A sensor arrangement method and system for scour force identification of a beam bridge pile foundation

Abstract

This invention discloses a sensor arrangement method and system for identifying the scour dynamics of beam bridge pile foundations, comprising the following steps: establishing a three-dimensional finite element structural dynamic model based on the beam bridge to be monitored; extracting the modal frequencies and mode shapes of the first N modes of the three-dimensional finite element structural dynamic model under various scour conditions; obtaining the frequency sensitivity of the first N modes; obtaining a set of sensitive states; obtaining the target mode shape vector under the corresponding sensitive modes; if monitoring a single mode of the beam bridge, arranging a single sensor on the candidate degree-of-freedom node with the largest vibration amplitude of the lowest-order sensitive mode in the set of sensitive states; if monitoring multiple modes of the beam bridge, selecting a target monitoring scheme from multiple multi-modal monitoring schemes. This invention can effectively improve the identification accuracy of the scour effect of beam bridge pile foundations in single-modal monitoring; and can reduce sensor redundancy and ensure the reliability of sensor monitoring of the bridge in multi-modal monitoring.

Description

Technical Field

[0001] This invention belongs to the field of bridge health monitoring, and particularly relates to a sensor arrangement method and system for identifying the scour dynamics of beam bridge pile foundations. Background Technology

[0002] Scouring is a major cause of bridge failure. It creates deep craters, weakens the stability of the bridge foundation, and can lead to overall structural collapse. The indirect costs of bridge collapse (such as traffic disruption and emergency response) are five times the direct repair costs, having a profound impact on society and the economy. During floods, increased water flow exacerbates the scouring effect, posing a particular threat to bridges built over waterways. The pile foundations of beam bridges are the main load-bearing components and are highly susceptible to scouring due to prolonged exposure to water flow. Scouring causes soil loss around the pile foundations, reducing their load-bearing capacity and potentially leading to bridge tilting or collapse. Monitoring the scouring process allows for timely assessment of pile foundation damage, enabling necessary maintenance measures to ensure the overall stability and safety of the bridge.

[0003] In order to obtain more comprehensive and accurate monitoring data, existing monitoring technologies deploy a large number of sensors on bridges. In actual applications, due to the large number of sensors, data redundancy will occur, which will undoubtedly increase the overall computing cost and reduce the overall computing efficiency. Summary of the Invention

[0004] Purpose of the invention: The first objective of this invention is to provide a sensor arrangement method for identifying the scour dynamics of beam bridge pile foundations that can reduce sensor redundancy and has high monitoring reliability.

[0005] A second objective of this invention is to provide a sensor arrangement system for identifying the scour dynamics of beam bridge pile foundations.

[0006] Technical solution: This invention discloses a sensor arrangement method for identifying the scour dynamics of beam bridge pile foundations, comprising the following steps:

[0007] A three-dimensional finite element structural dynamic model capable of expressing the coupling effect between pile foundation and soil was established based on the beam bridge to be monitored.

[0008] Excitation conditions were applied to the three-dimensional finite element dynamic model of the structure, and the modal frequencies and mode shapes of the first N modes of the three-dimensional finite element dynamic model under various scouring conditions were extracted respectively.

[0009] The influence of scouring conditions on the modal frequencies of the first N modes is quantified to obtain the frequency sensitivity of the first N modes; sensitive modes are selected from the first N modes based on the frequency sensitivity to form a set of sensitive modes.

[0010] The sensitive modes include the mode shapes of all degrees of freedom nodes of the beam bridge to be monitored, forming the initial mode shape vector of the sensitive modes; based on the initial mode shape vector, candidate degree-of-freedom nodes are selected from all degree-of-freedom nodes of the beam bridge to be monitored, and the mode shapes of all candidate degree-of-freedom nodes constitute the target mode shape vector under the corresponding sensitive modes;

[0011] If monitoring a single mode of a beam bridge, the single sensor is placed on the candidate degree of freedom node with the largest vibration amplitude of the lowest-order sensitive mode in the sensitive state set.

[0012] If monitoring the multimodal behavior of a beam bridge, multiple sensors are selectively arranged on candidate degree-of-freedom nodes to form multiple multimodal monitoring schemes, wherein the number of sensors is less than or equal to the number of candidate degree-of-freedom nodes; the signal-to-noise ratio (SNR) of the target mode shape vector under each sensitive mode is calculated under different multimodal monitoring schemes; the weighting coefficient of the target mode shape vector under each sensitive mode is calculated based on the frequency sensitivity; and the target monitoring scheme is selected from multiple multimodal monitoring schemes based on the weighting coefficients and SNR of all sensitive modes.

[0013] Furthermore, the coupling effect between the pile foundation and the soil is expressed as follows: nonlinear soil spring elements are arranged at the contact interface between the pile foundation and the soil in the three-dimensional finite element structural dynamic model, and constitutive models and corresponding constitutive parameters of the soil spring elements of each soil layer in the soil contact interface are set; wherein the constitutive model of the soil spring element includes the TZ curve for simulating shear slip response, the PY curve for simulating lateral deformation response, and the QZ curve for describing pile end resistance; the constitutive parameters include the stiffness parameters of the soil spring element.

[0014] Furthermore, when establishing a three-dimensional finite element dynamic model of a structure, constraint boundaries or damping boundaries are applied to the peripheral nodes of the three-dimensional finite element dynamic model to simulate the energy absorption and reflection characteristics of the foundation in the far field.

[0015] Furthermore, multiple scouring conditions refer to setting multiple different scouring depths in the three-dimensional finite element structural dynamic model, and the scouring depths of multiple scouring conditions show an arithmetic progression with fixed tolerance values.

[0016] Furthermore, the formula for the frequency sensitivity of the first N modes is obtained through quantization. ,in The modal frequency of the i-th mode is given by the scouring depth d. ; This refers to the scouring depth of The modal frequency of the i-th mode. The increment step size for scouring depth; Let be the frequency sensitivity of the i-th mode.

[0017] Furthermore, the sensitive mode set is obtained by sorting the first N modes in descending order of frequency sensitivity, taking the first u modes as sensitive modes, and forming the sensitive mode set from the u sensitive modes.

[0018] Furthermore, the first in the sensitive mode set The vector expression for the initial mode shape vector of each sensitive mode is: ,in Refers to the first The mode shape of the q-th degree-of-freedom node in a sensitive mode, where the mode shape includes the vibration amplitude and direction of the degree-of-freedom node, and ;n refers to the number of nodes with all degrees of freedom of the beam bridge to be monitored, and ; Represents a matrix. Represents an n-row, 1-column matrix;

[0019] The steps to obtain the target mode shape vector under the corresponding sensitive modes are as follows:

[0020] For the initial mode shape vector under each sensitive mode The vibration amplitude is normalized to obtain the initial mode shape vector under the corresponding sensitive mode. The normalized amplitude is denoted as the full-bridge mean under the corresponding sensitive mode;

[0021] The beam bridge to be monitored is divided into multiple areas;

[0022] Calculate the normalized mean amplitude and the normalized maximum amplitude of all degree-of-freedom nodes in each region under each sensitive mode. Record the obtained normalized mean amplitude as the region mean in the sensitive mode and the normalized maximum amplitude as the region maximum in the sensitive mode.

[0023] If the mean or maximum value of a region in any sensitive mode is greater than b times the mean of the full bridge in the corresponding sensitive mode, then the region is identified as a high-response region.

[0024] All nodes within the high-response region are selected as candidate nodes; the first node in the sensitive mode set... The vector expression for the target mode shape vector of each sensitive mode is: Where m refers to the number of candidate degree-of-freedom nodes. The first in the sensitive mode set The mode shape of the m-th degree-of-freedom node of a sensitive mode; This represents an m-row, 1-column matrix.

[0025] Furthermore, the arrangement of multiple sensors selectively placed on candidate degree-of-freedom nodes is denoted as the sensor placement matrix, and the sensor placement matrix is ​​denoted as L. ,in Refers to an m-row, I-column matrix; I refers to the number of sensors, and ;

[0026] The formula for calculating the signal-to-noise ratio (SNR) of the p-th sensitive mode in the sensitive mode set under the sensor deployment matrix L is as follows: ,in This represents the power spectral density of the p-th sensitive mode excitation. Let p be the damping ratios of the sensitive modes. To measure the channel noise power spectral density.

[0027] Furthermore, the formula for calculating the weighting coefficients of the target mode shape vector under each sensitive mode is as follows: ,in The weight coefficient of the p-th sensitive mode in the sensitive mode set. The frequency sensitivity of the p-th sensitive mode in the sensitive mode set; The frequency sensitivity of the j-th sensitive mode in the sensitive mode set;

[0028] The method for selecting a target monitoring scheme from multiple multimodal monitoring schemes based on the weighting coefficients of all sensitive modes and the signal-to-noise ratio index is as follows:

[0029] The overall signal-to-noise ratio (SNR) of all sensitive modes under the same sensor deployment matrix L is calculated based on weighting coefficients and SNR indices. The formula for calculating the overall signal-to-noise ratio is as follows: ;

[0030] With the goal of maximizing the overall signal-to-noise ratio, the Grey Wolf optimization algorithm is used to iteratively optimize the sensor deployment matrix L, and the iteratively optimized sensor deployment matrix L is taken as the final target monitoring scheme.

[0031] Based on the same inventive concept, this invention also discloses a sensor arrangement system for identifying the scour dynamics of beam bridge pile foundations, comprising,

[0032] The model simulation unit establishes a three-dimensional finite element structural dynamic model based on the beam bridge to be monitored, which can express the coupling effect between the pile foundation and the soil.

[0033] The data extraction unit applies excitation conditions to the three-dimensional finite element structural dynamic model and extracts the modal frequencies and mode shapes of the first N modes of the three-dimensional finite element structural dynamic model under various scouring conditions.

[0034] The modal screening unit quantifies the influence of scouring conditions on the modal frequencies of the first N modes, and obtains the frequency sensitivity of the first N modes; based on the frequency sensitivity, sensitive modes are screened from the first N modes to form a sensitive mode set;

[0035] The node screening unit extracts the mode shapes of all degrees of freedom nodes of the beam bridge to be monitored, forming the initial mode shape vector of the sensitive mode; based on the initial mode shape vector, candidate degree-of-freedom nodes are screened from all degree-of-freedom nodes of the beam bridge to be monitored, and the mode shapes of all candidate degree-of-freedom nodes constitute the target mode shape vector of the corresponding sensitive mode.

[0036] For a single-mode monitoring unit, if monitoring a single mode of a beam bridge, the single sensor is placed on the candidate degree of freedom node with the largest vibration amplitude of the lowest-order sensitive mode in the sensitive state set.

[0037] For a multimodal monitoring unit, if monitoring the multimodal behavior of a beam bridge, multiple sensors are selectively arranged on candidate degree-of-freedom nodes to form multiple multimodal monitoring schemes, wherein the number of sensors is less than or equal to the number of candidate degree-of-freedom nodes; the signal-to-noise ratio (SNR) index of the target mode shape vector under each sensitive mode is calculated under different multimodal monitoring schemes; the weighting coefficient of the target mode shape vector under each sensitive mode is calculated based on the frequency sensitivity; and the target monitoring scheme is selected from multiple multimodal monitoring schemes based on the weighting coefficients and SNR index of all sensitive modes.

[0038] Beneficial Effects: Compared with existing technologies, this invention has the following significant advantages: Firstly, it screens out sensitive modes that are sensitive to changes in scour depth. Then, it performs regional response intensity analysis on the beam bridge to be monitored, screening out candidate degree-of-freedom nodes within the high-response region of the beam bridge. Placing sensors at these candidate degree-of-freedom nodes effectively improves the reliability of bridge monitoring. This invention can select single-mode monitoring or multi-mode monitoring as needed. In single-mode monitoring, placing sensors at the candidate degree-of-freedom nodes with the largest amplitude effectively improves the accuracy of identifying the scour effect on the beam bridge pile foundation. In multi-mode monitoring, the historical signal-to-noise ratio and interference sensitivity of the candidate degree-of-freedom nodes are evaluated, quantifying the signal-to-noise ratio index of the sensitive modes. The Grey Wolf optimization algorithm is used to optimize the sensor deployment scheme, ensuring the reliability of bridge monitoring while reducing sensor redundancy. Attached Figure Description

[0039] Figure 1 This is a flowchart of the method of the present invention;

[0040] Figure 2 This is a diagram of the three-dimensional finite element structure dynamic model in an embodiment of the present invention;

[0041] Figure 3These are the first 6 mode shapes extracted in the embodiments of the present invention;

[0042] Figure 4 This is a diagram illustrating the sensor deployment scheme for the target monitoring method in this embodiment of the invention.

[0043] Figure 5 This is a schematic diagram of the iteration of the gray wolf optimization algorithm in an embodiment of the present invention;

[0044] Figure 6 This is a schematic diagram of the system of the present invention. Detailed Implementation

[0045] The technical solution of the present invention will be further described below with reference to the accompanying drawings.

[0046] Example 1

[0047] This invention discloses a sensor arrangement method for identifying the scour dynamics of beam bridge pile foundations, such as... Figure 1 As shown, it includes the following steps:

[0048] S1: Establish a three-dimensional finite element structural dynamic model based on the beam bridge to be monitored, which can express the coupling effect between the pile foundation and the soil.

[0049] Based on the design drawings and construction parameters of the beam bridge to be monitored, a three-dimensional finite element structural dynamic model was established. The three-dimensional finite element structural dynamic model includes the main load-bearing components of the beam bridge, such as the main beams, piers, abutments, and pile foundations. The relevant parameters of the load-bearing components in the three-dimensional finite element structural dynamic model are set based on actual engineering conditions, including the material properties, geometric dimensions, and boundary constraints of the load-bearing components.

[0050] Preferably, the beam grid method is used to model the bridge structure of the beam bridge, which is equivalent to a beam grid model composed of longitudinal beams and virtual crossbeams, simulating the stress and deformation of the bridge under different load conditions. The longitudinal stiffness of the main beam is provided by the longitudinal beams of the beam grid, and the transverse stiffness is provided by the virtual crossbeams. The virtual crossbeams are only used to provide stiffness and are not included in the mass calculation. The beam grid method follows the following equivalence principles: after the beam grid is divided, the centroids of all longitudinal beams should be located on the same horizontal straight line; the equivalent beam grid model should be consistent with the deflection, stress, and strain distribution of the actual bridge under the same load conditions, thereby ensuring the accuracy of the simulation results.

[0051] When establishing a three-dimensional finite element dynamic model of a structure, boundary conditions are set and Rayleigh damping is introduced. Constraint boundaries or damped boundaries are applied to the outer nodes of the three-dimensional finite element dynamic model to simulate the energy absorption and reflection characteristics of the foundation in the far field. Setting boundary conditions can absorb seismic waves and stress waves propagating outward from the beam bridge, preventing the waves from reflecting back and interfering with the calculation, thereby simulating an infinitely large site and eliminating artificial boundary reflections.

[0052] In practical applications, Rayleigh damping is introduced by combining the target frequency range and damping ratio parameter of the beam bridge under monitoring. The damping ratio is a dimensionless parameter describing the energy dissipation capacity of a structure during vibration; it represents the ratio of the actual damping of the structural system to the critical damping (the minimum damping that allows the beam bridge to return directly to its equilibrium position without oscillation after vibration). Rayleigh damping is used to simulate the material energy consumption of beam bridges, and its introduction accurately reflects the energy dissipation characteristics of the beam bridge structure.

[0053] The coupling effect between the pile foundation and the soil is expressed as follows: nonlinear soil spring elements are arranged at the interface between the pile foundation and the soil in the three-dimensional finite element dynamic model, and constitutive models and corresponding constitutive parameters of the soil spring elements of each soil layer in the soil contact interface are set. That is, the constitutive models and corresponding constitutive parameters of the soil spring elements of each soil layer are set using the layered assignment method. The key to the foundation scour effect lies in the interaction between the pile foundation and the soil interface. Therefore, this embodiment uses nonlinear soil spring elements to simulate the dynamic response relationship between the pile foundation and the surrounding soil.

[0054] The constitutive model of the soil spring element includes the TZ curve for simulating shear slip response, the PY curve for simulating lateral deformation response, and the QZ curve for describing pile end resistance; the constitutive parameters include the stiffness parameters of the soil spring element. In practical applications, the constitutive model and its constitutive parameters of the soil spring element are set according to the results of geological surveys and geotechnical tests. The constitutive parameters can also be set based on an engineering experience database. In practical applications, the distribution range and constitutive parameters of the soil spring element can be dynamically adjusted as scour conditions change, fully reflecting the physical changes in the interaction between the pile foundation and the soil at different scour depths.

[0055] Multiple scour conditions refer to setting multiple different scour depths in the three-dimensional finite element structural dynamic model, with the scour depths of the multiple scour conditions increasing in an arithmetic progression with fixed tolerance values. The multiple different scour depths include no scour (0% scour depth), light scour (20% scour depth), moderate scour (40%-60% scour depth), and heavy scour (80%-100% scour depth). In this embodiment, the multiple scour conditions are set to 0% scour depth, 20% scour depth, 40% scour depth, 60% scour depth, 80% scour depth, and 100% scour depth.

[0056] The constitutive parameters of soil springs are proportional to the bearing capacity of beam bridge pile foundations. The weakening (or strengthening) of pile foundation bearing capacity can be simulated by decreasing (or increasing) the stiffness parameters of the soil spring elements. In other words, by adjusting the constitutive parameters of the soil springs to set different scour depths, an equivalent variation model of foundation boundary conditions and soil bearing capacity under different scour depths can be formed.

[0057] S2: Apply excitation conditions to the three-dimensional finite element dynamic model of the structure, and extract the modal frequencies and mode shapes of the first N modes of the three-dimensional finite element dynamic model under various scouring conditions.

[0058] Preferably, a standardized excitation is applied to the three-dimensional finite element structural dynamic model; that is, the initial displacement of free vibration or unit pulse load of the three-dimensional finite element structural dynamic model is set to ensure the effectiveness and accuracy of subsequent modal analysis and dynamic response extraction.

[0059] In this embodiment, the modal frequencies and mode shapes of the first N modes are extracted when the scouring conditions are 0%, 20%, 40%, 60%, 80%, and 100% scouring depth. In this embodiment, the modal frequencies and mode shapes of the first 6 modes are taken, and the mode shapes of the first 6 modes are as follows: Figure 3 As shown.

[0060] S3: Quantify the influence of the scouring condition on the modal frequencies of the first N modes to obtain the frequency sensitivity of the first N modes; based on the frequency sensitivity, select sensitive modes from the first N modes to form a sensitive state set S.

[0061] This embodiment uses the finite difference method to quantify the scour sensitivity index of modal frequencies, that is, to quantify the influence of scour conditions on the modal frequencies of the first N modes. The method for quantifying the influence of scour conditions on the modal frequencies of the first N modes is as follows: the influence of changes in scour depth on the modal frequencies of each mode is defined as the frequency sensitivity. And based on modal frequencies Calculate the frequency sensitivity of each mode according to the corresponding scour depth. Frequency sensitivity The calculation formula is as follows:

[0062] ,

[0063] in The modal frequency of the i-th mode is given by the scouring depth d. ; This refers to the scouring depth of The modal frequency of the i-th mode. The increment step size for scouring depth; Let be the frequency sensitivity of the i-th mode.

[0064] During the calculation process, this invention adopts a uniform scour depth increment step size for all orders of modes. That is, the sensitivity calculation for each modal order. and In and The same scour depth sequence was used for all tests to ensure that the frequency sensitivity comparison had a consistent physical scale basis. The frequency sensitivity can comprehensively and intuitively reflect the degree of response of different order modal frequencies to changes in scour depth, providing theoretical support for subsequent sensitive mode screening.

[0065] The sensitive mode set S is obtained as follows: the first N modes are sorted according to their frequency sensitivity from high to low, and the first u modes are taken as sensitive modes, forming the sensitive mode set S. The preferred value range for u is [3, 5]. This sensitive mode set S will serve as the primary identification target for subsequent sensor deployment optimization.

[0066] Preferably, the frequency sensitivity to each mode is... Frequency sensitivity for all order modes before sorting Normalization is performed.

[0067] S4: Extract the mode shapes of all degrees of freedom nodes of the sensitive mode containing all degrees of freedom nodes of the beam bridge to be monitored, and form the initial mode shape vector of the sensitive mode; based on the initial mode shape vector, select candidate degree-of-freedom nodes from all degree-of-freedom nodes of the beam bridge to be monitored, and the mode shapes of all candidate degree-of-freedom nodes constitute the target mode shape vector under the corresponding sensitive mode.

[0068] Modal modes include the vibration amplitude and direction of the nodes of freedom. The first mode in the sensitive mode set S is the... The vector expression for the initial mode shape vector of each sensitive mode is: ,in Refers to the first The mode shape of the q-th degree-of-freedom node in a sensitive mode, where the mode shape includes the vibration amplitude and direction of the degree-of-freedom node, and ;n refers to the number of nodes with all degrees of freedom of the beam bridge to be monitored, and ; Represents a matrix. This represents an n-row, 1-column matrix.

[0069] After identifying u sensitive modes that are highly sensitive to scour depth, this invention further analyzes the regional response intensity of the bridge to be monitored to better assess the sensitivity of structural components to scour depth, and selects nodes with degrees of freedom within the high-response region of the bridge. The steps for obtaining the target mode shape vector under the corresponding sensitive modes are as follows:

[0070] S41: For the initial mode shape vector The vibration amplitude is normalized to obtain the normalized amplitude. The initial mode shape vectors under the corresponding sensitive modes are obtained. The normalized amplitude is denoted as the full-bridge mean under the corresponding sensitive mode.

[0071] The formula for normalization is as follows: ,in Describes the first in the sensitive mode set S. The sensitive mode is in the first Vibration amplitude at each degree of freedom node; Represents the initial mode shape vector The element-wise absolute value; Initial mode shape vector The normalized amplitude after normalization has a maximum value of 1.

[0072] S42: Divide the beam bridge to be monitored into multiple areas. In practical applications, the areas can be divided according to the bridge span, piers, and bridge deck functions.

[0073] S43: Calculate the normalized mean amplitude and the normalized maximum amplitude of all degree-of-freedom nodes in each region under each sensitive mode. Record the obtained normalized mean amplitude as the region mean in the sensitive mode and the normalized maximum amplitude as the region maximum in the sensitive mode.

[0074] S44: If the mean or maximum value of a region under any sensitive mode is greater than b times the mean of the full bridge under the corresponding sensitive mode, then the region is identified as a high-response region. Here, b is set according to actual engineering requirements, and the preferred value range for b is... .

[0075] S45: Select all nodes within the high-response region as candidate nodes; the first node in the sensitive mode set... The vector expression for the target mode shape vector of each sensitive mode is: Where m refers to the number of candidate degree-of-freedom nodes. The first in the sensitive mode set The mode shape of the m-th degree-of-freedom node of a sensitive mode; This represents an m-row, 1-column matrix.

[0076] The vibration modes (amplitude and direction) of all degrees of freedom nodes within the high-response region constitute the target mode shape vector. That is, removing the initial mode shape vector. The target mode shape vector is obtained from the degree-of-freedom nodes in the high-response region of Central Africa. .

[0077] S5: If monitoring a single mode of a beam bridge, place a single sensor on the candidate degree of freedom node with the largest vibration amplitude of the lowest-order sensitive mode in the sensitive state set.

[0078] Preferably, when the sensor is not convenient to be directly placed at the candidate degree of freedom node with the largest vibration amplitude of the lowest-order sensitive mode in the sensitive state set due to limitations such as on-site monitoring conditions, the sensor can be placed in the area to which the degree of freedom node belongs.

[0079] In practical engineering applications, due to limitations such as on-site monitoring conditions or sensor resources, dynamic observation of a single mode of a beam bridge is often limited. Therefore, existing technologies mostly monitor and analyze only a specific order of natural modes (such as the first or second order horizontal vibration modes) in the dynamic response of the beam bridge structure, acquiring only the natural frequencies, mode shapes, and dynamic response information corresponding to that specific order mode, without simultaneously observing the relevant parameters of other orders of modes. Single-mode monitoring strategies are suitable for scenarios with a limited number of sensors, limited signal processing capabilities, or where the monitoring system needs to focus on scour-sensitive modes.

[0080] Under the aforementioned single-modal monitoring conditions, this embodiment can determine the location with the largest amplitude (i.e., the location with the largest modal energy) by traversing the amplitude values ​​of all candidate degree-of-freedom nodes in the sensitive mode. Limited sensor resources are then preferentially allocated to this location, specifically at the degree-of-freedom node with the largest absolute amplitude value in the modal shape vector or within the region of that node. This maximizes the sensitivity to observing the dynamic changes of the mode. This invention can improve the accuracy of identifying the scour effect of beam bridge pile foundations under single-modal monitoring conditions, enabling real-time reflection of the stress state and stiffness changes of the structure at different scour depths. This further enhances the reliability and damage prediction capabilities of bridge monitoring using this sensor deployment scheme.

[0081] S6: If monitoring the multimodal behavior of a beam bridge, multiple sensors are selectively arranged on candidate degree-of-freedom nodes to form multiple multimodal monitoring schemes, wherein the number of sensors is less than or equal to the number of candidate degree-of-freedom nodes; the signal-to-noise ratio (SNR) index of the target mode shape vector under each sensitive mode is calculated under different multimodal monitoring schemes; the weighting coefficient of the target mode shape vector under each sensitive mode is calculated based on the frequency sensitivity; and the target monitoring scheme is selected from multiple multimodal monitoring schemes based on the weighting coefficients and SNR index of all sensitive modes.

[0082] The arrangement of multiple sensors selectively placed on candidate degree-of-freedom nodes is denoted as the sensor placement matrix, and the sensor placement matrix is ​​denoted as L. ,in Refers to an m-row, I-column matrix; I refers to the number of sensors, and Sensor deployment matrix This refers to selectively arranging I sensors on m degree-of-freedom nodes. If the k-th sensor is arranged on the h-th candidate degree-of-freedom node, the element in the k-th row and h-th column of the sensor arrangement matrix L is 1, and the other elements in the k-th row and h-th column are all 0. Only one sensor is arranged on each candidate degree-of-freedom node.

[0083] After screening candidate degree-of-freedom nodes, this invention evaluates the historical signal-to-noise ratio and interference sensitivity of the candidate degree-of-freedom nodes in order to further consider the engineering noise environment and actual monitoring needs. It quantifies the signal-to-noise ratio index of sensitive modes, so that when using the Grey Wolf optimization algorithm, it can prioritize the retention of candidate degree-of-freedom nodes with high signal-to-noise ratio and less affected by environmental noise.

[0084] The formula for calculating the signal-to-noise ratio (SNR) of the p-th sensitive mode in the sensor deployment matrix L is as follows: ,in This represents the power spectral density of the p-th sensitive mode excitation; Let p be the damping ratio for the sensitive modes; To measure the channel noise power spectral density, i.e., the sensor's noise power spectral density, a Bayesian frequency domain identification method was used to analyze the modes. It was found that the identification uncertainty of the sensitive mode parameters is inversely proportional to the mode signal-to-noise ratio (SNR). Therefore, this invention defines the SNR index as... .

[0085] The formula for calculating the weighting coefficient of the target mode shape vector under each sensitive mode is as follows: ,in The weight coefficient of the p-th sensitive mode in the sensitive mode set. The frequency sensitivity of the p-th sensitive mode in the sensitive mode set; The frequency sensitivity refers to the j-th sensitive mode in the set of sensitive modes.

[0086] The method for selecting a target monitoring scheme from multiple multimodal monitoring schemes based on the weighting coefficients of all sensitive modes and the signal-to-noise ratio index is as follows:

[0087] S61: Calculate the overall signal-to-noise ratio (SNR) of all sensitive modes under the same sensor deployment matrix L based on weighting coefficients and SNR indicators. The formula for calculating the overall SNR of all sensitive modes under the sensor deployment matrix L is as follows: .

[0088] S62: With the highest overall signal-to-noise ratio. To optimize the objective, the Grey Wolf optimization algorithm is used to iteratively optimize the sensor deployment matrix L. The optimized sensor deployment matrix is ​​then... As the final target monitoring scheme.

[0089] To avoid an overly concentrated spatial distribution of candidate degree-of-freedom nodes in practical applications, this invention aims to maximize the overall signal-to-noise ratio. To optimize the objective, the Grey Wolf optimization algorithm was used to optimize the sensor deployment scheme. That is, the spatial distribution of candidate degree-of-freedom nodes was optimized and adjusted according to the actual layout of the beam bridge to be monitored, so as to ensure that the sensor deployment points cover the key areas of the beam bridge to be monitored and have good regional representativeness.

[0090] With the highest overall signal-to-noise ratio To optimize the objective, the Gray Wolf optimization algorithm is used to optimize the sensor deployment scheme as follows: In each iteration, the three individuals with the best fitness values ​​in the current population are denoted as follows: (Optimal Wolf) (Suboptimal Wolf) and (The third superior wolf) is used to guide the other individuals to update their positions.

[0091] Define a linearly decreasing convergence factor 'a', which gradually decreases during iteration to control the smooth transition from global search to local search. The calculation formula is:

[0092] ,

[0093] in, This represents the current iteration number. This represents the maximum number of iterations. The initial value of 'a' is 2, which is eventually reduced to 0. Subsequently, two independent random vectors are generated for each dimension. and Their components all obey The uniform distribution among them is used to control the nondeterminism and diversity of the search.

[0094] Based on the above random vector and Define two core control parameter vectors:

[0095] ,

[0096] ,

[0097] in, This represents the encirclement intensity vector, which controls whether the search particles (i.e., the sensor deployment matrix) approach or move away from the alpha wolf's position. Control the weight of the alpha wolf's influence on the search particles.

[0098] Calculate the "virtual capture distance" vector between the search particle and the alpha wolf:

[0099]

[0100] in, It means alpha wolf or Continuous position vectors, This indicates the position of the w-th search particle. This represents the Hadamard element-wise product. This indicates the absolute value operation. The formula reflects the difference in the distribution of the search particle and the alpha wolf in the solution space.

[0101] Therefore, the new position of the w-th search particle under the guidance of the alpha wolf p is updated as follows:

[0102]

[0103] This formula represents the one-step positional movement of the search particle under the control of the alpha wolf, incorporating direction (from...). (determined) and step size (by) (Decisive) Two factors.

[0104] Based on respectively and After calculating the three updated positions, the three alpha wolves take the average of them to obtain the final position of the w-th search particle in the current iteration:

[0105] ,

[0106] This formula simulates the essence of the cooperative hunting behavior of gray wolf packs, that is, individuals make collective decisions based on the opinions of the three dominant wolves, thereby enhancing the stability and robustness of the solution.

[0107] Placing sensors on candidate degree-of-freedom nodes is essentially a binary optimization problem, requiring the aforementioned continuous solution to be implemented. Mapped to layout matrix This invention employs the sigmoid mapping function for continuous-binary transformation, the expression of which is as follows:

[0108] ,

[0109] in, For continuous variables, the Sigmoid function compresses any real number to a continuous value. This serves as the probability value for the corresponding dimension.

[0110] Continuous values ​​for each dimension k Generate a random number And perform preliminary binarization according to the following formula:

[0111] ,

[0112] The sensor deployment at each degree of freedom node is transformed into a probability sampling mechanism, effectively preserving the ranking weight information formed during the gray wolf search.

[0113] To satisfy the constraint of a fixed number of sensors, namely:

[0114] ,

[0115] The initial binarization results need to be corrected.

[0116] If the number of sensors is greater than If the value of S is large, then the positions with larger S values ​​will be retained, and the rest will be set to 0.

[0117] If the number of sensors is less than Then, the undeployed position with the largest S value is added.

[0118] After the above steps, M sets of sensor deployment matrices satisfying the constraints will be obtained after each iteration. Then, the objective function value of each set of sensor deployment matrices will be calculated. The objective function value Maximize as the optimization objective function.

[0119] Finally, after completing a preset number of iterations or meeting a preset convergence condition, the historically optimal sensor deployment matrix is ​​selected. This is the output of the target monitoring scheme. The iterative diagram of the gray wolf optimization algorithm in this embodiment is shown below. Figure 5 As shown; the final target monitoring scheme output in this embodiment is as follows. Figure 4 As shown, Figure 4 The "degrees of freedom number" refers to the number of the candidate degree-of-freedom nodes. In this embodiment, there are 400 candidate degree-of-freedom nodes. The sensitive modes selected in this embodiment are the second-order mode (mode 2) and the fourth-order mode (mode 4). The selection is made from all candidate degree-of-freedom nodes (the locations of the sensor candidates) as follows: Figure 4 Sensors are placed on the five candidate degree-of-freedom nodes shown (the actual selected sensor locations).

[0120] Example 2

[0121] This invention discloses a sensor arrangement system for identifying the scour dynamics of beam bridge pile foundations, such as... Figure 6 As shown, it includes a model simulation unit, a data extraction unit, a modal screening unit, a node screening unit, a single modal monitoring unit, and a multimodal monitoring unit.

[0122] The data extraction unit applies excitation conditions to the three-dimensional finite element structural dynamic model and extracts the modal frequencies and mode shapes of the first N modes of the three-dimensional finite element structural dynamic model under various scouring conditions. The data extraction unit executes step S1 in Example 1.

[0123] The modal screening unit quantifies the influence of the scouring condition on the modal frequencies of the first N modes, obtaining the frequency sensitivity of the first N modes; based on the frequency sensitivity, it screens sensitive modes from the first N modes to form a sensitive mode set. The modal screening unit executes step S2 in Example 1.

[0124] The node selection unit extracts the mode shapes of all degrees of freedom nodes of the beam bridge to be monitored, forming the initial mode shape vector of the sensitive mode. Based on the initial mode shape vector, it selects candidate degree-of-freedom nodes from all degree-of-freedom nodes of the beam bridge to be monitored. The mode shapes of all candidate degree-of-freedom nodes constitute the target mode shape vector under the corresponding sensitive mode, thus obtaining the target mode shape vector of the sensitive mode. The node selection unit executes step S3 in Example 1.

[0125] If the single-modal monitoring unit is monitoring a single mode of a beam bridge, then the single sensor is placed on the candidate degree-of-freedom node with the largest vibration amplitude of the lowest-order sensitive mode in the sensitive state set. The single-modal monitoring unit executes step S5 in Example 1.

[0126] The multimodal monitoring unit, if monitoring the multimodal behavior of a beam bridge, selectively arranges multiple sensors on candidate degree-of-freedom nodes to form multiple multimodal monitoring schemes, wherein the number of sensors is less than or equal to the number of candidate degree-of-freedom nodes; calculates the signal-to-noise ratio (SNR) of the target mode shape vector under each sensitive mode under different multimodal monitoring schemes; calculates the weighting coefficient of the target mode shape vector under each sensitive mode based on frequency sensitivity; and selects the target monitoring scheme from the multiple multimodal monitoring schemes based on the weighting coefficients and SNR of all sensitive modes. The multimodal monitoring unit executes step S6 in Example 1.

Claims

1. A sensor arrangement method for identifying the scour dynamics of beam bridge pile foundations, characterized in that: Includes the following steps, A three-dimensional finite element structural dynamic model capable of expressing the coupling effect between pile foundation and soil was established based on the beam bridge to be monitored. Excitation conditions were applied to the three-dimensional finite element dynamic model of the structure, and the modal frequencies and mode shapes of the first N modes of the three-dimensional finite element dynamic model under various scouring conditions were extracted respectively. The influence of scouring conditions on the modal frequencies of the first N modes is quantified to obtain the frequency sensitivity of the first N modes; sensitive modes are selected from the first N modes based on the frequency sensitivity to form a set of sensitive modes. The sensitive modes include the mode shapes of all degrees of freedom nodes of the beam bridge to be monitored, forming the initial mode shape vector of the sensitive modes; based on the initial mode shape vector, candidate degree-of-freedom nodes are selected from all degree-of-freedom nodes of the beam bridge to be monitored, and the mode shapes of all candidate degree-of-freedom nodes constitute the target mode shape vector under the corresponding sensitive modes; If monitoring a single mode of a beam bridge, the single sensor is placed on the candidate degree of freedom node with the largest vibration amplitude of the lowest-order sensitive mode in the sensitive state set. If monitoring the multimodal behavior of a beam bridge, multiple sensors are selectively arranged on candidate degree-of-freedom nodes to form multiple multimodal monitoring schemes, wherein the number of sensors is less than or equal to the number of candidate degree-of-freedom nodes. Calculate the signal-to-noise ratio of the target mode shape vector under each sensitive mode under different multimodal monitoring schemes; The weighting coefficients of the target mode shape vector under each sensitive mode are calculated based on frequency sensitivity. The target monitoring scheme is then selected from multiple multimodal monitoring schemes based on the weighting coefficients of all sensitive modes and the signal-to-noise ratio.

2. The sensor arrangement method for identifying the scour dynamics of beam bridge pile foundations according to claim 1, characterized in that: The method for expressing the coupling effect between the pile foundation and the soil is as follows: nonlinear soil spring elements are arranged at the contact interface between the pile foundation and the soil in the three-dimensional finite element structural dynamic model, and constitutive models and corresponding constitutive parameters of soil spring elements for each soil layer in the soil contact interface are set; wherein the constitutive model of the soil spring element includes TZ curve for simulating shear slip response, PY curve for simulating lateral deformation response, and QZ curve for describing pile end resistance; constitutive parameters include stiffness parameters of the soil spring element.

3. The sensor arrangement method for identifying the scour dynamics of beam bridge pile foundations according to claim 1, characterized in that: When establishing a three-dimensional finite element dynamic model of a structure, constraint boundaries or damping boundaries are applied to the outer nodes of the three-dimensional finite element dynamic model to simulate the energy absorption and reflection characteristics of the foundation in the far field.

4. The sensor arrangement method for identifying the scour dynamics of beam bridge pile foundations according to claim 1, characterized in that: Multiple scouring conditions refer to setting multiple different scouring depths in a three-dimensional finite element structural dynamic model, and the scouring depths of multiple scouring conditions increase in an arithmetic sequence with fixed tolerance values.

5. The sensor arrangement method for identifying the scour dynamics of beam bridge pile foundations according to claim 4, characterized in that: The formula for quantizing the frequency sensitivity of the first N modes is as follows: ,in The modal frequency of the i-th mode is given by the scouring depth d. ; This refers to the scouring depth of The modal frequency of the i-th mode. The increment step size for scouring depth; Let be the frequency sensitivity of the i-th mode.

6. The sensor arrangement method for identifying the scour dynamics of beam bridge pile foundations according to claim 5, characterized in that: The sensitive mode set is obtained by sorting the first N modes in descending order of frequency sensitivity, taking the first u modes as sensitive modes, and forming the sensitive mode set from the u sensitive modes.

7. The sensor arrangement method for identifying scour dynamics of beam bridge pile foundations according to claim 6, characterized in that: The first in the sensitive mode set The vector expression for the initial mode shape vector of each sensitive mode is: ,in Refers to the first The mode shape of the q-th degree-of-freedom node in a sensitive mode, where the mode shape includes the vibration amplitude and direction of the degree-of-freedom node, and ;n refers to the number of nodes with all degrees of freedom of the beam bridge to be monitored, and ; Represents a matrix. Represents an n-row, 1-column matrix; The steps to obtain the target mode shape vector under the corresponding sensitive modes are as follows: For the initial mode shape vector under each sensitive mode The vibration amplitude is normalized to obtain the initial mode shape vector under the corresponding sensitive mode. The normalized amplitude is denoted as the full-bridge mean under the corresponding sensitive mode; The beam bridge to be monitored is divided into multiple areas; Calculate the normalized mean amplitude and the normalized maximum amplitude of all degree-of-freedom nodes in each region under each sensitive mode. Record the obtained normalized mean amplitude as the region mean in the sensitive mode and the normalized maximum amplitude as the region maximum in the sensitive mode. If the mean or maximum value of a region in any sensitive mode is greater than b times the mean of the full bridge in the corresponding sensitive mode, then the region is identified as a high-response region. All nodes within the high-response region are selected as candidate nodes; the first node in the sensitive mode set... The vector expression for the target mode shape vector of each sensitive mode is: Where m refers to the number of candidate degree-of-freedom nodes. The first in the sensitive mode set The mode shape of the m-th degree-of-freedom node of a sensitive mode; This represents an m-row, 1-column matrix.

8. The sensor arrangement method for identifying scour dynamics of beam bridge pile foundations according to claim 7, characterized in that: The arrangement of multiple sensors selectively placed on candidate degree-of-freedom nodes is denoted as the sensor placement matrix, and the sensor placement matrix is ​​denoted as L. ,in Refers to an m-row, I-column matrix; I refers to the number of sensors, and ; The formula for calculating the signal-to-noise ratio (SNR) of the p-th sensitive mode in the sensitive mode set under the sensor deployment matrix L is as follows: ,in This represents the power spectral density of the p-th sensitive mode excitation. Let p be the damping ratios of the sensitive modes. To measure the channel noise power spectral density.

9. The sensor arrangement method for identifying the scour dynamics of beam bridge pile foundations according to claim 8, characterized in that: The formula for calculating the weighting coefficient of the target mode shape vector under each sensitive mode is as follows: ,in The weight coefficient of the p-th sensitive mode in the sensitive mode set. The frequency sensitivity of the p-th sensitive mode in the sensitive mode set; The frequency sensitivity of the j-th sensitive mode in the sensitive mode set; The method for selecting a target monitoring scheme from multiple multimodal monitoring schemes based on the weighting coefficients of all sensitive modes and the signal-to-noise ratio index is as follows: The overall signal-to-noise ratio (SNR) of all sensitive modes under the same sensor deployment matrix L is calculated based on weighting coefficients and SNR indices. The formula for calculating the overall signal-to-noise ratio is as follows: ; With the goal of maximizing the overall signal-to-noise ratio, the Grey Wolf optimization algorithm is used to iteratively optimize the sensor deployment matrix L, and the iteratively optimized sensor deployment matrix L is taken as the final target monitoring scheme.

10. A sensor arrangement system for identifying the scour dynamics of pile foundations in beam bridges, characterized in that: include, The model simulation unit establishes a three-dimensional finite element structural dynamic model based on the beam bridge to be monitored, which can express the coupling effect between the pile foundation and the soil. The data extraction unit applies excitation conditions to the three-dimensional finite element structural dynamic model and extracts the modal frequencies and mode shapes of the first N modes of the three-dimensional finite element structural dynamic model under various scouring conditions. The modal screening unit quantifies the influence of scouring conditions on the modal frequencies of the first N modes, and obtains the frequency sensitivity of the first N modes; based on the frequency sensitivity, sensitive modes are screened from the first N modes to form a sensitive mode set; The node screening unit extracts the mode shapes of all degree-of-freedom nodes of the beam bridge to be monitored, forming the initial mode shape vector of the sensitive mode; based on the initial mode shape vector, candidate degree-of-freedom nodes are screened from all degree-of-freedom nodes of the beam bridge to be monitored, and the mode shapes of all candidate degree-of-freedom nodes constitute the target mode shape vector under the corresponding sensitive mode. For a single-mode monitoring unit, if monitoring a single mode of a beam bridge, the single sensor is placed on the candidate degree of freedom node with the largest vibration amplitude of the lowest-order sensitive mode in the sensitive state set. If the multimodal monitoring unit is monitoring the multimodal behavior of a beam bridge, multiple sensors are selectively arranged on candidate degree-of-freedom nodes to form multiple multimodal monitoring schemes, wherein the number of sensors is less than or equal to the number of candidate degree-of-freedom nodes. Calculate the signal-to-noise ratio of the target mode shape vector under each sensitive mode under different multimodal monitoring schemes; The weighting coefficients of the target mode shape vector under each sensitive mode are calculated based on frequency sensitivity. The target monitoring scheme is then selected from multiple multimodal monitoring schemes based on the weighting coefficients of all sensitive modes and the signal-to-noise ratio.

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