Time-varying ellipsoid model structure reliability evaluation method and device, equipment and medium

Abstract

The invention provides a time-varying ellipsoid model structure reliability evaluation method and device, equipment and a medium, and belongs to the technical field of structural engineering reliability, and the method comprises the steps: obtaining a response sample set corresponding to a target structure; dispersing each response sample into a plurality of sub-intervals according to a fixed time interval; for each response sample, generating a respective corresponding sample point in the target coordinate system based on the response data of each subinterval in the response sample; for each subinterval, establishing a time-varying ellipsoid model enveloping all sample points in the subinterval, and determining a respective corresponding failure area based on each time-varying ellipsoid model; and determining the instantaneous spanning rate of the subinterval based on each failure area, and determining the reliability of the target structure based on each instantaneous spanning rate. According to the time-varying ellipsoid model structure reliability evaluation method and device, the equipment and the medium provided by the invention, the reliability of the target structure under the dynamic load condition can be accurately evaluated.

Description

Technical Field

[0001] This application belongs to the field of structural engineering reliability technology, and more specifically, relates to a method, device, equipment, and medium for evaluating the reliability of time-varying ellipsoidal model structures. Background Technology

[0002] Structural reliability is a core indicator for measuring the performance and safety of engineering structures. For transportation infrastructure such as bridges, their main beams are subjected to various dynamic external loads such as wind loads and vehicle dynamic loads over a long period of time. The dynamic characteristics of the loads will cause uncertainty in the structural response, which is directly related to the safe service and operational efficiency of the bridge. Therefore, accurately assessing the dynamic reliability of certain structures (such as the main beam of a bridge) in engineering structures is of great engineering significance.

[0003] In existing technologies, structural reliability analysis methods are mainly divided into two categories: probabilistic reliability models and non-probabilistic reliability models. Probabilistic reliability models rely on the precise probability distribution parameters of the input random variables. However, in practical engineering, obtaining sufficient probability distribution sample data often faces high economic costs or difficult technical challenges. To address the problem of insufficient sample data, non-probabilistic reliability models have been proposed and developed. These models describe uncertainties using bounded sets such as intervals and ellipsoids, reducing the data requirements. However, most existing non-probabilistic reliability models are designed for static uncertainty scenarios and cannot effectively capture and evaluate the time-varying reliability of structures (such as the main beam of the bridge mentioned above) under dynamic external loads.

[0004] Therefore, there is an urgent need for a method that can accurately assess the structural reliability under dynamic load conditions. Summary of the Invention

[0005] This application provides a method, apparatus, device, and medium for assessing the reliability of a time-varying ellipsoidal model structure, addressing the technical problem of lacking an effective method to accurately assess structural reliability under dynamic loads in the prior art, and achieving the goal of accurately assessing the reliability of the target structure under dynamic load conditions. To achieve the above objective, the technical solution provided by this application is as follows: Firstly, a method for assessing the structural reliability of a time-varying ellipsoidal model is provided, including: Obtain the response sample set corresponding to the target structure. The response sample set is used to reflect the dynamic behavior of the target structure. The response sample set includes multiple response samples. One response sample is the response data of the target structure model obtained by dynamic simulation under a dynamic load and changing over time, or one response sample is the real response data of the target structure obtained by actual detection of the target structure by sensors and changing over time within a preset time. Each response sample is discretized into several sub-intervals according to a fixed time interval. Each sub-interval in a response sample is characterized by the sub-interval response data, which is characterized by the response data corresponding to the first time of the sub-interval and the response data corresponding to the last time of the sub-interval. For each response sample, based on the response data of each sub-interval in the response sample, corresponding sample points are generated in the target coordinate system. The x-coordinate and y-coordinate of the sample point corresponding to the response data of the first time and the last time of the sub-interval are respectively. For each sub-interval, a time-varying ellipsoid model is established to enclose all sample points within the sub-interval. Based on each time-varying ellipsoid model, the corresponding failure region is determined. For a sub-interval, the failure region corresponding to the sub-interval is represented as the region corresponding to the failure response sample set in the target coordinate system. Each failure sample in the failure response sample set is the response data in the sub-interval where the response data at the first moment is safe but the response data at the last moment exceeds a set threshold under a certain external load. The instantaneous slack rate of each sub-interval is determined based on each failure region, and the reliability of the target structure is determined based on each instantaneous slack rate.

[0006] Secondly, a reliability assessment device for a time-varying ellipsoidal model structure is provided, comprising: The acquisition module is used to acquire the response sample set corresponding to the target structure. The response sample set is used to reflect the dynamic behavior of the target structure. The response sample set includes multiple response samples. One response sample is the response data of the target structure model obtained by dynamic simulation under a dynamic load and changing over time, or one response sample is the real response data of the target structure obtained by actual detection of the target structure by sensors and changing over time within a preset time. The discrete module is used to discretize each response sample into several sub-intervals according to a fixed time interval. Each sub-interval in a response sample is characterized by the sub-interval response data, which is characterized by the response data corresponding to the first time of the sub-interval and the response data corresponding to the last time of the sub-interval. The sample point generation module is used to generate corresponding sample points in the target coordinate system for each response sample based on the response data of each sub-interval in the response sample. The x-coordinate and y-coordinate of the sample point corresponding to the response data of the first time and the last time of the sub-interval are respectively. An ellipsoid model module is established to create a time-varying ellipsoid model that encloses all sample points within each sub-interval. Based on each time-varying ellipsoid model, the corresponding failure region is determined. For a sub-interval, the failure region corresponding to the sub-interval is represented as the region corresponding to the failure response sample set in the target coordinate system. Each failure sample in the failure response sample set is the response data in the sub-interval where the response data at the first moment is safe but the response data at the last moment exceeds a set threshold under a certain external load. The structural reliability determination module is used to determine the instantaneous span rate of each sub-interval based on each failure region, and to determine the reliability of the target structure based on each instantaneous span rate.

[0007] Thirdly, embodiments of this application also provide an electronic device, which includes a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the time-varying ellipsoid model structure reliability assessment method provided by any possible implementation of the first aspect.

[0008] Fourthly, embodiments of this application also provide a computer-readable storage medium storing a computer program that, when executed by a processor, implements the time-varying ellipsoid model structure reliability assessment method provided by any possible implementation of the first aspect.

[0009] The beneficial effects of the technical solution provided in this application are as follows: This application provides a method, apparatus, equipment, and medium for assessing the structural reliability of a time-varying ellipsoidal model. Compared with related technologies, this application first obtains response samples that can realistically reflect the dynamic behavior of the main beam of a bridge through dynamic simulation, without relying on a large number of probability distribution samples, thus solving the problem of high cost or difficulty in obtaining accurate probability distribution samples in actual engineering for probabilistic reliability models. Second, an ellipsoidal model enveloping all sample points can be directly established through response samples to describe the uncertainty of the dynamic response. Moreover, this model is time-varying, breaking through the limitations of existing non-probabilistic reliability model research that focuses on theoretical derivation and improvement. At the same time, the time-varying data used in the model construction process are mostly simulated data generated by mathematical time series, lacking deep integration with actual engineering structures. Finally, by determining the failure domain and calculating the instantaneous span rate, the structural reliability assessment under dynamic load conditions is accurately realized, solving the problem of lacking an effective method to accurately assess the structural reliability under dynamic loads in the prior art, and significantly improving the accuracy and engineering applicability of the assessment results. Attached Figure Description

[0010] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments of this application will be briefly introduced below.

[0011] Figure 1 A flowchart illustrating the reliability assessment method for a time-varying ellipsoidal model structure provided in this application embodiment; Figure 2 The bridge mid-span displacement time history diagram provided in the embodiments of this application; Figure 3 This is a schematic diagram illustrating the transformation of bridge mid-span displacement response sample points in the target coordinate system according to an embodiment of this application. Figure 4 This is a schematic diagram of the interval model provided in the embodiments of this application; Figure 5 A schematic diagram of an ellipsoidal model provided in an embodiment of this application; Figure 6 A schematic diagram of the standardized ellipsoid model provided in the embodiments of this application; Figure 7 A schematic diagram of the failure domain provided in the embodiments of this application; Figure 8 A schematic diagram of the limit function provided in the embodiments of this application; Figure 9 This is a schematic diagram of an ellipsoidal model under the [0, 1] time period provided in the embodiments of this application; Figure 10 This is a schematic diagram of the ellipsoidal model under the time period [7, 8] provided in the embodiments of this application; Figure 11 A comparison of the reliability of three methods under scenario 1 provided in the embodiments of this application; Figure 12 A comparison of the reliability of three methods under scenario 2 provided in the embodiments of this application; Figure 13 A comparison of the reliability of three methods under scenario 3 provided in the embodiments of this application; Figure 14 A comparison of the reliability of three methods under scenario 4 provided in the embodiments of this application; Figure 15 This is a structural block diagram of the time-varying ellipsoid model structure reliability assessment device provided in the embodiments of this application; Figure 16 A schematic block diagram of an electronic device provided in an embodiment of this application. Detailed Implementation

[0012] The embodiments of this application are described below with reference to the accompanying drawings. It should be understood that the embodiments described below with reference to the accompanying drawings are exemplary descriptions for explaining the technical solutions of the embodiments of this application, and do not constitute a limitation on the technical solutions of the embodiments of this application.

[0013] Those skilled in the art will understand that, unless specifically stated otherwise, the singular forms “a,” “an,” “the,” and “the” used herein may also include the plural forms. It should be further understood that the terms “comprising” and “including” as used in embodiments of this application mean that the corresponding feature can be implemented as the presented feature, information, data, step, operation, element, and / or component, but do not exclude implementation as other features, information, data, step, operation, element, component, and / or combinations thereof supported by the art. It should be understood that when we say that an element is “connected” or “coupled” to another element, the one element can be directly connected or coupled to the other element, or it can mean that the one element and the other element establish a connection relationship through an intermediate element. Furthermore, “connected” or “coupled” as used herein can include wireless connection or wireless coupling. The term “and / or” as used herein indicates at least one of the items defined by the term; for example, “A and / or B” can be implemented as “A,” or as “B,” or as “A and B.” When describing multiple (two or more) items, if the relationship between the multiple items is not explicitly defined, the multiple items can refer to one, several or all of the multiple items. For example, the description of "parameter A includes A1, A2, A3" can be implemented as parameter A includes A1 or A2 or A3, or it can be implemented as parameter A includes at least two of the three items A1, A2 and A3.

[0014] This application provides a method for assessing the reliability of a time-varying ellipsoidal model structure. This method can be executed by an electronic device, such as... Figure 1 As shown, the method may include: S101: Obtain the response sample set corresponding to the target structure. The response sample set is used to reflect the dynamic behavior of the target structure. The response sample set includes multiple response samples. One response sample is the response data of the target structure model obtained by dynamic simulation under a dynamic load and changing over time, or one response sample is the real response data of the target structure obtained by actual detection by sensors and changing over time within a preset time.

[0015] In this embodiment, the target structure can be a bridge main beam structure, an aircraft wing structure, or other structures from which response samples can be obtained; the response can be displacement response, deformation response, strain response, etc. The response samples can be obtained by simulating the target structure model. Specifically, the target structure model can be a bridge main beam model, an aircraft wing structure model, or other structures from which response samples can be obtained. In the simulation software, by establishing a structural model corresponding to the target structure and inputting the material performance parameters of the target structure and the external load data borne by the target structure, the dynamic behavior of the target structure under the simulated environment can be simulated to obtain the required response data. For example, a set of mid-span displacement time history data of the main beam structure model under different external loads can be obtained. This data can be a response dataset represented by a set of mid-span displacement curves that change over time. The response samples can also be measured by sensors on the actual target structure. Specifically, sensors capable of obtaining response data can be pre-deployed at fixed points on the target structure. The data obtained by the sensors on the target structure under actual external loads, showing changes over a preset time period, can be used as the response data. For example, the response data obtained each day can be used as a response curve over time. The final result is a set of real response datasets that change over a preset time period of one day. External loads refer to forces or actions applied to the structure that change over time. Furthermore, this change is random and cannot be described by a definite numerical value (dynamically uncertain external loads). In this embodiment, external loads can be wind loads, wave loads, vehicle loads, etc.

[0016] As can be concluded from the above, for time-varying uncertain parameters or loads on the target structure, a series of dynamic response data covering uncertain external loads can be obtained as a response dataset through dynamic simulation technology, or a set of dynamic response data can be obtained as a response dataset by using actual measured data with a preset time period of days. The embodiments of this application can obtain the dynamic behavior of the target structure in a real service environment through simulation when there are no sensors to obtain model response data, or obtain a response sample set based on measured data when only sensors are available, providing multiple means of obtaining the response sample set.

[0017] S102: Discretize each response sample into several sub-intervals according to a fixed time interval. Each sub-interval in a response sample is characterized by the sub-interval response data, which is characterized by the response data corresponding to the first time of the sub-interval and the response data corresponding to the last time of the sub-interval.

[0018] In this embodiment, by inputting the material property data of the target structure and the external loads it experiences into the simulation software, data such as... can be obtained. Figure 2The multiple response curves shown represent the response data of the mid-span displacement of the main beam model as a function of time. After determining the changes of the multiple mid-span displacement curves, upper and lower dashed lines are drawn according to the trend of mid-span displacement changes to characterize the interval in which the changes of the multiple mid-span displacement curves are located. The external load conditions of each response curve are different, and the external load conditions of each response curve can be set based on experience or calculated based on theoretical basis. For example, the wind and wave load can be calculated based on the wind and wave power spectrum. Figure 2 The horizontal axis represents time, and the vertical axis represents the mid-span displacement of the main beam model; the fixed time interval can be 1 second or 2 seconds, etc., and this fixed time interval is preset based on the response data. Figure 2 As shown to That is, a subinterval, in which... to In the middle, we can see that Time and If there are multiple response curves corresponding to the mid-span displacement response data at a given time, then the response data for that sub-interval is the first time interval. The corresponding mid-span displacement data and the final time () The data corresponds to multiple mid-span displacements.

[0019] As can be seen from the above, the embodiments of this application discretize continuous response samples into several sub-intervals at fixed time intervals, and characterize the response features of a sub-interval using only the response data at the beginning and end of the sub-interval. This provides a theoretical basis for calculating the instantaneous span rate of each sub-interval using the span rate theory, greatly reducing the computational complexity. On the other hand, the fixed time interval discretization method ensures uniform sampling in the time dimension, and the response data at the beginning and end of the sub-interval can effectively reflect the dynamic change trend of the structural response within the sub-interval. This not only preserves the core characteristics of time-varying uncertainty, but also provides regular and efficient basic data support for the subsequent construction of a time-varying ellipsoidal model, making subsequent uncertainty modeling based on sub-interval data more feasible and computationally efficient.

[0020] S103: For each response sample, based on the response data of each sub-interval in the response sample, generate corresponding sample points in the target coordinate system. The x-coordinate and y-coordinate of the sample point corresponding to the response data of the first time and the last time of the sub-interval are respectively.

[0021] In this embodiment, the response data of each sub-interval in step S102 is used to generate sample points for that sub-interval in the target coordinate system, such as... Figure 3 As shown, in the sub-interval to In the middle, the curve of each sample The response value at time t is used as the x-axis. The response value at time t is used as the ordinate and mapped to... The plane completes the mapping of corresponding points of all sample curves.

[0022] Specifically, in combination Figure 2 and Figure 3 Let's look at the sub-intervals. to middle, Figure 2 The response data corresponding to the first moment of the response curve where point A is located is taken as the abscissa value of the response data sample point of point A. Figure 3 The x-coordinate value of point A in the diagram ), Figure 2 The response data corresponding to the last moment of the response curve where point A is located is taken as the ordinate value of the response data sample point at point A. Figure 3 The ordinate value of point A in the diagram Similarly, it can be seen that in the subintervals... to middle, Figure 2 The response curve where point C is located and Figure 2 The sample points corresponding to the response curves at point B are generated in the same way as the sample points at point A, such as... Figure 3 The C sample point and the B sample point are shown in the figure.

[0023] As can be seen from the above, by mapping the response data of the first and last moments of each sub-interval to sample points in the target coordinate system, the dimensionality of the time-domain dynamic response data is compressed, transforming the originally continuously changing response curve over time into discrete sample points on a two-dimensional plane, which greatly reduces the computational complexity of subsequent modeling. Furthermore, by using the horizontal and vertical coordinates to correspond to the response values ​​of the first and last moments of the sub-interval, the dynamic change characteristics of the structural response within that sub-interval are fully preserved, ensuring that each sample point can reflect the response fluctuation information within the corresponding time period. At the same time, this unified coordinate mapping method allows the dynamic characteristics of all response samples in that sub-interval to be presented on the same plane, forming a regular distribution of sample points. This provides structured and intuitive basic data for the subsequent construction of the minimum volume ellipsoid model, effectively improving the efficiency and accuracy of subsequent uncertainty modeling.

[0024] S104: For each sub-interval, establish a time-varying ellipsoid model that encloses all sample points within the sub-interval. Based on each time-varying ellipsoid model, determine the corresponding failure region. For a sub-interval, the failure region corresponding to the sub-interval is represented as the region corresponding to the failure response sample set in the target coordinate system. Each failure sample in the failure response sample set is the response data in the sub-interval where the response data at the first moment is safe but the response data at the last moment exceeds a set threshold under a certain external load.

[0025] In one embodiment of this application, establishing a time-varying ellipsoid model encompassing all sample points within the sub-interval includes: Based on the x-coordinate and y-coordinate of each sample point in all sample points, determine the maximum, minimum, maximum and minimum x-coordinate values ​​of all sample points. Use the arithmetic mean of the maximum and minimum x-coordinate values ​​as the x-coordinate of the center point of the time-varying ellipsoid model, and use the arithmetic mean of the maximum and minimum y-coordinate values ​​as the y-coordinate of the center point of the time-varying ellipsoid model to characterize the center point coordinates of the time-varying ellipsoid model. Based on the x and y coordinates of each sample point in all sample points and the coordinates of the center point of the time-varying ellipsoid model, the feature matrix of the time-varying ellipsoid model is determined. Based on the center point coordinates and feature matrix of the time-varying ellipsoid model, a time-varying ellipsoid model with the smallest volume that encloses all sample points within the sub-interval is established.

[0026] In one embodiment of this application, based on the center point coordinates of the time-varying ellipsoid model and the feature matrix of the time-varying ellipsoid model, a time-varying ellipsoid model that encloses all sample points within the sub-interval and has the smallest volume is established, including: Establish the smallest two-dimensional rectangular interval model that encloses all sample points; Based on the center point coordinates and the characteristic matrix of the time-varying ellipsoid model, an ellipsoid model passing through each vertex of the two-dimensional rectangular interval model is drawn as the initial ellipsoid model. The initial ellipsoid model is rotated multiple times in the target coordinate system with the origin of the target coordinate system as the reference, and the coordinates of each sample point after rotation and the feature matrix of the time-varying ellipsoid model after rotation are determined. Based on the coordinates of each sample point after rotation and the feature matrix of the time-varying ellipsoid model after rotation, the volume of the ellipsoid model corresponding to each rotation is determined to obtain the ellipsoid model with the smallest volume.

[0027] In one embodiment of this application, based on the center point coordinates of the time-varying ellipsoid model and the characteristic matrix of the time-varying ellipsoid model, an ellipsoid model passing through each vertex of the two-dimensional rectangular interval model is drawn as an initial ellipsoid model, including: If sample points exist at each vertex of the two-dimensional rectangular interval model, then based on the semi-axis length of the two-dimensional rectangular interval model, the semi-axis length of the initial ellipsoid model is determined using the semi-axis length formula, and the initial ellipsoid model is determined. The semi-axis length formula is: (1) in, The semi-axis length of the initial ellipsoid model. This is the semi-axis length of the two-dimensional rectangular interval model. The dimension of the initial ellipsoid model; If there are no sample points at each vertex of the two-dimensional rectangular interval model, an adjustment factor is introduced. This adjustment factor is used to scale the major and minor axes of the initial ellipsoid model until sample points exist on the boundary of the ellipsoid model, thus determining the initial ellipsoid model. The formula for the adjustment factor is: (2) in, To adjust the factor, To obtain the maximum value among all calculation results, For summation, For the first The sample point at the th th dimensional coordinates, The center point of the time-varying ellipsoid model is at the th dimensional coordinates, This is the semi-axis length of the initial ellipsoid model.

[0028] In this embodiment, for each sub-interval, to ensure that all sample points within that sub-interval fall within the interior of the time-varying ellipsoid model corresponding to that sub-interval, the following relational constraint exists: (3) in, Let be the coordinates of any sample point inside the time-varying ellipsoid model. The coordinates of the center point of the time-varying ellipsoid model are: The feature matrix that determines the size and shape of the ellipsoid model, The symbol is for transpose. For the two-dimensional scene in this embodiment, to establish a time-varying ellipsoidal model encompassing all sample points within each sub-interval, it is necessary to determine the coordinates of the ellipsoid's center point and the feature matrix. Simultaneously, the optimization of the time-varying ellipsoidal model must be considered. To establish an ellipsoidal model containing all sample points and with the smallest volume, the ellipsoid can be rotated, and all rotation angles can be iterated to find an ellipsoidal model with the smallest volume.

[0029] As can be seen from the above, the relational constraint formula can strictly limit all sample points to be inside the time-varying ellipsoid model from a mathematical perspective, avoiding incomplete description of the uncertainty of the structural dynamic response due to the omission of sample points, and laying the foundation for the accuracy of subsequent reliability assessment. In the two-dimensional scenario, it is necessary to determine the coordinates of the ellipsoid center point and the feature matrix. The coordinates of the center point can anchor the core position of the model in the target coordinate system, ensuring that the central trend of the model and the sample distribution are consistent. The feature matrix can accurately define the size and shape of the ellipsoid, so that the model can match the difference in the degree of dispersion of samples in different sub-intervals, solving the problem that traditional static non-probabilistic models are difficult to dynamically adjust their shape according to the sample distribution.

[0030] In this embodiment, the interval model describes an uncertain mathematical model by defining the range of variation of an interval. It can be expressed by equation (4): (4) in, For the first Any real number value in the dimensional interval model; such as Figure 4 The diagram shows a schematic of an interval model, defining the midpoint of the interval model. and the radius of the interval model The midpoint of this interval model can be represented by equation (5): (5) The radius of this interval model can be expressed as shown in equation (6): (6) in, For the first Lower bound of the dimensional interval model For the first The upper limit of the dimensional interval model, in this embodiment, is applied to a two-dimensional scenario, so... .

[0031] In this embodiment, in order to establish a time-varying ellipsoidal model that encloses all sample points within the sub-interval, it is difficult to determine the boundary of the sample points by using the semi-axis length of the ellipsoidal model as an unknown quantity. The computational load is large and it is not easy to obtain results. However, the boundary of the interval model can be determined by knowing the maximum and minimum values ​​of the coordinates. Therefore, by equations (4), (5) and (6), the smallest two-dimensional rectangular interval model that encloses all sample points, as well as its midpoint and radius, can be obtained. The center point of the two-dimensional rectangular interval model and the center point of the time-varying ellipsoidal model are theoretically completely coincident. This provides a stable benchmark for subsequent rotation optimization to find the final time-varying ellipsoidal model.

[0032] In this embodiment, if there are sample points at all four vertices of the two-dimensional rectangular interval model, then the semi-axis length formula (1) is used. Determine the semi-axis length of the initial ellipsoid model. and (in, (where the radius or half-width of the two-dimensional rectangular interval model is used), and the diagonal matrix corresponding to the initial feature matrix is ​​used. It can be expressed by equation (7): (7) in, It is in English. The abbreviation for "(diagonal)" in mathematics and engineering refers to the construction of a diagonal matrix; in the two-dimensional scenario of this application embodiment, this diagonal matrix... It is A diagonal matrix, with elements placed sequentially along the main diagonal (the diagonal from the top left corner to the bottom right corner). and Elements not located on the main diagonal are all Since the initial ellipsoid does not rotate, the coordinate system is consistent with the target coordinate system of the two-dimensional rectangular interval model. Therefore, the feature matrix is ​​a diagonal matrix, which is the corresponding initial feature matrix in this case. .

[0033] If there are no sample points at any of the four vertices of the two-dimensional rectangular interval model, then an adjustment factor is introduced. The semi-axis length is adjusted by adjusting the factor formula. and Then we obtain the initial diagonal matrix, at which point the initial diagonal matrix is... It can be expressed by equation (8): (8) That is, the initial feature matrix corresponding to this case. .

[0034] After determining the initial feature matrix, and combining the coordinates of the center point of the time-varying ellipsoid model, an ellipsoid model passing through each vertex of the two-dimensional rectangular interval model is drawn as the initial ellipsoid model. The two-dimensional ellipsoid model can be represented as shown in equation (9): (9) in, Let be the coordinates of any point on the ellipsoid. The center point of the time-varying ellipsoid model, This is the transpose symbol.

[0035] In this embodiment, the origin of the target coordinate system is used as the reference, and the coordinates are located between 0 and... Within the angular range (due to the symmetry of the rotation matrix and the geometric symmetry of the ellipsoid model, 0 to...) The rotation within the range can cover the existence of all possible ellipsoids containing all sample points, with sufficiently small angular increments. The initial ellipsoid model is rotated multiple times, with each rotation corresponding to a rotation angle. (Angle increment) The value can be set based on experience; the smaller the value, the more accurate the subsequent calculation of the instantaneous span rate of each sub-interval will be. For each rotation, the coordinates of each sample point after rotation and the feature matrix of the time-varying ellipsoid model after rotation can be obtained.

[0036] Specifically, for each rotation, a two-dimensional rotation transformation matrix can be used. For the original coordinates of all sample points within each sub-interval Perform the transformation to obtain the sample coordinates in the new coordinate system after rotation. The transformation relationship can be expressed by equation (10): (10) Wherein, the rotation transformation matrix It can be expressed as follows (11): (11) The diagonal matrix in the new coordinate system after rotation Restore the characteristic matrix to the original coordinate system It can be restored using the following formula (12): (12) At the same time, we obtain the new coordinates point restored to the target coordinate system. : (13) The characteristic matrix is ​​obtained after each rotation and restoration to the original coordinate system. Then, the volume of the ellipsoid under the current rotation angle is calculated using the ellipsoid volume formula, which is shown in equation (14) below: (14) in, The symbol for cumulative multiplication indicates a series of multiplication operations; for the two-dimensional scene in this embodiment ( Represents dimension, so The volume factor formula is: (15) Therefore, volume factor .

[0037] In this embodiment, a heuristic algorithm (such as a genetic algorithm or a simulated annealing algorithm) can be used to traverse the volume values ​​of all ellipsoidal models corresponding to the rotation angles, compare and select the ellipsoidal model with the smallest volume, and the rotation angle corresponding to this model is the optimal rotation angle. The corresponding feature matrix is ​​the final time-varying ellipsoidal model feature matrix.

[0038] As can be seen from the above, the embodiments of this application define the interval range and calculate its midpoint and radius through an interval model. Compared with directly solving the sample point boundary using the semi-axis length of the ellipsoid as the unknown, it only needs to obtain the maximum and minimum values ​​of the sample point coordinates to quickly lock the interval boundary, which greatly simplifies the initial modeling process of the time-varying ellipsoid model. At the same time, it avoids the problems of large computational load and difficulty in determining the boundary when directly solving the ellipsoid parameters. Furthermore, for different scenarios where the vertices of the two-dimensional rectangular interval model have sample points or not, the initial feature matrix is ​​determined by the semi-axis length formula and adjustment factor, respectively, to ensure that the initial ellipsoid can completely enclose all sample points. (When none of the four vertices of the two-dimensional rectangular interval model contain sample points, the semi-axis length is scaled by adjusting the factor until the ellipsoid boundary contains sample points.) This achieves adaptability to different sample distribution scenarios and ensures the integrity of the initial model's envelope. Finally, the smallest ellipsoid is selected by traversing and filtering through a two-dimensional rotation transformation matrix and a heuristic algorithm. The minimum volume characteristic can eliminate the interference of redundant space on the description of uncertainty, making the ellipsoid model more consistent with the actual sample distribution. This significantly improves the accuracy of characterizing the structural response uncertainty within the sub-interval, laying a highly reliable model foundation for subsequent determination of failure regions and calculation of failure probabilities based on the time-varying ellipsoid model.

[0039] In one embodiment of this application, for each time-varying ellipsoidal model, the corresponding failure region is determined based on each time-varying ellipsoidal model, including: Determine the failure threshold of the response sample, and based on the failure threshold of the response sample, determine the horizontal and vertical failure thresholds in the target coordinate system. Based on the failure thresholds on the horizontal and vertical axes, two failure criterion lines are determined, which are parallel to the horizontal and vertical axes of the target coordinate system, respectively. Based on the two failure criterion lines and the time-varying ellipsoid model, the corresponding failure region is determined.

[0040] In this embodiment, a failure threshold for the target structure's response data is determined. This failure threshold characterizes the situation where the target structure fails when its dynamic response exceeds this threshold. Specifically, for example, in simulation software, a dynamic external load is applied to the main girder model of a bridge, and if the mid-span displacement response curve of the main girder model exceeds a set threshold at a certain moment, based on span theory, it is considered that the bridge structure may fail at that moment. In the smallest volume ellipsoidal model, the physical meaning of the horizontal and vertical axes of the target coordinate system are the response data of the target structure at the first and last moments of that sub-interval. Therefore, determining the failure threshold for the target structure's response data allows us to determine the horizontal and vertical failure thresholds in the target coordinate system. For a specific sub-interval, such as... Figure 5 As shown, this is the ellipsoidal model with the smallest volume that encloses all sample points in the target coordinate system. Figure 5 On Failure time criterion and The time-based failure criterion is the display of the horizontal and vertical failure thresholds in the target coordinate system. Specifically, it is determined by... Figure 5 It can be seen that within this sub-interval, the failure threshold of the target structure response data is 0.066 (the negative sign before the coordinate values ​​in the figure only represents the direction). Figure 5 The failure threshold of 0.066 shown is set based on experience. At this point, based on the two failure criterion lines and the ellipsoid model, the failure region within this sub-interval can be determined (based on the span theory, i.e., the structural safety response data at the first moment does not exceed 0.066, and the structural failure response data at the last moment exceeds 0.066; in this case, the failure region is the fourth quadrant region, which is defined as...). Failure time criterion and The failure criteria at any given moment are respectively used as the fourth quadrant region in a coordinate system established by the horizontal and vertical axes of a two-dimensional coordinate system.

[0041] As can be seen from the above, the embodiments of this application transform the critical failure state of the target structure into the horizontal and vertical coordinate failure thresholds in the target coordinate system, so that the physical meaning of the structural functional failure directly corresponds to the quantitative parameters of the coordinate system. Since both the horizontal and vertical axes represent the response data of the target structure, the determination of the threshold can accurately anchor the judgment criterion of "failure when the response exceeds the limit", avoiding the problem of failure boundary relying on experience judgment and lacking quantitative basis in traditional static evaluation. Combined with the time-varying ellipsoid model to determine the failure area, the high-risk range of the structural dynamic response in each sub-interval can be accurately locked, without omitting the uncertainty risk points covered by the ellipsoid model, and without including irrelevant areas, providing an accurate regional basis for subsequent calculation of the failure probability of the sub-interval, effectively improving the objectivity and accuracy of structural failure judgment under dynamic load.

[0042] In one embodiment of this application, for each time-varying ellipsoid model, the corresponding failure region is determined based on two failure criterion lines and the time-varying ellipsoid model, including: The time-varying ellipsoid model and the two failure criterion lines are simultaneously normalized and standardized to obtain the processed standard circle model and the standardized two failure criterion lines. Based on the two standardized failure criterion lines and the standard circle model, the corresponding failure regions are determined.

[0043] In this embodiment, for each sub-interval, the ellipsoid model that encloses all sample points within the sub-interval and has the smallest volume is normalized and standardized. The normalization and standardization of the model does not change the distribution shape of the sample points. The main purpose is to eliminate the influence of dimensions and scale, thereby more clearly analyzing the geometric characteristics of the ellipsoid.

[0044] Specifically, in order to eliminate the influence of dimensions and scale on the analysis of ellipsoidal geometric properties, the coordinates of the sample points of the time-varying ellipsoidal model in the original coordinate system are first transformed to the normalized space using formula (16). In the process, the normalized coordinates of the sample points are obtained. : (16) The original time-varying ellipsoidal model in normalized space Converted to: (17) The normalized feature matrix is ​​as follows: (18) To convert the ellipsoidal model into a standard circular model that is easier to analyze, the normalized feature matrix can be decomposed using Choleskey decomposition. Specifically, the normalized feature matrix can be... Decompose into a lower triangular matrix The product of its transpose: (19) To introduce a variable as the transpose symbol ,make The ellipsoidal model in normalized space is transformed into a standard circle model: (20) As can be seen from the above, this embodiment achieves the transformation from an ellipsoidal model to a standard circle model through normalization and standardization, eliminating the differences in dimensions and scales of response data of different dimensions, and avoiding misjudgment of ellipsoidal geometric characteristics caused by inconsistent dimensions; by transforming the ellipsoidal geometry into a regular circle, the problem of failure region determination caused by the complexity of the ellipsoidal boundary is solved, and the calculation process is simplified; at the same time, the entire transformation process does not change the shape of the sample point distribution, fully preserving the uncertainty information of the dynamic response of the structure within the sub-interval, improving the efficiency and accuracy of failure region determination, and providing a precise regional analysis basis for subsequent sub-interval failure probability calculation.

[0045] In this embodiment, as Figure 6 As shown, Figure 6 That is Figure 5 The standard circle model after normalization and standardization, and the standardized model Failure time criterion and standardized The failure criterion at this moment is that the failure area is... Figure 6 The region between the two failure criterion lines and within the area of ​​the standard circle model.

[0046] S105: Determine the instantaneous slack rate of each sub-interval based on each failure region, and determine the reliability of the target structure based on each instantaneous slack rate.

[0047] In one embodiment of this application, the instantaneous slack rate of the sub-interval is determined based on each failure region, and the reliability of the target structure is determined based on each instantaneous slack rate, including: Determine the circumscribed rectangle of the standard circular model, and generate sample points uniformly within the circumscribed rectangle; Determine the first number of points belonging to the generated sample points in the failed region; Determine the second number of points belonging to the generated sample points in the standard circle model; Based on the first and second quantities, determine the instantaneous crossing rate of the sub-interval; The total crossing rate of the target structure is determined based on the instantaneous crossing rate of each sub-interval; The reliability of the target structure is determined based on the total span rate of the target structure.

[0048] In this embodiment, to address the difficulty in calculating the area due to the irregular shape of the failure region, an approximate solution can be performed. Specifically, to improve sampling efficiency and uniformity, a Monte Carlo simulation method can be used: a circumscribed rectangle can be constructed outside the standard circular model as the generation area for uniform sample points; based on this, a rejection sampling strategy can be introduced, that is, only valid sample points falling within the standard circular model are retained, while sample points belonging to the circumscribed rectangle but not within the standard circular model are not retained. Figure 7 As shown, within the bounding rectangle, a preset number of sample points are uniformly generated (the preset number is set based on experience). Then, it is determined whether the failure area belongs to the failure domain. Figure 7 The number of generated sample points in the failure domain is taken as the first quantity, and the number of generated sample points in the standard circle model is taken as the second quantity. The ratio of the first quantity to the second quantity is calculated, and this ratio is the probability of transitioning from a safe state to a failure state within this sub-interval. Based on this probability Time step of sub-interval This allows us to obtain the instantaneous span rate of the sub-interval: (twenty one) In this embodiment, after obtaining the instantaneous sprint rate of each sub-interval, the instantaneous sprint rate and time step of each sub-interval are used as the basis for the calculation. ,calculate The data are then superimposed to determine the total span rate of the target structure over the entire time period, thereby determining the reliability of the target structure.

[0049] Specifically, each discrete subinterval has its corresponding instantaneous span rate. In a discretized scenario, the entire time period Divided into fixed time intervals There are sub-intervals, and the time step of each sub-interval is . (This time step can be set based on experience), then the total span rate over the entire time period can be approximated as the sum of the products of the instantaneous span rate and the time step in each sub-interval: (twenty two) in, For the first The instantaneous span rate of each sub-interval is determined by formula (21).

[0050] This embodiment can introduce Poisson process theory to calculate the probability of failure events occurring over the entire time period. At the initial moment of the entire time period... At that time, the initial failure probability of the target structural model is Then throughout the entire time period Within, the cumulative failure probability of the target structure is: (twenty three) in, The total traversal rate over the entire time period is the probability of transitioning from a safe state to a failure state in each sub-interval. The result of superposition is: (twenty four) At this point, the reliability of the target structure is the complement of the failure probabilities, and the reliability of the target structure can be expressed as: (25) From the above, it can be concluded that by uniformly generating sample points within the circumscribed rectangle of the standard circle model and introducing a rejection sampling strategy, the probability of transitioning from a safe state to a failure state within a sub-interval can be approximately obtained simply by statistically analyzing the ratio of the number of sample points within the failure domain (the first quantity) to the number of valid sample points within the standard circle (the second quantity). Combined with the time step, the instantaneous scramble rate of each sub-interval can be obtained. This effectively solves the technical problem of accurately calculating the area of ​​irregular failure domains and is more adaptable to small sample scenarios, avoiding errors in direct area calculation under small sample conditions. Based on the scramble rate theory, each sub-interval... The total scramble rate over the entire time period is obtained by superimposing the product of the instantaneous scramble rate of each interval and the time step. Poisson process theory is then introduced to calculate the cumulative failure probability. Since structural failure events under dynamic loads are rare, the Poisson process can accurately match this characteristic, making the calculation of the total failure probability more consistent with actual engineering scenarios. By calculating the instantaneous scramble rate of each sub-interval separately and integrating the evaluation over the entire time period, the accuracy of the instantaneous scramble rate calculation for each sub-interval is ensured, and continuous evaluation of the reliability of the target structure over the entire time domain is achieved, significantly improving the practicality and accuracy of reliability evaluation under dynamic loads.

[0051] Based on the above embodiments, this application provides a specific example: An existing related research method includes the following formulas (26), (27), Table 1, and Table 2: (26) (27)

[0052]

[0053] In the limit function (26), It is the system's output response. These are four random input variables, representing uncertainties in the system. The angle parameter is used to introduce time-varying or environment-related fluctuations. This limiting function is used to describe the output. With input variables and angle parameters The mathematical relationship between them.

[0054] In the time-varying formula for the mean (27), For variables At any moment The mean, For variables At the initial moment ( The mean of ) For the attenuation amplitude parameter, For decay rate parameters, The mean is an exponentially decaying term that increases over time; this time-varying formula characterizes each input variable. The mean over time The changing pattern.

[0055] Based on the formulas and tabular data of the above research methods, in the embodiments of this application, four parameter values ​​are considered, as shown in cases 1 to 4 in Table 2.

[0056] Calculate the dynamic reliability of the target structure using Case 1 in Table 2 as an example: Only In this embodiment, the variable is an interval variable. Given a certain external load with a variation range of [17, 23], 1000 data points are uniformly generated within the interval [17, 23]. Substituting the data from Case 1 in Table 2 into the time-varying mean formula (27), the values ​​at each time point are obtained. The value is set based on experience. Taking 10°, substituting it into the limit function formula (26), we can find the result under 1000 different external loads. Functional properties that change over time, such as Figure 8 As shown, each curve represents the condition under an external load. Different curves use different representations to depict how things change over time.

[0057] Will As a sample curve, the time period is divided according to a fixed time interval (the response sample is discretized into several sub-intervals according to a fixed time interval). In this embodiment, it is set to be divided into 16 sub-intervals with a time interval of 1×100h. The ellipsoid model at each time point is plotted and the span rate of each is calculated. The structural dynamic reliability is obtained based on the method of this application embodiment.

[0058] Specifically, data from the time interval [0, 1] is mapped onto a two-dimensional plane to create an ellipsoidal model, and the result is shown below. Figure 9 Because the sample points are approximately linearly distributed and the number of sample points is large, the set of all sample points can be approximated as a thick line (e.g., ...). Figure 9 The sample point set is shown, but when magnified, it appears as multiple sample points; at the same time, the ellipsoidal model approximates a line (as shown). Figure 9 The model is shown as an ellipsoid, but when magnified, it becomes an ellipse. The failure domain is the region where time t1 is greater than 0 and time t2 is less than 0 (0 is the response failure threshold in this embodiment), i.e., the region of the ellipse within the fourth quadrant (the fourth quadrant region in the coordinate system composed of the failure criteria at time t1 and time t2). Experiments show that at the first 7 time points, there are only sample points and no failure domain exists. After the 8th time point, the failure domain exists with sample points, as shown... Figure 10 As shown (at time point 8). The ellipsoidal model is standardized, and a large number of sample points are uniformly generated within the standard circle using rejection sampling. The ratio of the number of sample points in the failure domain to the total number of sample points within the standard circle is taken as the scramble rate at that time point. The total scramble rates are calculated as shown in Table 3. The calculated reliability results are compared with two methods mentioned in existing related research (scramble rate method and time point method), and the results are shown in Table 4. Figure 11 As shown (where, Figure 11 The sprint rate method mentioned is an important model-based sampling method in existing approaches, which differs from this method.

[0059]

[0060]

[0061] As can be seen from the calculation results in Case 1, the reliability of the two methods mentioned in an existing related research method (the stride rate method and the time point method) is 1 at the first 7 time points, meaning there is no failure. However, the structural dynamic reliability method does have failures because the ellipsoidal model captures cognitive uncertainty (i.e., uncertainty about the true state of the system due to limited knowledge and insufficient data). Even if all sample points are safe, the true boundary position of the system cannot be completely and accurately determined. The ellipsoidal model used in this application quantifies this "unknown," expressing "the worst possible outcome for the parameters under the current level of knowledge." Therefore, it can identify potential risks and determine the uncertainty domain of variables with a small sample size. The two methods mentioned in the existing related research method (the stride rate method and the time point method) ignore this cognitive limitation. This results in the cumulative failure probability of the two methods at the first 7 time points in Case 1 being 0, while the structural dynamic reliability analysis method is non-zero, resulting in a relative error of less than 9%, as shown in Table 5. Relative error 1 is compared with the stride rate method in this application, and relative error 2 is compared with the time point method in this application.

[0062]

[0063] The calculation process is the same for cases 2 through 4, and will not be described in detail again. Figures 12 to 14 The table shows the reliability comparison results of the two methods mentioned in the embodiments of this application and the related research methods under cases 2 to 4. As shown in Table 6, the relative error between the slack rate method mentioned in one of the existing related research methods in cases 2 to 4 and the method of this application (dynamic reliability method) is within 3%, and the relative error between the time point method and the method of this application (dynamic reliability method) is within 2%, which proves the feasibility of the method of this application.

[0064]

[0065] Based on the same principle as the time-varying ellipsoidal model structure reliability assessment method provided in the embodiments of this application, the embodiments of this application also provide a time-varying ellipsoidal model structure reliability assessment device, such as... Figure 15 As shown, the time-varying ellipsoid model structure reliability assessment device 20 may specifically include: an acquisition module 21, a discretization module 22, a sample point generation module 23, an ellipsoid model establishment module 24, and a structure reliability determination module 25.

[0066] The acquisition module 21 is used to acquire the response sample set corresponding to the target structure. The response sample set is used to reflect the dynamic behavior of the target structure. The response sample set includes multiple response samples. One response sample is the response data of the target structure model obtained by dynamic simulation under a dynamic load and changing over time, or one response sample is the real response data of the target structure obtained by actual detection by sensors and changing over time within a preset time.

[0067] Discretization module 22 is used to discretize each response sample into several sub-intervals according to a fixed time interval. Each sub-interval in a response sample is characterized by sub-interval response data, which is characterized by the response data corresponding to the first time of the sub-interval and the response data corresponding to the last time of the sub-interval.

[0068] The sample point generation module 23 is used to generate corresponding sample points in the target coordinate system for each response sample based on the response data of each sub-interval in the response sample. The x-coordinate and y-coordinate of the sample point corresponding to the response data of the first time and the last time of the sub-interval are respectively.

[0069] The ellipsoid model module 24 is used to establish a time-varying ellipsoid model that encloses all sample points within each sub-interval. Based on each time-varying ellipsoid model, the corresponding failure region is determined. For a sub-interval, the failure region corresponding to the sub-interval is represented as the region corresponding to the failure response sample set in the target coordinate system. Each failure sample in the failure response sample set is the response data in the sub-interval where the response data at the first moment is safe but the response data at the last moment exceeds a set threshold under a certain external load.

[0070] The structural reliability determination module 25 is used to determine the instantaneous span rate of the sub-interval based on each failure region, and to determine the reliability of the target structure based on each instantaneous span rate.

[0071] In one embodiment of this application, the ellipsoid model building module 24, when building a time-varying ellipsoid model encompassing all sample points within the sub-interval, is specifically used for: Based on the x-coordinate and y-coordinate of each sample point in all sample points, determine the maximum, minimum, maximum and minimum x-coordinate values ​​of all sample points. Use the arithmetic mean of the maximum and minimum x-coordinate values ​​as the x-coordinate of the center point of the time-varying ellipsoid model, and use the arithmetic mean of the maximum and minimum y-coordinate values ​​as the y-coordinate of the center point of the time-varying ellipsoid model to characterize the center point coordinates of the time-varying ellipsoid model. Based on the x and y coordinates of each sample point in all sample points and the coordinates of the center point of the time-varying ellipsoid model, the feature matrix of the time-varying ellipsoid model is determined. Based on the center point coordinates and feature matrix of the time-varying ellipsoid model, a time-varying ellipsoid model with the smallest volume that encloses all sample points within the sub-interval is established.

[0072] In one embodiment of this application, the ellipsoid model building module 24, when building a time-varying ellipsoid model that encloses all sample points within the sub-interval and has the smallest volume based on the center point coordinates and feature matrix of the time-varying ellipsoid model, is further used for: Establish the smallest two-dimensional rectangular interval model that encloses all sample points; Based on the center point coordinates and the characteristic matrix of the time-varying ellipsoid model, an ellipsoid model passing through each vertex of the two-dimensional rectangular interval model is drawn as the initial ellipsoid model. The initial ellipsoid model is rotated multiple times in the target coordinate system with the origin of the target coordinate system as the reference, and the coordinates of each sample point after rotation and the feature matrix of the time-varying ellipsoid model after rotation are determined. Based on the coordinates of each sample point after rotation and the feature matrix of the time-varying ellipsoid model after rotation, the volume of the ellipsoid model corresponding to each rotation is determined to obtain the ellipsoid model with the smallest volume.

[0073] In one embodiment of this application, the ellipsoid model building module 24, based on the center point coordinates of the time-varying ellipsoid model and the feature matrix of the time-varying ellipsoid model, draws an ellipsoid model passing through each vertex of the two-dimensional rectangular interval model. When used as the initial ellipsoid model, it is further specifically used for: If sample points exist at each vertex of the two-dimensional rectangular interval model, then based on the semi-axis length of the two-dimensional rectangular interval model, the semi-axis length of the initial ellipsoid model is determined using the semi-axis length formula, and the initial ellipsoid model is determined. The semi-axis length formula is:

[0074] in, The semi-axis length of the initial ellipsoid model. This is the semi-axis length of the two-dimensional rectangular interval model. The dimension of the initial ellipsoid model; If there are no sample points at each vertex of the two-dimensional rectangular interval model, an adjustment factor is introduced. This adjustment factor is used to scale the major and minor axes of the initial ellipsoid model until sample points exist on the boundary of the ellipsoid model, thus determining the initial ellipsoid model. The formula for the adjustment factor is:

[0075] in, To adjust the factor, To obtain the maximum value among all calculation results, For summation, For the first The sample point at the th th dimensional coordinates, The center point of the time-varying ellipsoid model is at the th dimensional coordinates, This is the semi-axis length of the initial ellipsoid model.

[0076] In one embodiment of this application, for each time-varying ellipsoidal model, an ellipsoidal model module 24 is established. When determining the corresponding failure region based on each time-varying ellipsoidal model, it is specifically used for: Determine the failure threshold of the response sample, and based on the threshold of the response sample, determine the horizontal and vertical failure thresholds in the target coordinate system. Based on the failure thresholds on the horizontal and vertical axes, two failure criterion lines are determined, which are parallel to the horizontal and vertical axes of the target coordinate system, respectively. Based on the two failure criterion lines and the time-varying ellipsoid model, the corresponding failure region is determined.

[0077] In one embodiment of this application, for each time-varying ellipsoidal model, an ellipsoidal model module 24 is established. When determining the corresponding failure region based on two failure criterion lines and the time-varying ellipsoidal model, it is further used for: The time-varying ellipsoid model and the two failure criterion lines are simultaneously normalized and standardized to obtain the processed standard circle model and the standardized two failure criterion lines. Based on the two standardized failure criterion lines and the standard circle model, the corresponding failure regions are determined.

[0078] In one embodiment of this application, the structural reliability determination module 25, when determining the instantaneous span rate of the sub-interval based on each failure region and determining the reliability of the target structure based on each instantaneous span rate, is specifically used for: Determine the circumscribed rectangle of the standard circular model, and generate sample points uniformly within the circumscribed rectangle; Determine the first number of points belonging to the generated sample points in the failed region; Determine the second number of points belonging to the generated sample points in the standard circle model; Based on the first and second quantities, determine the instantaneous crossing rate of the sub-interval; The total crossing rate of the target structure is determined based on the instantaneous crossing rate of each sub-interval; The reliability of the target structure is determined based on the total span rate of the target structure.

[0079] The apparatus of this application embodiment can execute the method provided in this application embodiment. The implementation principle is similar. The actions performed by each module in the apparatus of each embodiment of this application correspond to the steps in the method of each embodiment of this application. For detailed functional descriptions of each module of the apparatus, please refer to the descriptions in the corresponding methods shown above, which will not be repeated here.

[0080] Figure 16 A schematic diagram of the structure of an electronic device to which this application embodiment applies is shown, such as... Figure 16 As shown, the electronic device can be used to implement the methods provided in any embodiment of this application.

[0081] like Figure 16 As shown, the electronic device 300 may primarily include at least one processor 301. Figure 16 The diagram shows components such as a memory 302, a communication module 303, and an input / output interface 304. Optionally, these components can be connected and communicate with each other via a bus 305. It should be noted that... Figure 16 The structure of the electronic device 300 shown is merely illustrative and does not constitute a limitation on the electronic devices to which the methods provided in the embodiments of this application are applicable.

[0082] The memory 302 can be used to store operating systems and applications, etc. The applications can include computer programs that implement the methods shown in the embodiments of this application when invoked by the processor 301, and can also include programs for implementing other functions or services. The memory 302 can be ROM (Read Only Memory) or other types of static storage devices that can store static information and instructions, RAM (Random Access Memory) or other types of dynamic storage devices that can store information and computer programs, or it can be EEPROM (Electrically Erasable Programmable Read Only Memory), CD-ROM (Compact Disc Read Only Memory) or other optical disc storage, optical disc storage (including compressed optical discs, laser discs, optical discs, digital universal optical discs, Blu-ray discs, etc.), magnetic disk storage media or other magnetic storage devices, or any other medium that can be used to carry or store desired program code in the form of instructions or data structures and that can be accessed by a computer, but is not limited thereto.

[0083] Processor 301 is connected to memory 302 via bus 305 and implements corresponding functions by calling the application programs stored in memory 302. Processor 301 can be a CPU (Central Processing Unit), a general-purpose processor, a DSP (Digital Signal Processor), an ASIC (Application Specific Integrated Circuit), an FPGA (Field Programmable Gate Array), or other programmable logic devices, transistor logic devices, hardware components, or any combination thereof. It can implement or execute the various exemplary logic blocks, modules, and circuits described in conjunction with the disclosure of this application. Processor 301 can also be a combination that implements computing functions, such as a combination of one or more microprocessors, a combination of a DSP and a microprocessor, etc.

[0084] Electronic device 300 can connect to a network via communication module 303 (which may include, but is not limited to, components such as a network interface) to communicate with other devices (such as user terminals or servers) through the network and achieve data interaction, such as sending data to or receiving data from other devices. Communication module 303 may include wired network interfaces and / or wireless network interfaces, meaning the communication module may include at least one of wired or wireless communication modules.

[0085] The electronic device 300 can connect to necessary input / output devices, such as a keyboard and display device, via the input / output interface 304. The electronic device 300 itself may have a display device, and other display devices can also be connected externally via the interface 304. Optionally, a storage device, such as a hard drive, can also be connected via the interface 304 to store data from the electronic device 300, retrieve data from the storage device, or store data from the storage device in the memory 302. It is understood that the input / output interface 304 can be a wired interface or a wireless interface. Depending on the actual application scenario, the device connected to the input / output interface 304 can be a component of the electronic device 300 or an external device connected to the electronic device 300 when needed.

[0086] The bus 305 used to connect the components may include a path for transmitting information between the components. The bus 305 may be a PCI (Peripheral Component Interconnect) bus or an EISA (Extended Industry Standard Architecture) bus, etc. Depending on its function, the bus 305 may be divided into an address bus, a data bus, a control bus, etc.

[0087] Optionally, for the solution provided in the embodiments of this application, the memory 302 can be used to store a computer program that executes the solution of this application, and the processor 301 runs the computer program. When the processor 301 runs the computer program, it implements the operation of the method or apparatus provided in the embodiments of this application.

[0088] Based on the same principle as the method provided in the embodiments of this application, the embodiments of this application provide a computer-readable storage medium storing a computer program, which, when executed by a processor, can implement the corresponding content of the aforementioned method embodiments.

[0089] This application also provides a computer program product, which includes a computer program that, when executed by a processor, can implement the corresponding content of the aforementioned method embodiments.

[0090] It should be noted that the terms "first," "second," "third," "fourth," "1," "2," etc. (if present) in the specification, claims, and accompanying drawings of this application are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of this application described herein can be implemented in a sequence other than that shown in the figures or text.

[0091] In the embodiments of this application, the terms "module" or "unit" refer to a computer program or part of a computer program that has a predetermined function and works with other related parts to achieve a predetermined goal, and can be implemented wholly or partially using software, hardware (such as processing circuitry or memory), or a combination thereof. Similarly, a processor (or multiple processors or memory) can be used to implement one or more modules or units. Furthermore, each module or unit can be part of an overall module or unit that includes the functionality of that module or unit.

[0092] It should be understood that although arrows indicate various operation steps in the flowcharts of this application's embodiments, the order in which these steps are implemented is not limited to the order indicated by the arrows. Unless explicitly stated herein, in some implementation scenarios of this application's embodiments, the implementation steps in each flowchart can be executed in other orders as required. Furthermore, some or all steps in each flowchart, based on the actual implementation scenario, may include multiple sub-steps or multiple stages. Some or all of these sub-steps or stages can be executed at the same time, and each sub-step or stage can also be executed at different times. In scenarios where execution times differ, the execution order of these sub-steps or stages can be flexibly configured according to requirements, and this application's embodiments do not limit this.

[0093] The above description is only an optional implementation method for some implementation scenarios of this application. It should be noted that for those skilled in the art, other similar implementation methods based on the technical concept of this application without departing from the technical concept of this application also fall within the protection scope of the embodiments of this application.

Claims

1. A method for assessing the structural reliability of a time-varying ellipsoidal model, characterized in that, include: Obtain a response sample set corresponding to the target structure. The response sample set is used to reflect the dynamic behavior of the target structure. The response sample set includes multiple response samples. One response sample is the response data of the target structure model obtained by dynamic simulation under a dynamic load and changing over time. Or one response sample is the real response data of the target structure obtained by actual detection of the target structure by a sensor and changing over time within a preset time. Each response sample is discretized into several sub-intervals according to a fixed time interval. Each sub-interval in a response sample is characterized by the sub-interval response data, which is characterized by the response data corresponding to the first time of the sub-interval and the response data corresponding to the last time of the sub-interval. For each response sample, based on the response data of each sub-interval in the response sample, corresponding sample points are generated in the target coordinate system. The x-coordinate and y-coordinate of the sample point corresponding to the response data of the first time and the last time of the sub-interval are respectively. For each sub-interval, a time-varying ellipsoid model is established to enclose all sample points within the sub-interval. Based on each time-varying ellipsoid model, the corresponding failure region is determined. For a sub-interval, the failure region corresponding to the sub-interval is characterized as the region corresponding to the failure response sample set in the target coordinate system. Each failure sample in the failure response sample set is the response data in the sub-interval where the response data at the first moment is safe but the response data at the last moment exceeds a set threshold under a certain external load. The instantaneous traverse rate of the sub-interval is determined based on each of the failure regions, and the reliability of the target structure is determined based on each of the instantaneous traverse rates.

2. The reliability assessment method for time-varying ellipsoidal model structures as described in claim 1, characterized in that, The establishment of a time-varying ellipsoidal model encompassing all sample points within the sub-interval includes: Based on the x-coordinate and y-coordinate of each sample point in all sample points, determine the maximum, minimum, maximum and minimum x-coordinate values ​​of all sample points. Use the arithmetic mean of the maximum and minimum x-coordinate values ​​as the x-coordinate of the center point of the time-varying ellipsoid model, and use the arithmetic mean of the maximum and minimum y-coordinate values ​​as the y-coordinate of the center point of the time-varying ellipsoid model to characterize the center point coordinates of the time-varying ellipsoid model. Based on the x-coordinate and y-coordinate of each sample point in all the sample points and the coordinates of the center point of the time-varying ellipsoid model, the feature matrix of the time-varying ellipsoid model is determined. Based on the center point coordinates of the time-varying ellipsoid model and the feature matrix of the time-varying ellipsoid model, a time-varying ellipsoid model that encloses all sample points within the sub-interval and has the smallest volume is established.

3. The reliability assessment method for time-varying ellipsoidal model structures as described in claim 2, characterized in that, The step of establishing a time-varying ellipsoid model that encloses all sample points within the sub-interval and has the smallest volume, based on the center point coordinates of the time-varying ellipsoid model and its feature matrix, includes: Establish a minimum two-dimensional rectangular interval model that encloses all the sample points; Based on the center point coordinates of the time-varying ellipsoid model and the feature matrix of the time-varying ellipsoid model, an ellipsoid model passing through each vertex of the two-dimensional rectangular interval model is drawn as the initial ellipsoid model. The initial ellipsoid model is rotated multiple times within the target coordinate system with the origin of the target coordinate system as the reference, and the coordinates of each sample point after rotation and the feature matrix of the time-varying ellipsoid model after rotation are determined. Based on the coordinates of each sample point after rotation and the feature matrix of the time-varying ellipsoid model after rotation, the volume of the ellipsoid model corresponding to each rotation is determined to obtain the ellipsoid model with the smallest volume.

4. The reliability assessment method for time-varying ellipsoidal model structures as described in claim 3, characterized in that, The step of drawing an ellipsoid model passing through each vertex of the two-dimensional rectangular interval model, based on the center point coordinates of the time-varying ellipsoid model and the feature matrix of the time-varying ellipsoid model, as the initial ellipsoid model, includes: If sample points exist at each vertex of the two-dimensional rectangular interval model, then based on the semi-axis length of the two-dimensional rectangular interval model, the semi-axis length of the initial ellipsoid model is determined using the semi-axis length formula, and the initial ellipsoid model is determined. The semi-axis length formula is: in, Let be the semi-axis length of the initial ellipsoid model. The semi-axis length of the two-dimensional rectangular interval model is given. The dimension of the initial ellipsoid model; If there are no sample points at each vertex of the two-dimensional rectangular interval model, an adjustment factor is introduced. This adjustment factor is used to scale the major and minor axes of the initial ellipsoid model until sample points exist on the boundary of the ellipsoid model, thus determining the initial ellipsoid model. The formula for the adjustment factor is: in, The adjustment factor is... To obtain the maximum value among all calculation results, For summation, For the first The sample point at the th th dimensional coordinates, The center point of the time-varying ellipsoid model is at the th dimensional coordinates, Let be the semi-axis length of the initial ellipsoid model.

5. The reliability assessment method for time-varying ellipsoidal model structures as described in claim 1, characterized in that, For each of the time-varying ellipsoidal models, the step of determining the corresponding failure region based on each time-varying ellipsoidal model includes: Determine the failure threshold of the response sample, and based on the failure threshold of the response sample, determine the horizontal and vertical failure thresholds in the target coordinate system; Based on the failure thresholds of the horizontal and vertical axes, two failure criterion lines are determined, which are parallel to the horizontal and vertical axes of the target coordinate system, respectively. Based on the two failure criterion lines and the time-varying ellipsoid model, the corresponding failure region is determined.

6. The reliability assessment method for time-varying ellipsoidal model structures as described in claim 5, characterized in that, For each time-varying ellipsoid model, the determination of the corresponding failure region based on the two failure criterion lines and the time-varying ellipsoid model includes: The time-varying ellipsoid model and the two failure criterion lines are simultaneously normalized and standardized to obtain the processed standard circle model and the standardized two failure criterion lines. Based on the two standardized failure criterion lines and the standard circle model, the corresponding failure regions are determined.

7. The reliability assessment method for time-varying ellipsoidal model structures as described in claim 6, characterized in that, The step of determining the instantaneous traverse rate of the sub-interval based on each of the failure regions, and determining the reliability of the target structure based on each of the instantaneous traverse rates, includes: Determine the circumscribed rectangle of the standard circle model, and uniformly generate sample points within the circumscribed rectangle; Determine the first number of points belonging to the generated sample points in the failure region; Determine the second number of points belonging to the generated sample points in the standard circle model; Based on the first quantity and the second quantity, determine the instantaneous span rate of the sub-interval; The total traversal rate of the target structure is determined based on the instantaneous traversal rate of each sub-interval; The reliability of the target structure is determined based on the total span rate of the target structure.

8. A reliability assessment device for a time-varying ellipsoidal model structure, characterized in that, include: The acquisition module is used to acquire the response sample set corresponding to the target structure. The response sample set is used to reflect the dynamic behavior of the structure corresponding to the target structure. The response sample set includes multiple response samples. One response sample is the response data of the target structure model obtained by dynamic simulation under a dynamic load and changing over time, or one response sample is the real response data of the target structure obtained by actual detection of the target structure by a sensor and changing over time within a preset time. The discrete module is used to discretize each response sample into several sub-intervals according to a fixed time interval. Each sub-interval in a response sample is characterized by the sub-interval response data, which is characterized by the response data corresponding to the first time of the sub-interval and the response data corresponding to the last time of the sub-interval. The sample point generation module is used to generate corresponding sample points in the target coordinate system for each response sample based on the response data of each sub-interval in the response sample. The x-coordinate and y-coordinate of the sample point corresponding to the response data of the first time and the last time of the sub-interval are respectively. An ellipsoid model module is established to create a time-varying ellipsoid model that encloses all sample points within each sub-interval. Based on each time-varying ellipsoid model, the corresponding failure region is determined. For a sub-interval, the failure region corresponding to the sub-interval is characterized as the region corresponding to the failure response sample set in the target coordinate system. Each failure sample in the failure response sample set is the response data in the sub-interval where the response data at the first moment is safe but the response data at the last moment exceeds a set threshold under a certain external load. The structural reliability determination module is used to determine the instantaneous slack rate of the sub-interval based on each of the failure regions, and to determine the reliability of the target structure based on each of the instantaneous slack rates.

9. An electronic device, characterized in that, The electronic device includes a memory and a processor. The memory stores a computer program, and the processor executes the time-varying ellipsoid model structure reliability assessment method according to any one of claims 1 to 7 when running the computer program.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, implements the time-varying ellipsoid model structure reliability assessment method according to any one of claims 1 to 7.

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