in combination with the target parameters to be optimized;

[0051] Step 7: Evaluate the fitting performance of the response surface model with the determination coefficient and adjustment coefficient; combine the optimization algorithm, conduct multi-objective optimization analysis with the goal of minimizing the response surface function, and obtain the parameters of each device of the optimal energy consumption system.

[0052] Example 2

[0053] As a supplement to Example 1, this example discloses the following steps:

[0054] Step 1: Based on the design drawings and on-site parameters, clarify the influencing parameters of the shock absorption and energy dissipation system, such as the number of each energy dissipation device, the energy dissipation parameters of a single damper, the damper installation position and other parameters. Suppose u parameters are the influencing parameters of the shock absorption and energy dissipation system, recorded as x1, x2…x u ;

[0055] Step 2: The optimization targets are determined based on the design requirements, such as the lateral displacement of the main beam, pier damage, foundation response, concrete block damage, etc. There are t optimization targets, denoted as y1, y2…y t ;

[0056] Step 3: Use the central composite design method (CCD) to select the values ​​of each influencing parameter and obtain the design conditions of n groups of influencing parameters, as shown in Table 1

[0057] Table 1 CCD parameter sample value design

[0058]

[0059] Step 4: Generate artificial waves based on the geological information of the bridge site and the design specifications, or obtain seismic waves with better adaptability from PEER based on the design response spectrum. Assume that a total of N seismic waves are obtained;

[0060] Step 5: Combine the design drawings and on-site bridge information, and use the OpenSeesPy nonlinear finite element analysis platform to establish a full-bridge finite element analysis model of the target bridge that carefully considers the energy consumption system, and set n groups of bridge models corresponding to n groups of working conditions according to the design parameters obtained in step 3;

[0061] Step 7: Based on n types of bridge models, each type of model inputs N seismic waves for nonlinear dynamic time history analysis and calculation, and extracts the seismic response results of t optimization objectives, which are the structural seismic resistance demand D;

[0062] Step 8: Based on the probabilistic seismic demand analysis method, it is assumed that the structural responses of each optimization target obey the log-normal distribution; combined with the site information and the finite element model, the seismic intensity index IM of the site is determined, and it is assumed that there is an exponential correlation between the structural seismic resistance demand D and IM;

[0063] Step 9: Based on step 8, construct the exponential relationship between the structural seismic demand D and the site strength index IM, as shown in formula (1):

[0064] S D =a(IM) b or In(S D ) = In(a) + bIn(IM); (1)

[0066] Step 10: Based on the probabilistic seismic demand analysis method, construct the probability curve of the structural seismic demand D of the key response target reaching or exceeding its bearing capacity C. Its failure probability is shown in formula (2), where β C As shown in formula (3) and (4):

[0067]

[0068] S D =a(IM) b or In(S D ) = In(a) + bIn(IM); (4)

[0070] Where a and b are S D The exponential regression coefficient with IM, N is the number of ground motions, D i is the peak seismic demand under the ith earthquake motion, a and b are S D The exponential regression coefficient with IM, β C are the logarithmic standard deviations of demand and bearing capacity, respectively. COV is the covariance coefficient of the structure or component capacity, which is 0.25 for slight damage and moderate damage, and 0.50 for severe damage and complete damage. In order to obtain the probabilistic relationship between the earthquake demand D and the strength index IM, this paper selects the peak acceleration PGA of the earthquake as the earthquake intensity index;

[0071] Step 11: For n types of bridge models, based on the probabilistic seismic demand analysis method, repeat steps 8 to 10 to obtain the damage probability of t optimization targets corresponding to each type of bridge model, thereby obtaining the damage probability of each optimization target corresponding to each damping system parameter, that is, the damage probability value of t optimization targets corresponding to n groups of models with n groups of damping system parameters designed by the CCD method, as shown in Table 2;

[0072] Table 2 Earthquake damage probability corresponding to group n of shock absorption system models

[0073]

[0074] Step 12: Based on Table 2 and the response surface model (RSM), a quadratic polynomial is selected as the basic expression of the response surface function. Combined with the target parameter u to be optimized, the structural seismic response surface function is constructed as shown in (5):

[0075]

[0076] Where: y represents the target structure damage result, x1, x2…x u Corresponding to the influencing parameters of u types of shock absorption and energy dissipation systems, β0, β1…β k To fit the unknown parameters;

[0077] Step 13: Determine the coefficient R 2 , adjust R 2 Coefficient (AdjustedR 2 ) was used to evaluate the fitting performance of the response surface model, as shown in (6); the coefficient of determination R 2 It is a statistic that measures how well the model fits the experimental data; adjust R 2 The coefficient is the coefficient of determination R 2 The optimization of R adjusts the number of explanatory variables in the model by introducing a penalty term. 2 With adjustment R 2 The closer the coefficient is to 1, the more accurate the fitting effect of the data and the stronger the ability to explain the data;

[0078]

[0079] Where SSE is the residual sum of squares, which represents the sum of squares of the differences between the actual observed values ​​and the model predicted values; SST is the total sum of squares, which represents the sum of squares of the differences between the observed values ​​and the mean of the observed values; n is the number of samples; and p is the number of explanatory variables in the model.

[0080] Step 14: Obtain the response surface functions y1, y2…y from steps 12 and 13 t, combined with non-dominated genetic algorithm NSGA-Ⅱ and other optimization algorithms, to optimize the response surface functions y1, y2…y t As the goal, multi-objective optimization analysis is carried out to obtain the optimal energy consumption system parameters x1′, x2′Kx′ u .

[0081] Example 3

[0082] As a specific application of Example 1 and Example 2, the following technical solutions are disclosed:

[0083] Take a newly built cable-stayed bridge as an example. Figure 1 As shown in the figure. Due to the consolidation of the main tower and the asymmetric structural system, the shear force of the side pier column and the lateral displacement of the main beam under strong earthquakes are large, and it is often necessary to set up an energy dissipation system at the pier column to reduce seismic energy. At this time, the seismic response of the structure is controlled by setting metal dampers and elastic-plastic cables. In view of this, taking this example as the object, an energy dissipation system optimization design method based on earthquake damage probability fitting is explained.

[0084] The specific steps are:

[0085] Step 1: Figure 2(a)-Figure 2(c) Taking the energy dissipation system shown as an example, combined with the characteristics of the bridge type and the composition of the energy dissipation system, its sensitive parameters include the number of metal dampers x1, the number of elastic-plastic cables x2, and the length of the elastic-plastic cables x3.

[0086] Step 2: Clearly define the bridge pier damage probability y as the target to be optimized s , transverse displacement of the main beam y p ;

[0087] Step 3: First, based on the bridge design drawings, a refined nonlinear finite element analysis model is established using finite element analysis platforms such as OpenSeesPy. Figure 3 As shown, the finite element simulation of various parameters of the energy consumption system is refined;

[0088] Step 4: Generate artificial waves based on the geological information of the bridge site and the design specifications, or obtain seismic waves with good adaptability to the design response spectrum from PEER based on the design response spectrum. Suppose a total of N seismic waves are obtained, such as Figure 4 As shown;

[0089] Step 5: Using the central composite design method, taking the influencing parameters of the energy consumption system as the object, design n groups of working conditions to select the values ​​of the influencing parameters of the energy consumption system, as shown in Table 3;

[0090] Table 3 CCD parameter sample value design

[0091]

[0092] Step 6: Substitute the influencing parameters of the n groups of energy dissipation systems into the nonlinear finite element analysis model of the bridge to obtain n types of bridge models, group N seismic waves into a group, and bring them into the n types of nonlinear finite element analysis models for nonlinear dynamic time-history finite element analysis, and extract the seismic response peak value of each target to be optimized;

[0093] Step 7: Select the earthquake peak acceleration PGA as the site earthquake intensity index IM, The seismic response peak structure of each target to be optimized in the nonlinear finite element analysis model is exponentially linearly fitted with the seismic intensity index IM, and the fitting coefficients a and b corresponding to the i-th model are obtained;

[0094] Step 8: Combined with the critical thresholds of various damage states, based on the probabilistic seismic demand analysis, the probability curve of the structural seismic demand D of the key response target reaching or exceeding the bearing capacity C is constructed, such as Figure 5 As shown;

[0095] Step 9: Repeat steps 6 to 8 to obtain the damage probability of each optimization target corresponding to each damping system parameter, that is, y corresponding to n groups of models of n groups of damping system parameters designed by the CCD method. s ,y p The damage probability values ​​are shown in Table 4;

[0096] Table 4 Earthquake damage probability corresponding to group n of shock absorption system models

[0097]

[0098]

[0099] Step 10: Based on Table 4 and the response surface model, the quadratic polynomial is selected as the basic expression of the response surface function. Combined with the target parameters to be optimized as x1, x2, and x3, the structural seismic response surface function is constructed, as shown in equations (7) and (8);

[0100]

[0101] Step 11: Combine the response surface function y s ,y p The coefficient of determination R 2 , adjust R 2 The coefficient values ​​are used to determine the fitting accuracy and the ability to interpret the data, so as to obtain the response surface function with the best performance.

[0102] Step 12: Combine optimization algorithms such as non-dominated genetic algorithm NSGA-Ⅱ to minimize the response surface function y s ,y pAs the goal, multi-objective optimization analysis is carried out, combined with Pareto frontier analysis, such as Figure 6 As shown, the parameters x1′, x2′, and x3′ of each device of the optimal energy consumption system are obtained.

[0103] In this specification, each embodiment is described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the embodiments can be referred to each other. For the device disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant parts can be referred to the method part.

[0104] The above description of the disclosed embodiments enables one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to the embodiments shown herein, but rather to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. An energy consumption system optimization design method based on earthquake damage probability fitting, characterized in that: The following steps are involved: Step 1: Determine the influencing parameters of the shock absorption and energy dissipation system based on the design drawings and on-site parameters; determine the target to be optimized according to the design requirements; use the central composite design method to select the values ​​of the influencing parameters to obtain n groups of design conditions of the influencing parameters; Step 2: Based on the design drawings and on-site parameters, a full-bridge finite element analysis model of the target bridge with a detailed consideration of the energy consumption system is established, and n groups of bridge models corresponding to n groups of working conditions are set accordingly; Step 3: Based on n groups of bridge models, each type of model inputs N seismic waves for nonlinear dynamic time history analysis and calculation, and extracts the seismic response results of t optimization objectives, which are the structural seismic resistance demand D; Step 4: construct an exponential relationship between the structural seismic demand D and the site strength index IM, and construct a probability curve of the structural seismic demand D of the response target reaching or exceeding its bearing capacity C; Based on the probabilistic seismic demand analysis method, a probability curve of the structural seismic demand D of the key response target reaching or exceeding its bearing capacity C is constructed, and its failure probability is shown in the following formula: S D = a(IM) b or In(S D ) = In(a) + bIn(IM); Where N is the number of earthquakes, D i is the peak seismic demand under the ith earthquake motion, COV is the covariance coefficient of the structure or component capacity, a and b are S D The exponential regression coefficient with IM, β C are the logarithmic standard deviations of demand and affordability, respectively; Step 5: Repeat steps 3 and 4 to obtain the damage probability of the optimization target corresponding to each damping system parameter; Step 6: Based on the response surface model, a quadratic polynomial is selected as the expression of the response surface function, and the structural seismic response surface function is constructed in combination with the target parameters to be optimized; Step 7: Evaluate the fitting performance of the response surface model with the determination coefficient and adjustment coefficient; combine the optimization algorithm, take minimizing the response surface function as the goal, conduct multi-objective optimization analysis, and obtain the parameters of each device of the optimal energy consumption system.

2. The energy consumption system optimization design method based on earthquake damage probability fitting according to claim 1 is characterized in that: In step one, the influencing parameters include: the number of each energy dissipation device, the energy dissipation parameter of a single damper, and the damper installation position parameter.

3. The energy consumption system optimization design method based on earthquake damage probability fitting according to claim 1 is characterized in that: In step 1, the targets to be optimized include the lateral displacement of the main beam, the damage of the pier, the response of the foundation, and the damage of the concrete stopper.

4. The energy consumption system optimization design method based on earthquake damage probability fitting according to claim 1 is characterized in that: In step 2, the finite element analysis model of the full bridge is established using the OpenSeesPy nonlinear finite element analysis platform.

5. The energy consumption system optimization design method based on earthquake damage probability fitting according to claim 1 is characterized in that: In step three, the process of obtaining N seismic waves is as follows: N artificial seismic waves are generated by combining the geological information of the bridge site and the design specifications, or seismic waves are obtained from PEER in combination with the design response spectrum. It is assumed that a total of N seismic waves are obtained.

6. The energy consumption system optimization design method based on earthquake damage probability fitting according to claim 1 is characterized in that: In step 4, an exponential relationship between the structural seismic demand D and the site strength index IM is constructed as shown below: S D = a(IM) b or In(S D ) = In(a) + bIn(IM); Where: a and b are S D Exponential regression coefficient with IM.

7. The energy consumption system optimization design method based on earthquake damage probability fitting according to claim 1 is characterized in that: In step 7, the coefficient of determination is calculated as follows: The calculation formula of the adjustment factor is as follows: Among them, SSE is the residual sum of squares, which represents the sum of squares of the differences between the actual observed values ​​and the model predicted values; SST is the total sum of squares, which represents the sum of squares of the differences between the observed values ​​and the mean of the observed values; n is the number of samples; and p is the number of explanatory variables in the model.

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