An automatic load distribution method for load tests that can reduce the number of loading conditions

Abstract

The present invention belongs to the field of structural safety detection, and discloses an automatic load distribution method for load tests that can reduce the number of loading conditions. The method includes: (1) classifying the control sections corresponding to each loading condition based on the peak position of the influence surface; (2) determining the number and formation of loading vehicles corresponding to each loading condition based on grid division; (3) determining the positions of loading vehicles corresponding to each loading condition based on a multi-section target optimization method. The present invention can automatically give a load distribution plan according to pre-determined loading vehicle parameters, bridge deck geometric information, bridge influence surface and the expected number of load conditions, and the entire calculation process requires no human intervention; multiple bridge control sections can be used as optimization targets at the same time to find a load distribution plan that meets the loading efficiency requirements of multiple sections and has the fewest loading vehicles and loading conditions. The present invention has good potential for subsequent engineering applications.

Description

Technical Field

[0001] The present invention belongs to the field of structural safety detection, and particularly relates to an automatic load distribution method for a load test that can reduce the number of loading conditions. Background Art

[0002] The wave of large-scale bridge construction in China is approaching its end, and the development demand of bridge engineering is transforming from "construction-oriented" to "equal emphasis on construction and maintenance, with maintenance as the main focus". During the long-term service of bridges, due to fatigue, corrosion, and material deterioration, the resistance effect of bridges will continuously decay. At the same time, due to the increase in traffic loads, the load effect of bridges is also increasing continuously. To ensure the safe operation of bridges, technologies such as structural health monitoring and non-destructive testing have received increasing attention. However, there are still some deficiencies in these emerging management technologies: the bridge health monitoring system usually can only obtain the bridge response under the operating load, and the non-destructive testing technology usually can only detect local damage of the bridge. For these reasons, using a loading fleet with a known and stable weight for a load test is still an irreplaceable method to grasp the actual condition of the bridge and evaluate the bearing capacity of the bridge.

[0003] The implementation process of a load test can be divided into three stages: preparation, execution, and analysis. The preparation stage includes collecting design information, determining the target load and stop criteria; the execution stage includes stepwise applying the target load and measuring the response of key sections; the analysis stage includes evaluating and making decisions on the tested bridge. Among the different implementation stages of the load test, since it is directly related to the test cost and the reliability of the results, the load distribution of the target load and on-site loading are one of the most critical steps. Currently, there are two mainstream methods internationally to determine the target load of a load test. One is the method specified in the American code to directly use the design truck to drive for loading, and the other is the method specified in the Chinese code to use a fleet load to generate the internal force or deformation of the same section as the target load. This method requires converting the live load model in the code into an equivalent fleet load. Therefore, how to determine the number and position of loading trucks in different conditions has become a key issue in the implementation of this method.

[0004] To meet the equivalent requirements of different control sections, in engineering practice, it is necessary to design loading conditions composed of various numbers, formations, and positions of different trucks. For example, during the load test of the Nissibi cable-stayed bridge, 2 trucks were rented and 6 loading conditions were designed to load the bridge. During the load test of the Yangluo Yangtze River Bridge, 72 trucks were rented and 11 loading conditions were designed to load the bridge. In addition, the shape of the influence surface of long-span bridges is complex, and it is difficult to accurately achieve the internal force and deformation targets of the control section by manually adjusting the position of the loading trucks. Therefore, it is necessary to develop an automatic search algorithm for determining the position and formation of loading trucks. At the same time, the number of loading trucks and loading conditions is directly related to the implementation cost of the load test. Determining the minimum number of loading trucks and loading conditions that meet the loading efficiency requirements of each control section is of great significance.

[0005] To provide a reasonable method for arranging loading vehicles, and use the minimum number of loading vehicles and loading conditions to meet the equivalent objectives of internal forces or deformations of all control sections, the present invention proposes an automatic loading arrangement method for load tests that can reduce the number of loading conditions. First, classify the control sections corresponding to each loading condition based on the peak positions of the influence surfaces, then determine the number of loading vehicles and their formations corresponding to each loading condition based on grid division, and finally determine the positions of the loading vehicles corresponding to each loading condition based on the multi-section objective optimization method. Compared with the traditional method of independently designing loading conditions for each control section, the present invention simultaneously takes the equivalent internal forces or deformations of multiple control sections as the optimization objectives, and achieves the loading efficiency requirements of all control sections with the minimum number of loading vehicles and loading conditions. Summary of the Invention

[0006] The object of the present invention is to provide a reasonable method for arranging loading vehicles, and use the minimum number of loading vehicles and loading conditions to meet the equivalent objectives of internal forces or deformations of all control sections. The present invention proposes an automatic loading arrangement method for load tests that can reduce the number of loading conditions.

[0007] Technical Solution of the Present Invention:

[0008] An automatic loading arrangement method for load tests that can reduce the number of loading conditions, the steps are as follows:

[0009] Step 1, classify the control sections based on the peak positions of the influence surfaces:

[0010] (1) Initially determine the total number m of loading conditions to be implemented during the load test according to the load test budget and the characteristics of the bridge structure to be tested;

[0011] (2) Determine the control sections that need to meet the equivalent internal force or deformation requirements according to the specifications, with a total number of p, and classify all control sections according to the following formula:

[0012]

[0013] where, ct c is the c-th control section of the bridge to be tested; C n is the set of control sections included in the n-th loading condition; is the longitudinal position of the bridge corresponding to the peak of the influence surface of the c-th control section; is the element in the influence coefficient matrix IS c of the c-th control section, determined by the finite element model; x is the longitudinal coordinate of the bridge; y is the transverse coordinate of the bridge; L is the total longitudinal length of the bridge to be tested;

[0014] Step 2, determine the number of loading vehicles and their formations corresponding to each loading condition based on grid division:

[0015] (3) To make the loading vehicle formation in the cloth loading result more regular for convenient on-site loading, first evenly divide the bridge deck into grids with a quantity of k×t. The number of grids divided in the transverse direction of the bridge t is equal to the number of lanes, and the number of grids divided in the longitudinal direction of the bridge k is determined according to Equation (2):

[0016]

[0017] where s is the minimum spacing of loading vehicles in the same lane, D is the distance between the front and rear axles of the loading vehicle; int is the rounding function; (4) Establish a loading efficiency matrix E with dimensions of k×t c , E c represents the loading efficiency generated by arranging a single loading vehicle in each grid divided according to step (3) in sequence, and its element is calculated by Equation (3):

[0018]

[0019] where S c is the response of the c-th control section caused by the design live load; μ is the impact coefficient value taken according to the design code; is the response of the c-th control section caused by a single loading vehicle in grid i,j, and is calculated by Equation (4):

[0020]

[0021] where A k is the weight of the k-th wheel of the loading vehicle; w is the total number of wheels of the loading vehicle; is the influence coefficient of the k-th wheel of the loading vehicle on the c-th control section of the bridge;

[0022] (5) Sum the loading efficiency of each grid. When the sum of the loading efficiency of all control sections is between 1 and 1.5, the corresponding maximum number of grids is the number of loading vehicles;

[0023] (6) After determining the number of loading vehicles, determine the loading vehicle formation vector (p,q) required for cloth loading according to Formulas (5) and (6):

[0024]

[0025] where (p,q) is an n-dimensional loading vehicle formation vector; p i and q j are the elements in vectors p and q, representing the longitudinal and transverse positions of the loading vehicle in the grid respectively; is the element in the total loading efficiency matrix T, and the matrix T is determined by Formula (6):

[0026]

[0027] Among them, Ei c is the loading efficiency matrix E with dimension k×t c The matrix consisting of the maximum loading efficiency areas with the dimension of r×t separated from the matrix is ​​as follows; r is the maximum number of rows of loading vehicles in the same lane, which is determined according to formula (7);

[0028]

[0029] Step 3: Determine the loading vehicle position corresponding to each loading condition based on the multi-section target optimization method:

[0030] (7) The loading efficiency objective function of any control section is established as follows:

[0031]

[0032] Where z is the position of the axle closest to the origin of the coordinate system along the bridge; IL j (z) is the influence line function of the jth lane, which is represented by the influence coefficient matrix IS c The middle row vector is fitted; L k and P k is the distance and weight of the axle closest to the origin of the coordinate system at the kth wheelbase;

[0033] After establishing the loading efficiency objective function, the constraints of the loading efficiency objective function (8) are determined as follows according to the restriction that vehicles cannot leave the bridge deck during the load test:

[0034] 0≤z≤Lr·max(L t ) (9)

[0035] (8) Using genetic algorithm to search for the Pareto frontier of the objective function * , optimal loading fleet position z op The corresponding Pareto frontier point that minimizes the 2-norm of the sum of all distribution objective functions is shown in formula (10):

[0036] x op =argmin||f(z * )|z * ∈PS * || 2 (10)

[0037] (9) Calculate the loading efficiency of each control section under each loading condition. If it meets the requirements, the loading is completed; if it does not meet the requirements, increase the number of loading conditions m and re-load according to the process.

[0038] Beneficial effects of the present invention:

[0039] 1. The method of the present invention can automatically generate a loading plan based on pre-determined loading vehicle parameters, bridge deck geometric information, bridge influence surface, and the number of expected load conditions. The entire calculation process requires no human intervention, and an efficient automatic loading algorithm is established.

[0040] 2. The automatic loading method for load tests of the present invention that can reduce the number of loading conditions can simultaneously use multiple bridge control sections as optimization objectives, find a loading plan that meets the loading efficiency requirements of multiple sections and has the minimum number of loading vehicles, thereby achieving the purpose of reducing the implementation cost of load tests. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 is a flowchart of the method of the present invention;

[0042] Figure 2 is the basic situation and control sections of the arch bridge to be tested in Embodiment 1 of the method of the present invention;

[0043] Figure 3 is the finite element model of the arch bridge to be tested in Embodiment 1 of the method of the present invention;

[0044] Figure 4 are the influence surfaces of each control section of the arch bridge to be tested in Embodiment 1 of the method of the present invention, (a) deflection at the south 1 / 4 of the main girder; (b) displacement of the north side support seat; (c) moment at the south side arch foot; (d) mid-span deflection; (e) moment at the arch crown;

[0045] Figure 5 is the design live load of the arch bridge to be tested in Embodiment 1 of the method of the present invention;

[0046] Figure 6 is the Pareto front of the loading vehicle position optimization in Embodiment 1 of the method of the present invention, (a) loading conditions 1 and 3; (b) loading condition 2;

[0047] Figure 7 are the optimization results of the number, formation, and position of the loading vehicles under each working condition in Embodiment 1 of the method of the present invention, (a) loading condition 1: loading on the north side of the main girder; (b) loading condition 2: loading at the mid-span of the main girder; (c) loading condition 3: loading on the south side of the main girder. DETAILED DESCRIPTION OF THE INVENTION

[0048] The present invention will be further described in detail below with reference to the drawings and a numerical example.

[0049] The influence line identification method of the present invention is divided into three steps: "classifying control sections based on the peak position of the influence surface", "determining the number and formation of loading vehicles corresponding to each loading condition based on grid division", and "determining the position of loading vehicles corresponding to each loading condition based on the multi-section target optimization method". The specific implementation has been given above. Next, the usage method and characteristics of the invention will be described with a numerical example.

[0050] Implementation Example 1: Automatic Loading Example for the Load Test of a Suspender Arch Bridge

[0051] To verify the effectiveness of the proposed method, this implementation example introduces a loading example for the load test of a suspender arch bridge. The bridge to be tested has a total length of 150 m, a deck width of 30 m, a rise of 30 m, and the deck is a two-way six-lane. The loading vehicle uses a three-axle truck, and the wheelbase between the front axle and the rear axle is 1.4 m and 4.9 m respectively. The axle loads of each load test vehicle are 150 kN, 150 kN, and 75 kN respectively.

[0052] A total of 8 control section responses need to be tested in the load test of this arch bridge. The equivalent targets to be calculated include 5 section deformations and 3 section bending moments. The basic situation of the arch bridge to be tested and the control sections are shown in Figure 2 . After determining the control sections, a finite element model is established to calculate the influence surfaces of all control sections. The detailed drawings of the finite element model are shown in Figure 3 , and the influence surfaces of each control section calculated by the finite element model are shown in Figure 4 . According to the loading condition determination method proposed in step (2), the control sections are initially divided into three categories, corresponding to three different loading conditions. The control sections (north arch foot bending moment, north support lateral displacement, south 1 / 4 main girder deflection) whose influence surface peaks are located at the north 1 / 3 position of the deck can be classified as loading condition 1; the control sections (mid-span crossbeam bending moment, main girder mid-span deflection) whose influence surface peaks are located in the mid-span 1 / 3 interval can be classified as loading condition 2. The other control sections whose influence surface peaks are located at the south 1 / 3 position of the deck can be classified as loading condition 3.

[0053] After that, determine the number and formation of the load vehicles. Take the spacing s = 2 m between the load vehicles in the same lane. First, divide the deck into a 15×6 grid according to step (3). Then, according to the influence surface of each section, the load vehicle information, and the design live load, calculate the loading efficiency of each grid according to step (4). The design live load of the bridge to be tested is shown in Figure 5 . According to step (5), it can be determined that 7 load vehicles should be used for loading condition 1, and 6 load vehicles should be used for each of loading conditions 2 and 3. According to step (6), the formation of the load vehicles can be determined. For loading conditions 1 and 3, the 7 load vehicles should be divided into two rows. The 3 trucks in the front row are located in lanes 3 - 5, and the 4 trucks in the rear row are located in lanes 2 - 5. For loading condition 2, the 6 load vehicles should be divided into two rows. The 2 trucks in the front row are located in lanes 3 - 4, and the 4 trucks in the rear row are located in lanes 2 - 5.

[0054] After determining the number and positions of the load vehicles under each loading condition, use the multi-control section joint optimization method to determine the positions of the load vehicles. The objective function and its corresponding constraint conditions should be established according to step (7). The Pareto frontiers of each loading condition obtained by searching based on the genetic algorithm are shown in Figure 6As shown. Based on the symmetric characteristics of the bridge influence surface, the truck positions under Condition 3 can be obtained by symmetrically reversing the load distribution results. According to Step (8), the optimal loading truck positions correspond to the Pareto front with the minimum 2-norm. The two optimal loading truck positions for Loading Conditions 1 and 2 are at 26 m and 80 m from the north support of the rear axle distance, respectively.

[0055] The optimization results of the number, formation, and position of the loading trucks under each condition are as Figure 7 shown. The loading efficiency of each control section corresponding to each condition is shown in Table 1. As can be seen from Table 1, in the loading scheme optimized by the method of the present invention, each loading condition can meet the internal force or deformation objectives of all corresponding sections (the loading efficiency is between 0.85 and 1.05), and the loading efficiency of the internal force or deformation of other sections during the loading process does not exceed the limit. The final load distribution result obtained by the proposed method only uses 3 loading conditions to meet the loading efficiency objectives of 8 different control sections, effectively reducing the implementation cost of the load test.

[0056] Table 1 Loading efficiency of each control section under each condition

[0057]

Claims

1. An automatic load distribution method for load tests that can reduce the number of loading conditions, characterized in that, the steps are as follows: Step 1, classify control sections based on the peak position of the influence surface: (1) Based on the load test budget and the characteristics of the bridge structure to be tested, preliminarily determine the total number m of loading conditions to be implemented during the load test; (2) Determine the control sections that need to meet the equivalent internal force or deformation requirements according to the specifications, with a total number of p, and classify all control sections according to the following formula: Among them, ct c is the cth control section of the bridge to be tested; C n is the set of control sections included in the nth loading case; is the bridge longitudinal position corresponding to the peak value of the influence surface of the cth control section; IS is the influence coefficient matrix of the cth control section c The middle element is determined by the finite element model; x is the longitudinal coordinate of the bridge; y is the transverse coordinate of the bridge; L is the total length of the bridge to be tested in the longitudinal direction; Step 2, determine the number and formation of loading vehicles corresponding to each loading condition based on grid division: (3) To make the formation of the loading vehicle fleet in the load distribution result more regular for easy on-site loading, first evenly divide the bridge deck into grids with a number of k×t. The number t of transverse grid divisions is equal to the number of lanes, and the number k of longitudinal grid divisions is determined according to formula (2): where s is the minimum distance between loading vehicles in the same lane, D is the distance between the front and rear axles of the loading vehicle; int is the rounding function; (4) Establish a loading efficiency matrix E with dimensions k×t c , E c represents the loading efficiency generated by arranging single loading vehicles in each grid divided according to step (3) in sequence, and its elements are calculated by Equation (3): Among them, S c is the response of the c-th control section caused by the design live load; μ is the impact coefficient value taken according to the design code; is the response of the c-th control section caused by a single loading vehicle in the grid i, j, which is calculated by Equation (4): Among them, A k is the weight of the k-th wheel of the loading vehicle; w is the total number of wheels of the loading vehicle; is the influence coefficient of the c-th control section of the bridge corresponding to the k-th wheel of the loading vehicle; (5) Sum the loading efficiencies of each grid. When the sum of the loading efficiencies of all control sections is between 1 and 1.5, the corresponding maximum number of grids is the number of loading vehicles; (6) After determining the number of loading vehicles, determine the loading vehicle formation vector (p,q) required for load distribution according to formulas (5) and (6): Among them, \((p, q)\) is an \(n\)-dimensional loading vehicle formation vector; \(p\) i and \(q\) j are the elements in vectors \(p\) and \(q\), representing the longitudinal and transverse positions of the loading vehicle in the grid respectively; is the element in the total loading efficiency matrix \(T\), and the matrix \(T\) is determined by formula (6): Among them, Ei c is a matrix composed of the maximum loading efficiency region with dimensions of r×t separated from the loading efficiency matrix E with dimensions of k×t c ; r is the maximum number of rows of the loading vehicles in the same lane, which is determined according to formula (7). Step 3, determine the positions of loading vehicles corresponding to each loading condition based on the multi-section target optimization method: (7) Establish the following loading efficiency objective function for any control section: Among them, z is the longitudinal position along the bridge of the axle closest to the coordinate origin; IL j (z) is the influence line function of the j-th lane, which is obtained by fitting the row vector in the influence coefficient matrix IS c ; L k and P k are the distance and weight of the k-th axle from the axle closest to the coordinate origin; After establishing the loading efficiency objective function, determine the constraint of the loading efficiency objective function (8) according to the restriction that vehicles must not leave the bridge deck during the load test: 0 ≤ z ≤ L - r·max(L t ) (9) (8) Use the genetic algorithm to search for the Pareto front PS of the objective function * , the optimal loading fleet position z op corresponds to the Pareto front point that minimizes the 2-norm of the sum of all loading objective functions, as shown in Equation (10): x op = argmin ||f(z * )|z * ∈PS * || 2 (10) (9) Calculate the loading efficiencies of each control section under each loading condition. If the requirements are met, the load distribution ends; if not, increase the number m of loading conditions and re-perform the load distribution according to the process.

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