CN117852150A

CN117852150A - Linear measuring method and system for cable-stayed bridge

Info

Publication number: CN117852150A
Application number: CN202410059860.6A
Authority: CN
Inventors: 唐刚祥; 王威; 韩小雷; 马攀辉; 冯海波; 郭晓涛; 张振杰; 牛朋辉; 张兵兵; 吕宪闯
Original assignee: Road and Bridge International Co Ltd; China Communications Road and Bridge North China Engineering Co Ltd
Current assignee: Road and Bridge International Co Ltd; China Communications Road and Bridge North China Engineering Co Ltd
Priority date: 2024-01-16
Filing date: 2024-01-16
Publication date: 2024-04-09

Abstract

The invention discloses a line type measuring method and a line type measuring system for a cable-stayed bridge; the actual measurement line shape of the main girder before cable replacement is X _r Based on the actual measurement line shape, combining the original design line shape to design a target line shape X after cable replacement _o . Obtaining a vertical displacement influence matrix D _h And cable stress shadow matrix D _σ On the basis of (1) establishing an optimization target of the bridge girder forceThe following requirements are also satisfied: delta T is the difference vector of the optimized cable force relative to the measured cable force; the invention uses LHS algorithm to execute the overpull Ding Lifang sampling, realizes the sectional consideration of the inhaul cable, and samples the parameter space thereof, thereby ensuring that the sample points are uniformly distributed in the whole parameter range. This improves the efficiency and comprehensiveness of the sampling, especially if multiple input parameters are considered to be mutually influencing.

Description

Linear measuring method and system for cable-stayed bridge

Technical Field

The invention relates to the technical field of cable-stayed bridges, in particular to a line type measuring method and a line type measuring system for a cable-stayed bridge.

Background

Along with the development of highway bridge construction industry in China, the highway bridge gradually develops towards the direction of large span and light weight, and the cable-stayed bridge is suitable for the development trend and rapidly develops.

Stay cable is used as main bearing member of large-span cable-stayed bridge, and in bridge health monitoring system, cableForce monitoring takes a vital role. Display according to related statistics ^[1] In the last twenty years, of the subsequent projects of 30 cable-stayed bridges on average, approximately 50% of the projects take construction measures including reinforcement and even dismantling, the causes of which are directly related to the degradation of the mechanical properties of the cables. In addition, in terms of actual operation observation conditions of a plurality of established cable-stayed bridges, cable replacement becomes an indispensable link after the cable-stayed bridges are used for a certain period of time.

In the existing cable replacement engineering, the cable force optimization method mainly can be divided into three main categories ^[2] : cable force optimization for a given stress state, unconstrained cable force optimization, and constrained cable force optimization. Wherein, the constrained cable force optimization method ^[3] The method aims at determining reasonable bending moment distribution in a bridge formation state by taking the equality of positive and negative absolute values of a bending moment envelope graph formed by load combination in a normal use limit state as a target. For the constrained cable force optimization method, the cable force optimization in the cable replacement engineering is substantially consistent with the cable force optimization in the design stage of the cable-stayed bridge. However, in the cable replacement engineering, additional consideration is also required for improvement of the bridge deck line shape.

When the constrained cable force optimization method is used for linear improvement, displacement targets of certain control points are required to be taken into an optimization equation as hard constraint conditions. This practice often results in an unreasonable distribution of internal forces and non-uniformity of cable forces ^[4] . More importantly, only a limited number of control point displacement targets are used as constraint conditions, and severe change of elevation near the control point can be caused ^[5] Thus, the original purpose of improvement of the linearity cannot be achieved.

Based on the above analysis, the technical problems to be solved in the current prior art and the coping mechanism thereof can be categorized into the following two points:

(1) The internal force change and the shape change of the cable are interrelated. On the premise of meeting the stress specification, improvement of the linearity should be pursued as much as possible.

(2) In consideration of various errors in the construction process of the inclined bridge, the cable-changing design must be based on the current internal force and linear state of the cable-stayed bridge. The purpose of the design is to ensure that the stress of the bridge in the operation stage meets the requirement after the replacement of the cable is completed, and simultaneously, the line shape is improved to the maximum extent. Therefore, the original design state should not be simply taken as the target of the cable replacement design.

In addition, the cable replacement engineering, namely the stay cable installation engineering, can effectively prolong the service life of the stay cable if the quality control of the stay cable installation process is considered in the initial construction process of the cable-stayed bridge.

Therefore, the invention aims to provide an intelligent measuring and evaluating method, which takes the technical problems to be solved into consideration, and provides corresponding cable replacement strategy guidance information for the stay cable installation project of initial construction and the subsequent cable replacement project. Therefore, a linear measuring method and a linear measuring system for a cable-stayed bridge are provided.

The citations in this application are:

[1]Li S L，Wei S Y，Bao Y Q，et al.Condition assessment of cables by pattern recognition of vehicle induced cable tension ratio[J].Engineering Structures，2018，155：1-15.

[2] shore Ru Cheng, xiang Haifan impact on optimization of stay cable forces matrix method [ J ]. University of same university, 1998, 26 (3): 235-240.

[3] Weng Shaling the constant-load cable force optimization research [ C ] of main span cable-stayed bridge of sea-facing bridge, chinese society of computational mechanics, 2003, 1053-1058

[4] Chen Zhigang and Zhang Qiwei Cable force optimization and cable replacement primary tension determination in cable-stayed bridge cable replacement project [ R ]. National bridge academy of sciences in China highway society bridge and structural engineering.

[5]Kim,K.S.,Lee,H,S,(2001).Analysis of target configurations under dead loads for cable supported bridges[J].Computers&Structures，79(29-30):2681-2692.

[6] Tang Chenghua practical equation for measuring Soxhlet force by frequency method taking boundary conditions into consideration [ J ]. University of Hunan university report: 2012, 39 (08): 7-13.

[7] Ren Weixin, chedden, practical formula for calculating cable tension from fundamental frequency [ J ]. Journal of civil engineering, 2005, 38 (11): 26-31.

[8] Kong Fanlong influence the application of matrix method in secondary cable adjusting of bridge crane rod of bridge construction [ J ]. Traffic science, 2005, 251:7-9.

Disclosure of Invention

In view of this, it is desirable to provide a line type measuring method and system for a cable-stayed bridge according to an embodiment of the present invention:

in a first aspect, a method for determining the linearity of a cable-stayed bridge comprises:

summary (one) overview

The method aims to solve or alleviate the technical problems in the prior art, namely how to provide corresponding cable changing strategy guidance information for the subsequent cable changing engineering, and under the premise of considering that the stress specification is met in the process, the improvement of the line shape is pursued as much as possible, and the original design state is not taken as the target of cable changing design.

The method takes LHS algorithm as core, and adds several auxiliary algorithms including linear interpolation algorithm, cumulative distribution function algorithm, knuth shuffling algorithm, etc. to realize different linear schemes N _i Comprehensive consideration of uniformity of cable force distribution helps staff obtain more guiding information. Meanwhile, if the D-S evidence theory algorithm is considered to be further executed, different line type schemes N can be adopted for the LHS algorithm _i Provides an adaptive correction mechanism.

And (II) establishing a model:

firstly, the technical scheme needs to determine a cable force optimization model of a cable replacement project: the improvement of the line shape is aimed at, and the uniformity of stress and cable force distribution under combined load is taken as a constraint condition.

The actual measurement line shape of the main girder before cable replacement is X _r Based on the actual measurement line shape, combining the original design line shape to design a target line shape X after cable replacement _o . Based on literature ^[8] Providing a formula to obtain a vertical displacement influence matrix D _h And cable stress shadow matrix D _σ On the basis of (symbols and literature of the two matrices in the present solution) ^[8] To establish an optimization objective Min (Δt) of the bridge forming force:

meanwhile, in the constraint relation, the following needs to be satisfied:

in the above formula: delta T is the difference vector of the optimized cable force relative to the measured cable force;

σ _min is X _r Actually measuring minimum stress vectors of upper and lower edges of the inhaul cable under the combined load of the cable force;

σ _max is X _r Measuring maximum stress vectors of upper and lower edges of the inhaul cable under the combined load of the cable force;

is X _r In the normal use limit state, the minimum limit value of the tensile stress (determined by engineering design);

is X _r In the normal use limit state, the maximum limit value of the tensile stress (determined by engineering design);

the difference vector Δt needs to be further constrained because consideration is given to ensuring uniformity of the stay cable safety coefficient. Since the parameter specification (model) of the stay cable is determined according to the cable force at the beginning of the cable-stayed bridge, the cable force delta T after cable replacement is set _lb And design cable force delta T _lu The difference limit determines the difference vector Δt constraint:

△T _lb ≤△T≤△T _lu

however, in summary of the above equations, the current difference vector Δt has only theoretical guiding significance, but does not have actual guiding significance. Because it captures only the change in the line shape, and its effectiveness is insufficient for the guidance of the actual engineering. But we also suggest from the side that we need to further consider the multidimensional parameter space if a uniform distribution of sampling points in each dimension can be ensured to better represent the whole parameter space. The linear feasibility of the mapping type reaction cable replacement scheme can be realized.

Taking Min (delta T) as an optimization target through the four constraint conditions; based on the measured cable force before cable replacement, the reasonable bridge cable forming force after cable replacement can be obtained.

The context of the present technology has been clarified so far. What follows is: on the premise of reasonably forming the bridge cable force (namely optimizing the target Min (delta T)) after cable replacement, the feasibility of different inhaul cable linear schemes is considered.

(III) technical content:

the actual feasibility of the improvement scheme of the inhaul cable line shape is determined by the following steps:

3.1 step S1, executing LHS algorithm (Latin Hypercube Sampling, LHS, latin hypercube sampling algorithm):

The LHS algorithm is a method for approximate random sampling from the multivariate parameter distribution, and belongs to a Monte Carlo method. It has the property of uniform layering, and can obtain tail sample values with fewer samples, which makes the LHS algorithm more efficient than the normal sampling method. In the technical scheme, the LHS algorithm is used for dividing steel ropes and carrying out stress analysis. Because the LHS algorithm can also be regarded as an efficient sampling method for a multiple function, it is particularly suitable for cases where multiple input parameters need to be considered to interact. By ensuring an even distribution of sampling points in each dimension, the LHS algorithm helps map the entire parameter space, thus better representing possible variations.

3.1.1 step S100, parameter acquisition:

first, key parameters affecting the cable stress are determined. Including the difference vector DeltaT obtained above, and literature-based ^[6-7] Calculating the dimensionless parameters xi, xi of the reflected relative bending rigidity of the current inhaul cable, wherein the smaller the value xi is, the larger the relative rigidity of the inhaul cable is ^[6] 。

3.1.2 step S101, line type development:

and (3) drawing out different line-type schemes for replacing the cable, namely, drawing out a line-type scheme Ni with curve characteristics of cable sweep. There are n linear schemes:

[N ₁ ,N ₂ ,...,N _n ]

Then the segment modeling and overpull Ding Lifang sampling needs to be performed so that the effect of different linear solution characteristics on the rope stress is studied more systematically. The advantage of the overpull Ding Lifang sampling is that it can provide relatively comprehensive parameter space coverage with a relatively small number of samples, which is very helpful for efficient analysis of complex systems. The LHS algorithm ensures that sampling points are evenly distributed in each dimension, thus enabling a more comprehensive consideration of the various conditions within the multidimensional parameter space.

3.1.2.1 step S1010, overpull Ding Lifang sample:

the overpull Ding Lifang sampling will sample in this two-dimensional parameter space, ensuring a uniform distribution of sample points throughout the range.

3.1.2.1.1 parameter space S:

firstly, a parameter space S of a currently selected linear scheme Ni is formulated based on a difference vector delta T and a dimensionless parameter zeta:

S＝[△T _min ,△T _max ]*[ξ _min ,ξ _max ]

△T _min and DeltaT _max Is the minimum and maximum range in which the difference vector DeltaT can take values;

ξ _min and xi _max Is the minimum and maximum range in which the dimensionless parameter ζ can take values.

3.1.2.1.2 distribution:

if the distribution of parameters is considered to help in the robustness analysis of the system. Even if certain changes occur to the system parameters, the sensitivity of the system performance to the parameter changes can be estimated by considering the distribution of the parameters, so that the subsequent LHS algorithm is more robust. It is therefore also necessary to perform probability distribution on the difference vector Δt and the dimensionless parameter ζ. The technical scheme provides two optional modes:

1) Mode one, evenly distributed:

if the construction conditions of the construction site are advanced enough to ensure that the difference vector delta T and the dimensionless parameter zeta can be uniformly distributed in a given range, the probability density function f of uniform distribution _uniform The method comprises the following steps:

wherein a is less than or equal to x is less than or equal to b

x is the difference vector delta T or the dimensionless parameter xi, and a and b are the minimum and maximum values of the difference vector delta T or the dimensionless parameter xi respectively;

2) Mode two, normal distribution:

if the condition of mode one cannot be met in practice, mode two may be a sub-option. Although not as effective as mode one, it can also make the subsequent LHS algorithm more robust; probability density function f of normal distribution _normal The method comprises the following steps:

wherein μ is the mean and σ is the standard deviation; exp is the base of the natural logarithm. The staff is required to give play to subjective activity to carry out assignment according to the ground conditions.

3.1.2.1.3 samples in parameter space S using the surla Ding Lifang sampling method:

this ensures that there are evenly distributed sample points throughout the parameter range. The method comprises the following steps:

a. determining the number of samples M: representing a linear scheme N _i I.e. how many sample points are obtained in the parameter space S.

b. Dividing the (0, 1) interval into M sections: ensuring that each segment contains a uniform distribution.

c. Randomly extracting a value: a value is randomly extracted in each segment. These values represent positions within the respective parameter ranges:

for each segment i, a value u is randomly extracted one at a time _i Where i=1, 2, …, M, u _i Is a random number within the (0, 1) interval. The number of extraction is M.

d. The inverse function mapping by standard normal distribution is the sample: the extracted values are mapped to samples of the standard normal distribution by an inverse function of the standard normal distribution. This helps to ensure that samples are obtained that fit a normal distribution:

the value u to be extracted _i By an inverse function phi of a standard normal distribution ^-1 (inverse transform function) mapping to a standard normal distribution of samples z _i ：

z _i ＝Φ ^-1 (u _i )

Where Φ is the cumulative distribution function of the standard normal distribution:

wherein z is a standard normal distributed random variable, and the calculation mode is as follows:

wherein exp is the base of natural logarithms;

where erf is the error function, which describes the cumulative distribution function of a standard normal distribution, which involves gaussian integration:

t is an integration variable representing an independent variable during integration. dt represents a small change in t, i.e., a infinitesimal. T is divided into tiny portions, each of which has a width dt.

Finally, the cumulative distribution function (Cumulative Distribution Function, CDF) is the integral of the probability density function. For a standard normal distribution, its CDF can be obtained by integrating the probability density function described above:

since this integral does not have a closed form solution, it is necessary to calculate the cumulative distribution function value of the standard normal distribution by means of MATLAB.

e. The sampling order is disordered: executing a Knuth shuffling algorithm to shuffle the sampling order of the samples to ensure randomness of the sample points:

the Knuth shuffling algorithm begins at the end of the array, randomly selects an element to exchange for the element at the current location, and then proceeds to forward selection. This process is random, and thus can effectively shuffle the order of the arrays:

taking all the values extracted in the step d as an array a, wherein the length is M, and the initial sequence is a ₁ ,a ₂ ,...,a _M ；

Generating a random number r from M, wherein the value range is [1, M]Then extract an array a _r Step d is performed again to obtain another sample z _i ；

After reaching this step e again, exchange a _r And a _M Then subtracting 1 from M, obtaining a corresponding array, and then executing the step d again to obtain another sample z _i ；

After reaching this step e again, the above-mentioned exchange is performed again and reduced by 1 until M becomes 1. Thus, after several iterations, the order of array a is disturbed. This process ensures that each element is randomly placed in a different location of the array, thereby achieving the goal of scrambling the sampling order.

This helps to ensure an even distribution of sampling points in the parameter space, thus exploring more fully the various possible linear schemes. If the order of sample points is not disturbed, some bias may result and a particular range of parameters may be more easily selected. Thus by using a random arrangement, this potential bias can be eliminated, making the sampling more fair and comprehensive. This helps to increase the efficiency of the sampling in terms of selecting Knuth shuffling algorithm, especially when a large number of sample points are required.

3.1.2.1.4 the partition number m for each variable is formulated:

latin hypercube sampling requires the same number of partitions m per variable, but does not require the same increase in the number of samples m as the variable increases. Two proposed modes are given in the technical scheme; but no matter which mode is selected, the problem of data excessive aggregation during simple random sampling can be solved, and more uniform parameter space coverage is ensured:

mode one), consider a uniform distribution of the number of partitions m:

if the total number of samples M can be kept unchanged in practice, the sampling points in each dimension are uniformly distributed as much as possible:

where M is the total number of samples. d is the total number of variables (number of dimensions).

This formula determines the number of partitions in each dimension based on the cube root of M1/d. This is designed to distribute the sampling points uniformly in each dimension as much as possible while keeping the total number of samples M unchanged.

Mode two), consider a normal distribution of partition number m:

if the total number of samples M cannot be kept unchanged in practice, especially in latin hypercube sampling, then to ensure that the sampling points in each dimension obey a normal distribution, the number of partitions M in each dimension is determined using a relationship of quantiles and a standard normal distribution.

In the quantiles Q (p) of the normal distribution, p is the probability of the quantiles. The Z (p) representation is used for a standard normal distribution:

alpha significance level, selected to be 0.05.d is the total number of variables (number of dimensions).

This formula is based on the two-sided alpha/2 quantiles of a normal distribution byTo determine the sampling point in each dimension. Taking ceiling function->For ensuring that m is an integer.

3.1.2.2 step S1011, segment modeling:

sample z based on sampling result _i And dimensionless parameters xi, calculate the linear scheme N _i Is defined by the difference vector DeltaT'; the steel cable I is then divided into several sections I, each of which is passed through a distribution function F1 to obtain a corresponding set of difference vectors DeltaTi'.

3.1.2.2.1 the difference vector DeltaT':

in step S1010, the number M of samples represents the linear scheme N to be extracted _i I.e. how many sample points are to be obtained from the parameter space S. These sample points are used to represent different possibilities of variation of the linear scheme. Then dividing the (0, 1) interval into M sections, each section corresponding to a sample point z _i . Such that each sample point z _i Representing one possible variation in the linear scheme.

α _j The weight coefficient, which is a linear interpolation, is a value considered in advance when the allocation function F1 is executed later (the value is set to 0.5 when the allocation function F1 is executed for the first time). The weight coefficient alpha is subjected to subjective activity of staff by combining with the actual environment information _j And performing assignment.

The difference vector deltat' is obtained by adding a correction term based on the value of the dimensionless parameter zeta and the weight of the linear interpolation on the basis of the theoretical difference vector deltat. Thus, Δt' contains the actual adjustment information, making it more practical instructive. Specifically:

1) (theoretical) difference vector Δt: an initial difference vector obtained based on a theoretical model; it has some theoretical guidance, but may not adequately take into account variations and errors in actual engineering.

2) (corrected) difference vector Δt': deltaT' is based on DeltaT according to the corresponding linear scheme N _i After performing the LHS algorithm, the value of the dimensionless parameter ζ and the sample point z are taken into account _i To correct for deltat. It contains more information about the actual project, through sample point z _i The influence of different line type schemes on the difference vector is better reflected.

While these sample points will be used for subsequent segment modeling. Thus, in step S1011, each sample point z _i The wire rope is divided uniformly into segments i and a set of difference vectors Δti' for each segment is obtained by the distribution function F1. Thus, each sample point z _i Corresponding to the linear scheme N _i I, is defined as one segment i of the block.

3.1.2.2.2 performs the allocation function F1:

the allocation function F1 is used to allocate the difference vector Δt' in the sampling result to each segment i:

F1(ΔTi′)＝ΔT

Δti 'is the difference vector of the i-th segment, which is distributed from the total sampling result Δt' by the distribution function F1.

While the assignment function F1 may take the specific form of a linear interpolation algorithm. Because there are M sample points z _i Each sample point feeds back a linear scheme N _i One possible variation of (a) is described. After the (0, 1) interval is divided into M sections, each section corresponds to one sample point z _i 。

The difference vector Δti' can be calculated by linear interpolation for each segment i of the cable. Let ΔTi ' be the difference vector of the ith section, and ΔTa ' and ΔTb ' be two adjacent sample points z, respectively _a And z _b Corresponding difference vector:

this formula shows that for each segment i, its difference vector Δti' is calculated by linear interpolation. Thus, the sample z passing through the sample point is completed _i A process of assigning a difference vector to each segment.

3.2 step S2, stress analysis:

the conversion function F2 is applied to combine the difference vector delta Ti' of all the segment bodies i and the dimensionless parameter xi to obtain the linear scheme N _i Is defined by the correction difference vector deltat ":

ΔT”＝F2(ξ,{ΔTi’})

{ Δti '} is the set of all difference vectors Δti'.

The specific form of the conversion function F2 is:

ΔT”＝∑ _i w·ξ+∑ _i b·{ΔTi′}

w and b are weight coefficients.

3.3. Step S3, judging:

judging the linear scheme N _i Is of the difference vector DeltaT "(N) _i ) Whether the cable force delta T after cable replacement is set _lb And design cable force delta T _lu The difference limit to determine the difference vector Δt constraint:

△T _lb ≤△T”(N _i )≤△T _lu

if the above condition is satisfied, then the scheme N is determined _i Pass, remain in the final set of linear schemes. If the condition is not satisfied, the linear scheme is deleted from the consideration set.

Through the execution of a plurality of rounds of steps S1-S3, m linear schemes which can meet the design requirement are obtained:

[N ₁ ,N ₂ ,...,N _m ]

the engineer can conduct deeper consideration in the subsequent engineering according to the policy guidance of the m linear schemes, including finite element calculation, cost analysis and the like, so as to finally determine the linear scheme which is most suitable for the actual cable replacing engineering. The whole process is a multi-step iterative process, and combines the sampling and analysis of parameter space, the consideration of linear and nonlinear relations and the determination of the final engineering actual conditions.

3.4 second scenario, step S4 is introduced:

for steps S1 to S3 provided in 3.1 to 3.3, the calculation of the difference vector Δt' of S1011 is one of the core points, as described previously: each segment corresponds to a sample point z _i . Such that each sample point z _i Representing one possible variation in the linear scheme.

α _j The weight coefficient, which is a linear interpolation, is a value considered in advance when the allocation function F1 is executed later (the value is set to 0.5 when the allocation function F1 is executed for the first time).

However, the weight coefficient α _j It is not possible to always stay at 0.5 because it is adjusted to environmental factors. The manner given in the previous step S1 is to combine the actual environmental information by the subjective activity of the staff versus the weight coefficient α _j And performing assignment.

In this scenario, however, the D-S evidence theory algorithm of step S4 will be used for the weighting coefficients α _j Assignment is performed, and the introduction of the D-S evidence theory algorithm can also realize an adaptive adjustment mechanism for the steps S1-S3 as a whole.

3.4.1 step S400, obtaining an evidence set A and an evidence set B:

firstly, based on the N linear schemes obtained by linear planning in the step S101, selecting the linear scheme N of the LHS algorithm to be executed currently _i And to the linear scheme N _i Another linear scheme N with minimal differences (e.g. curvature between lines, length of line, etc.) _o ；

Then, through step S1, a plurality of samples of each of the two linear schemes are obtainedz _i And are respectively aggregated to form an evidence set A (linear scheme N _i ) And evidence set B (linear scheme N _o )。

3.4.2Dempster's combination principle:

combining the evidence set A and the evidence set B through a Dempster's combination principle, and outputting a joint trust degree function Bel (A U B); mapping the joint trust function Bel (A U.B) to a [0,1 ]]The interval value between them is used as the weight coefficient alpha _j 。

3.4.2.1 step S4010, calculate the combined confidence score Bel (C):

indicating that evidence A and evidence B have an intersection, < ->Indicating that evidence a and evidence B have no intersection. Likewise, the number of the cells to be processed, And->Indicating that evidence a and evidence B intersect with the set of assumptions C. Bel (C) represents the confidence level for the hypothesis set C (one at [0, 1)]Values within the range).

3.4.2.1 step S4011, combined uncertainty allocation Pl (C):

pl (C) represents the uncertainty for the hypothesis set C (a value in the range of [0,1 ]), which is complementary to Bel (C).

In S4010 to S4011, A _i And B _i Respectively are provided withIs a subset of the evidence A and the evidence B (i.e. sample z _i ) The method comprises the steps of carrying out a first treatment on the surface of the mass is a weight (average of the total number of subsets is selected); c is the "possible set";representing an empty set;

3.4.2.2 step S4013, obtain a joint trust function Bel (A U B):

bel (A) and Pl (A) are trust and uncertainty allocations for the set of evidence A;

bel (B) and Pl (B) are trust and uncertainty allocations for the set of evidence B;

(Pl (a) Σpl (B)) is an uncertainty allocation of the intersection of each of the evidence a and the evidence B.

The specific acquisition mode of (Pl (A) ≡Pl (B)) is as follows:

A _i and B _i Respectively, a subset of evidence a and evidence B. The molecules are the sum of wi of evidence supporting A.cndot.B, and 1 minus this sum gives Pl (A.cndot.B), representing the degree of uncertainty for A.cndot.B.

3.4.2.3 step S402, mapping:

Mapping the joint trust function Bel (A U.B) to a [0,1 ] by a sigmoid function]The interval value between them is used as the weight coefficient alpha _j ：

e is the base of natural logarithms (approximately equal to 2.718); the output value of the sigmoid function approaches 1 when Bel (a ≡b) is large and approaches 0 when Bel (a ≡b) is small. Thus weightingCoefficient alpha _j The size of (a) reflects the size of Bel (a u B).

α _j The method is a linear interpolation weight coefficient, and reflects the overall credibility of different schemes, so that the weight adjustment is more targeted and reasonable. When the overall reliability is higher, the system is more believed about the influence of the relevance evidence of different schemes, and when the overall reliability is lower, the system is more prone to smoothly adjusting the weight to keep the stability of the system.

Second aspect: a line-type assay system for a cable-stayed bridge, the system comprising a processor, a register coupled to the processor, the register having stored therein program instructions which, when executed by the processor, cause the processor to perform a line-type assay method and system for a cable-stayed bridge as described above.

Summarizing, compared with the prior art, the linear measuring method and system for the cable-stayed bridge provided by the invention have the following beneficial effects:

1. Super latin cube sampling: the invention uses LHS algorithm to execute the overpull Ding Lifang sampling, realizes the sectional consideration of the inhaul cable, and samples the parameter space thereof, thereby ensuring that the sample points are uniformly distributed in the whole parameter range. This improves the efficiency and comprehensiveness of the sampling, especially if multiple input parameters are considered to be mutually influencing.

2. The linear scheme considers: the invention introduces the consideration of different linear schemes, systematically researches the influence of different linear scheme characteristics on the cable stress through LHS algorithm and piecewise modeling, and is superior to the traditional technology which relies on experience or intuition. Meanwhile, when judging whether the linear scheme is qualified, the limit value of the difference between the cable force after cable replacement and the designed cable force is considered, so that the method is closer to the requirement of actual engineering.

3. Adaptive correction mechanism: the invention can further introduce the D-S evidence theory, considers different environmental factors encountered by the LHS algorithm and applies the factors to form a weight distribution conversion adjustment strategy, so that the LHS algorithm can take into consideration different factors encountered by different linear schemes and conflicts and uncertainties generated by the factors of the current linear schemes, and can carry out autonomous adjustment and correction, thereby being beneficial to the system to be more adaptive and robust in the face of new data and changes.

On the basis of the three-point beneficial effects, the service life of the stay cable can be effectively prolonged in the installation process of the stay cable in the initial construction of the cable-stayed bridge.

Drawings

In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings that are required in the embodiments or the technical descriptions will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present application, and other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.

FIG. 1 is a schematic flow chart of the method of the present invention;

FIG. 2 is an abstract view of cable segmentation of the present invention;

Detailed Description

In order that the above objects, features and advantages of the invention will be readily understood, a more particular description of the invention will be rendered by reference to the appended drawings. In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention. This invention may be embodied in many other forms than described herein and similarly modified by those skilled in the art without departing from the spirit of the invention, whereby the invention is not limited to the specific embodiments disclosed below;

Embodiment one: as shown in fig. 1, in the line type measuring method of the cable-stayed bridge, the primary task is to determine a cable force optimizing model of a cable replacement project. Wherein the actual measurement line of the main girder is X before cable replacement _r Based on the actual measurement line shape, combining the original design line shape to design a target line shape X after cable replacement _o . Based on literature ^[8] The provided formula obtains a vertical displacement influence matrix D _h And cable stress shadow matrix D _σ On the basis of (a), the optimization objective aims at minimizing the difference between the measured cable force and the target cable force. Concrete embodimentsIn other words, by calculating the vertical displacement influence matrix D _h The norm between the bridge forming cable force and the optimized cable force difference vector delta T is measured, and an optimized target Min (delta T) of the bridge forming cable force is established as a core; meanwhile, the constraint condition ensures that the cable force after cable replacement is within a certain range, and considers the minimum and maximum stress of the upper edge and the lower edge caused by the combined load of the inhaul cable under the actually measured cable force:

meanwhile, in the constraint relation, it is also necessary to ensure that the difference vector Δt is within a certain range:

the model aims at optimizing the line shape of the bridge by adjusting the cable force so as to meet the design requirement and ensure the stability of the structure.

In the present embodiment, it is necessary to develop a plurality of cable line patterns N in advance _i For a pair ofEach cable line type scheme executes the model to obtain each line type scheme N _i Corresponding delta T with theoretical guidance significance; the different line schemes of the replacement rope are drawn, namely the line scheme N of the curve characteristic of the steel rope sweep _i . There are n linear schemes:

[N ₁ ,N ₂ ,...,N _n ]

then based on the cable force optimization model of the cable replacement engineering, executing an LHS algorithm (Latin Hypercube Sampling, LHS, latin hypercube sampling algorithm) of the step S1: the LHS algorithm is considered as a sampling for the multiple function for the cable type scheme N that needs to be considered _i The case where the plurality of segments i of (a) affect each other. By ensuring an even distribution of sampling points in each dimension, the LHS algorithm helps map the entire parameter space, thereby better representing the cable-line type scheme N _i Possible variations. It comprises substeps S100 to S101. The process of sub-steps S100-S101 ensures that there are evenly distributed sample points in each dimension to better represent the entire parameter space. In this way, the engineer can pass through a plurality of guy cable type schemes N _i The influence of different linear schemes on the cable stress is known, so that cable replacement engineering of the cable-stayed bridge is guided more comprehensively.

In the present embodiment, regarding step S101: segment modeling and overpull Ding Lifang sampling were performed so that the effect of different linear solution characteristics on rope stress was studied more systematically. The advantage of the overpull Ding Lifang sampling is that it can provide relatively comprehensive parameter space coverage with a relatively small number of samples, which is very helpful for efficient analysis of complex systems. The LHS algorithm ensures that sampling points are evenly distributed in each dimension, thus enabling a more comprehensive consideration of the various conditions within the multidimensional parameter space. Which will specifically include sub-steps S1010-S1011.

In the present embodiment, regarding step S1010, the overpull Ding Lifang samples:

the overpull Ding Lifang sampling will sample in this two-dimensional parameter space, ensuring a uniform distribution of sample points throughout the range. Wherein the current selection is firstly based on the difference vector delta T and the dimensionless parameter zeta One selected line type scheme N _i Is drawn up in the parameter space S; it is a two-dimensional region, denoted as:

S＝[△T _min ,△T _max ]*[ξ _min ,ξ _max ]

ξ _min and xi _max Is the minimum and maximum range in which the dimensionless parameter ζ can take values. This value requires engineers to make a conservative determination based on the design parameters of their cable-stayed bridges.

The sample may then be super-pulled Ding Lifang to sample in this two-dimensional parameter space, ensuring a uniform distribution of sample points throughout the range. Among other things, the advantage of overpull Ding Lifang sampling is that it provides relatively comprehensive parameter space coverage with a relatively small number of samples. Because at relatively small sample numbers, the overpull Ding Lifang sampling can provide relatively comprehensive parameter space coverage. By designing the distribution of sample points, the sampling method can better capture the change of the parameter space, thereby reflecting the behavior of the system more comprehensively. This is critical for complex system analysis of cable-stayed bridges, as the performance of the system is often affected by a number of parameters. By ensuring that there are evenly distributed sample points throughout the parameter range, it effectively helps to analyze complex systems such as cable linear stresses of cable stayed bridges. Because a uniform distribution throughout the parameter space helps to avoid excessive aggregation or excessive dispersion of samples, the quality of sampling of the parameter space is improved. This is critical to ensure that the representativeness of the sample and the change in system behavior under different parameter combinations is accurately captured. Under the situation of a cable-stayed bridge, sample points which are uniformly distributed in the whole parameter range of the wire rope linear scheme are ensured, and the stress change corresponding to the wire rope linear scheme can be more comprehensively known.

In the present embodiment, regarding step S1010, it is also necessary to consider the distribution setting of the parameters:

if the distribution of parameters is considered to help in the robustness analysis of the system. Even if certain changes occur to the system parameters, the sensitivity of the system performance to the parameter changes can be estimated by considering the distribution of the parameters, so that the subsequent LHS algorithm is more robust. It is therefore also necessary to perform probability distribution on the difference vector Δt and the dimensionless parameter ζ. This embodiment provides two alternative modes:

1) Mode one, evenly distributed:

wherein a is not less than x is not less than b

2) Mode two, normal distribution:

wherein mu is the mean value, sigma is the standard deviation, and staff is required to perform subjective activity assignment according to the actual field conditions; exp is the base of the natural logarithm.

In this embodiment, regarding the sampling of the parameter space S in step S1010 using the overpull Ding Lifang sampling method, the operation steps include a to e:

in this scheme, step a. Determine the number of samples M: representing a linear scheme N _i The number of samples to be extracted, i.eHow many sample points are obtained in the parameter space S.

In particular, in practical applications, the choice of the number of samples M is generally based on a balance of complexity and sampling accuracy of the parameter space S. In general, the larger M, the more accurate the sampling, but the computation cost increases accordingly.

In the scheme, step b, the (0, 1) interval is divided into M sections: ensuring that each segment contains a uniform distribution.

In particular, step b may divide the interval (0, 1) uniformly into M segments to ensure a sufficient uniform distribution of sample points throughout the range. Each segment has a width of 1/M. This can be achieved by simple mathematical calculations, for example, the start of the ith segment is (i-1)/M and the end is i/M.

In this scheme, step c. Randomly extract a value: a value is randomly extracted in each segment. These values represent positions within the respective parameter ranges:

for each segment i, a value u is randomly extracted _i Where i=1, 2, …, M, u _i Is a random number within the (0, 1) interval.

Specifically, the random number can be realized by using a random number generation algorithm, ensuring each u _i Are uniformly distributed random numbers.

Specifically, steps a-c are the bedding of subsequent steps d-e, which aim to generate evenly distributed sample points in the parameter space S by overpull Ding Lifang sampling, providing a comprehensive parameter range coverage for subsequent analysis. This sampling method is very helpful for efficient analysis of complex systems, especially in view of the multidimensional parameter space and parameter interactions of the cable-stayed bridge.

In this scheme, step d. Mapping into samples by an inverse function of the standard normal distribution: the extracted values are mapped to samples of the standard normal distribution by an inverse function of the standard normal distribution. This helps to ensure that samples are obtained that fit a normal distribution:

the value u to be extracted _i By an inverse function phi of a standard normal distribution ^-1 Mapping (inverse transform function) to standard normal distributed samples z _i ：

z _i ＝Φ ^-1 (u _i )

Where Φ is a cumulative distribution function of the standard normal distribution, the cumulative distribution function Φ (z) of the standard normal distribution describes the probability that the random variable is equal to or smaller than z in the standard normal distribution:

where z is a random variable of a standard normal distribution, describing the probability density of the random variable at z in the standard normal distribution. The calculation mode is as follows:

wherein exp is the base of natural logarithms;

Specifically, the MATLAB procedure described above is:

% random variable

z_values＝[X,X,X,X,X]；

% calculation of cumulative distribution function value of standard normal distribution

cdf_values＝normcdf(z_values)；

% display results

disp ('random variable z:');

disp(z_values)；

disp ('cumulative distribution function value of normal distribution:');

disp(cdf_values)；

the norm cdf (z_values) in the above procedure calculates the cumulative distribution function value of the standard normal distribution corresponding to these variables.

In this scheme, step e. Scramble the sampling order: executing a Knuth shuffling algorithm to shuffle the sampling order of the samples to ensure randomness of the sample points:

taking all the values extracted in the step d as an array a, wherein the length is M, and the initial sequence is as follows:

a ₁ ,a ₂ ,...,a _M

It will be appreciated that the purpose of step e is to ensure an even distribution of sample points in the parameter space, thereby exploring more fully the various possible linear schemes. If the order of sample points is not disturbed, some bias may result and a particular range of parameters may be more easily selected. By using a random arrangement, this potential bias can be eliminated, making the sampling more fair and comprehensive. The Knuth shuffling algorithm is chosen to help increase the efficiency of sampling, especially when a large number of sample points are required, as it is an efficient random permutation algorithm. This helps to better represent the entire parameter space, providing more accurate results for subsequent simulations and analyses.

In this embodiment, when executing steps a to e, the specific implementation manner of the partition number m of each variable needs to be formulated is as follows:

Specifically, mode one considers a uniform distribution of the partition number m:

It will be appreciated that pattern one ensures an even distribution of sampling points in each dimension by the cube root calculation based on M1/d. This helps to maintain full coverage of the sample points in the parameter space, avoiding situations where certain regions are over-sampled or under-sampled. The partition number in each dimension can be flexibly controlled by adjusting the total sample number M and the variable total number d, so that different sampling requirements can be met.

Specifically, mode two considers the normal distribution of partition number m:

It will be appreciated that the pattern two takes into account the normal distribution, ensuring that the sampling points in each dimension follow the normal distribution. It may be more consistent with the distribution characteristics of the dynamic real data, helping to reflect the characteristics of the parameter space more accurately. By taking into account the quantiles and significance level of the normal distribution, the pattern two can flexibly adjust the number of partitions in each dimension even if the total number of samples M is not fixed. This provides greater flexibility in adapting to data sets of different sizes and characteristics.

In the present embodiment, regarding step S1011, segment modeling: sample z based on sampling result _i And dimensionless parameters xi, calculate the linear scheme N _i Is defined by the difference vector DeltaT'; the steel cable I is then divided into several sections I, each of which is passed through a distribution function F1 to obtain a corresponding set of difference vectors DeltaTi'.

Specifically, referring to fig. 2, the black thick lines in the drawing are inhaul cable illustrations, and the black thick lines on the left and right sides are two different inhaul cable line type schemes N _i The method comprises the steps of carrying out a first treatment on the surface of the The broken line squares in the figure are "the wire rope I is uniformly divided into a plurality of segments I", i.e. each broken line square represents a segment I. Fig. 2 can also be understood as a geometric visualization of the LHS algorithm.

Specifically, the steel cable I is uniformly divided into a plurality of sections I, the sections I can be divided based on the characteristics and the requirements of actual engineering, and each section after division can fully reflect the characteristics of the steel cable.

Specifically, with respect to calculating the difference vector Δt': this vector represents the linear scheme N _i Changes in parameter space. This calculation is based on the number of samples M and the manner of linear interpolation.

Specifically, regarding the number of samples M and the sampling point z _i : the number of samples M represents the linear scheme N to be extracted _i I.e. how many sample points are obtained from the parameter space S. Dividing the (0, 1) interval into M sections, each section corresponding to a sample point z _i . Such that each sample point z _i Representing one possible variation in the linear scheme. The calculation of the difference vector Δt' is accomplished by means of linear interpolation, expressed as follows:

α _j The weight coefficient, which is a linear interpolation, is a value considered in advance when the allocation function F1 is executed later (the value is set to 0.5 when the allocation function F1 is executed for the first time). The actual environment information is combined later, and the weight is given by the subjective activity of the staffCoefficient alpha _j And performing assignment.

Sample z _i The sampling points are considered in this expression, representing one possible variation of the linear scheme.

This calculation is based on the idea of linear interpolation, which results in an overall difference vector Δt' by linear combination of M sample points. Thus, each sample point corresponds to one Δti', representing the variation of the linear scheme at different parameter points.

It will be appreciated that the core idea of a linear interpolation algorithm is to estimate the value of an unknown point from the linear relationship of known data points. In a linear version of the cable-stayed bridge, linear interpolation is used to estimate the difference vector Δti' at each sampling point.

Specifically, the interpolation weight coefficient α _j The function of (3): in the interpolation process, the weight coefficient alpha _j Can be seen as the contribution of each sample point in the interpolation. It represents the sampling point z _i The degree of influence on the difference vector Δti'. The initial setting of 0.5 is to treat the effect of two adjacent sample points equally in interpolation.

Specifically, calculation of linear combination: the difference vector DeltaT' is obtained by combining the theoretical difference vector DeltaT with M sample points z _i And linearly combining. This combination is weighted by interpolation alpha _j And dimensionless parameters ζ.

Further, by linear interpolation, other points can be estimated between known sample points, enabling a more comprehensive coverage of the entire parameter space. This helps to more fully understand the behavior of the linear scheme at different parameter points. Linear interpolation makes the transition between adjacent sample points smooth, as it is estimated by a linear relationship. This helps to better understand the continuity of the parameters during the course of the change. Interpolation weight coefficient alpha _j The subjective assignment of (2) enables engineers to adjust interpolation results to a certain extent, and subjective experience is flexibly applied according to actual conditions, so that actual engineering requirements are better met.

Thus, linear interpolation is an effective method by taking a step between known pointsThe linear estimation obtains more comprehensive parameter space information and is helpful for better understanding the linear scheme N _i Is described herein).

Meanwhile, the difference vector delta T' is obtained by adding a correction term based on the theoretical difference vector delta T according to the value of the dimensionless parameter zeta and the weight of linear interpolation. Thus, Δt' contains the actual adjustment information, making it more practical instructive. Specifically:

Further, the allocation function F1 is executed in step S1011: the allocation function F1 is used to allocate the difference vector Δt' in the sampling result to each segment i:

F1(ΔTi′)＝ΔT

Preferably, the specific form of the allocation function F1 may be a linear interpolation algorithm. Because there are M sample points z _i Each sample point feeds back a linear scheme N _i One possible variation of (a) is described. After the (0, 1) interval is divided into M sections, eachThe segment corresponds to a sample point z _i . The difference vector Δti' can be calculated by linear interpolation for each segment i of the cable. The expression of the linear interpolation algorithm is:

this algorithm shows that for each segment i its difference vector Δti' is calculated by linear interpolation. Thus, the sample z passing through the sample point is completed _i A process of assigning a difference vector to each segment. Wherein,

Δti': the difference vector of the i-th segment is represented, which is distributed from the total sampling result Δt' by the distribution function F1.

z _i : the expression indicates the sample point corresponding to each segment i of the rope, reflecting the linear scheme N _i One possible variation of (a). After the (0, 1) interval is divided into M sections, each section corresponds to one sample point z _i 。

Δta 'and Δtb': respectively two adjacent sample points z _a And z _b A corresponding difference vector.

Specifically, the specific implementation manner of the linear interpolation algorithm is as follows:

p1, determining the neighboring sample points z _a And z _b : for each segment i, two adjacent sample points z are found _a And z _b These two points correspond to two possible variations in the linear scheme, respectively.

P2, linear interpolation calculation ΔTi': by using the linear interpolation algorithm, the sample point z is passed _i The position in the (0, 1) interval and the adjacent sample point z _a And z _b And calculating the difference vector delta Ti' of the ith section.

P3, repeating P1 to P2: the calculation process is repeatedly executed for each segment i, and the distribution process of the difference vector delta T' of the sampling result to each segment is completed.

It will be appreciated that since the stress points of the cable are at the two points of its head, and therefore its stress distribution is uniform for each segment i, performing linear interpolation is provided that the variation between two adjacent points is linear, and when the variation between the difference vectors Δta ' and Δtb ' is relatively small and linear, the linear interpolation maintains the linear relationship between the adjacent points by the principle of a similar triangle, and thus Δti ' can be accurately calculated. I.e. in two similar triangles the proportion of corresponding sides is equal. Here, the triangle formed by Δta ' and Δtb ' is similar to the triangle formed by Δti '.

Thus, the linear interpolation algorithm can perform efficient estimation between known difference vectors, so that the difference vector Δti' of each segment shows a smooth trend of variation as a whole, which helps to more fully understand the possibility of the linear scheme.

In the present embodiment, regarding step S2, stress analysis: the conversion function F2 is applied to combine the difference vectors delta Ti 'of all the segment bodies i and the dimensionless parameters xi to obtain a corrected difference vector delta T' of the linear scheme Ni:

ΔT”＝F2(ξ,{ΔTi’})

{ Δti '} is the set of all difference vectors Δti'.

Preferably, the specific form of the conversion function F2 is:

ΔT”＝F2(ξ,{ΔTi’})＝∑ _i w·ξ+∑ _i b·{ΔTi′}

w and b are weight coefficients.

Specifically, the effect of the weight coefficient w: and the dimensionless parameters xi are linearly combined through the weight coefficient w, and the correction of the dimensionless parameters to the linear scheme is introduced to reflect the influence of the dimensionless parameters to the overall stress.

Preferably, the assignment formula of the weight coefficient w is:

MinJ(w)＝[w ₁ ,w ₂ ,...,w _n ]

j is Particle Swarm Optimization (PSO), minJ is a minimization objective function, targeting at minimization stress uniformity; w (w) ₁ ,w ₂ ,...,w _n Is the search space for the weight coefficient w.

Illustratively, the minimization of the objective function minJ is performed by an existing particle swarm algorithm, and this embodiment illustratively provides a MATLAB procedure:

function stress_uniformity＝StressUniformityFunction(w)

% measure of calculated stress uniformity

% w is the weight coefficient vector

% represents the matrix stress of each section of the inhaul cable, each column corresponds to one section, and each row corresponds to one sample

% stress_matrix (i, j) represents stress of the j-th segment in the i-th sample

% calculation of average stress per segment

mean_stress＝mean(stress_matrix,1)；

% calculation of the weighted average stress corresponding to the weight coefficient

weighted_mean_stress＝w*stress_matrix；

% calculate the difference between stress at each segment and the weighted average stress

stress_difference＝abs(stress_matrix-weighted_mean_stress)；

% calculate the standard deviation of stress for each segment as a measure of stress uniformity

stress_uniformity＝std(stress_difference,0,1)；

% PSO parameter settings

options＝optimoptions(@particleswarm,'SwarmSize',50,'MaxIterations',100)；

% execution of PSO algorithm

[w_optimal,cost_optimal]＝particleswarm(@objectiveFunction,num_varia bles,lb,ub,options)；

% output results

disp ('optimal weight coefficient:'); disp (w_optimal); disp ('minimum objective function value:'); disp (cost_optimal);

end

in the above procedure, the stressuniformyl function accepts as input a weight coefficient vector w and calculates the difference between each segment stress and the weighted average stress. Finally, the standard deviation of the stress of each segment is calculated as a measure of the stress uniformity. The objective function is an objective function that needs to be minimized, and parameters of the StressUniformityFunction, PSO algorithm called inside this function can be adjusted according to actual problems. The particle swarm size was set to 50 and the maximum number of iterations was 100 in this procedure. The staff member may draw other values as appropriate based on actual computing resources.

Specifically, the effect of the weight coefficient b: the difference vector delta Ti' is linearly combined through the weight coefficient b, and the correction of the difference vector to the linear scheme is introduced to reflect the influence of the difference vector of each section on the overall stress.

Preferably, the weight coefficient b is also obtained using a particle swarm algorithm, the MATLAB procedure of which is as follows:

function optimized_weights＝particleSwarmOptimization()

% delta_T_matrix represents a matrix of difference vectors, one for each column and one for each row

% delta_T_matrix (i, j) represents the difference vector of the j-th segment in the i-th sample

The objective function of the% particle swarm algorithm is a negative value of stress uniformity, i.e., minimizing stress uniformity

objective_function＝@(weights)-StressUniformityFunction(weights,delta_T_matrix)；

Parameter setting of a% particle swarm algorithm

options＝optimoptions('particleswarm','SwarmSize',50,'MaxIterations',100)；

% run particle swarm algorithm for optimization

optimized_weights＝particleswarm(objective_function,numel(delta_T_ma trix),[],[],options)；

end

functionstress_uniformity＝StressUniformityFunction(b,delta_T_matrix)

% the function is used to calculate a measure of stress uniformity

% b is the vector of weight coefficients

% calculation of the linear combinations corresponding to the weight coefficients

weighted_delta_T＝weights*delta_T_matrix；

% calculation of the difference between the stress of each segment and the linear combined stress

stress_difference＝abs(delta_T_matrix-weighted_delta_T)；

stress_uniformity＝std(stress_difference,0,1)；

% output results

end

in this scenario, the principle is similar for the weight coefficients w and b described above, and the particle swarm algorithm starts with a randomly generated particle swarm. Each particle represents a potential solution (i.e., the value of a weight coefficient). Initially, each particle has a random position and velocity. The goal of the population of particles is to minimize a specific objective function by adjusting the weighting coefficients. In the above procedure, the objective function is a negative value of stress uniformity, i.e., minimizing stress uniformity. The definition of the objective function is in the function StressUniformityFunction.

Updating the position and velocity of the particles: each particle updates its location and velocity based on its current location and velocity, as well as the optimal solution in the population and the historical optimal solution for the individual. This is achieved by the following formula:

υ _ij ＝w·υ _ij +c ₁ ·r ₁ ·(pbest _ij -x _ij )+c ₂ ·r ₂ ·(gbest _j -x _ij )

where vij is the velocity of the particle, xij is the position of the particle, pbestj is the individual optimal solution of the particle, gbestj is the historical optimal solution of the whole population, w is the inertial weight, c1 and c2 are acceleration coefficients, and r1 and r2 are random numbers. The value of the objective function, i.e. the stress uniformity, is then calculated from the current position of the particles. If the fitness corresponding to the current position is better than the individual history optimal solution of the particles, updating the individual history optimal solution; and if the fitness corresponding to the current position is better than the historical optimal solution of the whole group, updating the historical optimal solution of the whole group. The above steps are then repeated until a stop condition is met (e.g., a maximum number of iterations is reached or the objective function value is sufficiently small). And after the particle swarm algorithm is finished, the optimal weight coefficient is a solution when the stress uniformity is minimized. These optimal weighting coefficients are in optimized_weights.

It will be appreciated that the above weight coefficients w and b are not limited to the assignment of the above procedure either. The subjective activity of the cable can be given by a person skilled in the art by combining the actual cable stress parameter and the actual form.

In the present embodiment, regarding step S3, the criterion of judgment is:

△T _lb ≤△T”(N _i )≤△T _lu

Through the execution of several rounds of steps S1 to S3 as described in the present embodiment, m linear schemes capable of satisfying the design requirement are obtained:

[N ₁ ,N ₂ ,...,N _m ]

engineers can take more in-depth consideration in subsequent projects according to the policy guidelines of the m linear schemes.

It will be appreciated that this step completes the final screening of the wire-type solution, ensuring that the selected solution meets design requirements in terms of cable force. The final obtained linear scheme set can be used as the basis for the more deeply considered by engineers in the subsequent engineering, including finite element solution, cost analysis and the like, so as to finally determine the linear scheme which is most suitable for the actual cable changing engineering. The linear scheme not only can meet the premise of stress specification, but also pursues improvement of the linear structure, and does not simply take the original design state as the target of cable replacement design; the whole process is a multi-step iterative process, and combines the sampling and analysis of parameter space, the consideration of linear and nonlinear relations and the determination of the final engineering actual conditions. The comprehensive method can effectively guide engineering decisions and ensure that the cable-changing engineering of the cable-stayed bridge can meet design requirements.

Embodiment two: the present embodiment further provides a step S4 on the basis of the first embodiment:

in steps S1 to S3 of the first embodiment, the calculation of the difference vector Δt' of step S1011 is one of the core points, as described previously: each segment corresponds to a sample point z _i . Such that each sample point z _i Representing one possible variation in the linear scheme.

α _j The weight coefficient, which is a linear interpolation, is a value considered in advance when the allocation function F1 is executed later (the value is set to 0.5 when the allocation function F1 is executed for the first time). In the scheme of the present embodiment, however, the D-S evidence theory algorithm of step S4 will be used for the weighting coefficients α _j Assignment is performed, and the introduction of the D-S evidence theory algorithm can also realize an adaptive adjustment mechanism for the steps S1-S3 as a whole.

In the present embodiment, with respect to step S400, evidence set a and evidence set B are acquired:

Then, through step S1, a plurality of samples z of each of the two linear schemes are obtained _i And are respectively aggregated to form an evidence set A (linear scheme N _i ) And evidence set B (linear scheme N _o )。

In this embodiment, the Dempster's combination principle then needs to be performed:

Specifically, with respect to step S4010, a combined trust allocation Bel (C) is calculated:

indicating that evidence A and evidence B have an intersection, < ->Indicating that evidence a and evidence B have no intersection. Likewise, the number of the cells to be processed,and->Indicating that evidence a and evidence B intersect with the set of assumptions C. Bel (C) represents the confidence level for the hypothesis set C (one at [0, 1)]Values within the range). By means of the Dempster's combination principle, the two sets of Bel (C) information are combined to obtain a more comprehensive and reliable assessment of the confidence level of the hypothesis set C. This step helps to integrate information from different evidence and increase confidence levels for different states.

Specifically, evidence set a (linear scheme N _i ) And evidence set B (linear scheme N _o ) By considering a similar linear scheme, the system is able to more fully evaluate confidence levels in different states. This helps to increase the robustness of the model, making it more adaptive to potential uncertainties and variations. Similarity line Scheme N _o For the currently calculated linear scheme N _i Additional information about the system behavior is provided, which helps introduce more evidence of diversity. By comprehensively considering the confidence levels of different states, the system can be better adapted to various engineering situations.

Specifically, the evidence set a (linear scheme N _i ) And evidence set B (linear scheme N _o ) By doing the synthesis, the system can more deeply understand the differences between different line patterns. This provides a more comprehensive basis for engineering decisions and solution selections, and engineers can better understand the merits of each solution. Also in engineering practice, design conditions may vary or there may be some degree of uncertainty. The confidence level of the different states is considered to make the system more flexible and better able to accommodate possible future changes and uncertainties. At the same time comprehensively considering evidence set A (linear scheme N _i ) And evidence set B (linear scheme N _o ) Confidence levels for different states of (c) may provide a more reliable basis for engineering decisions. This helps engineers make more intelligent choices, reducing the risk of decision making.

Specifically, regarding step S4011, the combined uncertainty allocation Pl (C): pl (C) is the uncertainty allocation to hypothesis set C from the perspective of evidence sets A and B, respectively. In a system, both of these can be considered in combination:

Pl (C) represents the uncertainty for the hypothesis set C (a value in the range of [0,1 ]), which is complementary to Bel (C). By combining Pl (C) of different evidence, a more comprehensive, more reliable assessment of uncertainty of the set of hypotheses C can be obtained. The use of Bel (C) in combination may provide a more comprehensive understanding, including a confidence level for a state and consideration of uncertainty for that confidence level.

In S4010 to S4011, A _i And B _i The respectively are thatEvidence a and a subset of the evidence B (i.e. sample z _i ) The method comprises the steps of carrying out a first treatment on the surface of the mass is a weight (an average value of the total number of subsets is selected, or the weight can be automatically assigned according to subjective activity based on the credibility of staff corresponding to each subset); c is the "possible set";representing an empty set;

after obtaining Pl (C), it can be integrated with the previously computed joint confidence function Bel (a u B) to more fully evaluate the uncertainty for the hypothesis set C. The system can more fully and accurately understand the confidence for different states and the consideration of uncertainty for the confidence through such comprehensive information.

Specifically, regarding step S4013, a joint trust function Bel (a u B) is obtained:

This formula represents that the trust and uncertainty allocation of evidence sets A and B are comprehensively considered through the Dempster's combination principle, and a joint trust function Bel (A U B) is obtained. This process combines the information of the two evidence sets, providing an assessment of the confidence level of the entire hypothesis set A U B.

The specific acquisition mode of (Pl (A) ≡Pl (B)) is as follows:

A _i and B _i Evidence A and evidence respectivelyAnd a subset of B. The molecules are the sum of wi of evidence supporting A.cndot.B, and 1 minus this sum gives Pl (A.cndot.B), representing the degree of uncertainty for A.cndot.B.

It can be appreciated that the joint confidence function Bel (a u B) integrates the information of two independent evidence sets, so that the system can more comprehensively understand the confidence of the whole hypothesis set. This is of great importance for processing multisource information, fusing different observations. The joint trust function Bel (a u B) also takes into account the uncertainty between the two evidence sets by introducing an uncertainty allocation Pl (a u B). This makes the system more robust in handling uncertainty issues. Most importantly, the joint confidence function Bel (A U B) provides a comprehensive assessment of confidence for the system based on multiple evidence sets. Such information has a guiding role in decision making, problem solving, especially when multiple factors need to be comprehensively considered.

Further, by comparing the similar evidence sets a (linear scheme N _i ) And evidence set B (linear scheme N _o ) The system can fuse the information of both to form a more comprehensive understanding of the change in the thread type scheme. This helps the system more accurately capture the characteristics of the linear scheme, improving understanding of the actual problem. Comparison of similar schemes helps to reduce problems due to systematic errors or model uncertainties. By comparing similar schemes, the system can correct the judgment of the system when the information is insufficient or interference exists, and the overall accuracy and reliability are improved.

Specifically, regarding step S402, mapping:

e is the base of natural logarithms (approximately equal to 2.718);

through sigmoid mapping, the system introduces relevance evidence for different schemesUncertainty correction of the degree of confidence. Under the condition that Bel (A U B) is larger, the output of the sigmoid function approaches to 1, which indicates that the trust of the system to the evidence is higher, and the weight coefficient alpha _j Larger. Conversely, when Bel (A U B) is smaller, the output of the sigmoid function approaches 0, which means that the trust of the system to the evidence is lower, and the weight coefficient alpha _j Smaller. Due to the nature of the sigmoid function, the weight coefficient α _j A sensitive and smooth response is maintained to variations in Bel (a u B). This design allows the system to be more adaptive and robust in the face of new data and changes without drastic fluctuations due to some evidence or changes in the relevance information of different schemes.

It will be appreciated that during the mapping process, α _j The variation of (a) is consistent with that of Bel (A U B), and the causal relationship is reserved. The method and the system enable the change of the weight to be more interpretable, and can better reflect the relevance of the system to different schemes or the understanding of the credibility of the evidence of similar information.

It will be appreciated that the principle of this mechanism of adaptive correction is that:

(1) And (3) overall information synthesis: the joint confidence function considers two linear schemes N _i And N _o By comprehensively considering the evidence of the relevance of the different schemes of the two schemes, the characteristics of the different schemes in the system can be more fully understood. This helps the calculation of Δti' to be more accurate because of the weight α _j Can be adjusted according to the integral evidence.

(2) Flexibility and adaptability: mapping by sigmoid function, alpha _j A smooth, nonlinear response appears to the change in confidence. This non-linear response makes the adjustment of the weights more flexible and adaptable, enabling a relatively smooth adjustment in the face of different situations, rather than abrupt changes. This mechanism helps the system to be more adaptive and robust in the face of new data and changes.

(3) Weight adjustment of relevance evidence for different schemes: mapping of joint confidence functions preserves causal relationships, i.e., α _j Is consistent with the change in confidence. This assists the workerThe engineer understands the reason for the adjustment of the weights, and α _j The changes in (a) are well documented and do not occur unexplained. The weight adjustment of the relevance evidence for different schemes is reasonable because it fully considers the similarity and variability between schemes.

(4) Adaptive adjustment: bel (A U B) in the mapping is the embodiment of the whole credibility, and the adaptive adjustment of the whole credibility is realized by mapping to the [0,1] interval. Such adaptation helps the system introduce some uncertainty correction when considering the confidence level of the relevance evidence of different schemes, so that the system adapts better to the changes.

(5) Overall reliability reflects: alpha _j The method is a linear interpolation weight coefficient, and reflects the overall credibility of different schemes, so that the weight adjustment is more targeted and reasonable. When the overall reliability is higher, the system is more believed about the influence of the relevance evidence of different schemes, and when the overall reliability is lower, the system is more prone to smoothly adjusting the weight to keep the stability of the system.

Embodiment III: the present embodiment further provides several assignment schemes of the weight coefficient w and the weight coefficient b on the basis of the first embodiment or the second embodiment:

scheme one, balance both:

weight coefficient w: w=0.5;

weight coefficient b: b=0.5;

the scheme balances the influence of linear interpolation and difference vectors, and the contributions of the linear interpolation and the difference vectors are equal.

In particular, in practice, the solution considers the overall performance of the engineering, and it is desirable to balance the effects of linear interpolation and difference vectors, so as to ensure that the overall system has better linear properties, and can flexibly perform fine tuning through the difference vectors.

Scheme II, biased linear interpolation:

weight coefficient w: w=0.8;

weight coefficient b: b=0.2;

the scheme emphasizes the effect of linear interpolation, and the effect of the difference vector is relatively small.

In particular, in practice, if engineering requirements emphasize linear properties more, this requirement can be better met by a larger linear interpolation weight, for example, for cable force situations where a more uniform distribution is required.

Scheme three, bias difference vector:

weight coefficient w: w=0.2;

weight coefficient b: b=0.8;

the scheme emphasizes the effect of the difference vector, and the effect of linear interpolation is relatively small.

In particular, in practice when there is a need for nonlinear variation or local adjustment in the actual engineering, this scenario three may be considered if the engineering is more prone to achieve a more flexible system response by adjusting the difference vector.

Scheme four, emphasizes the first half:

weight coefficient w: w= [0.7,0.3];

weight coefficient b: b= [0.5,0.5];

in the scheme, in two sections, the influence of the first half section is stronger, and the influence of the second half section is relatively smaller.

Specifically, in practice, if the cable force is more critical in the first half of the bridge (e.g., affected by a larger external force or requiring more precise adjustment), the weight may be emphasized in the first half.

Scheme five, emphasizes the second half:

weight coefficient w: w= [0.3,0.7];

weight coefficient b: b= [0.5,0.5];

in the scheme, in two sections, the influence of the second half section is stronger, and the influence of the first half section is relatively smaller.

In particular, like solution four, in practice it is more critical if the latter half of the bridge is more critical, so the effect of the latter half is more emphasized in the trade-off to meet the specific requirements of the latter half.

Embodiment four: the embodiment discloses a line type measurement system for a cable-stayed bridge:

the system comprises a processor and a register coupled with the processor, wherein program instructions are stored in the register, and when the program instructions are executed by the processor, the processor is caused to execute the linear measuring method and the linear measuring system for the cable-stayed bridge according to the first to third embodiments in the specific implementation manner.

The above examples merely illustrate embodiments of the invention that are specific and detailed for relevant practical applications and are not to be construed as limiting the scope of the invention. It should be noted that it will be apparent to those skilled in the art that several variations and modifications can be made without departing from the spirit of the invention, which are all within the scope of the invention. Accordingly, the scope of protection of the present invention is to be determined by the appended claims.

Claims

1. A line type measuring method for cable-stayed bridge includes such steps as planning several different line-type schemes N for cable-changing _i Characterized by also comprising a pair-line type scheme N _i Establishing a cable force optimization model of cable replacement engineering to obtain a difference vector delta T of the optimized cable force relative to the actually measured cable force, and then executing steps S1-S3:

s1, executing an LHS algorithm: scheme N of opposite line type _i Dividing into i segments, performing segment modeling and overpull Ding Lifang sampling on each segment i, extracting a value u _i Sample z mapped to a standard normal distribution _i Each segment i obtains a corresponding group of difference vectors delta Ti' through a distribution function F1;

s2, stress analysis: the conversion function F2 is applied to combine the difference vector delta Ti' of all the segment bodies i and the dimensionless parameter xi to obtain the linear scheme N _i Is defined by the correction difference vector deltat ":

s3, judging the linear scheme N _i Is of the difference vector DeltaT "(N) _i ) Whether the cable force delta T after cable replacement is set _lb And design cable force delta T _lu The difference limit value and further determine the linear scheme N _i Whether the requirement of cable replacement engineering is met.

2. The line-type measuring method for a cable-stayed bridge according to claim 1, wherein: the cable replacement engineering cable force optimization model is used for solving an optimization target Min (delta T) of Cheng Qiaosuo force:

wherein X is _r Is the actual measurement line shape of the main beam before cable replacement, X _o Is of the target linear shape, D _h Is a vertical displacement influence matrix, D _σ Is a cable stress shadow matrix;

in the context of the constraints of the present invention,

is X _r In a normal use limit state, the minimum limit value of the tensile stress;

is X _r In the normal use limit state, the maximum limit value of the tensile stress.

3. The line-type measuring method for a cable-stayed bridge according to claim 1, wherein: in the S1, it includes:

s100, parameter acquisition: obtaining a difference vector delta T and a dimensionless parameter zeta of the current inhaul cable relative bending stiffness;

S101, line type planning, wherein n line type schemes are provided:

[N ₁ ,N ₂ ,...,N _n ]

s101 further comprises substeps S1010-S1011:

s1010, overpull Ding Lifang sampling: a parameter space S is formulated, and a superpull Ding Lifang sampling method is used for parameter nullingSampling in S to obtain sample z _i ；

S1011, segment modeling: sample z based on sampling result _i And dimensionless parameters xi, calculate the linear scheme N _i Is defined by the difference vector DeltaT'; the steel cable I is then divided into several sections I, each of which is passed through a distribution function F1 to obtain a corresponding set of difference vectors DeltaTi'.

4. A line-type assay for a cable-stayed bridge according to claim 3, characterized in that: in the step S1010, the parameter space S is a currently selected linear scheme N based on the difference vector DeltaT and the dimensionless parameter xi _i And the proposed:

S＝[△T _min ,△T _max ]*[ξ _min ,ξ _max ]

5. The method for determining the linearity of a cable-stayed bridge according to claim 4, characterized in that: in S1010, the sampling is performed by:

a. determining the number of samples M: determining how many sample points are obtained in the parameter space S;

b. Dividing the (0, 1) interval into M sections: so that each segment contains a uniform distribution;

c. randomly extracting a value:

for each segment i, a value u is randomly extracted _i Where i=1, 2, …, M, u _i Is a random number within the (0, 1) interval;

d. by an inverse function phi of a standard normal distribution ^-1 Mapping to sample z _i ；

e. The sampling order is disordered: the sampling order of the samples is disturbed to ensure randomness of the sample points.

6. According to claimThe line type measuring method for a cable-stayed bridge according to claim 5, wherein: in the step d, the inverse function Φ of the normal distribution ^-1 The method comprises the following steps:

z _i ＝Φ ^-1 (u _i )

where z is a standard normal distribution of random variables.

7. A line-type assay for a cable-stayed bridge according to claim 3, characterized in that: in said S1010, the latin hypercube sampling is performed, requiring the same number of partitions m per variable, but not requiring the same increase in the number of samples m as the variable increases.

8. The line-type measuring method for a cable-stayed bridge according to claim 1, wherein: in S1011, it includes:

calculating a difference vector DeltaT': the number of samples M represents the linear scheme N to be extracted _i Equally dividing the (0, 1) interval into M segments, each segment corresponding to one sample point z _i Representing a change in the linear scheme:

α _j is a weight coefficient of linear interpolation;

an allocation function F1 is performed, the allocation function F1 being used to allocate the difference vector Δt' in the sampling result to each segment i:

F1(ΔTi′)＝ΔT

9. A line-type assay for a cable-stayed bridge according to claim 1 or 3, characterized in that:

in the step S2, a conversion function F2 is applied to combine the difference vectors DeltaTi' and dimensionless parameters xi of all the segment bodies i to obtain the linear scheme N _i Is defined by the correction difference vector deltat ":

ΔT”＝F2(ξ,{ΔTi’})

{ Δti '} is a set of all difference vectors Δti';

in the S3, the linear scheme N is judged _i Is of the difference vector DeltaT "(N) _i ) Whether the cable force delta T after cable replacement is set _lb And design cable force delta T _lu The difference limit to determine the difference vector Δt constraint:

△T _lb ≤△T”(N _i )≤△T _lu

if the above constraint is satisfied, then the scheme N is determined _i Qualified, remain in the final linear scheme set; if the constraint condition is not satisfied, deleting the linear scheme from the consideration set;

Through the execution of a plurality of rounds of steps S1-S3, m linear schemes which can meet the design requirement are obtained: [ N ] ₁ ,N ₂ ,...,N _m ]。

10. A line-type measuring system for a cable-stayed bridge, characterized by: the system comprising a processor, a register coupled to the processor, the register having stored therein program instructions which, when executed by the processor, cause the processor to perform a line-type assay method for a cable-stayed bridge as claimed in any one of claims 1 to 9.