A prestress optimization method for large-span dome structure

Abstract

This invention discloses a prestress optimization method for large-span dome structures. The steps include: acquiring information about the large-span dome structure; determining an initial Q-table based on the acquired information; updating the Q-table and imposing individual constraints using a screening model, and adding newly constrained individuals to a set R; calculating performance evaluation values ​​based on a prestress evaluation model using the prestress evaluation values; determining the individual state and reward value based on the prestress evaluation values, and updating the Q-table; calculating the optimization degree corresponding to each newly added individual using an optimization degree model based on set R, and iterating back to the Q-table update step until the maximum number of iterations is reached, ultimately selecting the individual with the maximum optimization degree P. max And query the maximum optimization degree P. max For each individual component, prestress optimization is achieved. This invention can better meet optimization requirements when multiple structural deformation considerations are needed.

Description

Technical Field

[0001] This invention relates to the field of prestress optimization technology for dome structures, specifically a prestress optimization method for large-span dome structures. Background Technology

[0002] A large-span dome structure with a spatially stressed cable-stayed prestressed steel structure system, the level of prestress is a key factor affecting the shape and load-bearing characteristics of the large-span dome structure. Before the application of prestress, the structure's own stiffness cannot maintain its shape, and the system is in a relaxed state. Only by applying a certain amount of prestress can it take shape and bear loads; moreover, the magnitude and distribution of the prestress directly affect the structural performance. Only when the magnitude and distribution of prestress in the structure are reasonable can the structure have good mechanical properties.

[0003] Many scholars have conducted fruitful research and achieved rich results in the prestressing optimization of dome structures. However, previous studies have been limited to single-objective optimizations such as minimizing mass and prestressing level. In practical research and design, it is often necessary to consider the optimal solution achievable in multiple aspects of performance, which is a multi-objective optimization problem. In terms of optimization algorithms, previous methods have mostly used criterion methods and programming methods. These methods often rely on the setting of criteria and require other auxiliary information such as the derivative value of the objective function to determine the search direction, making them prone to getting trapped in local optima. Moreover, current optimization methods often cannot simultaneously consider multiple optimization variables, nor can they account for the interactions between optimization variables. Summary of the Invention

[0004] The purpose of this invention is to provide a prestress optimization method for large-span dome structures, which uses Q-learning to achieve constrained multi-objective optimization of prestress.

[0005] To solve the above-mentioned technical problems, the present invention provides the following technical solution: a prestress optimization method for a large-span dome structure, comprising the following steps:

[0006] Obtain structural information of large-span domes;

[0007] The initial Q-table is determined based on the obtained information about the large-span dome structure;

[0008] Based on the Q-table, the Q-table is updated and individual constraints are applied using a screening model, and the newly added individuals with constraints are placed into the set R.

[0009] Based on set R, the optimal prestress is determined by iterative optimization model.

[0010] According to the above technical solution, the information of the large-span dome structure includes: self-stress mode information, initial prestress, optimization variables, objective function, large-span dome structure information, and constraint condition information.

[0011] The constraint information includes overall feasibility conditions, stress conditions under working load, and displacement limit conditions.

[0012] According to the above technical solution, the steps for establishing the screening model include:

[0013] The initial Q-table is determined, the state space s is the initial prestress, and the action set is the prestress optimization action;

[0014] Calculate the performance evaluation value based on the prestressing evaluation model;

[0015] Based on the prestress assessment value, determine the individual state and reward value, and update the Q-table, state vector, action chain, and reward chain;

[0016] Based on the updated Q-table, a constraint algorithm is used to impose conditional constraints on individuals within the population, and newly added individuals with constraints are placed into the set R.

[0017] Q-table updates are a model-free reinforcement learning algorithm with advantages such as low computational complexity and good learning performance. For any finite environment and actions, it can select the appropriate action based on feedback obtained from interacting with the environment, thereby achieving the learning objective and maximizing overall gains. The machine learns the policy through continuous trials in the environment and predicts the action to be performed in the next state. Utilizing the Q-learning method broadens the search scope and removes limitations on the search direction, avoiding the tendency to get trapped in local optima.

[0018] Each row in the Q-table represents a state, and each column represents an action. Q(s,a) is the state-action function, which represents the expected reward that can be obtained by taking action a in state s at a certain moment.

[0019] According to the above technical solution, the prestressing evaluation model is as follows:

[0020]

[0021] Where H represents the span of the large-span dome structure, ζ represents the damping ratio; h is a constant; M represents the structural mass; l x Represents the displacement vector of the current individual; l x-1 Represented as the displacement vector of the previous body; s i This refers to the values ​​for newly added individuals.

[0022] The prestressing assessment model is established based on overall feasibility conditions, stress conditions under working loads, and displacement limit conditions, taking into account the actual situation of the dome structure.

[0023] According to the above technical solution, the Q-table update formula is:

[0024] Q(s,a)=(1-h)Q(s,a)+h(r+βQ(s′,a′));

[0025] Where Q(s,a) is the state-action function, a represents the current action, s represents the current state, h is a constant representing the update step size, r represents the prestress evaluation value, β represents the bonus discount, s′ represents the state at the next moment, and a′ represents the best action in state s′.

[0026] According to the above technical solution, the constraint algorithm is as follows:

[0027] F = a1f1 + a2f2 + ... + a n f n +C;

[0028] Among them, f1, f2, f n These are the individual constraint functions after regularization; a1, a2, a... n These are the weighting coefficients for the corresponding objective functions; C is a constant term. The constant term C represents the critical values ​​for the overall feasibility condition, the stress condition under the working load, and the displacement limit condition. By utilizing a constraint algorithm to consider the optimal solution achievable from multiple performance aspects, prestress optimization becomes more realistic and accurate.

[0029] According to the above technical solution, the steps for establishing the optimization model include:

[0030] Based on the individual values ​​within set R, the optimization degree corresponding to each individual is calculated using the optimization degree model.

[0031] The optimization degree of each individual is sorted in descending order, and the maximum optimization degree is placed into the maximum optimization degree set U;

[0032] Determine whether the maximum number of iterations has been reached. If the maximum number of iterations has not been reached, return to the step of using the screening model to screen the population and iterate until the maximum number of iterations is reached and then stop iterating.

[0033] Select the set U with the maximum optimization degree P max And query the maximum optimization degree P. max The corresponding individual.

[0034] According to the above technical solution, the optimization degree model is as follows:

[0035]

[0036] Where K is the number of new individuals added based on the initial individual x0, and P i Let f(x0) be the optimization degree of the i-th individual in the set of newly added individuals based on the initial individual x0, and f(s) be the initial individual value.i Let be the value of the i-th individual in the set of individuals added based on the initial individual x0.

[0037] The closer an individual's function value is to the target, the higher its optimization degree and the larger the corresponding probability region. By comparing the optimization degrees, the maximum optimization degree after iteration can be obtained to achieve prestress optimization.

[0038] Compared with existing technologies, the beneficial effects achieved by this invention are as follows: This invention constructs a Q-table based on the actual information of the large-span dome structure, and continuously optimizes the prestress using the Q-learning method based on the prestress evaluation model. The establishment of the prestress evaluation model considers the conditions for prestress evaluation, including overall feasibility, stress and displacement limits under working load, making the prestress evaluation more in line with the actual situation. The optimized prestress is constrained using a constraint algorithm, which transforms multi-objective optimization into single-objective optimization. The optimization model is then iterated until the maximum number of iterations is reached. Finally, the optimal prestress is selected using the optimization degree model. This invention not only considers optimization variables of multiple parameters, but also transforms multi-objective optimization into single-objective optimization, which can better meet the optimization requirements when multiple structural deformation requirements need to be considered. At the same time, it reduces the complexity of calculation and can easily determine the prestress level that meets the actual design requirements. Attached Figure Description

[0039] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used in conjunction with embodiments of the invention to explain the invention and do not constitute a limitation thereof. In the drawings:

[0040] Figure 1 This is a flowchart of the prestressing optimization method for a large-span dome structure according to the present invention. Detailed Implementation

[0041] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0042] This invention uses a rib-ring cable dome structure as an example to illustrate a prestress optimization method for large-span dome structures.

[0043] like Figure 1 As shown, this invention proposes a prestressing optimization method for large-span dome structures:

[0044] S1. Obtain information on the large-span dome structure, including: self-stress mode information, initial prestress, optimization variables, large-span dome structure information, and constraint information. Specifically, the large-span dome structure has a span of 100m, two ring cables, 117 members, and 47 nodes, of which 38 are unconstrained. The overall feasible prestress mode is 1. Constraint information includes overall feasibility, stress and displacement limits under load conditions, and the unit overall feasible prestress modes for each group of members are shown in Table 1.

[0045] Table 1. Feasible prestressed modes for the structural unit as a whole

[0046] Prestressed modes 0.79 0.28 0.34 0.51 0.54 -0.18 1.00 0.45 -0.09 1.01 0.04

[0047] S2. Determine the initial Q-table based on the obtained information on the large-span dome structure;

[0048] S3. Based on the Q-table, update the Q-table and impose individual constraints using a screening model, and put the newly added individuals into set R. Each row in the Q-table represents a state, and each column represents an action. The Q-table has a total of 11 columns corresponding to the lever groups.

[0049] The specific steps are as follows: determine the initial Q-table, the state space s is the initial prestress, and the action set is the prestress optimization action;

[0050] The performance evaluation value is calculated based on the prestressing evaluation model; the prestressing evaluation model is:

[0051]

[0052] Where H represents the span of the large-span dome structure, ζ represents the damping ratio; h is a constant, representing the update step size; M represents the current mass of the individual structure; l x Represents the displacement vector of the current individual; l x-1 Represented as the displacement vector of the previous body; s i This refers to the values ​​for newly added individuals.

[0053] By using the prestress assessment value, the individual state and reward value are determined, and the Q-table, state vector, action chain and reward chain are updated using the Q-table update formula;

[0054] The Q-table update formula is:

[0055] Q(s,a)=(1-h)Q(s,a)+h(r+βQ(s′,a′));

[0056] Where Q(s,a) is the state-action function, a represents the current action, s represents the current state, h is a constant representing the update step size, r represents the prestress evaluation value, β represents the bonus discount, s′ represents the state at the next moment, and a′ represents the best action in state s′.

[0057] Based on the updated Q-table, a constraint algorithm is used to impose conditional constraints on individuals within the population, and newly added individuals with constraints are placed into the set R.

[0058] The constraint algorithm is as follows:

[0059] F = a1f1 + a2f2 + ... + a n f n +C;

[0060] Among them, f1, f2, f n These are the individual constraint functions after regularization; a1, a2, a... n These are the weighting coefficients for the corresponding objective functions; C is the constant term.

[0061] S4. Based on set R, the optimal prestress is determined by iterative optimization model. Specifically, the optimization degree is calculated for each individual based on the individual values ​​in set R using the optimization degree model.

[0062] The optimization degree of each individual is sorted in descending order, and the maximum optimization degree is placed into the maximum optimization degree set U;

[0063] Determine whether the maximum number of iterations has been reached. If the maximum number of iterations has not been reached, return to the step of using the screening model to screen the population and iterate until the maximum number of iterations is reached and then stop iterating.

[0064] Select the set U with the maximum optimization degree P max And query the maximum optimization degree P. max For the corresponding individual, the prestress optimization result is 5.33β / MN.

[0065] The optimization model is as follows:

[0066]

[0067] Where K is the number of new individuals added based on the initial individual x0, and P i Let f(x0) be the optimization degree of the i-th individual in the set of newly added individuals based on the initial individual x0, and f(s) be the initial individual value. i Let be the value of the i-th individual in the set of individuals added based on the initial individual x0.

[0068] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus.

[0069] Finally, it should be noted that the above descriptions are merely preferred embodiments of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for optimizing prestressing in a large-span dome structure, characterized by the following steps: include: Obtain structural information of large-span domes; The initial Q-table is determined based on the obtained information about the large-span dome structure; Based on the Q-table, the Q-table is updated and individual constraints are applied using a screening model, and the newly added individuals with constraints are placed into the set R. Based on set R, the optimal prestress is determined by iterative optimization model. The steps for establishing the optimization model include: Based on the individual values ​​within set R, the optimization degree corresponding to each individual is calculated using the optimization degree model. The optimization degree of each individual is sorted in descending order, and the maximum optimization degree is placed into the maximum optimization degree set U; Determine whether the maximum number of iterations has been reached. If the maximum number of iterations has not been reached, return to the step of using the screening model to screen the population and iterate until the maximum number of iterations is reached and then stop iterating. Filter out the set with the maximum optimization degree in set U And query the maximum optimization degree The corresponding individual; The optimization model is as follows: ； Where K is based on the initial individual The number of newly added individuals, To be based on the initial individual The optimization degree of the i-th individual in the newly added set of individuals. These are the initial individual values. To be based on the initial individual The value of the i-th individual in the newly added set of individuals.

2. The prestressing optimization method for a large-span dome structure according to claim 1, characterized in that: The steps for establishing the screening model include: Determine the initial Q-table; Calculate the performance evaluation value based on the prestressing evaluation model; The individual status and reward value are determined by the prestress assessment value, and the Q-table is updated accordingly; Based on the updated Q-table, a constraint algorithm is used to impose conditional constraints on individuals within the population, and newly added individuals with constraints are placed into the set R.

3. The prestressing optimization method for a large-span dome structure according to claim 2, characterized in that: The prestressing evaluation model is as follows: ； Where H represents the span of the large-span dome structure. Indicates the damping ratio; It is a constant, representing the update step size; M represents the structural mass; Represents the displacement vector of the current individual; Represented as the displacement vector of the previous body; For newly added individuals, r represents the prestress assessment value.

4. The prestressing optimization method for a large-span dome structure according to claim 3, characterized in that: The Q-table update formula is: ； in, It is a state-action function-value function, where 'a' represents the current action and 's' represents the current state. It is a constant, representing the update step size; r represents the prestress evaluation value. Indicates a reward discount, Indicates the state at the next moment. Indicated as in The best action in a given state.

5. The prestressing optimization method for a large-span dome structure according to claim 3, characterized in that: The constraint algorithm is as follows: ； in, , , These are the individual constraint functions after regularization; , , These are the weighting coefficients for the corresponding objective functions; C is the constant term.

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