A method for identifying weak points in loading and unloading arms and optimizing reinforcement rings

Abstract

The present invention discloses a method for identifying weak points in a loading and unloading arm and optimizing reinforcement rings, which specifically includes: simulating the random fluctuation characteristics in natural wind, constructing a non-steady-state wind load model, and generating a pulsating wind speed time history based on the Davenport spectrum by superimposing the harmonics of multiple frequency components; establishing a nonlinear Euler beam structural dynamic model of the material, and using the Newmark-β method to calculate the response of the loading and unloading arm under wind load; extracting displacement, structural stress, and strain energy density indicators to identify weak nodes and weak sections; introducing an adjustable reinforcement ring structure to optimize the local stiffness of the weak section area, forming a multi-objective optimization scheme for stiffness enhancement and quality control. The present invention can achieve efficient identification of weak points in the loading and unloading arm under non-steady-state wind loads and response-driven reinforcement optimization, with the advantages of high precision, strong adaptability, and good structural lightweighting effect, effectively solving many problems in traditional wind-resistant design.

Description

Technical Field

[0001] The invention belongs to the technical field of port loading and unloading equipment structure optimization, and particularly relates to a method for identifying weak parts of a loading and unloading arm and optimizing a reinforcement ring. Background Art

[0002] In industrial scenarios such as port operations, ship loading and unloading, and logistics, large loading and unloading arms are critical components used for lifting, transporting, and positioning cargo. With the increasing automation and scale of loading and unloading operations, the size of loading and unloading arms is increasing, and their wind resistance in high-altitude working environments is becoming increasingly problematic. This is especially true in complex environments such as strong winds, gusty winds, and sudden weather events. The loading and unloading arm structure can produce dramatic dynamic responses, directly impacting operational efficiency, equipment safety, and service life.

[0003] In current engineering design, traditional wind resistance analysis methods generally adopt the static wind load assumption, that is, simplified estimation through fixed wind pressure or gust factor. This method has obvious limitations. It is difficult to accurately simulate the non-steady-state disturbance characteristics in the actual wind field. It ignores the transient nature of wind speed in time and space, resulting in significant deviations between the response of the structure under actual working conditions and the simulation results. In addition, in terms of structural reinforcement design, existing schemes often rely on empirical rules to select reinforcement areas and lack a quantitative identification mechanism based on the structural response under actual wind loads. This is prone to problems such as redundant reinforcement or omission of key parts, which not only increases the weight of the system (typical weight increase of 15%-20%), but also reduces the dynamic response performance and flexible execution capability of the loading and unloading arm.

[0004] More critically, as a long, highly compliant structure, the loading and unloading arm is subject to the combined effects of varying wind angles, fluctuating wind loads, and turbulent fluctuations in actual wind fields, which can easily lead to structural vibration instability, such as vortex-induced vibration and flutter. If these vibrations are not controlled, they can not only cause structural fatigue damage, but can also lead to reduced end-of-line precision, abnormal mechanism operation, and even accidents in severe cases. Existing research lacks systematic dynamic failure mode identification methods and adaptive response control means, making it impossible to achieve full-process dynamic safety assurance for the loading and unloading arm in complex wind environments.

[0005] In summary, how to construct a wind-resistant optimization system that can consider the effects of non-steady-state wind loads, identify structural weak points, and achieve efficient strengthening design has become a key technical issue for improving the structural performance and safety of loading and unloading arms. Summary of the Invention

[0006] In response to the problems existing in the above-mentioned prior art, the present invention proposes a method for identifying weak points in loading and unloading arms and optimizing reinforcement rings. First, a non-steady-state pulsating wind field is constructed using the Davenport wind speed spectrum, and the Fourier superposition method is used to generate a time-varying wind speed history. The wind load time series at the node is calculated by combining the structural geometry and the wind attack angle. Subsequently, the loading and unloading arm structure is discretized into Euler beam units, and a finite element model including a stiffness matrix, a lumped mass matrix, and a Rayleigh damping matrix is ​​constructed. The Newmark-β method is then used to perform time-step integration on the structural response to obtain response data such as node displacement, stress, and curvature. On this basis, a multi-criteria criterion is constructed based on indicators such as stress, strain energy density, and curvature to identify weak nodes and areas of the structure. Based on the identification results, a parameterized reinforcement ring is placed in the weak section. The optimized moment of inertia is calculated by adjusting its outer diameter, wall thickness, and length, and an equivalent stiffness increment target is set. A multi-objective optimization function, aiming to minimize structural weight gain and maximize local stiffness, was further constructed. Combining geometric, strength, and weight constraints, a non-dominated sorting genetic algorithm (NSGA-II) was employed to determine the optimal reinforcement ring configuration. This invention aims to address issues such as simplified wind load modeling, blind reinforcement design, and a lack of response-driven optimization mechanisms in traditional loading arm wind-resistant designs. This approach enables efficient identification of weak points in loading arms under unsteady wind loads and response-driven reinforcement optimization, achieving high precision, strong adaptability, and effective structural lightweighting.

[0007] In order to achieve the above technical objectives, the present invention provides the following technical solutions:

[0008] A method for identifying weak points of a loading and unloading arm and optimizing a reinforcement ring comprises the following steps:

[0009] S1. Simulate the random fluctuation characteristics of natural wind, build an unsteady wind load model, and generate a fluctuating wind speed time history based on the Davenport spectrum by superimposing the harmonics of multiple frequency components;

[0010] S2. Establish a nonlinear Euler beam structural dynamic model and use the Newmark-β method to calculate the response of the loading arm under wind load.

[0011] S3. Extract displacement, structural stress, and strain energy density indicators to identify weak locations, including weak nodes and weak segments;

[0012] S4. Introduce an adjustable reinforcement ring structure to optimize the local stiffness of the weak section area, forming a multi-objective optimization scheme for stiffness enhancement and quality control.

[0013] Furthermore, step S1 is specifically as follows:

[0014] Simulate the random fluctuation characteristics of natural wind and synthesize the fluctuating wind speed time history; the formula is expressed as:

[0015] ;

[0016] in, express The instantaneous wind speed at the moment represents the real-time change of the pulsating wind, which is determined by the average wind speed. and random pulsating components; The average wind speed is the stable wind speed component over a long time scale, which is given by meteorological data and design specifications; Indicates the number of discrete frequency components; Represents the random phase angle of each frequency component;

[0017] The Davenport wind speed power spectral density function is expressed in terms of frequency The value at is expressed as:

[0018] ;

[0019] in, Represents the center frequency of the nth frequency component, which is generated as follows: ; Indicates frequency resolution, that is, the interval between adjacent frequency components; Indicates the surface roughness coefficient; Indicates the average wind speed at a height of 10 meters; Indicates the cutoff frequency, which determines the peak position of the spectrum. L is the turbulence integral scale, which is the preset value.

[0020] Furthermore, step S2 specifically includes:

[0021] S21. Discretize the loading arm structure into Euler beam units and establish a finite element model including material nonlinearity; define the loading arm parameters including: total length of Euler beam , elastic modulus , mass distribution density along the beam and yield strength ; Discrete the loading and unloading arm Euler beam into Nodes, remember represents the initial node position; Indicates the Node locations, , Indicates the node spacing; For the The cross-sectional diameter at each node is the cross-sectional moment of inertia. ;

[0022] S22. The Newmark-β method is used to solve the dynamic response of the structure under wind load. The calculation formula is:

[0023] ;

[0024] in, The mass matrix calculated for the lumped mass method; is the stiffness matrix calculated based on beam bending theory; is the Rayleigh damping matrix; 、 and are the nodal displacement, nodal velocity and nodal acceleration; It is the external load, also known as the variable wind load;

[0025] Time-varying wind load The node distribution is expressed as:

[0026] ;

[0027] in, Indicates the air density; Indicates the Nodes are in t The instantaneous wind speed at the moment; Indicates the angle between the loading arm and the incoming wind direction; It is The resistance coefficient of each node.

[0028] Furthermore, step S3 specifically includes:

[0029] S31, in At time , the node displacement is known to be , then any node Curvature The formula is expressed as:

[0030] ;

[0031] The bending stress ;

[0032] The plastic strain energy density per unit volume is ;in, , represents the bending stress under unit elastic modulus; for The first derivative of ;

[0033] S32, determine the weak nodes, when any node A node is considered a weak node if it satisfies the following three constraints at the same time:

[0034] I. Node Maximum stress at , ;

[0035] II. Node Stress concentration factor at ,in is the mean stress;

[0036] III. Node The plastic strain energy density per unit volume at ;

[0037] in, is the preset threshold coefficient;

[0038] S33, remember the weak node sequence is , K is the total number of weak nodes; the area where the weak node sequence is located is the weak segment area.

[0039] Furthermore, step S4 specifically includes:

[0040] S41, based on the weak nodes and weak sections identified in step S3, an adjustable reinforcement ring is arranged in each weak section according to the overrun index corresponding to each weak node; the reinforcement ring parameters include: outer diameter , wall thickness , Reinforcement ring length , reinforcement ring volume , material density , material elastic modulus , the moment of inertia of the cross section where the reinforcement ring and the original loading and unloading arm structure are combined ;

[0041] S42. Install adjustable reinforcement rings to control the maximum stress of the loading and unloading arm structure in the weak section area. Reduced to yield strength When the maximum stress exceeds the safety range, the adjustable parameters of the reinforcement ring are adjusted to enhance the local stiffness of the weak section.

[0042] S43. A balance is achieved between the improvement of the local wind resistance stiffness of the reinforcement ring and the overall quality of the reinforcement ring through an optimization algorithm, specifically including:

[0043] First, the adjustable parameters of the reinforcement ring are recorded as 、 、 , forming a vector group ;

[0044] Then set the dual objective function for strengthening ring optimization 、 , the formula is:

[0045] ;

[0046] ;

[0047] in, For the weight control objective function, minimize To minimize the overall mass of the reinforcement ring; is the wind resistance performance objective function, maximizing Achieve the maximum improvement in the local wind resistance stiffness of the weak section of the loading and unloading arm structure;

[0048] The non-dominated sorting genetic algorithm (NSGA-II) is used to process the two objective functions in parallel, and the optimal balance between wind resistance and lightweight is solved by constructing the Pareto front solution set.

[0049] More specifically, step S42 is as follows:

[0050] After the adjustable reinforcement ring is installed, the maximum stress of the loading and unloading arm structure in the weak section area is controlled The following inequality is satisfied:

[0051] ;

[0052] in, The total equivalent wind stiffness of the loading and unloading arm structure in the weak section area after the reinforcement ring is introduced. is the equivalent wind stiffness of the original structure at the weak section;

[0053] When the maximum stress exceeds the safety range, the adjustable parameters of the reinforcement ring are automatically adjusted according to the degree of excess, including: outer diameter , wall thickness , Reinforcement ring length , to achieve stiffness enhancement in weak section areas.

[0054] More specifically, the specific process of using the non-dominated sorting genetic algorithm NSGA-II to solve the optimal balance in step S43 is as follows:

[0055] P1. Initialize the population, for each individual in the population Calculate separately and ;

[0056] P2. Group all individuals according to the Pareto dominance relationship. If a solution is not inferior to another solution in all objectives and is better in at least one objective, it is considered to dominate it. According to the dominance relationship between individuals, the best individuals are formed into the first-level non-dominated solution set, the second-best individuals are formed into the second-level non-dominated solution set, and so on. Group all individuals.

[0057] P3. Within the same frontier, calculate the crowding distance between individuals, prioritize evenly distributed solutions, and prevent all individuals from concentrating on one side;

[0058] P4. After completing selection, crossover, and mutation, a new generation of individuals is generated. The offspring and parent generations are merged to form a candidate set. The objective function is calculated and the non-dominated sorting is repeated. If the maximum algebra and convergence criterion is reached, a set of mutually non-dominated optimal solutions is output to form the Pareto frontier. Otherwise, repeat P1-P4.

[0059] Based on the above technical solution, the present invention has at least the following beneficial effects:

[0060] The present invention constructs a non-steady-state wind load model that takes into account pulsating wind, turbulent energy spectrum and changes in wind attack angle, and combines finite element dynamic response analysis with multi-dimensional response criteria to achieve accurate identification of weak parts of the loading and unloading arm structure under complex wind load conditions. Compared with the traditional reinforcement method that relies on experience, the present invention scientifically determines the positions that need to be strengthened based on dynamic indicators such as node stress, curvature, and strain energy density, significantly improving the reliability and pertinence of identification. For the identified weak areas, the present invention introduces a parameterized reinforcement ring design, and combines the moment of inertia increment model to construct an optimization objective function, and uses a multi-objective genetic algorithm to search for the optimal solution to achieve a balance between stiffness improvement and structural weight gain. This method can not only effectively suppress the vibration and deformation of the loading and unloading arm under wind load and improve its overall structural stability, but also avoid excessive reinforcement while meeting engineering safety requirements, significantly reduce redundant weight, and improve the operating efficiency and flexibility of loading and unloading equipment. The loading and unloading arm structure design is suitable for various complex wind environments. It has the advantages of strong versatility, flexible deployment, and good engineering adaptability. It effectively solves technical problems existing in traditional wind-resistant design, such as rough wind load modeling, blind reinforcement, and lack of quantitative basis for response control. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] The drawings described herein are used to provide a further understanding of the present application and constitute a part of the present application. The illustrative embodiments of the present application and their descriptions are used to explain the present application and do not constitute an improper limitation on the present application. In the drawings:

[0062] Figure 1 This is a method for identifying weak points in loading and unloading arms and optimizing reinforcement rings proposed by the present invention;

[0063] Figure 2 The time-varying wind speed history diagram is generated based on the Davenport spectrum;

[0064] Figure 3 It is a schematic diagram of the loading and unloading arm structure;

[0065] Figure 4The flowchart of the genetic algorithm based on NSGA-II to process two objective functions. DETAILED DESCRIPTION

[0066] In order to make the above-mentioned objects, features and advantages of the present invention more clearly understood, the following Figure 1-4 The present invention is further described in detail with specific implementation methods, so that the application can fully understand how to use technical means to solve technical problems and achieve technical effects and implement them accordingly.

[0067] Those skilled in the art will appreciate that all or part of the steps in the above-mentioned embodiment methods can be accomplished by instructing the relevant hardware through a program. Therefore, the present application may take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Furthermore, the present application may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0068] See Figures 1-4 , showing a specific implementation of this embodiment. Based on time-varying wind load-structural response coupled modeling, this invention provides a method for identifying weak points in loading and unloading arms and optimizing reinforcement rings. By integrating unsteady wind load modeling, structural dynamic response solution, response index analysis, and multi-objective optimization, this method achieves intelligent reinforcement design for loading and unloading arm structures in complex wind environments.

[0069] This embodiment first constructs a non-steady-state wind field model that takes into account the fluctuating wind, turbulent energy spectrum and wind attack angle changes, and uses the Davenport wind spectrum combined with the Fourier superposition method to generate a wind speed time history with statistical characteristics. The wind load is then input into the finite element model of the loading and unloading arm, and the Newmark-β method is used to solve the dynamic response of the structure under time-varying wind excitation, and obtain multi-dimensional response data such as node-level displacement, stress, curvature and strain energy density. During the response monitoring process, the key weak areas of the loading and unloading arm structure are automatically identified by combining stress thresholds, energy indicators and stress concentration coefficients through a customized multi-criteria weakness identification method. The identification results are used as input for the optimization design of the reinforcement ring, and a multi-objective optimization model with the goal of minimum structural weight gain and maximum stiffness improvement is further constructed. The outer diameter, wall thickness and length parameters of the reinforcement ring are input as variables into the genetic algorithm for iterative optimization to obtain the optimal reinforcement configuration that meets the performance constraints. Figure 1 As shown, the method proposed in the present invention specifically includes the following steps:

[0070] S1. Simulate the random fluctuation characteristics of natural wind and build an unsteady wind load model by superimposing the harmonics of multiple frequency components, such as Figure 2As shown, the fluctuating wind speed time history is generated based on the Davenport spectrum;

[0071] As a preferred embodiment, step S1 is specifically as follows:

[0072] Simulate the random fluctuation characteristics of natural wind and synthesize the fluctuating wind speed time history; the formula is expressed as:

[0073] ;

[0074] in, express The instantaneous wind speed at the moment represents the real-time change of the pulsating wind, which is determined by the average wind speed. and random pulsating components; The average wind speed is the stable wind speed component over a long time scale (e.g., 10 minutes), which is given by meteorological data and design specifications. In this embodiment, the average wind speed for the port loading and unloading arm is 25 m / s. Represents the number of discrete frequency components. Its physical meaning is: through Fourier series expansion, the continuous wind spectrum is discretized into The superposition of frequency components, Determines the simulation accuracy, usually ; Represents the random phase angle of each frequency component;

[0075] The Davenport wind speed power spectral density function is expressed in terms of frequency The value at is expressed as:

[0076] ;

[0077] in, Represents the center frequency of the nth frequency component, which is generated as follows: ; Represents the frequency resolution, that is, the interval between adjacent frequency components ( , usually take ); represents the surface roughness coefficient, which is 0.03 in this embodiment; Indicates the average wind speed at a height of 10 meters; Indicates the cutoff frequency, which determines the peak position of the spectrum. L is the turbulence integral scale, which is a preset value and is 1200m in this embodiment.

[0078] S2. Establish a nonlinear Euler beam structural dynamic model and use the Newmark-β method to calculate the response of the loading arm under wind load.

[0079] As a preferred embodiment, Figure 3 As shown, step S2 specifically includes:

[0080] S21. Discretize the loading arm structure into Euler beam units and establish a finite element model including material nonlinearity; define the loading arm parameters including: total length of Euler beam , elastic modulus , mass distribution density along the beam and yield strength ; Discrete the loading and unloading arm Euler beam into Nodes, remember represents the initial node position; Indicates the Node locations, , Indicates the node spacing; For the The cross-sectional diameter at each node is the cross-sectional moment of inertia. ;

[0081] S22. The Newmark-β method is used to solve the dynamic response of the structure under wind load. The calculation formula is:

[0082] ;

[0083] in, The mass matrix calculated for the lumped mass method; is the stiffness matrix calculated based on beam bending theory; is the Rayleigh damping matrix; 、 and are the nodal displacement, nodal velocity and nodal acceleration; It is the external load, also known as the variable wind load;

[0084] Time-varying wind load The node distribution is expressed as:

[0085] ;

[0086] in, Indicates the air density; Indicates the Nodes are in t The instantaneous wind speed at the moment; Indicates the angle between the loading arm and the incoming wind direction (also known as the wind attack angle); It is The resistance coefficient of each node.

[0087] S3. Extract displacement, structural stress, and strain energy density indicators to identify weak locations, including weak nodes and weak segments;

[0088] As a preferred embodiment, step S3 specifically includes:

[0089] S31, in At time , the node displacement is known to be , then any node Curvature The formula is expressed as:

[0090] ;

[0091] The bending stress ;

[0092] The plastic strain energy density per unit volume is ;in, , represents the bending stress under unit elastic modulus; for The first derivative of ;

[0093] S32, determine the weak nodes, when any node A node is considered a weak node if it satisfies the following three constraints at the same time:

[0094] I. Node Maximum stress at , ;

[0095] II. Node Stress concentration factor at ,in is the mean stress;

[0096] III. Node The plastic strain energy density per unit volume at ;

[0097] in, is the preset threshold coefficient;

[0098] S33, remember the weak node sequence is , K is the total number of weak nodes; the area where the weak node sequence is located is the weak segment area.

[0099] In this application, it is set that the weak section area is determined by the above three conditions. When the three conditions are not met at the same time, that is, as long as one condition is not met, the section area is not considered to be a weak section area. Considering that the three conditions are actually related to the maximum stress, this application is designed to locally strengthen the rigidity of the weak section area by limiting the maximum stress threshold.

[0100] S4. Introduce an adjustable reinforcement ring structure to optimize the local stiffness of the weak section area, forming a multi-objective optimization scheme for stiffness enhancement and quality control.

[0101] As a preferred embodiment, step S4 specifically includes:

[0102] S41, based on the weak nodes and weak sections identified in step S3, an adjustable reinforcement ring is arranged in each weak section according to the overrun index corresponding to each weak node; the reinforcement ring parameters include: outer diameter , wall thickness , Reinforcement ring length , reinforcement ring volume , material density , material elastic modulus , the moment of inertia of the cross section where the reinforcement ring and the original loading and unloading arm structure are combined ;

[0103] S42. Install adjustable reinforcement rings to control the maximum stress of the loading and unloading arm structure in the weak section area. Reduced to yield strength Within the safety range, that is, the maximum stress after increasing the equivalent stiffness satisfies ;in, The total equivalent wind stiffness of the loading and unloading arm structure at the weak section after the reinforcement ring is introduced. is the equivalent wind stiffness of the original structure at the weak section;

[0104] When the maximum stress exceeds the safety range, the adjustable parameters of the reinforcement ring are automatically adjusted according to the degree of excess: outer diameter , wall thickness , Reinforcement ring length , to achieve stiffness enhancement in weak section areas;

[0105] S43. A balance is achieved between the improvement of the local wind resistance stiffness of the reinforcement ring and the overall quality of the reinforcement ring through an optimization algorithm, specifically including:

[0106] First, the adjustable parameters of the reinforcement ring are recorded as 、 、 , forming a vector group ;

[0107] Then set the dual objective function for strengthening ring optimization 、 , the formula is:

[0108] ;

[0109] ;

[0110] in, For the weight control objective function, minimize To minimize the overall mass of the reinforcement ring; is the wind resistance performance objective function, maximizing Achieve the maximum improvement in the local wind resistance stiffness of the weak section of the loading and unloading arm structure;

[0111] Finally, the constraints of various parameters including geometric dimensions, yield strength, stiffness, and weight are set, and the non-dominated sorting genetic algorithm NSGA-II is used to process the two objective functions in parallel. By constructing the Pareto front solution set, the optimal balance between wind resistance and lightweight is solved.

[0112] More specifically, Figure 4 As shown, the specific process of using the non-dominated sorting genetic algorithm NSGA-II to solve the optimal balance in step S43 is:

[0113] P1. Initialize the population, for each individual in the population Calculate separately and ;

[0114] P2. Group all individuals according to the Pareto dominance relationship. If a solution is not inferior to another solution in all objectives and is better in at least one objective, it is considered to dominate it. According to the dominance relationship between individuals, the best individuals are formed into the first-level non-dominated solution set, the second-best individuals are formed into the second-level non-dominated solution set, and so on. Group all individuals.

[0115] P3. Within the same frontier (i.e., the same level of non-dominated solution set), calculate the crowding distance between individuals, prioritize evenly distributed solutions, and prevent all individuals from concentrating on one side;

[0116] P4. After completing selection, crossover, and mutation, a new generation of individuals is generated. The offspring and parent generations are merged to form a candidate set. The objective function is calculated and the non-dominated sorting is repeated. If the maximum algebra and convergence criterion is reached, a set of mutually non-dominated optimal solutions is output to form the Pareto frontier. Otherwise, repeat P1-P4.

[0117] At this point, the method proposed in the present invention realizes the accurate identification of weak parts of the loading and unloading arm structure and adaptive stiffness enhancement control, which not only improves the wind resistance and stability of the structure, but also takes into account the lightweight design requirements, and has strong engineering practicality and promotion value.

[0118] In the description of this specification, the reference terms "one embodiment," "some embodiments," "example," "specific example," or "some examples" mean that the specific features, structures, materials, or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present application. Moreover, the specific features, structures, materials, or characteristics described may be combined in any appropriate manner in any one or more embodiments or examples. In addition, those skilled in the art may combine and combine different embodiments or examples described in this specification, as well as features of different embodiments or examples, unless they are mutually inconsistent.

[0119] The logic and / or steps represented in the flowchart or otherwise described herein may be considered, for example, as an ordered list of executable instructions for implementing logical functions, and may be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (such as a computer-based system, a system including a processor, or other system that can fetch and execute instructions from an instruction execution system, apparatus, or device).

[0120] The above embodiments provide a detailed introduction to the present invention. Specific examples are used herein to illustrate the principles and implementation methods of the present invention. The description of the above embodiments is only used to help understand the method of the present invention and its core ideas. At the same time, for those skilled in the art, according to the ideas of the present invention, there may be changes in the specific implementation methods and application scopes. In summary, the contents of this specification should not be understood as limiting the present invention.

Claims

1. A method for identifying weak points of loading and unloading arms and optimizing reinforcement rings, characterized in that: The specific steps include: S1. Simulate the random fluctuation characteristics of natural wind, build an unsteady wind load model, and generate a fluctuating wind speed time history based on the Davenport spectrum by superimposing the harmonics of multiple frequency components; S2. Establish a nonlinear Euler beam structural dynamic model and use the Newmark-β method to calculate the response of the loading arm under wind loads. This includes: S21. Discretize the loading arm structure into Euler beam units and establish a finite element model including material nonlinearity; define the loading arm parameters including: total length of Euler beam , elastic modulus , mass distribution density along the beam and yield strength ; Discrete the loading and unloading arm Euler beam into Nodes, remember represents the initial node position; Indicates the Node locations, , Indicates the node spacing; For the The cross-sectional diameter at each node is the cross-sectional moment of inertia. ; S22. The Newmark-β method is used to solve the dynamic response of the structure under wind load. The calculation formula is: ； in, The mass matrix calculated for the lumped mass method; is the stiffness matrix calculated based on beam bending theory; is the Rayleigh damping matrix; 、 and are the nodal displacement, nodal velocity and nodal acceleration; It is the external load, also known as the variable wind load; Time-varying wind load The node distribution is expressed as: ； in, Indicates the air density; Indicates the Nodes are in t The instantaneous wind speed at the moment; Indicates the angle between the loading arm and the incoming wind direction; It is The resistance coefficient of each node; S3. Extract displacement, structural stress, and strain energy density indicators to identify weak locations, including weak nodes and weak sections. Specifically, S31, in At time , the node displacement is known to be , then any node Curvature The formula is expressed as: ； The bending stress ; The plastic strain energy density per unit volume is ;in, , represents the bending stress under unit elastic modulus; for The first derivative of ; S32, determine the weak nodes, when any node A node is considered a weak node if it satisfies the following three constraints at the same time: I. Node Maximum stress at , ; II. Node Stress concentration factor at ,in is the mean stress; III. Node The plastic strain energy density per unit volume at ; in, is the preset threshold coefficient; S33, remember the weak node sequence is , K is the total number of weak nodes; the area where the weak node sequence is located is marked as the weak segment area; S4. Introduce an adjustable reinforcement ring structure to optimize the local stiffness of the weak section area, forming a multi-objective optimization scheme for stiffness enhancement and quality control.

2. The method for identifying weak points of loading and unloading arms and optimizing reinforcement rings according to claim 1, characterized in that: Step S1 is specifically as follows: Simulate the random fluctuation characteristics of natural wind and synthesize the fluctuating wind speed time history; the formula is expressed as: ； in, express The instantaneous wind speed at the moment represents the real-time change of the pulsating wind, which is determined by the average wind speed. and random pulsating components; The average wind speed is the stable wind speed component over a long time scale, which is given by meteorological data and design specifications; Indicates the number of discrete frequency components; Represents the random phase angle of each frequency component; The Davenport wind speed power spectral density function is expressed in terms of frequency The value at is expressed as: ； in, Represents the center frequency of the nth frequency component, which is generated as follows: ; Indicates frequency resolution, that is, the interval between adjacent frequency components; Indicates the surface roughness coefficient; Indicates the average wind speed at a height of 10 meters; Indicates the cutoff frequency, which determines the peak position of the spectrum. L is the turbulence integral scale, which is the preset value.

3. The method for identifying weak points of loading and unloading arms and optimizing reinforcement rings according to claim 1, characterized in that: Step S4 specifically includes: S41, based on the weak nodes and weak sections identified in step S3, an adjustable reinforcement ring is arranged in each weak section according to the overrun index corresponding to each weak node; the reinforcement ring parameters include: outer diameter , wall thickness , Reinforcement ring length , reinforcement ring volume , material density , material elastic modulus , the moment of inertia of the cross section where the reinforcement ring and the original loading and unloading arm structure are combined ; S42. Install adjustable reinforcement rings to control the maximum stress of the loading and unloading arm structure in the weak section area. Reduced to yield strength When the maximum stress exceeds the safety range, the adjustable parameters of the reinforcement ring are adjusted to enhance the local stiffness of the weak section. S43. A balance is achieved between the improvement of the local wind resistance stiffness of the reinforcement ring and the overall quality of the reinforcement ring through an optimization algorithm, specifically including: First, the adjustable parameters of the reinforcement ring are recorded as 、 、 , forming a vector group ; Then set the dual objective function for strengthening ring optimization 、 , the formula is: ； ； in, For the weight control objective function, minimize To minimize the overall mass of the reinforcement ring; is the wind resistance performance objective function, maximizing Achieve the maximum improvement in the local wind resistance stiffness of the weak section of the loading and unloading arm structure; The non-dominated sorting genetic algorithm (NSGA-II) is used to process the two objective functions in parallel, and the optimal balance between wind resistance and lightweight is solved by constructing the Pareto front solution set.

4. The method for identifying weak points of loading and unloading arms and optimizing reinforcement rings according to claim 3, characterized in that: Step S42 is specifically as follows: After the adjustable reinforcement ring is installed, the maximum stress of the loading and unloading arm structure in the weak section area is controlled The following inequality is satisfied: ； in, The total equivalent wind stiffness of the loading and unloading arm structure in the weak section area after the reinforcement ring is introduced. is the equivalent wind stiffness of the original structure at the weak section; When the maximum stress exceeds the safety range, the adjustable parameters of the reinforcement ring are automatically adjusted according to the degree of excess, including: outer diameter , wall thickness , Reinforcement ring length , to achieve stiffness enhancement in weak section areas.

5. The method for identifying weak points of loading and unloading arms and optimizing reinforcement rings according to claim 3, characterized in that: The specific process of using the non-dominated sorting genetic algorithm NSGA-II to solve the optimal balance in step S43 is as follows: P1. Initialize the population, for each individual in the population Calculate separately and ; P2. Group all individuals according to the Pareto dominance relationship. If a solution is not inferior to another solution in all objectives and is better in at least one objective, it is considered to dominate it. According to the dominance relationship between individuals, the best individuals are formed into the first-level non-dominated solution set, the second-best individuals are formed into the second-level non-dominated solution set, and so on. Group all individuals. P3. Within the same frontier, calculate the crowding distance between individuals, prioritize evenly distributed solutions, and prevent all individuals from concentrating on one side; P4. After completing selection, crossover, and mutation, a new generation of individuals is generated. The offspring and parent generations are merged to form a candidate set. The objective function is calculated and the non-dominated sorting is repeated. If the maximum algebra and convergence criterion is reached, a set of mutually non-dominated optimal solutions is output to form the Pareto frontier. Otherwise, repeat P1-P4.

Images