A numerical combination fast calculation method based on mutual exclusion group extreme value decomposition

Abstract

The application discloses a numerical combination fast calculation method based on mutual exclusion group extreme value decomposition, which comprises the following steps: according to the physical mutual exclusion of load working conditions, all load working conditions are divided into M mutual exclusion groups; finite element analysis is carried out on all working conditions in each mutual exclusion group, the structural effect is calculated, the positive maximum value and the negative minimum value in the group are recorded respectively, and the working condition number corresponding to the effect is generated; based on multiple load types, all mutual exclusion groups are combined to obtain P mutual exclusion group combinations, the effect positive extreme value and the effect negative extreme value of each mutual exclusion group combination are calculated; the effect positive extreme value and the effect negative extreme value of the P mutual exclusion group combinations are enveloped to obtain the final positive extreme value and the final negative extreme value; the method in the application realizes that the calculation time is greatly shortened, the calculation complexity is reduced from an exponential order to a linear order, and only the extreme values and the numbers of the mutual exclusion groups need to be stored, so that the memory demand of a large project is sharply reduced.

Description

A Fast Numerical Combinatorial Computation Method Based on Extrema Decomposition of Mutually Exclusive Sets Technical Field

[0001] This invention belongs to the field of structural mechanics and structural engineering calculation and analysis technology. Specifically, it relates to a rapid numerical combination calculation method based on the extreme value decomposition of mutually exclusive groups. It is applicable to the rapid combination analysis of various structural effects that satisfy the principle of linear superposition, such as component internal forces, support reactions, and nodal displacements. It is particularly suitable for rapid calculation in large and complex structures with a large number of mutually exclusive load conditions. At the same time, this calculation method is applicable not only to structural mechanics but also to all fields such as mechanics of materials that require superposition calculations for multiple load conditions. Background Technology

[0002] In structural design, according to the requirements of engineering specifications (GB50009-2012 "Code for Design of Building Structures", GB0068-2018 "Unified Standard for Reliability of Building Structures", etc.), it is necessary to conduct multi-condition load combination analysis on the structure.

[0003] Existing analysis methods employ traditional load combination calculations. These methods first analyze the structural effects of various load cases using finite element analysis, then perform linear superposition calculations on all possible load combinations according to specifications. Finally, they iterate through all combination results to find the maximum and minimum effect values ​​(i.e., envelope values) for each component. However, these methods have the following problems: 1. Because they require calculations for all possible load combinations, the number of combinations is extremely large. This massive exhaustive list of combinations still creates a significant computational burden, which is unacceptable in practical engineering. 2. The above calculation method requires storing the effect results of all combinations, leading to huge memory resource consumption. Multiple servers are needed to store all the data during the calculation process, resulting in low feasibility in engineering practice.

[0004] To address the aforementioned issues, various optimization solutions have been developed in the existing technology: the working condition screening method, which relies on subjective judgment, may overlook control conditions, and poses safety hazards.

[0005] Sampling method: It has the problem that it cannot guarantee finding the true extreme value, and the calculation results are biased and unsafe.

[0006] The experience database method suffers from the problem of large differences between different projects and poor prediction accuracy.

[0007] None of the above-mentioned improved solutions can fundamentally solve the problem of a large number of combinations, and they generally suffer from accuracy loss or security risks.

[0008] Based on this, the purpose of the present invention is to address the shortcomings of the prior art by providing a fast numerical combination calculation method based on mutual exclusion group extremum decomposition, so as to solve the problems of excessive calculation time caused by the exponential growth of the number of load combinations and the huge memory consumption required to store all combination effect results in traditional calculation methods. Summary of the Invention

[0009] In view of the deficiencies in the prior art, the purpose of this invention is to provide a fast numerical combination calculation method based on the extremum decomposition of mutually exclusive groups, so as to overcome the problems mentioned in the background art.

[0010] Specifically, the technical problem to be solved by the present invention is to address the shortcomings of the prior art. In the first aspect, the present invention provides a numerical combination fast calculation method based on the extreme value decomposition of mutually exclusive groups, including the following steps: Step 1: According to the physical mutual exclusivity of the load conditions, all load conditions are divided into M mutually exclusive groups.

[0011] Step 2: Perform finite element analysis on all operating conditions within each mutually exclusive group, calculate the structural effects, and record the positive maximum and negative minimum values ​​within the group, as well as the operating condition number that produces the corresponding effect.

[0012] Step 3: Combine all mutually exclusive groups based on multiple load types to obtain P mutually exclusive group combinations, and calculate the positive and negative extreme values ​​of the load effect for each mutually exclusive group combination.

[0013] Step 4: Calculate the envelope of the positive and negative extreme values ​​of the effects of the P mutually exclusive combinations to obtain the final positive and negative extreme values.

[0014] In one embodiment of the numerical combination fast calculation method based on the extremum decomposition of mutually exclusive groups according to the present invention, the mutually exclusive group is a set of working conditions, wherein any two working conditions cannot occur simultaneously in the same mutually exclusive group at the same time; working conditions between different mutually exclusive groups can occur simultaneously.

[0015] In one embodiment of the numerical combinatorial fast calculation method based on mutual exclusion set extremum decomposition according to the present invention, an extremum database EVD is established, and the calculation results in step two are stored in the extremum database EVD.

[0016] The data structure of the calculation results is as follows: positive maximum value, working condition number that produces the positive maximum value, negative maximum value, and working condition number that produces the negative maximum value.

[0017] In one embodiment of the numerical combination fast calculation method based on mutual exclusion group extreme value decomposition according to the present invention, the data of the extreme value database EVD is calculated and updated according to the working conditions.

[0018] In one embodiment of the numerical combination fast calculation method based on mutual exclusion group extreme value decomposition according to the present invention, the positive maximum value and negative minimum value of all types of structural effects are calculated and recorded simultaneously in a single finite element analysis, and the positive maximum value and negative minimum value of all types of structural effects are obtained simultaneously in a single working condition traversal, thus avoiding repeated calculations.

[0019] In one embodiment of the numerical combination fast calculation method based on mutual exclusion group extreme value decomposition according to the present invention, the load combination type in step three includes basic combination, standard combination, and quasi-permanent combination.

[0020] In one embodiment of the numerical combination fast calculation method based on mutual exclusion group extremum decomposition according to the present invention, the envelope calculation in step four is performed by an algorithm based on linear superposition for linear structural analysis, and by other methods or correction calculations for geometric nonlinearity and material nonlinearity structural analysis.

[0021] In one embodiment of the numerical combination fast calculation method based on mutual exclusion group extreme value decomposition according to the present invention, the method further includes step five: designing and verifying the component cross-section based on the final positive extreme value and the final negative extreme value; if the preset conditions are met, output the calculation results; if the preset conditions are not met, update the parameters of the working condition in step two, and repeat steps two to five until the preset conditions are met, and output the calculation results.

[0022] In a second aspect, the present invention provides an electronic device, comprising: at least one processor; and a memory storing instructions that, when executed by the at least one processor, cause the at least one processor to perform the numerical combination fast calculation method based on mutual exclusion set extremum decomposition as described above.

[0023] Thirdly, the present invention provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the steps of the numerical combination fast calculation method based on mutual exclusion set extremum decomposition as described above.

[0024] Compared with existing technologies, the positive effects of this invention are as follows: 1. Addressing the problem of excessively long calculation time caused by the exponential growth in the number of load combinations in existing calculation methods, the numerical combination fast calculation method based on mutually exclusive group extreme value decomposition proposed in this invention divides all load conditions into several mutually exclusive groups (groups that cannot occur simultaneously) according to physical mutual exclusivity. For each group, the envelope values ​​(maximum positive and minimum negative values) of various structural effects (including but not limited to component internal forces, support reactions, and nodal displacements) are calculated and recorded separately. Then, the combination coefficient is multiplied by the corresponding extreme value for linear combination, thereby directly obtaining the total envelope value of various effects, avoiding the need to enumerate all combinations in traditional calculation methods. The method in this invention significantly reduces the calculation time, reducing the calculation complexity from exponential to linear, with a speedup of hundreds to tens of thousands of times.

[0025] 2. To address the issue of massive memory consumption caused by storing all combined effect results in existing calculation methods, this invention proposes a fast numerical combination calculation method based on mutual exclusion group extreme value decomposition. This method conceives a data structure EVD for storing the extreme values ​​of mutual exclusion groups. For each triple (mutual exclusion group i, effect object k, effect component c), it stores the maximum and minimum values ​​of the group, object, and component, as well as the corresponding working condition number. This method is applicable to various effects such as component internal forces, support reactions, and nodal displacements. Compared to the storage requirements of traditional calculation methods, this invention only needs to store the extreme values ​​and numbers of each mutual exclusion group, drastically reducing the memory requirements for large projects. This allows ordinary workstations (32-64GB memory) to handle large projects that originally required high-performance servers.

[0026] 3. The numerical combination fast calculation method based on mutually exclusive group extreme value decomposition proposed in this invention can provide a unified calculation framework, applicable to all structural effects that satisfy the principle of linear superposition, such as component internal forces, support reactions, and nodal displacements. It can handle multiple types of effects in one calculation; in one finite element analysis, it can simultaneously calculate and record the extreme values ​​of multiple types of structural effects (component internal forces, support reactions, nodal displacements, etc.), and obtain the envelope values ​​of all types of effects in one working condition traversal, avoiding repeated calculations.

[0027] 4. The numerical combination fast calculation method based on mutual exclusion set extremum decomposition proposed in this invention achieves fast and accurate calculation of envelope value while ensuring calculation accuracy, without introducing any approximation or error, and ensures that the calculation result is completely consistent with the exhaustive method; that is, it can provide a complete mathematical proof to ensure the correctness of the algorithm in all cases, and avoids the uncertainty of approximation methods such as heuristic algorithms and sampling methods.

[0028] 5. The numerical combination fast calculation method based on the extremum decomposition of mutually exclusive groups proposed in this invention can provide a rigorous theoretical guarantee in mathematics. Based on strict mathematical theorems, the calculation results are equivalent to those of the traditional exhaustive method, fully meet the requirements of the specifications, have no safety hazards, and meet the structural safety design requirements. Attached Figure Description

[0029] Figure 1 is a flowchart of the numerical combination fast calculation method in this invention.

[0030] Figure 2 is a diagram illustrating the specific steps of dividing mutually exclusive groups in this invention.

[0031] Figure 3 is a flowchart of envelope value calculation in the traditional calculation method.

[0032] Figure 4 is a flowchart of the envelope value calculation method in an embodiment of the present invention.

[0033] Figure 5 is a flowchart of the envelope value calculation method in another embodiment of the present invention. Detailed Implementation

[0034] Hereinafter, exemplary embodiments according to this application will be described in detail with reference to the accompanying drawings. Obviously, the described embodiments are merely some embodiments of this application, and not all embodiments of this application. It should be understood that this application is not limited to the exemplary embodiments described herein.

[0035] It is understood that the term "a" should be understood as "at least one" or "one or more," meaning that in one embodiment, the number of an element can be one, while in another embodiment, the number of the element can be multiple. The term "a" should not be construed as a limitation on the quantity. "Multiple" means two or more.

[0036] While ordinal numbers such as “first,” “second,” etc., will be used to describe various components, there is no limitation on which components are used herein. The term is used only to distinguish one component from another. For example, a first component may be referred to as a second component, and similarly, a second component may be referred to as a first component, without departing from the teachings of this application. The term “and / or” as used herein includes any and all combinations of one or more of the associated listed items.

[0037] The terminology used herein is for the purpose of describing various embodiments only and is not intended to be limiting. As used herein, the singular form also includes the plural form, unless the context clearly indicates otherwise. It will also be understood that the terms “comprising” and / or “having” as used in this specification specify the presence of the described features, numbers, operations, components, elements or combinations thereof, without excluding the presence or addition of one or more other features, numbers, operations, components, elements or combinations thereof.

[0038] The present invention will be further described below with reference to Figures 1-5 and specific embodiments.

[0039] In structural design, according to the requirements of engineering specifications (GB50009-2012 "Code for Design of Building Structures", GB0068-2018 "Unified Standard for Reliability of Building Structures", etc.), it is necessary to conduct multi-condition load combination analysis on the structure.

[0040] Basic combination formula for ultimate limit state of bearing capacity:

[0041] S = γ_G × S_GK + Σγ_Qi × ψ_ci × S_QiK;

[0042] In the formula:

[0043] S is the design value of the effect of the load combination.

[0044] γ_G is the partial factor for permanent loads.

[0045] γ_Qi is the partial factor for the i-th variable load.

[0046] ψ_ci is the combination value coefficient of the i-th variable load.

[0047] S_GK is the standard value of the permanent load effect.

[0048] S_QiK is the standard value of the i-th variable load effect;

[0049] Definition of structural effect:

[0050] Structural effects refer to the various responses of a structure under load that satisfy the principle of linear superposition, including but not limited to:

[0051] Internal forces of the component: axial force N, shear force V_y / V_z, torque T, bending moment My / M_z;

[0052] Support reactions: vertical reaction force R_y, horizontal reaction force R_x / R_z, reaction moment M_Rx / M_Ry / M_Rz;

[0053] Nodal displacements: translational displacements u_x / u_y / u_z, rotational displacements θ_x / θ_y / θ_z;

[0054] Foundation internal forces: foundation bottom pressure, pile foundation axial force / shear force / bending moment;

[0055] Other effects: inter-story drift angle, component stress, etc.;

[0056] Each of the above applicable effects is E, with a total of N_components dimensions, and each component can constitute a dimension.

[0057] First, we need to demonstrate the traditional calculation method:

[0058] In structural engineering, within the linear elastic range, the load effect satisfies the superposition principle:

[0059] S_combination = Σ(γ_i × S_condition_i);

[0060] in:

[0061] S_combination: Structural effects (internal forces, displacements, etc.) under a certain combination;

[0062] S_condition i: The structural effect of the i-th condition;

[0063] γ_i: Combination coefficient for the i-th working condition;

[0064] The size of S is at least the number of elements N_elements * the effect dimension N_components;

[0065] Traditional methods require:

[0066] First: Perform finite element analysis on each working condition (to obtain S_working condition i);

[0067] Second: Perform linear superposition calculation for each combination (calculate S_combination);

[0068] Third: Calculate the envelope of all combination results;

[0069] All known structural design software uses a similar workflow:

[0070] The traditional calculation method involves the following steps: Traditional load combination calculation process:

[0071] Step 1: Finite element analysis of various working conditions:

[0072] Finite element analysis was performed for each load case to obtain the structural effects under each case:

[0073] Working condition 1 → FEM solution → {S1(component 1), S1(component 2), ..., S1(component n)}

[0074] Working Case 2 → FEM Solution → {S2(Component 1), S2(Component 2), ..., S2(Component n)}, ...,

[0075] Working condition k → FEM solution → {S k (Component 1), S k (Component 2), ..., S k (component n)};

[0076] The calculation method is similar for other effects such as support reactions and nodal displacements;

[0077] K represents the total number of operating conditions.

[0078] Step 2: Generate all possible combinations and superimpose them linearly:

[0079] According to the specifications, a linear superposition calculation is performed for all possible load combinations:

[0080] Combination 1: S_Combination 1 = γ1×S1 + γ2×S2 + ... + γ k ×S k ,

[0081] Combination 2: S_Combination 2 = γ1×S1 + γ3×S3 + ... + γ m ×S m ,...,

[0082] Combination N: S_combination N = γ1×S1+ γ n ×S n + ... + γ p ×S p ;

[0083] Where γᵢ is the combination coefficient (e.g., 1.2, 1.4, etc.), and N_total = ∏ᵢnᵢ combinations need to be calculated. nᵢ is the number of working conditions that can be combined in each category, and the total number of working conditions K=Σᵢnᵢ is the total number of all working conditions (summation).

[0084] Step 3: Calculate the envelope value:

[0085] Iterate through all combinations to find the maximum and minimum effect values ​​for each component:

[0086] For each component j:

[0087] Positive maximum value: S_max + (j) = max{S_combination i(j) | S_combination i(j)>0, i=1,2,...,N};

[0088] If all combinations are ≤ 0, then S_max + (j) = 0 (most unfavorable positive effect);

[0089] Negative minimum value: S_min - (j) = min{S_combination i(j) | S_combination i(j)<0, i=1,2,...,N};

[0090] If all combinations are ≥ 0, then S_min - (j) = 0 (most unfavorable negative effect);

[0091] Physical meaning:

[0092] S_max + : Maximum tensile force, maximum positive bending moment, etc. (used for configuring tensile reinforcement and verifying tensile stress);

[0093] S_min - : Maximum pressure, maximum negative bending moment, etc. (used for verifying buckling and configuring compression reinforcement);

[0094] Step 4: Component Design

[0095] The component cross-section is designed and verified based on the envelope value.

[0096] Step 5: Iterative optimization until convergence

[0097] Repeat the above steps until the preset conditions are met, such as the stress ratio not exceeding the limit.

[0098] Addressing the technical problems of traditional technologies:

[0099] The following case studies are actual examples that have occurred in engineering design:

[0100] Case Study: Large-Span Industrial Plant;

[0101] Crane load: 3 cranes, each with 100 critical positions;

[0102] Wind load: 36 directions;

[0103] Roof live load: 3 layouts;

[0104] Temperature: 2 operating conditions;

[0105] Number of operating conditions = 1 type of static load + 3 types of cranes × 100 types + 36 types of wind + 3 types of live load + 2 types of temperature = 342 types;

[0106] Total number of combinations: N_total = 100^3 × 36 × 3 × 2 = 216,000,000;

[0107] This setting has been simplified to the number of permutations and combinations of participating working conditions. In reality, when forming working condition combinations, even when the participating working conditions are exactly the same, there can be different coefficient combinations. That is, the permutations and combinations of working conditions need to be multiplied by as many as tens or hundreds of coefficient combinations.

[0108] Problem 1: The explosion of combinations leads to increased computation time.

[0109] Assuming a single analysis takes approximately 30 seconds, and the linear superposition of combinations takes only 0.01 seconds, then:

[0110] Finite element method solution for 342 operating conditions: 342 × 30 seconds ≈ 2.85 hours;

[0111] Combining linear superposition 216 million times: 216 million × 0.01 seconds ≈ 25 days;

[0112] Assuming iterative optimization for 10 cycles takes approximately 251 days.

[0113] Although the simplification principle of linear superposition avoids the high-load finite element solution for each combination and uses more efficient linear computational superposition, the sheer number of exhaustive combinations still creates a huge computational burden, which is unacceptable in practical engineering.

[0114] Question 2: Huge memory resource consumption:

[0115] The effects of all combinations need to be stored. Assuming only the internal forces of 6 components are calculated, for a factory building with 20,000 components:

[0116] Memory requirement = N_total × N_components × N_elements × sizeof(double);

[0117] = 216,000,000 × 6 × 20000 × 8 bytes;

[0118] = 207,360,000,000,000 bytes;

[0119] ≈ 207TB;

[0120] Even using top-of-the-line servers equipped with 2TB of memory, 104 servers would be needed to store all the data, which is completely impractical in engineering practice.

[0121] Question 3: Limitations of existing optimization methods:

[0122] Since problems 1 and 2 pose significant challenges to practical engineering applications, the following methods are often used in engineering practice to reduce practical requirements:

[0123] Operating condition screening method: relies on subjective judgment, which may overlook control conditions and pose safety hazards;

[0124] Sampling method: cannot guarantee finding the true extreme value, and the calculation results are biased and unsafe;

[0125] Empirical database method: Significant differences exist between different projects, resulting in poor prediction accuracy;

[0126] None of these methods can fundamentally solve the problem of combined explosions, and they generally suffer from loss of accuracy or safety risks.

[0127] Based on this, the present invention proposes a fast numerical combinatorial calculation method based on the extremum decomposition of mutually exclusive groups, including the following steps, the specific flowchart of which is shown in Figure 1:

[0128] Step S1: Based on the physical mutual exclusivity of the load conditions, divide all load conditions into M mutually exclusive groups;

[0129] Step S2: Perform finite element analysis on all working conditions within each mutually exclusive group, calculate the structural effects, and record the positive maximum and negative minimum values ​​within the group, as well as the working condition number that produces the corresponding effect.

[0130] Step S3: Based on multiple load types, combine all mutually exclusive groups to obtain P mutually exclusive group combinations, and calculate the positive and negative extreme values ​​of the load effect for each mutually exclusive group combination.

[0131] Step S4: Calculate the envelope of the positive and negative extreme values ​​of the effects of the P mutually exclusive combinations to obtain the final positive and negative extreme values;

[0132] It also includes step S5: Design and verify the component section based on the final positive extreme value and the final negative extreme value. If the preset conditions are met, output the calculation results; if the preset conditions are not met, update the parameters of the working condition in step S2 and repeat steps S1 to S5 until the preset conditions are met and output the calculation results.

[0133] The mutual exclusion group is a set of operating conditions, in which any two operating conditions cannot occur simultaneously in the same mutual exclusion group at the same time; operating conditions in different mutual exclusion groups can occur simultaneously.

[0134] Establish an extreme value database EVD, and store the calculation results from step S2 into the extreme value database EVD.

[0135] The data structure of the calculation results is as follows: positive maximum value, working condition number that produces the positive maximum value, negative maximum value, and working condition number that produces the negative maximum value.

[0136] Data in the extreme value database EVD is updated based on operating conditions;

[0137] In a single finite element analysis, the maximum positive value and minimum negative value of all types of structural effects are calculated and recorded simultaneously. In a single traversal of operating conditions, the maximum positive value and minimum negative value of all types of structural effects are obtained simultaneously, avoiding repeated calculations.

[0138] The load combination types in step S3 include basic combination, standard combination, quasi-permanent combination, and other types;

[0139] In step S4, the envelope calculation is performed using an algorithm based on linear superposition for linear structural analysis. For structural analysis involving geometric nonlinearity or material nonlinearity, other methods or modified calculations are required.

[0140] As can be seen, the fast numerical combination calculation method based on mutual exclusion set extremum decomposition in this invention includes the following features:

[0141] (1) The calculation method in this invention solves the problem of excessive calculation time caused by the exponential growth of the number of load combinations, and reduces the calculation complexity from exponential O(∏n_i) to linear O(Σn_i);

[0142] (2) The calculation method in this invention solves the problem of huge memory consumption required to store all combined effect results, and only needs to store the extreme values ​​of each mutually exclusive group, reducing the memory requirement for large projects by 10%. 6 More than twice;

[0143] (3) The calculation method in this invention provides a unified calculation framework, which is applicable to all structural effects that satisfy the principle of linear superposition, such as component internal forces, support reactions, and nodal displacements, and can handle multiple types of effects at the same time in one calculation;

[0144] (4) The calculation method in this invention achieves fast and accurate calculation of the envelope value while ensuring calculation accuracy, without introducing any approximation or error, and ensures that the calculation result is completely consistent with the exhaustive method;

[0145] (5) The calculation method in this invention provides a rigorous mathematical theoretical guarantee and meets the structural safety design requirements.

[0146] Example 1:

[0147] A fast numerical combinatorial calculation method based on the extremum decomposition of mutually exclusive groups includes the following steps:

[0148] Step S1: Mutual Exclusion Group Partitioning:

[0149] Based on the physical mutual exclusivity of the load conditions, all load conditions are divided into M mutually exclusive groups.

[0150] Definition of a mutual exclusion group: A mutual exclusion group Gᵢ is a set of operating conditions in which any two operating conditions cannot occur simultaneously at the same time.

[0151] Taking a common mutual exclusion relationship as an example, the specific steps for dividing the mutual exclusion group are shown in Figure 2:

[0152] Wind load in different directions: G_wind = {W_0°, W_10°, ..., W_350°};

[0153] Different positions of the crane: G_crane = {C_pos1, C_pos2, ..., C_posn};

[0154] Temperature rise and fall: G_temp = {T_heat, T_cool, T_zero} (T_zero indicates that the beneficial effects of temperature are not considered)

[0155] Construction stage: G_stage = {S1, S2, ..., S} n};

[0156] Different live load arrangements: G_live = {L_full, L_pattern1, L_pattern2, L_zero};

[0157] In this context, all positions of each crane form a mutually exclusive group.

[0158] Step S2: Calculation of operating conditions and recording of positive and negative extreme values:

[0159] Finite element analysis is performed on all load cases within each mutually exclusive group to calculate the structural effects and record the positive maximum and negative minimum values ​​within each group, as well as the load case number that produces the corresponding effect. The envelope value and the "positive maximum and negative minimum values" are interchangeable in this chapter.

[0160] Establish an Extreme Value Database (EVD), taking the internal forces of a component (symbolized as F) as an example:

[0161] Data Structures:

[0162] EVD[i][e][c] = {

[0163] F_max + : The maximum positive effect value of the internal force component c of component e in mutually exclusive group i;

[0164] LC_max + : The operating condition number that produces the maximum positive effect;

[0165] F_min - : The minimum negative effect value of the internal force component c of member e in mutually exclusive group i;

[0166] LC_min - : The operating condition number that produces the minimum negative effect};

[0167] in:

[0168] i — Mutex group index (i = 1, 2, ..., m);

[0169] e — Component index (e = 1, 2, ..., N_elements);

[0170] c — index of internal force components (c ∈ {N, V_y, V_z, T, M_y, M_z});

[0171] Among them, F_max + F_min - It can be a single value for the current internal force component c, depending on the actual calculation needs, or it can be an array of all effect values ​​(including multiple dimensions generated simultaneously) corresponding to the extreme value of the current component c, which can be used for subsequent synchronization calculations. For simplicity, it will be assumed to be a single value for the current internal force component c. If synchronization calculation is required, the array data at the extreme value is selected for the calculation in step S3, using the same system, and details are not elaborated here.

[0172] Envelope value recording rules:

[0173] Initial value settings:

[0174] F_max + = 0 (meaning that if all operating conditions in the group have negative effects, then the maximum positive effect is 0).

[0175] F_min - = 0 (meaning that if all operating conditions in the group have positive effects, then the minimum negative effect is 0);

[0176] Physical meaning:

[0177] F_max + Used to design components that withstand positive forces such as tension and positive bending moment;

[0178] F_min - Used to design components that withstand negative forces such as pressure and negative bending moment;

[0179] For each component e in each working condition j within the mutually exclusive group Gᵢ, calculate the effect value with combination coefficients. Fj is the effect matrix of the current working condition, which is obtained by solving the finite element method for the current working condition. This part is similar to the traditional method.

[0180] After obtaining the effect matrix Fj for the current operating condition, the envelope value of EVD is updated:

[0181] if(Fj[e][c]>0&&Fj[e][c]>EVD[i][e][c].F_max+ ) ;

[0182] {EVD[i][e][c].F_max + = Fj[e][c]; LC_max + = j};

[0183] if(Fj[e][c]<0&&Fj[e][c] <EVD[i][e][c].F_min_) ;

[0184] {EVD[i][e][c].F_min_ = Fj[e][c];LC_min - = j};

[0185] Simultaneous recording of multiple types of effects:

[0186] In a single finite element analysis, multiple types of effect extrema can be calculated and recorded simultaneously:

[0187] Extreme values ​​of internal forces in a component: EVD_Force[i][e][c];

[0188] Extreme values ​​of support reaction force: EVD_Reaction[i][s][c];

[0189] Node displacement extreme values: EVD_Displ[i][n][c];

[0190] The above extreme value databases have the same structure and recording method, differing only in their symbols (F represents internal force, R represents reaction force, and U represents displacement). F_max + F_min - It can be a single value for the current internal force component c, depending on the actual calculation needs, or it can be an array of all effect values ​​corresponding to the extreme value of the current component c, which can be used for subsequent synchronization calculations.

[0191] Step S3: Envelopes with multiple combinations:

[0192] Standards typically require consideration of multiple load combination types (such as basic combination, standard combination, quasi-permanent combination, etc.), with different dominant loads in each type; and combination of mutually exclusive groups.

[0193] The load effect for each mutually exclusive group combination type k is:

[0194] Positive extreme value of the effect: E_k_max + =Σ(γ_i × EVD[i].F_max + );

[0195] Negative extreme value of the effect: E_k_min -=Σ(γ_i × EVD[i].F_min_);

[0196] Where i is the index of the mutual exclusion group.

[0197] Then calculate the envelope of all combinations of mutual exclusion pairs:

[0198] Final positive extreme value: E_final_max + = max{E_k_max + | k = 1, 2, ..., p};

[0199] Final negative extreme value: E_final_min - = min{E_k_min - | k = 1, 2, ..., p};

[0200] Where P represents the total number of mutually exclusive group combinations.

[0201] Computational efficiency: Even considering P combinations, the computational complexity is still O(P×N_components), which is much smaller than the traditional method's O(N_total).

[0202] Step S4: Component Design

[0203] Based on the final positive extreme value: E_final_max + And the final negative extreme value: E_final_min - Perform component cross-section design and verification.

[0204] Step S5: Iterate and optimize until convergence:

[0205] Repeat the above steps until the preset conditions are met, such as the stress ratio not exceeding the limit.

[0206] Through the above embodiments, the present invention provides a complete and operable solution for realizing fast numerical combination calculation based on mutual exclusion set extremum decomposition.

[0207] To verify the performance of the calculation method of this invention, this invention compares the traditional calculation method with the calculation method of this invention and provides mathematical proof of the equivalence of the two methods:

[0208] The following conditions must be met in the existing standards and the above process design:

[0209] Combination coefficient γᵢ k ≥ 0 (compliant with current regulations);

[0210] The positive and negative extreme values ​​are recorded separately (F_max) + ≥ 0, F_min- ≤0);

[0211] Traditional calculation method (exhaustive search):

[0212] Suppose there are m mutually exclusive groups G1, G2, ..., G m The i-th group contains nᵢ working conditions; the traditional method requires enumerating all possible combinations:

[0213] C = {(j1, j2, ..., j m ) | jᵢ ∈ Gᵢ, i = 1,2,...,m};

[0214] Total number of combinations: N_total = ∏nᵢ;

[0215] For combination type k, the effect value of each combination on component e, c, is:

[0216] E(j1, j2, ..., j m ) = Σγᵢ k × Fᵢⱼᵢ[e][c];

[0217] in:

[0218] γᵢ k Let i be the combination coefficient of the i-th group in combination type k;

[0219] Fᵢⱼᵢ[e][c] represents the effect of the jᵢth working condition in the i-th group on component e, c;

[0220] Traditional methods for finding positive extremum envelopes:

[0221] E_traditional_max + = max{E(j1, j2, ..., j m ) | (j1, j2, ..., j m )∈C};

[0222] The calculation method of this invention:

[0223] Step 1: Record the positive extreme values ​​for each group:

[0224] EVD[i][e][c].F_max + = max{Fᵢⱼ[e][c]| j∈Gᵢ, Fᵢⱼ[e][c]≥0};

[0225] If there are no positive values ​​in the group, then F_max + = 0;

[0226] Step 2: Calculate the envelope using linear superposition:

[0227] E_new_max + = Σγᵢ k × EVD[i][e][c].F_max + ;

[0228] Equivalence Theorem:

[0229] Theorem (Positive Extremum Equivalence):

[0230] In the combination coefficient γᵢ k Under the premise that ≥0, the positive extremum calculated by the method of this invention is completely equivalent to the traditional exhaustive method:

[0231] E_traditional_max + = max{Σγᵢ k × Fᵢⱼᵢ[e][c]| jᵢ∈ Gᵢ, i=1,...,m};

[0232] Because the max operation has a distributive property for addition, when all γᵢ k When ≥0, the summation can be split:

[0233] E_traditional_max + = max{γ 1k × F 1j1 [e][c]+ γ 2k × F 2j2 [e][c]+ ... + γ mk ×F mjm [e][c]};

[0234] For any fixed combination (j1, j2, ..., j...) m To maximize the sum, each term needs to be as large as possible. Since the mutually exclusive groups are independent of each other, the choice of one group does not affect the other groups. Therefore, the overall maximum value is equal to the sum of the maximum values ​​of each group independently.

[0235] E_traditional_max + = max{γ 1k × F 1j1 [e][c]} + max{γ 2k × F 2j2 [e][c]} + ... +max{γ mk × F mjm [e][c]}

[0236] =Σ i=1ᵐ max{γᵢ k × F iji[e][c]| j i ∈Gᵢ};

[0237] Due to γᵢ k Values ​​≥ 0 (non-negative constants) can be extracted outside of the max function:

[0238] E_traditional_max + =Σ i=1ᵐ γᵢ k × max{F iji [e][c]| j i ∈Gᵢ};

[0239] Case 1: There exists a working condition in the i-th group such that Fᵢⱼ[e][c]>0:

[0240] max{Fᵢⱼᵢ[e][c]| jᵢ ∈ Gᵢ} = max{Fᵢⱼ[e][c]| j ∈ Gᵢ, Fᵢⱼ[e][c]>0}

[0241] = EVD[i][e][c].F_max + ;

[0242] Case 2: All operating conditions in the i-th group ensure that Fᵢⱼ[e][c]≤ 0.

[0243] max{Fᵢⱼᵢ[e][c]| jᵢ ∈ Gᵢ ∪ {0}} = 0 = EVD[i][e][c].F_max + ;

[0244] In summary, E_traditional_max + = Σγᵢ k × EVD[i][e][c].F_max + = E_new_max + Corollary: The proof of equivalence for negative extrema is completely symmetric. Replacing max with min in the above proof, F_max + Replace with F_min - Replace ≥0 with ≤0 to get:

[0245] E_new_min - = E_traditional_min - ;

[0246] This theorem requires γᵢ kThe value is ≥0, which is satisfied in current engineering specifications (GB50009-2012 "Code for Design of Building Structures", GB0068-2018 "Unified Standard for Reliability of Building Structures", etc.). All partial factors and combination factors are non-negative, so this method is fully applicable in actual engineering.

[0247] Comparative analysis shows that the traditional calculation method's envelope value calculation flowchart is shown in Figure 3; Figure 4 is an embodiment of the envelope value calculation flowchart in the calculation method of the present invention; Figure 5 is another embodiment of the envelope value calculation flowchart in the calculation method of the present invention. Local optimization of FEM solution and EVD improves the spatial and temporal coherence of related memory, which can significantly improve memory and cache utilization.

[0248] Comparison of complexity optimizations:

[0249] The complexity of the original algorithm (traditional calculation method): T_traditional = K×T_FEM + N_total×T_combine;

[0250] The complexity of the new algorithm (calculated using the method of this invention): T_new = K×T_FEM + K×N_elements×T_update + P×T_combine;

[0251] in:

[0252] T_FEM = Finite element solution time (relatively long);

[0253] T_combine = Combinatorial linear time (smaller);

[0254] T_update = EVD envelope value update time (very small);

[0255] K =Σᵢnᵢ represents the total number of operating conditions / the total number of all operating conditions (summation);

[0256] N_total = ∏ᵢnᵢ is the number of work condition combinations, where nᵢ is the number of work conditions that can be combined in each category;

[0257] M = Σᵢmᵢ represents the number of mutually exclusive groups;

[0258] P = ∏ᵢmᵢ is the number of mutually exclusive combinations, where mᵢ is the number of mutually exclusive groups that can be combined in each class;

[0259] Key Relationships:

[0260] N_total >> K (typically differing by thousands to millions of times);

[0261] P is much smaller than N_total;

[0262] M≪K (The number of mutually exclusive groups is much smaller than the number of operating conditions);

[0263] T_FEM >> T_combine >> T_update;

[0264] In addition to the theoretical advantages in algorithmic complexity, this invention also has significant advantages in caching and memory utilization at the computer architecture level:

[0265] Alternatively, in the above method as an executable solution, memory usage can be optimized.

[0266] Traditional memory access patterns:

[0267] Phase 1: Calculate and store the results for each working condition;

[0268] Second stage: Traverse all combinations and frequently and randomly access the results of each working condition to sum them up;

[0269] Memory access characteristics: frequent random reads, low cache hit rate;

[0270] Memory access mode of the method of this invention:

[0271] Single stage: The EVD extreme value database is updated in real time during calculations based on operating conditions;

[0272] Data access characteristics: sequential read / write, good locality;

[0273] Memory footprint: Only extreme value data (M groups) need to be maintained, resulting in a small memory footprint;

[0274] Improved caching efficiency:

[0275] Spatial locality: EVD data structures are compact and can be better loaded into the CPU cache;

[0276] Temporal locality: When extreme data of the same component is accessed consecutively, the cache hit rate is close to 100%.

[0277] Reduce memory bandwidth requirements: No need for repeated retrievals in terabyte-scale data;

[0278] By combining reduced algorithm complexity and improved caching efficiency, actual performance improvements can reach tens to hundreds of times, and in extreme cases, even hundreds of thousands of times.

[0279] As can be seen, the fast numerical combination calculation method based on mutual exclusion set extremum decomposition in this invention has the following characteristics:

[0280] First: A general structural effect combination calculation method based on mutual exclusion group extremum decomposition:

[0281] A rapid calculation method for structural load combinations is characterized by: dividing all load cases into several mutually exclusive groups (groups that cannot occur simultaneously) according to physical exclusivity; calculating and recording the envelope values ​​(maximum positive and minimum negative values) of various structural effects (including but not limited to component internal forces, support reactions, and nodal displacements) for each group; and then performing linear combinations by multiplying the combination coefficients by the corresponding extreme values ​​to directly obtain the total envelope value of various effects, thus avoiding enumerating all combinations.

[0282] Second: Storage structure of the general extreme value database:

[0283] An EVD data structure for storing extreme values ​​of mutually exclusive groups is characterized in that: for each triple (mutually exclusive group i, effect object k, effect component c), the maximum value, minimum value and corresponding working condition number of the component of the object in the group are stored. It is applicable to various effects such as component internal force, support reaction force and nodal displacement, and the total storage capacity is O(m×N_elements×N_components).

[0284] Third: Application of the linear effect combination extreme value decomposition theorem:

[0285] Application of the theorem:

[0286] max{Σ(γ_i × E_i)} = Σ[γ_i×max{E_i}] (γ_i≥0) (γ_i<0);

[0287] The same applies to min;

[0288] For the calculation of the envelope of structural effects, the complexity is reduced from exponential O(∏n_i) to linear O(Σn_i), and it is applicable to all structural effects that satisfy the principle of linear superposition.

[0289] Fourth: Strategies for simultaneous calculation of multiple effects:

[0290] The extreme values ​​of multiple types of structural effects (component internal forces, support reactions, nodal displacements, etc.) can be calculated and recorded simultaneously in a single finite element analysis, and the envelope values ​​of all types of effects can be obtained simultaneously in a single traversal of working conditions, thus avoiding redundant calculations.

[0291] (Fifth: Local update strategy for extreme value database in iterative optimization:)

[0292] Optionally, during the structural optimization iteration process, after the finite element analysis is completed and various types of structural effects are obtained, the data structure EVD for updating the extreme values ​​is compactly updated to achieve better memory-time and spatial coherence and improve cache and memory utilization.

[0293] The key technical points of the fast numerical combinatorial calculation method based on mutual exclusion group extremum decomposition in this invention are as follows:

[0294] Key point 1: Correct division of mutual exclusion groups:

[0295] Mutual exclusion group partitioning must ensure that:

[0296] It is physically impossible for any two operating conditions within the group to occur simultaneously.

[0297] The operating conditions of different groups can occur simultaneously.

[0298] Key Point 2: Correct handling of the sign of combination coefficients:

[0299] All combination coefficients must meet the engineering application restriction of ≥0.

[0300] Key Point 3: Independent handling of grouped working conditions:

[0301] For each mutually exclusive group, record the extreme values ​​for all operating conditions and calculate the envelope independently to ensure that the extreme value combinations for each dimension are correct.

[0302] Key Point 4: Applicability of the Linear Superposition Principle:

[0303] The algorithm is based on the principle of linear superposition and is suitable for linear structure analysis. For cases involving geometric nonlinearity, material nonlinearity, etc., other methods or appropriate modifications are required.

[0304] Key Point 5: Guarantee of Mathematical Rigor

[0305] The algorithm is based on rigorous mathematical theorems, ensuring that the calculation results are completely consistent with the exhaustive method, with zero error, and meets the structural safety design requirements.

[0306] Key Point 6: Universality and Scalability

[0307] The algorithmic framework is general and applicable to any structural effect that satisfies linear superposition, including but not limited to:

[0308] Internal forces of a component (axial force, shear force, bending moment, torque)

[0309] Support reactions (vertical, horizontal, bending moment)

[0310] Nodal displacements (translation and rotation)

[0311] Other effects such as stress, strain, and internal forces in the foundation.

[0312] The effects and advantages of the fast numerical combinatorial calculation method based on mutual exclusion set extremum decomposition in this invention are as follows:

[0313] First: Computational efficiency is significantly improved.

[0314] The calculation time has been greatly reduced;

[0315] The computational complexity is reduced from exponential O(∏n_i) to linear O(Σn_i), resulting in a speedup of hundreds to tens of thousands of times.

[0316] Small and medium-sized projects: Accelerate by 2-10 times;

[0317] Large-scale projects: Accelerate by 100-1000 times;

[0318] For mega-projects (tens of thousands of operating conditions): speeding up by more than 10,000 times;

[0319] Memory consumption has been significantly reduced;

[0320] Memory requirements are reduced from O(∏n_i×N_elements) to O(m×N_elements), resulting in savings of over 1000 times. This enables ordinary workstations (32-64GB of memory) to handle large projects that would otherwise require high-performance servers.

[0321] High-efficiency memory architecture access;

[0322] This method exhibits temporal and spatial locality, allowing for efficient utilization of modern computer memory architectures. Theoretically, it can achieve performance improvements of over 10,000 times in extreme cases.

[0323] Second: Calculation accuracy is fully guaranteed.

[0324] Theoretical rigor;

[0325] Based on rigorous mathematical theorems, the calculation results are equivalent to those of the traditional exhaustive method, fully meet the requirements of the specifications, and pose no safety risks.

[0326] It provides a complete mathematical proof to ensure the correctness of the algorithm in all cases, avoiding the uncertainty of approximation methods such as heuristic algorithms and sampling methods.

[0327] Third: High versatility and practicality:

[0328] Wide range of applications;

[0329] Applicable to all structural effects based on linear superposition, including:

[0330] Internal forces of structural components (steel structures, concrete structures, bridge structures, etc.);

[0331] Support reaction force (used in foundation design);

[0332] Nodal displacements (used for stiffness verification);

[0333] Other linear effects (stress, strain, etc.);

[0334] Simultaneous calculation of multiple effects;

[0335] A single analysis can process multiple types of effects simultaneously, avoiding double counting.

[0336] Traditional method: Calculating internal forces, reactions, and displacements separately takes 3 times longer;

[0337] This invention: Simultaneously calculates all effects without increasing the total time consumed;

[0338] Supports design iteration and optimization;

[0339] During the optimization design process, after each parameter adjustment, only the operating condition effect and the extreme value need to be recalculated, without the need to regenerate all combinations, which greatly improves the iteration efficiency.

[0340] Fourth: High engineering application value:

[0341] Reduce hardware costs;

[0342] With significantly reduced memory requirements, engineers can use ordinary workstations to perform computing tasks that would otherwise require high-performance servers, reducing hardware investment costs.

[0343] Shorten the design cycle;

[0344] The calculation time has been reduced from several days to several hours, enabling the design team to complete the comparison and optimization of solutions in a shorter time and speed up the project progress.

[0345] Improve design quality;

[0346] Because of the fast computation, designers can try more design options, optimize more thoroughly, and eliminate the risk of overlooking important combinations.

[0347] 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.

[0348] It should be noted that the various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the systems or apparatus disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the descriptions are relatively simple, and relevant parts can be referred to the method section.

[0349] It should be understood that in this invention, "at least one (item)" refers to one or more, and "more than one" refers to two or more. "And / or" describes the relationship between related objects, indicating that three relationships can exist. For example, "A and / or B" can represent three cases: only A exists, only B exists, and both A and B exist simultaneously, where A and B can be singular or plural. The character " / " generally indicates that the preceding and following related objects are in an "or" relationship. "At least one (item) of the following" or similar expressions refer to any combination of these items, including any combination of single or plural items. For example, at least one (item) of a, b, or c can represent: a, b, c, "a and b", "a and c", "b and c", or "a and b and c", where a, b, and c can be single or multiple.

[0350] It should also be noted that, in this invention, relational terms such as "first" and "second" are used merely 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 a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0351] The steps of the methods or algorithms described in conjunction with the embodiments disclosed in this invention can be implemented directly by hardware, a software module executed by a processor, or a combination of both. The software module can be located in random access memory (RAM), main memory, read-only memory (ROM), electrically programmable ROM, electrically erasable programmable ROM, registers, hard disk, removable disk, CD-ROM, or any other form of storage medium known in the art.

[0352] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined in this invention may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A fast numerical combinatorial calculation method based on the extremum decomposition of mutually exclusive sets, characterized in that, Includes the following steps: Step 1: Based on the physical exclusivity of the load cases, divide all load cases into M mutually exclusive groups; Step 2: Perform finite element analysis on all load cases within each mutually exclusive group, calculate the structural effects, and record the positive maximum and negative minimum values ​​within the group, as well as the load case number that produces the corresponding effect; Step 3: Combine all mutually exclusive groups based on multiple load types to obtain P mutually exclusive group combinations, and calculate the positive and negative extreme values ​​of the load effects for each mutually exclusive group combination; Step 4: Perform envelope calculation on the positive and negative extreme values ​​of the effects of the P mutually exclusive group combinations to obtain the final positive and final negative extreme values; An extreme value database (EVD) is established, and the calculation results from step two are stored in the extreme value database EVD. The data structure of the calculation results is as follows: positive maximum value, working condition number that produces the positive maximum value, negative maximum value, and working condition number that produces the negative maximum value. The data in the extreme value database EVD is updated according to the working condition. In one finite element analysis, the positive maximum value and negative minimum value of all types of structural effects are calculated and recorded simultaneously. In one working condition traversal, the positive maximum value and negative minimum value of all types of structural effects are obtained simultaneously to avoid duplicate calculations.

2. The numerical combinatorial fast calculation method based on mutual exclusion set extremum decomposition as described in claim 1, characterized in that, The mutual exclusion group is a set of operating conditions, in which any two operating conditions cannot occur simultaneously in the same mutual exclusion group at the same time; operating conditions in different mutual exclusion groups can occur simultaneously.

3. The numerical combinatorial fast calculation method based on mutual exclusion set extremum decomposition as described in claim 1, characterized in that, The load combination types in step three include basic combination, standard combination, and quasi-permanent combination.

4. The fast numerical combinatorial calculation method based on extremum decomposition of mutually exclusive sets as described in claim 1, characterized in that, In step four, the envelope calculation is performed using an algorithm based on linear superposition for linear structural analysis. For structural analysis involving geometric nonlinearity or material nonlinearity, a correction calculation is required.

5. The fast numerical combinatorial calculation method based on mutual exclusion set extremum decomposition as described in claim 1, characterized in that, It also includes step five: design and verify the component section based on the final positive and negative extreme values. If the preset conditions are met, output the calculation results; if the preset conditions are not met, update the parameters of the working condition in step two, and repeat steps two to five until the preset conditions are met, and output the calculation results.

6. An electronic device, characterized in that, include: At least one processor; And a memory storing instructions that, when executed by the at least one processor, cause the at least one processor to perform the fast numerical combination calculation method based on mutual exclusion set extremum decomposition as described in any one of claims 1 to 5.

7. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, implements the steps of the fast numerical combination calculation method based on mutual exclusion set extremum decomposition as described in any one of claims 1 to 5.

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