A reliability analysis method for static irregularity of track on dual-use highway-railway bridges based on higher-order moment method

Abstract

The invention discloses a reliability analysis method for static irregularity of rail tracks on a road-rail dual-use bridge based on a high-order moment method, including establishing a finite element model of a real bridge structure; constructing a structural function function; generating fitting values ​​of random variables in the structural function function according to measured data; converting the fitting values ​​of random variables to the same standard normal space by Rosenblatt inverse transformation, and obtaining the estimated point values ​​and weight values ​​of the fitting values ​​of random variables by Gauss-Hermite quadrature formula; substituting the estimated point values ​​and weight values ​​of the fitting values ​​of each random variable into the finite element model of the real bridge structure, and taking the mean of other random variables to obtain the univariate structural function function corresponding to each random variable; solving the first four moments according to the fourth-order moment theory, and calculating the structural failure probability and reliability through all the first four moments. The scheme of the invention realizes the quantitative analysis of the reliability of static irregularity of rail tracks on road-rail dual-use bridges based on the high-order moment method.

Description

Technical Field

[0001] The invention relates to the technical field of bridge engineering, and in particular to a reliability analysis method for static irregularity of a highway-railway dual-purpose bridge track based on a high-order moment method. Background Art

[0002] There are many factors that affect the static acceptance of ballastless track on large-span dual-use bridges. Unlike conventional high-speed railway bridges, the live load of the highway in large-span dual-use bridges will inevitably cause the bridge to deform, which in turn drives the deformation of the ballastless track on the bridge, and has a certain impact on the linear shape of the seamless line. Therefore, it is very necessary to explore the linear reliability of the ballastless track on the dual-use bridge during the operation period.

[0003] At present, the design of ballastless track in my country is mainly based on the allowable stress method of materials. However, for the large-span bridge-ballastless track system under complex loads, its load parameters and environmental changes are random, and the allowable stress method cannot fully meet the needs of structural design. The reliability theory based on probabilistic design has gradually been applied to the limit state design of ballastless track structure, which has attracted the attention of many scholars in recent years.

[0004] For simple engineering structures, when the structural performance function can be obtained relatively conveniently, its reliability can be directly solved by integration through the definition formula. If the expression of the structural performance function is complex and it is difficult to obtain its analytical solution by direct integration, the Taylor expansion method is generally chosen to approximately expand the structural performance function into a polynomial and then solve it by integration.

[0005] However, for the reliability analysis of static track irregularities on dual-use bridges for highway and railway, its load-response action mode is difficult to directly reflect through functional expressions. The structural function function is an implicit expression, and it is very difficult to directly integrate or solve the high-order moments of the structural function function through Taylor expansion. Summary of the invention

[0006] In order to solve the technical problem that the load-response action mode of the reliability analysis of the static irregularity of the track on the highway-railway dual-use bridge is difficult to obtain and solve through a function expression, the linear reliability of the ballastless track on the highway-railway dual-use bridge during the operation period is calculated. An embodiment of the present invention provides a reliability analysis method for the static irregularity of the track on the highway-railway dual-use bridge based on the high-order moment method.

[0007] The technical solution of the embodiment of the present invention is achieved as follows:

[0008] The embodiment of the present invention provides a reliability analysis method for static irregularity of a highway-railway dual-purpose bridge track based on a high-order moment method, the method comprising:

[0009] According to the design and construction drawings, a finite element model of the actual bridge structure is established; according to the track static irregularity specification indicators, a structural function function is constructed; according to the measured highway bridge deck vehicle data and the measured local climate conditions, the fitting values ​​of the random variables in the structural function function are generated; the fitting values ​​of the random variables are converted to the same standard normal space through the Rosenblatt inverse transformation, and the estimated point values ​​and weight values ​​of the fitting values ​​of the random variables in the standard normal space are obtained through the Gauss-Hermite quadrature formula; the estimated point values ​​and weight values ​​of the fitting values ​​of each random variable are substituted into the finite element model of the actual bridge structure, and the other random variables are averaged to obtain the univariate structural function function corresponding to each random variable; the first four moments of the univariate structural function function corresponding to each random variable are solved according to the fourth-order moment theory, and the structural failure probability and reliability are calculated through the first four moments of all the univariate structural function functions.

[0010] In one embodiment, the structure function comprises:

[0011]

[0012] in, G Lmax ( x 1, x 2… x n ) is the long-wave irregularity amplitude of ballastless track on long-span bridge under the action of various random variables, x 1- x n for n A random variable, when Z L >0, the structure is in a reliable state. Z L <0, the structure is in failure state. Z L =0, the structure is in the limit state.

[0013] In one embodiment, the fitted values ​​of the random variables are converted to the same standard normal space by an inverse Rosenblatt transformation, including:

[0014] The fitted values ​​of the random variables are transformed into the same standard normal space by Rosenblatt inverse transformation using the following calculation formula:

[0015]

[0016] in, T -1 ( U ) is the inverse Rosenblatt transform, Uis a random variable with standard normal distribution, X is a random variable with any distribution.

[0017] In one embodiment, the estimated point value and the weight value of the fitted value of the random variable in the standard normal space are obtained by using the Gauss-Hermite quadrature formula, including:

[0018] For a random variable in the standard normal space, we determine k The expression of the central moment is:

[0019]

[0020] in, is a random variable after inverse Rosenblatt transformation, k for k Order central moment; is the weight function;

[0021] The Gauss-Hermite quadrature formula for determining the weight function is expressed as:

[0022]

[0023] in, ; x j and A j They are weight functions exp(- x 2 )’s estimated point values ​​and weight values ​​for the Gauss-Hermite quadrature formula; m is the number of estimated points; k for k Order central moment;

[0024] Substitute the fitted value of the random variable in the standard normal space into the k From the order central moment expression and the Gauss-Hermite quadrature formula expression of the weight function, the estimated point value and weight value of the fitting value of the random variable in the standard normal space are obtained.

[0025] In one embodiment, solving the first four moments of the univariate structure function function corresponding to each random variable according to the fourth-order moment theory includes:

[0026] The first four moments of the univariate structural function function corresponding to each random variable are solved using the following calculation formula according to the fourth-order moment theory:

[0027]

[0028] in, is the first four moments of the univariate structure function, P j is the weight value corresponding to each estimated point, m To estimate the number of points, For estimated points x j The structural function value at ; , k for k Order central moment; .

[0029] In one embodiment, the structural failure probability and reliability are calculated by the first four moments of all the univariate structural function functions, including:

[0030] Obtaining the first four moments of the structure function function through the first four moments of all the univariate structure function functions;

[0031] The structural failure probability and reliability are calculated based on the first four moments of the structural performance function.

[0032] In one embodiment, the first four moments of the structure function function are obtained by using the first four moments of all the univariate structure function functions, including:

[0033] The first four moments of the structure function function are obtained by using the following calculation formula through the first four moments of all the univariate structure function functions:

[0034]

[0035] in, , , , is the first four moments of the univariate function Gi, n To estimate the number of points, is the value of the structural function when all random variables take their mean value, is a single variable function G j The variance of .

[0036] In one embodiment, the calculation of the structural failure probability and reliability based on the first four moments of the structural performance function includes:

[0037] The following calculation formula is used to calculate the structural failure probability and reliability based on the first four moments of the structural performance function:

[0038]

[0039] in, is the reliability of the structure, P fis the probability of structural failure, , , , , , , , , is the third-order central moment of the structure function; is the fourth-order central moment of the structure function, It is the second-order reliability index of the structural performance function.

[0040] This embodiment has the following beneficial effects:

[0041] This embodiment is based on the high-order moment method. By calculating the high-order moment of the structure function function, no matter what distribution the structure function function conforms to, the sample distribution characteristics can be described by the high-order moment, and then the failure probability of the structure can be solved. The real bridge finite element model is combined with the high-order moment method to calculate the linear reliability of the ballastless track on the road-rail dual-use bridge, which can reflect the influence of various loads on the linear shape of the ballastless track on the road-rail dual-use bridge during the operation period, and realize the quantitative calculation of the linear reliability of the ballastless track on the road-rail dual-use bridge. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 It is a flow chart of a reliability analysis method for static irregularity of a highway-railway dual-purpose bridge track based on a high-order moment method according to an embodiment of the present invention;

[0043] Figure 2 It is a schematic diagram of a specific process of a reliability analysis method for static irregularity of a highway-railway dual-purpose bridge track based on a high-order moment method according to an embodiment of the present invention;

[0044] Figure 3 This is a schematic diagram of the loading position of the random variable of the highway load according to an embodiment of the present invention;

[0045] Figure 4 It is a schematic diagram of a probability density fitting function curve of a highway load vehicle weight according to an embodiment of the present invention;

[0046] Figure 5 For the embodiment of the present invention x 1 is a schematic diagram of a univariate structural function curve of a random variable;

[0047] Figure 6 For the embodiment of the present invention x 2 is a schematic diagram of a univariate structural function curve of a random variable;

[0048] Figure 7 For the embodiment of the present invention x 3 is a schematic diagram of a univariate structural function curve of a random variable;

[0049] Figure 8 For the embodiment of the present invention x 4 is a schematic diagram of a univariate structural function curve of a random variable;

[0050] Fig. 9 For the embodiment of the present invention x 5 is a schematic diagram of a univariate structural function curve of a random variable;

[0051] Fig.10 For the embodiment of the present invention x 6 is a schematic diagram of a univariate structural function curve of a random variable;

[0052] Fig.11 1 is a diagram showing the internal structure of a computer device according to an embodiment of the present invention. DETAILED DESCRIPTION

[0053] The present invention will be described in further detail below with reference to the accompanying drawings and embodiments.

[0054] The embodiment of the present invention provides a reliability analysis method for static irregularity of a highway-railway dual-purpose bridge track based on a high-order moment method. Figure 1 As shown, the method includes:

[0055] Step 101: Establish a finite element model of the actual bridge structure according to the design and construction drawings;

[0056] Step 102: constructing a structural function function according to the track static irregularity specification index;

[0057] Step 103: generating fitting values ​​of random variables in the structure function function according to measured highway bridge deck vehicle data and measured local climate conditions;

[0058] Step 104: converting the fitted value of the random variable into the same standard normal space by Rosenblatt inverse transformation, and obtaining the estimated point value and weight value of the fitted value of the random variable in the standard normal space by Gauss-Hermite quadrature formula;

[0059] Step 105: Substitute the estimated point value and weight value of the fitting value of each random variable into the finite element model of the real bridge structure, and take the average of other random variables to obtain the univariate structural function corresponding to each random variable;

[0060] Step 106: Solve the first four moments of the univariate structural function function corresponding to each random variable according to the fourth-order moment theory, and calculate the structural failure probability and reliability through the first four moments of all the univariate structural function functions.

[0061] This embodiment provides a reliability analysis method for static irregularity of track on a highway-railway dual-use bridge based on a high-order moment method. By adopting a point estimation method combined with a finite element analysis method, the reliability of a seamless track on a highway-railway dual-use bridge can be effectively calculated.

[0062] Specifically, see Figure 2 , the method of this embodiment includes the following steps:

[0063] S1. Establish a finite element model of the real bridge structure;

[0064] S2. Constructing a structural function function according to the track static irregularity specification index;

[0065] S3. Determine the random variables to be considered and their distribution types;

[0066] S4, transform each random variable into the same standard normal space through inverse Rosenblatt transformation;

[0067] S5. Obtain the estimated point value and weight of each random variable according to the Gauss-Hermite quadrature formula;

[0068] S6, substituting each random variable estimation point into the finite element model to obtain a single variable structural performance function value;

[0069] S7. Solve the first four moments of the structure function function according to the fourth-order moment theory;

[0070] S8. The structural failure probability and its reliability are obtained through the first four moments of the structural performance function.

[0071] Here, in step S3, the random variables to be considered refer to the random variables that have a greater impact on the static irregularity of the track on the highway-railway dual-use bridge, such as overall temperature rise and fall, track system temperature rise, highway live load, etc. In actual calculation, the temperature random variable can be obtained through field measurement data, and the highway live load random variable can be fitted into the vehicle load probability density function according to the local highway vehicle load sample value, and then substituted into the finite element model for calculation.

[0072] In this embodiment, in step S4, any random variable X of any distribution can be transformed into a random variable U of a standard normal distribution through an inverse Rosenblatt transformation, as shown in the following formula, where T-1(U) is the inverse Rosenblatt transformation.

[0073]

[0074] In step S5, for the random variable U~N(0,1) of the standard normal distribution, its k-order central moment expression is as follows:

[0075]

[0076] The weight function is The Gauss-Hermite quadrature formula is as follows:

[0077]

[0078] The nodes of the quadrature formula u j (i.e., estimated points) and weight values P j It can be obtained by the following formula:

[0079]

[0080] In the formula, x j and A j They are the nodes and weight values ​​of the Gauss-Hermite quadrature formula of the weight function exp(-x2).

[0081] Since the estimated points of the standard normal distribution and their corresponding weight values ​​can be directly obtained through the Gauss-Hermite quadrature formula, m The estimated points in the standard normal space ( u 1, u 2… u m ) and the corresponding weight value ( P 1, P 2… P m ) after which the structure function G = G ( X )of k Order central moment It can be written as follows:

[0082]

[0083] The estimated nodes and their weight values ​​in the standard normal space can correspond one-to-one with the nodes and weight values ​​in the Gauss-Hermite quadrature formula. Taking the 7-point estimate as an example, the estimated nodes in the standard normal space are u j and weight value P j As shown in Table 1 below.

[0084] Table 1 Nodes and weights of 7-point estimation in standard normal space

[0085]

[0086] In step S6, for a structure-performance function containing multiple random variables, assuming that the random variables are independent of each other, the structure-performance function can be approximately replaced by the following formula:

[0087]

[0088] In the formula, Represents the value of the structural function when all random variables take their mean value; G i represents only random variables x i is the only random variable, and the value of the structural function function when the other variables take the mean value, G i Only x i A single variable function of ; T -1 ( x i ) is the inverse Rosenblatt transform.

[0089] The first four moments of the univariate structure function It can be obtained by the following formula:

[0090]

[0091] In the formula, x j ( j =1,2… m )for m Estimated points; P j ( j =1,2… m ) is the weight value corresponding to each estimated point.

[0092] Correspondingly, the first four moments of the structure performance function Z = G (X) can be expressed as follows:

[0093]

[0094] In the formula, , , , is a single variable function G i The first four moments of .

[0095] In steps S7 and S8, after obtaining the first four moments of the structural performance function, the reliability index of the structure is and failure probability P f It can be obtained by the following formula:

[0096]

[0097] In the formula, , , , , , , .

[0098] This embodiment is based on the high-order moment method, takes into account the randomness of the load during the operation of the actual dual-use highway-railway bridge, realizes the quantitative analysis of the reliability of static irregularity of the track on the dual-use highway-railway bridge, and provides guidance for the track operation and maintenance of similar projects.

[0099] The following is an explanation with reference to a specific example. This example is a road-rail dual-use cable-stayed bridge, and the track system on the bridge adopts CRTSⅢ type ballastless slab track.

[0100] S1: In this embodiment, a refined finite element model of the entire bridge is established using plate and shell elements, and the correctness of the model is verified by comparing it with the results of the design file.

[0101] S2: Construct the structural function function according to the track static irregularity specification index. The revised article of the specification "High-speed Railway Design Specification" stipulates that for high-speed railway long-span bridges, the track long-wave static irregularity adopts the 60m chord length method 7mm allowable deviation as the track long-wave static acceptance standard, so the track long-wave static irregularity structural function function can be constructed as follows:

[0102]

[0103] In the formula, G Lmax ( x 1, x 2… x n ) is the long-wave irregularity amplitude of ballastless track on long-span bridge under the action of various random variables, x 1- x n for n There are random variables to be considered, when Z L >0, the structure is in a reliable state. Z L <0, the structure is in failure state. Z L =0, the structure is in the limit state.

[0104] S3: The calculation of static irregularity of ballastless track on a highway-railway dual-use bridge needs to consider the effects of random loads such as highway and temperature during operation. In this example, the highway bridge deck adopts a two-way 6-lane system, and each lane is divided into a fast lane, a middle lane and a slow lane. The vehicle speed in each lane is constant; each lane only uses the vehicle weight as a random variable, ignoring the influence of the wheelbase, and it is assumed that the vehicles in each lane are traveling along the center line of the lane; the vehicle weight between lanes is considered to be an independent random variable; according to the speed requirements of the expressway, the distance between vehicles in each lane is 100m, and the vehicle load loading position diagram is as follows: Figure 3 shown.

[0105] According to the measured highway bridge deck vehicle data, the probability density of vehicle load distribution usually presents a multi-peak distribution, which can be expressed by n The probability distribution lines of the unimodal distributions are combined together to fit, assuming that i The probability density function of the vehicle load is ,Will n The probability density function of the combined vehicle load is as follows:

[0106]

[0107] The vehicle load probability density function was fitted to the measured highway bridge deck vehicle data. It was found that the weighted sum of two log-normal distribution probability density functions and one normal distribution probability density function was used to describe the probability density function of the vehicle load between lanes. The vehicle load probability density function can be expressed as follows:

[0108] The probability density function curve of vehicle load in each lane is as follows: Figure 4 The specific parameter values ​​are shown in Table 2 below:

[0109] Table 2 Highway load fitting function parameter value table

[0110]

[0111] After measuring the local climate conditions and fitting the data, the temperature load considers three types of temperature random loads: uniform heating, track system heating, and cable-beam temperature difference. The distribution characteristics of the random variables are shown in Table 3 below:

[0112] Table 3 Random variable distribution characteristics

[0113]

[0114] S4, S5: The random variables in Table 3 are transformed into the standard normal space using the Rosenblatt inverse transformation method, and then the 7-point estimated values ​​in the standard normal space are used to obtain the 7-point inverse normal transformation values ​​of the random variables, as shown in Table 4 below:

[0115] Table 4 Summary of 7-point inverse normal transformation values ​​of random variables

[0116]

[0117] S6: Substituting the load value into the finite element model when a single random variable changes and the rest of the random variables take the average value, we can get the curve of the long wave irregularity of the ballastless track on the highway-railway dual-use bridge under the change of each single random variable; this example considers 6 kinds of random variables in total, and a total of 36 curves of the long wave irregularity of the ballastless track on the highway-railway dual-use bridge can be obtained, such as Figure 5-Figure 10 As shown in the figure G ij ( i =1~6, j =1~7) indicates the i The random variable in j The long-wave static irregularity curve of ballastless track at the estimated points.

[0118] S7, S8: By counting the first four moments of the structural function function of each single variable, the first four moments of the structural function function of the long wave irregularity of the ballastless track on the highway-railway dual-use bridge can be obtained, which are summarized in the following Table 5:

[0119] Table 5 Summary of the first four moments of the single variable structural function functions and the long wave irregularity structural function functions

[0120]

[0121] Substitute the following formula:

[0122]

[0123] The fourth-order reliability index of long-wave static irregularity of ballastless track on highway-railway dual-use bridge can be obtained =2.879, and the corresponding failure probability is =1.988×10-3.

[0124] This embodiment is based on the high-order moment method. By calculating the high-order moment of the structure function function, no matter what distribution the structure function function conforms to, the sample distribution characteristics can be described by the high-order moment, and then the failure probability of the structure can be solved. The real bridge finite element model is combined with the high-order moment method to calculate the linear reliability of the ballastless track on the road-rail dual-use bridge, which can reflect the influence of various loads on the linear shape of the ballastless track on the road-rail dual-use bridge during the operation period, and realize the quantitative calculation of the linear reliability of the ballastless track on the road-rail dual-use bridge.

[0125] In order to implement the method of the embodiment of the present invention, the embodiment of the present invention also provides a computer program product, which includes computer instructions, and the computer instructions are stored in a computer-readable storage medium. The processor of the computer device reads the computer instructions from the computer-readable storage medium, and the processor executes the computer instructions, so that the computer device performs the steps of the above method.

[0126] Based on the hardware implementation of the above program modules, and in order to implement the method of the embodiment of the present invention, the embodiment of the present invention further provides an electronic device (computer device). Specifically, in one embodiment, the computer device may be a terminal, and its internal structure diagram may be as follows: Fig.11 As shown. The computer device includes a processor A01, a network interface A02, a display screen A04, an input device A05 and a memory (not shown in the figure) connected through a system bus. Among them, the processor A01 of the computer device is used to provide computing and control capabilities. The memory of the computer device includes an internal memory A03 and a non-volatile storage medium A06. The non-volatile storage medium A06 stores an operating system B01 and a computer program B02. The internal memory A03 provides an environment for the operation of the operating system B01 and the computer program B02 in the non-volatile storage medium A06. The network interface A02 of the computer device is used to communicate with an external terminal through a network connection. When the computer program is executed by the processor A01, the method of any one of the above embodiments is implemented. The display screen A04 of the computer device can be a liquid crystal display screen or an electronic ink display screen, and the input device A05 of the computer device can be a touch layer covered on the display screen, or a key, trackball or touchpad set on the computer device housing, or an external keyboard, touchpad or mouse, etc.

[0127] Those skilled in the art will understand that Fig.11 The structure shown in the figure is only a block diagram of a part of the structure related to the solution of the present application, and does not constitute a limitation on the computer device to which the solution of the present application is applied. The specific computer device may include more or fewer components than those shown in the figure, or combine certain components, or have a different arrangement of components.

[0128] The device provided by the embodiment of the present invention includes a processor, a memory, and a program stored in the memory and executable on the processor. When the processor executes the program, the method of any one of the above embodiments is implemented.

[0129] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Moreover, the present application may adopt the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program codes.

[0130] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0131] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0132] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0133] In a typical configuration, a computing device includes one or more processors (CPU), input / output interfaces, network interfaces, and memory.

[0134] The memory may include non-permanent memory in a computer-readable medium, random access memory (RAM) and / or non-volatile memory in the form of read-only memory (ROM) or flash RAM. The memory is an example of a computer-readable medium.

[0135] Computer readable media include permanent and non-permanent, removable and non-removable media that can be implemented by any method or technology to store information. Information can be computer readable instructions, data structures, program modules or other data. Examples of computer storage media include, but are not limited to, phase change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technology, compact disk read-only memory (CD-ROM), digital versatile disk (DVD) or other optical storage, magnetic cassettes, magnetic tape disk storage or other magnetic storage devices or any other non-transmission media that can be used to store information that can be accessed by a computing device. As defined herein, computer readable media does not include temporary computer readable media (transitory media), such as modulated data signals and carrier waves.

[0136] It can be understood that the memory of the embodiment of the present invention can be a volatile memory or a non-volatile memory, and can also include both volatile and non-volatile memories. Among them, the non-volatile memory can be a read-only memory (ROM), a programmable read-only memory (PROM), an erasable programmable read-only memory (EPROM), an electrically erasable programmable read-only memory (EEPROM), a magnetic random access memory (FRAM), a flash memory, a magnetic surface memory, an optical disc, or a compact disc read-only memory (CD-ROM); the magnetic surface memory can be a disk memory or a tape memory. The volatile memory can be a random access memory (RAM), which is used as an external cache. By way of example and not limitation, many forms of RAM are available, such as static random access memory (SRAM), synchronous static random access memory (SSRAM), dynamic random access memory (DRAM), synchronous dynamic random access memory (SDRAM), double data rate synchronous dynamic random access memory (DDRSDRAM), enhanced synchronous dynamic random access memory (ESDRAM), synchronous link dynamic random access memory (SLDRAM, SyncLink Dynamic Random Access Memory), and direct RAMbus random access memory (DRRAM, Direct Rambus Random Access Memory).The memories described in the embodiments of the present invention are intended to include, but are not limited to, these and any other suitable types of memories.

[0137] It should also be noted that the terms "include", "comprises" or any other variations thereof are intended to cover non-exclusive inclusion, so that a process, method, commodity or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, commodity or device. In the absence of more restrictions, the elements defined by the sentence "comprises a ..." do not exclude the existence of other identical elements in the process, method, commodity or device including the elements.

[0138] The above are only embodiments of the present application and are not intended to limit the present application. For those skilled in the art, the present application may have various changes and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application should be included within the scope of the claims of the present application.

Claims

1. A reliability analysis method for static irregularity of rail-road dual-use bridge track based on high-order moment method, characterized in that: The method comprises: Establish the finite element model of the actual bridge structure according to the design and construction drawings; According to the track static irregularity specification index, the structural function function is constructed; Generating fitting values ​​of random variables in the structural function according to measured highway bridge deck vehicle data and measured local climate conditions; the random variables are vehicle weights of each lane; The fitted values ​​of the random variables are converted into the same standard normal space by Rosenblatt inverse transformation, and the estimated point values ​​and weight values ​​of the fitted values ​​of the random variables in the standard normal space are obtained by Gauss-Hermite quadrature formula; Substituting the estimated point value and weight value of the fitting value of each random variable into the finite element model of the real bridge structure, and taking the mean of other random variables to obtain the univariate structural function function corresponding to each random variable; Solve the first four moments of the univariate structural function function corresponding to each random variable according to the fourth-order moment theory, and calculate the structural failure probability and reliability through the first four moments of all the univariate structural function functions; The fitting values ​​of random variables in the structural function function are generated according to the measured highway bridge deck vehicle data and the measured local climate conditions, including: Assume i The probability density function of the vehicle load is ,Will n The probability density function of the combined vehicle load is as follows: in, ; The probability density function of the vehicle load between lanes is described by the weighted sum of two log-normal distribution probability density functions and one normal distribution probability density function. The probability density function of the vehicle load is expressed as; Among them, p1, p2, p3, , , , , , All are fitting parameters; Measure local climate conditions and fit the data; The structural function includes: in, G Lmax ( x 1, x 2… x n ) is the long-wave irregularity amplitude of ballastless track on long-span bridge under the action of various random variables, x 1- x n for n A random variable, when Z L >0, the structure is in a reliable state. Z L <0, the structure is in failure state. Z L =0, the structure is in the limit state.

2. The reliability analysis method for static irregularity of rail-road dual-purpose bridge track based on high-order moment method according to claim 1 is characterized in that: The fitted values ​​of the random variables are transformed into the same standard normal space by inverse Rosenblatt transformation, including: The fitted values ​​of the random variables are transformed into the same standard normal space by Rosenblatt inverse transformation using the following calculation formula: in, T -1 ( U ) is the inverse Rosenblatt transform, U is a random variable with standard normal distribution, X is a random variable with any distribution.

3. The reliability analysis method for static irregularity of rail-road dual-purpose bridge track based on high-order moment method according to claim 2 is characterized in that: The estimated point value and weight value of the fitting value of the random variable in the standard normal space are obtained by the Gauss-Hermite quadrature formula, including: For a random variable in the standard normal space, we determine k The expression of the order central moment is: in, is a random variable after inverse Rosenblatt transformation, k for k Order central moment; is the weight function; The Gauss-Hermite quadrature formula for determining the weight function is expressed as: in, ; x j and A j They are weight functions exp(- x 2 )’s estimated point values ​​and weight values ​​for the Gauss-Hermite quadrature formula; m is the number of estimated points; k for k Order central moment; Substitute the fitted value of the random variable in the standard normal space into the k From the order central moment expression and the Gauss-Hermite quadrature formula expression of the weight function, the estimated point value and weight value of the fitting value of the random variable in the standard normal space are obtained.

4. The reliability analysis method for static irregularity of rail-road dual-purpose bridge track based on high-order moment method according to claim 3 is characterized in that: Solving the first four order moments of the univariate structure function function corresponding to each random variable according to the fourth order moment theory includes: The first four moments of the univariate structural function function corresponding to each random variable are solved using the following calculation formula according to the fourth-order moment theory: in, is the first four moments of the univariate structure function, P j is the weight value corresponding to each estimated point, m To estimate the number of points, For estimated points x j The structural function value at ; , k for k Order central moment; .

5. The reliability analysis method for static irregularity of rail-road dual-purpose bridge track based on high-order moment method according to claim 4 is characterized in that: The structural failure probability and reliability are calculated by the first four moments of all the univariate structural function functions, including: Obtaining the first four moments of the structure function function through the first four moments of all the univariate structure function functions; The structural failure probability and reliability are calculated based on the first four moments of the structural performance function.

6. The reliability analysis method for static irregularity of rail-road dual-purpose bridge track based on high-order moment method according to claim 5 is characterized in that: The first four moments of the structure function function are obtained by using the first four moments of all the univariate structure function functions, including: The first four moments of the structure function function are obtained by using the following calculation formula through the first four moments of all the univariate structure function functions: in, , , , is a univariate function G i The first four moments of n To estimate the number of points, is the value of the structural function when all random variables take their mean value, is a single variable function G j The variance of .

7. The reliability analysis method for static irregularity of rail-road dual-purpose bridge track based on high-order moment method according to claim 5 is characterized in that: The structural failure probability and reliability are calculated based on the first four moments of the structural performance function, including: The following calculation formula is used to calculate the structural failure probability and reliability based on the first four moments of the structural performance function: in, is the reliability of the structure, P f is the probability of structural failure, , , , , , , , , is the third-order central moment of the structure function; is the fourth-order central moment of the structure function, It is the second-order reliability index of the structural performance function.

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