Gradient lifting-based suspension bridge construction stage suspender force intelligent optimization method

Abstract

The invention discloses a gradient lifting-based suspension bridge construction stage suspender force intelligent optimization method, and relates to the technical field of bridge construction intelligent optimization. The method sequentially comprises the following steps of: preparing data; defining a model and optimizing a target; training a first tree; determining a splitting point based on the gain; updating the leaf nodes; performing iterative training; predicting new data; analyzing errors; optimizing the suspender force in the construction stage through a particle swarm optimization algorithm; and outputting an optimization result. The accurate mapping relation between the construction stage suspender force and the bridge forming stage suspender force can be efficiently established, the optimal construction stage suspender force distribution is quickly and reversely solved through the global optimization algorithm, and the optimization efficiency and precision are comprehensively improved.

Description

Technical Field

[0001] The present invention relates to the technical field of intelligent optimization of bridge construction, and in particular to a method for intelligent optimization of hanger force during the construction phase of a suspension bridge based on gradient lifting. Background Art

[0002] As an important structural form in modern bridge engineering, suspension bridges are widely used in various complex terrains and long span bridge projects due to their large span and high performance. The hanger is an important load-bearing component connecting the main cable and the bridge deck system in a suspension bridge. The hanger force during the construction phase not only affects the line shape of the completed bridge, but also affects the overall safety, durability and operational performance of the bridge. Therefore, how to reasonably allocate the hanger force during the construction phase to ensure that the hanger force during the completed bridge phase meets the design objectives is a key technical issue in the design and construction of suspension bridges.

[0003] The optimization of the suspender force in the traditional construction stage usually adopts a combination of finite element analysis, manual trial calculation, and repeated iteration. The suspender force in the bridge completion stage is calculated by establishing a finite element model of the suspension bridge and performing iterative calculations, and the suspender force in the construction stage is inferred from this. However, finite element analysis needs to process large-scale bridge models, which has high requirements on computer performance and is time-consuming. It is difficult to meet the needs of rapid adjustment during the construction process. Moreover, due to model simplification and parameter uncertainty, the results of finite element analysis may deviate from the actual situation, resulting in unsatisfactory optimization results. Therefore, the optimization and adjustment of the suspender force currently mainly relies on construction experience for trial-and-error repeated adjustments, which lacks systematicity and automation and is prone to human errors. In addition, there is a complex nonlinear mapping relationship between the suspender force in the construction stage and the bridge completion stage. It is difficult for traditional optimization methods to accurately describe this relationship. With the continuous increase in bridge spans and the rapid development of construction technology, the optimization problem of suspender force gradually presents multi-dimensional and high-complexity characteristics. Traditional optimization methods are often prone to fall into local optimality in high-dimensional search space and lack global search capabilities, resulting in low optimization efficiency and difficult to ensure the quality of optimization results.

[0004] In summary, the traditional optimization method has the disadvantages of long calculation time, insufficient accuracy, reliance on manual adjustment, and difficulty in dealing with nonlinear problems in the optimization of the boom force during the construction phase. Therefore, a new intelligent optimization method is urgently needed to effectively solve the shortcomings of the traditional optimization method. Summary of the invention

[0005] In order to address the shortcomings of the background technology, the present invention provides an intelligent optimization method for the hanger force in the construction stage of a suspension bridge based on gradient boosting, which can efficiently establish an accurate mapping relationship between the hanger force in the construction stage and the hanger force in the bridge completion stage, and quickly inversely calculate the optimal hanger force distribution in the construction stage through a global optimization algorithm, thereby comprehensively improving the optimization efficiency and accuracy.

[0006] To achieve the above object, the present invention adopts the following technical solution: a method for intelligent optimization of the hanger force during the construction phase of a suspension bridge based on gradient lifting, comprising the following steps:

[0007] Step 1: Data preparation

[0008] Assume that there are m hangers in the construction stage of the suspension bridge and the number of samples is n. For the i-th sample, the hanger force in the construction stage is expressed as: X i =[x i1 ,x i2 ,…,x im ], x ij Y represents the construction stage suspender force of the jth suspender of the i-th sample, and the corresponding suspender force in the bridge completion stage is expressed as: i =[y i1 ,y i2 ,…,y im ],y ij represents the suspender force of the jth suspender of the i-th sample at the completion stage, i = 1, 2, ..., n, j = 1, 2, ..., m, and the input suspender force data set at the construction stage is: X = {X 1 ,X 2 ,…,X n}, the output data set of the suspender force in the bridge completion stage is: Y = {Y 1 ,Y 2 ,…,Y n};

[0009] Step 2: Model definition and optimization objectives

[0010] Model mapping relationship: Establish a mapping function f to map the suspender force in the construction stage to the suspender force in the bridge completion stage. The goal of the model is to learn f so that the predicted value and the true value Y i Minimize the error of

[0011] Optimization objective: Use square error as loss function L, Represents y ij The predicted value of

[0012] Objective formula: Minimize the loss function for:

[0013] Step 3: Train the first tree

[0014] Initialization prediction value: In the initial state, the model prediction value is the mean of the objective function,

[0015] Calculate initial residuals: Residuals Represented as the true value yij The current model prediction value The difference:

[0016] Step 4: Determine the split point based on gain

[0017] Gradient and second-order derivative: Using Taylor's second-order expansion of the loss function, the gradient and second-order derivative of each sample are calculated, expressed as follows:

[0018]

[0019] For the sample set D in the current node, we have:

[0020]

[0021] Gain formula: For the split point v t , divide the data into left child node D L and right child node D R ,have:

[0022]

[0023] In the formula, G L and G R Represents the gradient sum of the left child node and the right child node, H L and H R Represent the sum of the second-order derivatives of the left child node and the right child node respectively, λ represents the regularization parameter, and γ represents the splitting penalty term;

[0024] Select the best split point: traverse all split points v t , select the split point with the largest gain:

[0025] Step 5: Update leaf nodes

[0026] Leaf node output value: For a leaf node, its output value is:

[0027] Update prediction value: The model prediction value is updated to: η represents the learning rate;

[0028] Step 6: Iterative training

[0029] Recalculate the residuals:

[0030] Termination condition: the maximum number of trees T is reached or the decrease of the loss function is less than the threshold ε;

[0031] Step 7: Predict new data

[0032] Enter new data: Xnew =[x new,1 ,x new,2 ,…,x new,m ];

[0033] Model prediction: Using the accumulated results of all trees, calculate new prediction values:

[0034]

[0035] Where, T κ (·) represents the prediction function of the κth tree, T κ (X new ) indicates that the new data X is input new Above, the prediction result made by the κth tree;

[0036] Step 8: Error Analysis

[0037] Comparison of the hanger forces predicted by the model at the completion stage and the ideal bridge-building stage suspender force Y * , calculate the error using the following formula:

[0038]

[0039] In the formula, is the predicted suspender force of the jth suspender at the completion stage, is the ideal target suspender force of the jth suspender at the bridge completion stage;

[0040] If the error E is greater than the allowable threshold set by the project, further adjust X new , so that the suspender force in the bridge completion stage meets the ideal target;

[0041] Step 9: Particle swarm optimization algorithm optimizes the boom force during the construction phase

[0042] Optimization goal definition:

[0043] 1) Objective function: The optimized construction phase suspender force X needs to minimize the error between the predicted suspender force in the bridge completion phase and the ideal target. The objective function is as follows:

[0044]

[0045] Where f(X) j represents the suspender force of the jth suspender at the bridge completion stage predicted by the model after optimization;

[0046] 2) Constraints: Define the upper and lower limits of a single boom:

[0047]

[0048] In the formula, and They represent the minimum and maximum allowable values ​​of the j-th boom force respectively;

[0049] Particle Swarm Optimization Algorithm:

[0050] 1) Particle initialization: Initialize N particles, each particle represents a set of construction stage boom forces P i , which is expressed as follows:

[0051] P i =[x i1 ,x i2 ,…,x im ],i=1,2,…,N

[0052] Initialize the particle velocity, expressed as follows:

[0053] v ij =Uniform(-v max ,v max )

[0054]

[0055] Where α is the proportionality coefficient;

[0056] 2) Calculate the fitness of particles:

[0057] 3) Update the particle's historical optimal position and global optimal position:

[0058] The particle's historical optimal position update is expressed as: P i best =P i , if F(P i )<F(P i best );

[0059] The global optimal position update is expressed as: P global =P i , if F(P i )<F(P global );

[0060] 4) Update particle speed and position:

[0061] The particle velocity update is calculated as follows:

[0062]

[0063] The particle position update is calculated as follows:

[0064]

[0065] In the formula, represents the velocity of the ith particle in the jth dimension after the tth iteration, w represents the inertia weight, c 1 represents the individual learning factor, c 2 represents the group learning factor, r 1 and r 2 To randomly select a value in the interval [0,1], represents the value of the position of the i-th particle in the j-th dimension at the t-th iteration;

[0066] 5) Constraint processing:

[0067] Particle Speed ​​Limit:

[0068] Particle position constraints:

[0069] 6) Termination condition: When the global optimal fitness value changes to meet When , stop the iteration;

[0070] Step 10: Output optimization results

[0071] The optimized construction phase boom force: Output the global optimal position P of the particle swarm global :

[0072]

[0073] Verify the optimization effect: The optimized construction stage boom force X opt Input the xgboost model to predict the suspender force at the bridge completion stage:

[0074] Y opt =f(X opt )

[0075] Calculate the error after optimization: Compare the predicted hanger force Y in the bridge completion stage after optimization opt and the ideal value Y * :

[0076]

[0077] Where Y opt,j represents the predicted suspender force of the jth suspender at the bridge completion stage after optimization;

[0078] Output results: Output the optimized construction stage suspender force X opt , Predicted suspender force Y at the bridge completion stage after optimization opt And the optimization error F(X opt ).

[0079] Furthermore, in step nine, the maximum allowable value and the minimum allowed value Respectively meet:

[0080]

[0081] In the formula, σ max Indicates the maximum allowable stress of the hanger material, A j represents the cross-sectional area of ​​the jth hanger rod, x safe Indicates the safety threshold.

[0082] Compared with the prior art, the beneficial effects of the present invention are as follows: the present invention collects a large amount of hanger forces in the construction stage and the bridge completion stage of suspension bridges, combines the gradient boosting algorithm with the particle swarm optimization algorithm, and proposes a high-precision and high-efficiency hanger force optimization method for suspension bridge construction. The method can efficiently establish an accurate mapping relationship between the hanger forces in the construction stage and the bridge completion stage, and quickly inversely calculate the optimal hanger force distribution in the construction stage through the global optimization algorithm, thereby comprehensively improving the optimization efficiency and accuracy, providing scientific support for the hanger tensioning in the construction stage of suspension bridges, effectively improving the construction accuracy and bridge completion quality of the bridge, and ensuring the structural safety and performance of the bridge. BRIEF DESCRIPTION OF THE DRAWINGS

[0083] Figure 1 It is a flowchart of the method of the present invention. DETAILED DESCRIPTION

[0084] The technical solution of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0085] like Figure 1 As shown, a method for intelligent optimization of the hanger force in the construction stage of a suspension bridge based on gradient lifting includes the following steps:

[0086] Step 1: Data preparation

[0087] ① Input data:

[0088] Assume that there are m hangers in the construction stage of a suspension bridge, the hanger force of each hanger is a feature, the number of samples is n, and for the i-th sample, the hanger force in the construction stage is expressed as:

[0089] X i =[x i1 ,x i2 ,…,x im ]

[0090] In the formula, xij represents the construction phase hanger force of the jth hanger of the ith sample, i = 1, 2, …, n, j = 1, 2, …, m.

[0091] ② Output data:

[0092] The corresponding hanger force in the bridge completion stage is expressed by vector as follows:

[0093] Y i =[y i1 ,y i2 ,…,y im ]

[0094] In the formula, y ij It represents the hanger force of the jth hanger of the i-th sample at the bridge completion stage.

[0095] ③Collection representation of data sets:

[0096] Input construction stage suspender force data set: X = {X 1 ,X 2 ,…,X n};

[0097] Output bridge construction stage suspender force data set is: Y = {Y 1 ,Y 2 ,…,Y n}.

[0098] Step 2: Model definition and optimization objectives

[0099] ①Model mapping relationship:

[0100] A mapping function f is established to map the hanger force in the construction stage to the hanger force in the bridge completion stage, which is expressed as follows:

[0101] f:X i →Y i

[0102] The goal of the model is to learn f so that the predicted value and the true value Y i Minimize the error.

[0103] ②Optimization objectives:

[0104] Using square error as the loss function L, it is expressed as follows:

[0105]

[0106] In the formula, Represents y ij The predicted value of .

[0107] ③Target formula:

[0108] Minimize the loss function for:

[0109] Step 3: Train the first tree

[0110] ① Initialize the predicted value:

[0111] In the initial state, the model predicts the value is the mean of the objective function, expressed as:

[0112] ②Calculate the initial residual:

[0113] Residual Represented as the true value y ij The current model prediction value The difference:

[0114] Step 4: Determine the split point based on gain

[0115] ① Gradient and second-order derivative:

[0116] Using Taylor's second-order expansion of the loss function, the gradient and second-order derivative of each sample are calculated, expressed as follows:

[0117]

[0118] For the sample set D in the current node, we have:

[0119]

[0120] ②Gain formula:

[0121] For the split point v t , divide the data into left child node D L and right child node D R ,have:

[0122]

[0123] In the formula, G L and G R Represents the gradient sum of the left child node and the right child node, H L and H R They represent the second-order derivatives of the left child node and the right child node respectively, λ represents the regularization parameter, and γ represents the splitting penalty term.

[0124] ③Choose the best split point:

[0125] Traverse all split points v t , select the split point with the largest gain:

[0126] Step 5: Update leaf nodes

[0127] ①Leaf node output value:

[0128] For a leaf node, the output value is:

[0129]

[0130] ②Update the predicted value:

[0131] The model prediction value is updated to:

[0132]

[0133] In the formula, η represents the learning rate.

[0134] Step 6: Iterative training

[0135] ① Recalculate the residual:

[0136]

[0137] ②Termination conditions:

[0138] Reach the maximum number of trees T:

[0139] κ=T

[0140] When the data scale is small (500 rows or less, 10 features or less), it is recommended that T is [50, 100); when the data scale is medium (greater than 500 rows and less than 100,000 rows, greater than 10 features and less than 100 features), it is recommended that T is [100 to 300); when the data scale is large (more than 100,000 rows, 100 features or more), it is recommended that T is [300 to 500].

[0141] Or, the decrease in the loss function is less than the threshold ε:

[0142] |L (κ) -L (κ-1) |<ε

[0143] When the data size is small, ε=10 is recommended -3 ; For medium data size, ε=10 is recommended -4 ; When the data scale is large, it is recommended that ε = 10 -5 .

[0144] Step 7: Predict new data

[0145] ①Enter new data:

[0146] X new =[x new,1 ,x new,2 ,…,xnew,m ]

[0147] ②Model prediction:

[0148] Using the accumulated results from all trees, calculate new predictions:

[0149]

[0150] Where, T κ (·) represents the prediction function of the κth tree, T κ (X new ) indicates that the new data X is input new The prediction result made by the κth tree.

[0151] Step 8: Error Analysis

[0152] Comparison of the hanger forces predicted by the model at the completion stage and the ideal bridge-building stage suspender force Y * , calculate the error using the following formula:

[0153]

[0154] In the formula, is the predicted suspender force of the jth suspender at the completion stage, is the ideal target suspender force of the jth suspender in the bridge completion stage.

[0155] If the error E is greater than the allowable threshold set by the project, it is necessary to further adjust X new , so that the hanger force in the bridge completion stage meets the ideal target.

[0156] Step 9: Particle swarm optimization algorithm optimizes the boom force during the construction phase

[0157] ①Optimization target definition:

[0158] 1) Objective function:

[0159] Defining the optimized construction phase suspender force X requires minimizing the error between the predicted suspender force in the completed bridge phase and the ideal target. The objective function is as follows:

[0160]

[0161] Where f(X) j It represents the suspender force of the jth suspender in the bridge completion stage predicted by the model after optimization.

[0162] 2) Constraints:

[0163] Define the upper and lower limit constraints of a single hanger:

[0164]

[0165] In the formula, and They respectively represent the minimum and maximum allowable values ​​of the j-th hanger force.

[0166] According to the design standards and engineering requirements, the construction phase of each suspender force needs to meet the material strength limit, so the maximum allowable value The following formula must be satisfied:

[0167]

[0168] In the formula, σ max Indicates the maximum allowable stress of the hanger material, A j represents the cross-sectional area of ​​the jth hanger rod.

[0169] In order to ensure that the boom is always in tension during the construction phase and avoid loosening or failure of the boom, a safety threshold lower than the minimum tension needs to be set, so the minimum allowable value The following formula must be satisfied:

[0170]

[0171] In the formula, x safe Indicates the safety threshold.

[0172] ②Particle Swarm Optimization Algorithm:

[0173] 1) Particle initialization:

[0174] Initialize N particles, each particle represents a set of construction stage suspender forces P i , which is expressed as follows:

[0175] P i =[x i1 ,x i2 ,…,x im ],i=1,2,…,N

[0176] Initialize the particle velocity, expressed as follows:

[0177] v ij =Uniform(-v max ,v max )

[0178] v max Related to the particle position range (i.e., the upper and lower limits of the boom force during the construction phase), in order to prevent particles from moving too fast and jumping out of the search space, v max Determined by the following formula:

[0179]

[0180] In the formula, α is a proportional coefficient, and its value range is 0.1~1.

[0181] 2) Calculate the fitness of particles:

[0182] The fitness value of each particle is calculated by the following formula:

[0183]

[0184] 3) Update the particle's historical optimal position and global optimal position:

[0185] The particle's historical optimal position update is expressed as: P i best =P i , if F(P i )<F(P i best );

[0186] The global optimal position update is expressed as: P global =P i , if F(P i )<F(P global ).

[0187] 4) Update particle speed and position:

[0188] The particle velocity update is calculated as follows:

[0189]

[0190] The particle position update is calculated as follows:

[0191]

[0192] In the formula, represents the velocity of the ith particle in the jth dimension after the tth iteration, w represents the inertia weight, which controls the influence of the current velocity of the particle in the next iteration. The recommended range of w is 0.4 to 0.9, and c 1 represents the individual learning factor, which controls the tendency of the particle to move toward its own historical optimal position, c 2 represents the group learning factor, which controls the tendency of particles to move toward the global optimal position, c 1 and c 2 Recommended range 1.5~2.5, r 1 and r 2 is a random value in the interval [0,1], which is used to increase the randomness of particles. represents the position of the i-th particle in the j-th dimension (the force of the boom during the construction phase) at the t-th iteration, P i best is the optimal historical position of the i-th particle itself, Pglobal is the global optimal position.

[0193] 5) Constraint processing:

[0194] In order to avoid the particle speed being too large or too small, it is usually necessary to constrain the speed to prevent the particle from jumping out of the search space or falling into invalid search. The particle speed is limited by the following formula:

[0195]

[0196] For the particle position, the upper and lower limits of the boom force during the construction phase need to be met:

[0197]

[0198] 6) Termination conditions:

[0199] When the global optimal fitness value changes to meet When , stop the iteration.

[0200] Step 10: Output optimization results

[0201] ① Optimized boom force during construction:

[0202] Output the global optimal position P of the particle swarm global :

[0203]

[0204] ②Verify the optimization effect:

[0205] The optimized construction stage boom force X opt Input the xgboost model to predict the suspender force at the completion stage:

[0206] Y opt =f(X opt )

[0207] ③Calculate the error after optimization:

[0208] Compare the predicted suspender force Y at the bridge completion stage after optimization opt and the ideal value Y * :

[0209]

[0210] Where Y opt,j It represents the hanger force of the j-th hanger in the bridge completion stage predicted after optimization.

[0211] ④Output results:

[0212] Output optimized construction stage boom force X opt, Predicted suspender force Y at the bridge completion stage after optimization opt And the optimization error F(X opt ).

[0213] Example

[0214] This embodiment applies the method of the present invention to the Songhua River Yangmingtan Bridge, specifically as follows:

[0215] Step 1: Data preparation

[0216] ① The Songhua River Yangmingtan Bridge has 30 hangers and a total of 100 samples. Take one of the samples as an example. The hanger force during the construction phase is as follows:

[0217]

[0218] ②The corresponding hanger force at the bridge completion stage is as follows:

[0219]

[0220] ③ Take the first 5 of the 100 samples to display the input construction stage hanger force data set as follows:

[0221]

[0222] The output data set of the suspender force in the bridge completion stage is as follows:

[0223]

[0224] Step 2: Model definition and optimization objectives

[0225] ① Establish a mapping function f to map the suspender force in the construction stage to the suspender force in the bridge completion stage, f:X i →Y i , the goal of the model is to learn f so that the predicted value and the true value Y i Minimize the error.

[0226] ②Use square error as the loss function L, expressed as:

[0227] ③Minimize the loss function for:

[0228] Step 3: Train the first tree

[0229] ①In the initial state, the model predicts the value is the mean of the objective function:

[0230]

[0231] ② The previous 5 samples are shown, the residual Represented as the true value y ij The current model prediction value The difference:

[0232]

[0233] Step 4: Determine the split point based on gain

[0234] Find the best split point v based on the above residual t , let the candidate splitting point of the boom force X be the middle value:

[0235]

[0236] Taking the first split point 881.43 as an example, the data is divided into the left child node D L and right child node D R :

[0237]

[0238] In this embodiment, λ=1 and γ=0.

[0239] Split rules:

[0240] The boom force x≤881.43 enters the left child node, and x>881.43 enters the right child node.

[0241] Split results:

[0242] Left child node (suspender force x≤881.43)

[0243] X L =[922.85], r L =[-296.59]

[0244] Right child node (suspender force x>881.43)

[0245]

[0246] Compute the gradient and:

[0247] G L =∑r L =-296.59, G R =∑r R =-19816.1, H L =1,H R =29

[0248] Calculate the gain:

[0249]

[0250] Taking the first five samples as an example, traverse all split points v t , select the split point with the largest gain:

[0251]

[0252] Step 5: Update leaf nodes

[0253] ①For the leaf node, taking the first 5 samples as an example, its output value is:

[0254]

[0255] ② Update the predicted value and list an update:

[0256]

[0257] The learning rate is 0.01. Taking the first 5 samples as an example, the updated prediction values ​​are as follows:

[0258]

[0259] Step 6: Iterative training

[0260] ① Recalculate the residual:

[0261] ② Termination condition (one of them is met): the maximum number of trees T = 50 is reached, or the decrease in the loss function is less than the threshold ε = 10 -3 .

[0262] Step 7: Predict new data

[0263] ①Enter new data:

[0264]

[0265] ②Model prediction:

[0266] Using the accumulated results from all trees, calculate new predictions:

[0267]

[0268] Step 8: Error Analysis

[0269] The suspender force at the ideal bridge completion stage is:

[0270]

[0271] Comparison of the hanger forces predicted by the model at the completion stage and the ideal bridge-building stage suspender force Y * , calculation error

[0272] Step 9: Particle swarm optimization algorithm optimizes the boom force during the construction phase

[0273] ①Optimization target definition:

[0274] 1) Objective function:

[0275]

[0276] 2) Constraints:

[0277] The force of a single hanger is constrained within the range of [500, 10000].

[0278] ②Particle Swarm Optimization Algorithm:

[0279] 1) Particle initialization:

[0280] The number of particles is set to N = 50, the dimension of each particle is equal to the number of booms m = 30, and the initial position of each particle is P i The random generation range is the same as the boom force constraint range.

[0281] Take α = 1,

[0282] v max =0.1×(10000-500)=950

[0283] The initial velocity of each particle is randomly generated in the range [-950, 950].

[0284] The positions and velocities of the first five particles are shown below:

[0285]

[0286] 2) Calculate the fitness of particles:

[0287] The fitness values ​​of the first 5 particles are as follows:

[0288]

[0289] 3) Update the particle's historical optimal position and global optimal position:

[0290] The particle's historical optimal position update is expressed as: P i best =P i , if F(P i )<F(P i best );

[0291] The global optimal position update is expressed as: P global =P i , if F(P i )<F(Pglobal ).

[0292] 4) Update particle speed and position:

[0293] Taking the first five particles as an example, this embodiment takes one update as an example. Since the initial position of the first generation of particles is its historical optimal position, P i best =P i (0) , P global =P i (0) , w=0.6, c 1 =c 2 =2.0, r 1 =[0.3,0.5,0.6,0.8,0.2], r 2 =[0.7,0.4,0.3,0.5,0.9].

[0294] After one iteration, the speed of the second generation particles is as follows:

[0295]

[0296] The positions of the second generation particles are updated as follows:

[0297]

[0298] 5) Constraint processing:

[0299] In order to avoid the particle speed being too large or too small, it is usually necessary to constrain the speed to prevent the particle from jumping out of the search space or falling into invalid search. The particle speed is limited by the following formula:

[0300]

[0301] For the particle position, the upper and lower limits of the boom force during the construction phase need to be met:

[0302]

[0303] 6) Termination conditions:

[0304] After calculation and iteration:

[0305]

[0306] Stop iteration.

[0307] Step 10: Output optimization results

[0308] ① Output the global optimal position P of the particle swarm global :

[0309]

[0310] ② The optimized construction stage boom force X opt Input the xgboost model to predict the suspender force at the completion stage:

[0311]

[0312] ③ Compare the predicted suspender force Y at the completed bridge stage after optimization opt and the ideal value Y * :

[0313]

[0314] ④ Output the optimized construction stage boom force X opt , Predicted suspender force Y at the bridge completion stage after optimization opt And the optimization error F(X opt ).

[0315] It will be apparent to those skilled in the art that the invention is not limited to the details of the exemplary embodiments described above and that the invention can be implemented in other forms of assembly without departing from the spirit or essential features of the invention. Therefore, the embodiments should be considered in all respects as exemplary and non-restrictive, and the scope of the invention is defined by the appended claims rather than the foregoing description, and it is intended that all variations within the meaning and range of equivalents of the claims be included in the invention. Any reference numeral in a claim should not be considered as limiting the claim to which it relates.

[0316] In addition, it should be understood that although the present specification is described according to implementation modes, not every implementation mode contains only one independent technical solution. This description of the specification is only for the sake of clarity. Those skilled in the art should regard the specification as a whole. The technical solutions in each embodiment may also be appropriately combined to form other implementation modes that can be understood by those skilled in the art.

Claims

1. An intelligent optimization method for the suspender force during the construction phase of a suspension bridge based on gradient lifting, characterized in that: The following steps are involved: Step 1: Data preparation Assume that there are m hangers in the construction stage of the suspension bridge and the number of samples is n. For the i-th sample, the hanger force in the construction stage is expressed as: X i =[x i1 ,x i2 ,…,x im ], x ij Y represents the construction stage suspender force of the jth suspender of the i-th sample, and the corresponding suspender force in the bridge completion stage is expressed as: i =[y i1 ,y i2 ,…,y im ],y ij represents the suspender force of the jth suspender of the ith sample at the completion stage, i = 1, 2, ..., n, j = 1, 2, ..., m, and the input suspender force data set at the construction stage is: X = {X1, X2, ..., X n }, the output data set of the suspender force in the bridge completion stage is: Y = {Y1, Y2, …, Y n }; Step 2: Model definition and optimization objectives Model mapping relationship: Establish a mapping function f to map the suspender force in the construction stage to the suspender force in the bridge completion stage. The goal of the model is to learn f so that the predicted value and the true value Y i Minimize the error of Optimization objective: Use square error as loss function L, Represents y ij The predicted value of Objective formula: Minimize the loss function for: Step 3: Train the first tree Initialization prediction value: In the initial state, the model prediction value is the mean of the objective function, Calculate initial residuals: Residuals Represented as the true value y ij The current model prediction value The difference: Step 4: Determine the split point based on gain Gradient and second-order derivative: Using Taylor's second-order expansion of the loss function, the gradient and second-order derivative of each sample are calculated, expressed as follows: For the sample set D in the current node, we have: Gain formula: For the split point v t , divide the data into left child node D L and right child node D R ,have: In the formula, G L and G R Represents the gradient sum of the left child node and the right child node, H L and H R Represent the sum of the second-order derivatives of the left child node and the right child node respectively, λ represents the regularization parameter, and γ represents the splitting penalty term; Select the best split point: traverse all split points v t , select the split point with the largest gain: Step 5: Update leaf nodes Leaf node output value: For a leaf node, its output value is: Update prediction value: The model prediction value is updated to: η represents the learning rate; Step 6: Iterative training Recalculate the residuals: Termination condition: the maximum number of trees T is reached or the decrease of the loss function is less than the threshold ε; Step 7: Predict new data Enter new data: X new =[x new,1 ,x new,2 ,…,x new,m ]; Model prediction: Using the accumulated results of all trees, calculate new prediction values: Where, T κ (·) represents the prediction function of the κth tree, T κ (X new ) indicates that the new data X is input new Above, the prediction result made by the κth tree; Step 8: Error Analysis Comparison of the hanger forces predicted by the model at the completion stage and the ideal bridge-building stage suspender force Y * , calculate the error using the following formula: In the formula, is the predicted suspender force of the jth suspender at the completion stage, is the ideal target suspender force of the jth suspender at the bridge completion stage; If the error E is greater than the allowable threshold set by the project, further adjust X new , so that the suspender force in the bridge completion stage meets the ideal target; Step 9: Particle swarm optimization algorithm optimizes the boom force during the construction phase Optimization goal definition: 1) Objective function: The optimized construction phase suspender force X needs to minimize the error between the predicted suspender force in the bridge completion phase and the ideal target. The objective function is as follows: Where f(X) j represents the suspender force of the jth suspender at the bridge completion stage predicted by the model after optimization; 2) Constraints: Define the upper and lower limits of a single boom: In the formula, and They represent the minimum and maximum allowable values ​​of the j-th boom force respectively; Particle Swarm Optimization Algorithm: 1) Particle initialization: Initialize N particles, each particle represents a set of construction stage boom forces P i , which is expressed as follows: P i =[x i1 ,x i2 ,…,x im ],i=1,2,…,N Initialize the particle velocity, expressed as follows: v ij =Uniform(-v max ,v max ) Where α is the proportionality coefficient; 2) Calculate the fitness of particles: 3) Update the particle's historical optimal position and global optimal position: The particle's historical optimal position update is expressed as: P i best =P i , if F(P i )<F(P i best ); The global optimal position update is expressed as: P global =P i , if F(P i )<F(P global ); 4) Update particle speed and position: The particle velocity update is calculated as follows: The particle position update is calculated as follows: In the formula, represents the velocity of the ith particle in the jth dimension after the tth iteration, w represents the inertia weight, c1 represents the individual learning factor, c2 represents the group learning factor, r1 and r2 are randomly selected in the interval [0,1], represents the value of the position of the i-th particle in the j-th dimension at the t-th iteration; 5) Constraint processing: Particle Speed ​​Limit: Particle position constraints: 6) Termination condition: When the global optimal fitness value changes to meet When , stop the iteration; Step 10: Output optimization results The optimized construction phase boom force: Output the global optimal position P of the particle swarm global : Verify the optimization effect: The optimized construction stage boom force X opt Input the xgboost model to predict the suspender force at the bridge completion stage: Y opt =f(X opt ) Calculate the error after optimization: Compare the predicted hanger force Y in the bridge completion stage after optimization opt and the ideal value Y * : Where Y opt,j represents the predicted suspender force of the jth suspender at the bridge completion stage after optimization; Output results: Output the optimized construction stage suspender force X opt , Predicted suspender force Y in the completed bridge stage after optimization opt And the optimization error F(X opt ).

2. According to claim 1, a method for intelligent optimization of suspender force during the construction phase of a suspension bridge based on gradient lifting, characterized in that: In step nine, the maximum allowable value and the minimum allowed value Respectively meet: In the formula, σ max Indicates the maximum allowable stress of the hanger material, A j represents the cross-sectional area of ​​the jth hanger rod, x safe Indicates the safety threshold.

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