A multi-objective optimization layout scheme for multiple sensors for structural damage identification

Abstract

The present invention discloses a multi-objective optimization layout scheme for multiple sensors for structural damage identification. It uses damage identification indicators based on multivariate data fusion to perform damage sensitivity analysis and correlation analysis of measurement data, and establishes two objective functions for the optimal placement of multiple sensors. The first objective function is constructed based on response covariance sensitivity, and the second objective function aims to obtain independent responses through correlation analysis. When the two objective functions take their minimum values, the measurement data maximizes damage indicator sensitivity and response independence. The sensor optimization layout problem is thus formulated as selecting an optimized sensor arrangement and combination from all candidate locations to achieve the optimal solution for both optimization objectives. A non-dominated sorting genetic algorithm is then used for the solution. The technical solution provided by the present invention can simultaneously perform comprehensive optimization of the placement of multiple sensors, balancing multiple contradictions such as sensitivity and independence of multiple sensors to local damage, thereby better meeting engineering needs.

Description

Technical Field

[0001] The present invention relates to the technical field of sensor optimization layout, and in particular to a multi-sensor multi-objective optimization layout method and system for structural damage identification. Background Art

[0002] Over decades, even centuries, of service, civil engineering structures inevitably experience the combined effects of environmental erosion, material aging, load effects, and man-made or natural sudden changes, leading to the accumulation of structural damage and a reduction in resistance. This in turn reduces their ability to withstand natural disasters, normal loads, and environmental stresses, potentially triggering catastrophic accidents. Countless tragedies have been caused by the failure to promptly detect structural damage. To promptly identify safety hazards and ensure structural safety, research in structural health monitoring and damage identification technologies is crucial and in high demand. Health monitoring of engineering structures involves deploying a variety of intelligent sensors, along with data acquisition, data transmission, data management, data analysis, and early warning systems, to perceive, identify, diagnose, and assess the structure's damage and safety status and their evolution in real time. This approach reveals the lifecycle behavior of real structures under the coupled effects of real loads and the environment, mimicking the self-perception and self-diagnosis capabilities of humans.

[0003] The performance of a structural health monitoring system depends largely on the quality of the sensor system, including the number, type, and placement of sensors. Previous studies have shown that haphazardly placed sensors can even lead to erroneous identification results. Because civil engineering structures are often large and complex, they often require thousands of degrees of freedom to describe their responses. Consequently, the number of possible sensor locations is enormous. However, due to cost and other factors, the number of sensors available is very limited compared to the number of candidate locations. Therefore, how to rationally select the type, placement, and number of sensors to fully utilize the limited number of sensors to obtain comprehensive structural information is a key issue that must be addressed in the design of structural health monitoring systems. This problem is known as the optimal sensor placement problem. Numerous methods have been proposed over the past few decades for various purposes. Existing sensor placement criteria include the modal assurance criterion, the effective independence criterion, the singular value decomposition ratio criterion, the Fisher information matrix criterion, the probability-based damage identification criterion, the information entropy criterion, the shared information criterion, the representative least squares criterion, and the modal visualization degree criterion. Most current sensor placement optimization methods are only applicable to a single sensor type. However, the proper selection, installation, and use of multiple sensor types (such as accelerometers, displacement sensors, and strain gauges) is crucial for the design of structural health monitoring systems. The data measured by each sensor has distinct characteristics. For example, acceleration responses can be easily measured with a high signal-to-noise ratio and contain higher kinetic energy in higher-order vibration modes. In contrast, displacement responses contain more kinetic energy in lower-order vibration modes. Strain or stress responses are sensitive to local changes near the sensor but insensitive to changes farther away. Due to the varying strengths and limitations of these sensors, the combined use of multiple sensor types can complement their data, but also complicates optimal sensor placement. If single-type sensor placement optimization methods are used to independently design each sensor type, the resulting sensor configuration, combining the individual designs, will inevitably result in redundant measurements and suboptimal overall performance. The varying strengths and limitations of multiple sensor types often require the design of multiple optimization objective functions to balance common engineering conflicts such as cost and accuracy, and sensitivity and redundancy. These conflicting objectives cannot be addressed using existing sensor placement optimization methods that focus on single-objective optimization. Summary of the Invention

[0004] (1) Technical issues to be solved

[0005] Different types of smart sensors have different advantages and limitations. The combined use of multiple types of sensors can complement each other's data advantages, but it also complicates the optimal sensor layout. If the traditional single-type sensor optimization layout method is used to independently design each type of sensor, the final sensor configuration of the combined designs will not be able to avoid redundant measurements and will not achieve the best overall performance. In addition, the traditional sensor optimization layout method only optimizes a single objective function for the sensor, resulting in a structural health monitoring system composed of multiple sensors that cannot meet multiple optimization design goals at the same time. Engineering practice experience shows that the different advantages and limitations of multiple types of sensors often lead to the need for multiple optimization objective functions in the optimization to balance the contradictions commonly found in engineering, such as cost and accuracy, sensitivity and redundancy. Such conflicting objectives cannot be solved using the existing sensor optimization layout method for single-objective optimization.

[0006] Therefore, the traditional sensor optimization layout method only optimizes a single sensor and a single objective function, resulting in the structural health monitoring system composed of multiple sensors unable to achieve optimal performance.

[0007] (2) Technical solution

[0008] A multi-objective optimization placement method for multiple sensors for structural damage identification is proposed. It features comprehensive multi-objective optimization placement of multiple sensors, employs multivariate data fusion damage identification indicators to perform damage sensitivity analysis and measurement data correlation analysis, and then employs a non-dominated sorting genetic algorithm to solve the multi-objective optimization placement problem, balancing the various contradictions between the sensitivity and independence of multiple sensors to local damage. The specific process includes:

[0009] S1: Establish a finite element model of a preset civil structure where multiple sensors can be deployed, and obtain structural response data of all candidate sensor locations among the multiple sensors by inputting excitations;

[0010] S2: normalizing and dimensionless processing the structural response data of the candidate sensor position, and using a covariance function to perform multivariate data fusion and construct an index sensitive to local damage, thereby obtaining a damage identification index fused by the multivariate data;

[0011] The standardization and dimensionless processing are used to convert data with different dimensions and variation characteristics; the covariance function is used to fuse multi-source heterogeneous data; the damage identification index of multivariate data fusion is used to improve the sensitivity of the damage identification index to structural damage and reduce the impact of measurement noise on damage identification;

[0012] S3: Using the damage identification index of the multivariate data fusion to perform damage sensitivity analysis and redundancy analysis, and establish a comprehensive objective function for the optimal placement of the two sensors; wherein the first objective function corresponds to damage sensitivity, and the second objective function corresponds to data redundancy;

[0013] S4: Using a non-dominated sorting genetic algorithm to solve the objective function of the optimal arrangement of the two competing sensors and obtain an optimal compromise solution, thereby determining the optimized number and position of each sensor.

[0014] A multi-sensor multi-objective optimization placement system for structural damage identification is provided. The system is used to execute the multi-sensor multi-objective optimization placement method for structural damage identification as described above, and includes:

[0015] (1) a sensor position structural response data acquisition module, which is used to establish a finite element model of a preset civil structure on which multiple sensors can be deployed, and to acquire structural response data of all candidate sensor positions among the multiple sensors by inputting excitations;

[0016] (2) a multivariate data fusion damage identification index calculation module, which is used to standardize and dimensionlessly process the structural response data of the candidate sensor positions, and use a covariance function to perform multivariate data fusion and construct an index sensitive to local damage to obtain a multivariate data fusion damage identification index;

[0017] The standardization and dimensionless processing are used to convert data with different dimensions and variation characteristics; the covariance function is used to fuse multi-source heterogeneous data; the damage identification index of multivariate data fusion is used to improve the sensitivity of the damage identification index to structural damage and reduce the impact of measurement noise on damage identification;

[0018] (2) an objective function construction module, configured to perform damage sensitivity analysis and redundancy analysis using the damage identification index of the multivariate data fusion, and to establish an objective function for optimizing the placement of two sensors; wherein the first objective function corresponds to damage sensitivity, and the second objective function corresponds to data redundancy;

[0019] (3) An optimal solution solving module, which is used to solve the objective function of the optimal arrangement of the two sensors using a non-dominated sorting genetic algorithm to determine the optimal number and position of each sensor.

[0020] A damage identification system based on a multi-sensor multi-objective optimization arrangement scheme includes the aforementioned multi-sensor multi-objective optimization arrangement system for structural damage identification, and uses a plurality of sensors with a multi-objective optimization arrangement to perform structural damage identification; the damage identification system includes:

[0021] (1) a structural dynamic index acquisition module, which is used to acquire structural dynamic response monitoring data of the target civil structure in real time, and to perform multi-objective optimization layout calculation of multiple sensors using the multi-objective optimization layout system for structural damage identification, and then to extract structural dynamic indicators sensitive to structural damage based on the structural dynamic response monitoring data obtained from the optimized arrangement of sensors;

[0022] (2) A damage location and extent identification module, which is used to identify the damage location and extent of the target civil structure based on the structural dynamic indicators that are sensitive to structural damage.

[0023] (3) Beneficial effects

[0024] The multi-objective optimization arrangement method for multiple sensors for structural damage identification provided by the present invention has the following advantages:

[0025] (1) In order to solve the problem that most existing structural damage identification methods use the optimization layout method of a single type of sensor and cannot perform comprehensive optimization layout of multiple sensors at the same time, the sensor optimization layout algorithm adopted in the present invention is suitable for the mixed layout of multiple different types of sensors, which can effectively improve the measurement effect when multiple sensors are mixed, and provide better quality measurement data for the fusion of multi-dimensional heterogeneous data.

[0026] (2) In view of the problem that most existing sensor optimization layout methods for structural damage identification can only consider a single optimization target, the present invention proposes a multi-target optimization layout method suitable for multiple sensors, targeting two contradictory targets: the sensitivity of sensors to local damage and the redundancy of different types of sensors. This method can achieve the optimal overall sensitivity of multiple sensors to structural damage, while also minimizing the redundancy of measurement information between sensors of different or same categories. While ensuring damage sensitivity, information redundancy is avoided, so that damage identification can achieve the optimal damage identification result using the least number of sensors. Finally, a sensor layout scheme with the best performance and construction cost is provided for the structural health monitoring system, which can balance the contradictions in various aspects such as sensitivity, accuracy, and installation cost of multiple sensors to local damage, and better meet engineering needs.

[0027] The damage identification method provided by the present invention is based on a multi-objective optimization layout scheme of multiple sensors. Through the optimal solution provided by the multi-objective optimization layout scheme of multiple sensors for structural damage identification, a multi-sensor data fusion method is used to jointly extract structural dynamic indicators sensitive to structural damage from various structural dynamic response data such as acceleration, displacement, and strain. The different characteristics of various types of data can be used to effectively improve the quality of structural dynamic indicator data. By combining the finite element model of the engineering structure for structural damage identification, high-sensitivity and high-precision damage location and quantitative analysis can ultimately be achieved. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 Flowchart of a multi-objective optimization arrangement method of multiple sensors for structural damage identification according to an embodiment of the present invention;

[0029] Figure 2 This is a flowchart of the multi-objective optimization layout calculation of multiple sensors using the non-dominated sorting genetic algorithm in an embodiment of the present invention;

[0030] Figure 3 The Pareto front obtained by multi-objective optimization arrangement calculation of multiple sensors for structural damage identification in a three-dimensional cantilever beam structure according to an embodiment of the present invention;

[0031] Figure 4 The optimal arrangement scheme obtained based on the utility function method and the inflection point method in the embodiment of the present invention;

[0032] Figure 5 This is a calculation flow chart for damage identification based on multiple sensors with optimized arrangement in an embodiment of the present invention;

[0033] Figure 6 The results of structural damage identification using two optimized sensor layout schemes for a three-dimensional cantilever beam in an embodiment of the present invention are shown;

[0034] Figure 7 This is a framework diagram of a damage identification system based on a multi-sensor multi-objective optimization arrangement scheme in an embodiment of the present invention. DETAILED DESCRIPTION

[0035] In order to make the technical problems, technical solutions and beneficial effects to be solved by the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0036] In one embodiment, a multi-objective optimization arrangement method for multiple sensors for structural damage identification is provided, and its flow chart is as follows: Figure 1 As shown, and includes the following steps:

[0037] S1: Establish a finite element model of a preset civil structure where multiple sensors can be deployed, and obtain the structural response data of all candidate sensor locations among the multiple sensors through input excitation.

[0038] The preset civil structure is a pre-set building structure model, and the corresponding finite element model includes a variety of sensors, including but not limited to acceleration sensors, displacement sensors, strain sensors, etc. The sensors are installed in different locations in the civil structure, such as floors and cantilever beams.

[0039] Specifically, the external excitation vector is input into the finite element model to obtain the position structure response data of all candidate sensors in the multiple sensors. These sensor position structure response data are multivariate heterogeneous data.

[0040] Assume that all measured responses of structural health monitoring, including acceleration, displacement, strain and other structural dynamic response data, can be expressed by the following state equation:

[0041] y(t)=C c x(t)+D c f(t) (1)

[0042] in

[0043]

[0044] in, is the observation vector, which includes the strain response time history ε(t), displacement response time history z(t) and acceleration response time history is the state vector, satisfying the dynamic equation:

[0045]

[0046] in

[0047]

[0048] Where Ψ=BGL d Φ is the strain modal matrix; L d is the selection matrix of node displacements for matching strain calculation; matrix G is the coordinate transformation matrix from global coordinates to local coordinates; vector B defines the local strain-displacement relationship, Φ is the modal matrix, ω and ξ are diagonal matrices composed of the structural natural frequency and damping ratio, respectively, and q and are the displacement and velocity in modal coordinates respectively, and f(t) is the external excitation vector.

[0049] S2: The structural response data of the candidate sensor locations are normalized and dimensionless, and the covariance function is used to perform multivariate data fusion and construct an index sensitive to local damage to obtain a damage identification index based on multivariate data fusion;

[0050] Among them, standardization and dimensionless processing are used to convert data with different dimensions and change characteristics; multivariate data fusion is used to obtain multi-source heterogeneous data; and the damage identification index of multivariate data fusion is used to improve the sensitivity of the damage identification index to structural damage and reduce the impact of measurement noise on damage identification.

[0051] Specifically, the multivariate heterogeneous measurement data are standardized and dimensionless through formula (5), and the original structural response data are divided by their respective standard deviations to obtain the standardized and dimensionless structural response, which facilitates the subsequent data fusion of data with different dimensions and change characteristics.

[0052]

[0053] Among them, y p (t) is the original structural response data, is the standard deviation, is the normalized and dimensionless structural response obtained.

[0054] The covariance function is used to fuse multivariate heterogeneous data and reduce measurement noise. The formula for calculating the cross-covariance function of any two standardized structural responses is as follows:

[0055]

[0056] After the cross-covariance function of the structural response is obtained according to formula (6), it can be further assembled into the damage identification index vector V of multivariate data fusion pq , the calculation method is as follows:

[0057]

[0058] Among them, y p is the structural response recorded by sensor p, is the normalized structural response, represents the standard deviation of the response recorded by sensor p on the intact structure. E represents the expectation, the variable τ is the time interval, and the subscripts p and q represent the responses calculated from the responses measured by sensors p and q. i ∈[p1,p s ],q j ∈[q1,q s ], the subscript s represents the total number of selected sensors; nt is the total number of time intervals selected for damage identification.

[0059] S3: Use damage identification indicators based on multivariate data fusion to perform damage sensitivity analysis and redundancy analysis, and establish two objective functions for sensor optimization. The first objective function corresponds to damage sensitivity, and the second objective function corresponds to data redundancy.

[0060] Sensitivity to local stiffness changes and independence of multi-element structural responses are two conflicting sensor optimization layout criteria that determine the effectiveness of structural damage identification. Therefore, to balance the contradiction between the two optimization objectives, multiple optimization objective functions are considered, and two objective functions are selected for structural damage identification, which are applicable to the case of mixed optimization layout of multiple types of sensors. The first objective function corresponds to loss sensitivity analysis; the second objective function corresponds to data redundancy, or information correlation. The resulting sensor layout scheme is made sensitive to damage while avoiding information redundancy, thereby converting the problem into finding the optimal multi-type sensor layout that simultaneously satisfies both objective functions.

[0061] Specifically, the two optimization objectives of the multi-type sensor optimization layout problem are expressed as a comprehensive optimization objective function:

[0062]

[0063] in

[0064] Among them, F(θ) is a multi-objective function based on the sensitivity and correlation analysis of the covariance index of the structural dynamic response, and the variable θ represents the vector of the optimal arrangement and combination of sensors; is a dimensionless objective function normalized by its maximum value; and are the lower and upper limits of the number of sensors of type i, N oi is the total number of candidate positions, and the optimal arrangement of the above multi-type sensors can be obtained by solving this equation.

[0065] Compared with the currently commonly used single-sensor single-target sensor optimization layout method, the multi-target optimization layout method of multiple sensors proposed in the present invention can simultaneously optimize the number and position of multiple sensors and balance the contradiction between two different optimization objectives, thereby improving the measurement effect when multiple sensors are mixed, and ultimately improving the sensitivity and effectiveness of dynamic indicators for structural damage identification.

[0066] Furthermore, the first objective function f SA It is constructed based on the response covariance sensitivity, aiming to maximize the response covariance increase relative to the local stiffness change, f SA The sensor position with the minimum value is most sensitive to the local stiffness change of the damaged unit. The background of damage sensitivity and the first objective function f SA is defined as follows:

[0067] The stiffness matrix of the damaged structure can be expressed mathematically as:

[0068]

[0069] where α i ∈α is the coefficient of the stiffness matrix corresponding to the i-th unit. Δα i ∈Δα is the local stiffness change of the i-th element, ne is the total number of elements, α is the vector of stiffness matrix coefficients, and Δα is the vector of local stiffness change of the damaged element.

[0070] Measured damage indicators and the damage index calculated based on the finite element model of the structure in good condition The following damage identification equation is satisfied:

[0071]

[0072] In the formula It is the damage sensitivity, which is the partial derivative of the damage index with respect to the change in unit stiffness. It indicates the change in the damage index when the unit stiffness decreases. It can measure the sensitivity of the index to damage. Since α is a vector, the damage sensitivity It can be expressed in matrix form:

[0073]

[0074] The first objective function is taken as follows to conveniently measure the size of the sensitivity matrix S and characterize the damage sensitivity of the sensor layout scheme:

[0075]

[0076] At the same time, for the second objective function, since it is only based on the first objective function f SA The sensor arrangement of may be chosen to be clustered around certain structural units with similar sensitivity to local damage, so that the information from these sensors may be redundant. Therefore, the second objective function f CA Correlation analysis is performed to help reduce this redundant information by collecting more independent structural responses. Response independence has the potential to improve the quality of damage identification results and significantly reduce redundant sensors. The second objective function f CA Aiming to obtain independent responses through correlation analysis, f CA The smallest sensor position maximizes response independence.

[0077]

[0078] in

[0079]

[0080] where the vector θ represents the optimal sensor configuration; S is the sensitivity matrix, which can be calculated using formula (9); R is the correlation matrix of the selected response; the subscript p l ∈[p1,ps ],q k ∈[q1,q s ]; correlation coefficient r plqk It is the sensor p l and q k A scalar calculated from the logged response.

[0081] S4: Use the non-dominated sorting genetic algorithm to solve the objective function of the optimal arrangement of the two sensors and determine the optimal number and position of each sensor.

[0082] For the multi-objective optimization function of various sensors established by S3, a non-dominated sorting genetic algorithm is used to solve it and obtain the optimal compromise solution, thereby determining the optimization scheme of the sensor.

[0083] Specifically, see Figure 2 The non-dominated sorting genetic algorithm used in the present invention is customized for this problem. The possible sensor positions θ are the optimized design variables. Each possible sensor position is represented by an integer ("gene"), and the optimal sensor configuration θ is represented by an integer string ("chromosome"). In addition, forced mutation is embedded in the sensor optimization process to replace duplicate genes to avoid installing the same type of sensor in the same location. The specific calculation process of the non-dominated sorting genetic algorithm includes:

[0084] S41: The initial sensor position is specified as between 1 and N o Therefore, the non-dominated sorting genetic algorithm starts with a set of chromosomes of generation 0, which are between 1 and N. o A string of random integers uniformly distributed between ;

[0085] S42: In newly generated chromosomes or chromosomes that will subsequently undergo crossover and mutation operations, the same sensor can be placed more than once at the same position (e.g., the same integer can be repeatedly used for chromosome θ). Therefore, it is necessary to apply a forced mutation mechanism to replace the duplicate genes in each chromosome with non-repeated and uniformly distributed random integers from the difference between the set θ and the entire set of candidate sensor positions;

[0086] S43: Calculate the standardized objective function of each chromosome θ, and

[0087] S44: perform elite non-dominated sorting on all chromosomes of the current generation and determine the non-dominated frontier;

[0088] S45: Execute the genetic algorithm operations, including selection, crossover, and mutation, to generate a new population Q(θ). The forced mutation introduced in step S42 is then performed to replace duplicate genes in each chromosome, and the standardized objective function is calculated as in step S43. The old and new populations are merged into P(θ)∪Q(θ), and the elite non-dominated sorting described in step (4) is performed to generate the next population.

[0089] S46: Repeat step S45 until the maximum number of generated sensors is reached, and finally, the optimal solution under different optimal sensor configurations is obtained for the multi-target multi-type sensor optimization layout problem.

[0090] The Pareto front obtained by the non-dominated sorting genetic algorithm contains a series of Pareto solutions, each of which has a different weight factor of the objective function and corresponds to an optimal sensor layout scheme. Figure 3 As shown in Figure 1, the Pareto front is obtained by calculating the multi-objective optimization layout of multiple sensors for structural damage identification, taking a three-dimensional cantilever beam structure as an example.

[0091] Furthermore, since the aforementioned multi-objective and multi-type sensor optimization placement problem is a multi-solution problem, the Pareto front obtained by the non-dominated sorting genetic algorithm contains a series of Pareto solutions, each of which corresponds to a sensor optimization placement. However, not all solutions on the Pareto front are optimal sensor optimization placement solutions for damage identification. Rather, they are a set of compromise solutions resulting from the simultaneous optimization of two conflicting objectives, which are called non-dominated or Pareto suboptimal solutions.

[0092] To balance the trade-off between the two conflicting objectives, an inflection point-based approach can be used to select the optimal sensor layout from the Pareto front as the final solution. Typically, decision makers are unclear about or have difficulty evaluating these weighting factors, and without understanding user preferences, the inflection point of the Pareto optimal frontier is preferred as the optimal sensor placement solution. This involves fitting the Pareto solution obtained through multi-objective optimization into a smooth and differentiable Pareto frontier curve using a spline curve function. By calculating the curvature of the curve, the inflection point of the Pareto frontier curve is obtained at the point where the curvature is maximum. This inflection point represents the optimal compromise solution to the multi-objective optimization problem.

[0093] At the same time, an algorithm for determining the Pareto optimal OSP based on the utility function method is proposed, and the expression of the utility function is defined as follows:

[0094]

[0095] Among them, I SCA (θ Pa ) is the utility function; θ Pa is the Pareto solution of the sensor optimization placement problem; wSCA is a weighting factor, typically chosen based on the importance of the objective. That is, by selecting different weighting factors, this method can obtain multiple optimal solutions on the Pareto front. Each of these solutions is unique, corresponding to a specific pair of weighting factors. Utility function-based methods are one feasible approach to quantify the decision maker's preference for selecting the desired optimal sensor placement from Pareto solutions. The selection of weighting factors is based on the decision maker's knowledge and judgment. Generally, if the decision maker is clear about the weighting factors for each optimization objective, this method can be used to select the final optimal sensor placement solution.

[0096] Therefore, by determining the utility function or selecting the inflection point solution, we can finally determine an optimal solution on the Pareto front, such as Figure 4 As shown, the optimal layout solutions obtained based on the utility function method and the inflection point method.

[0097] In one embodiment, a multi-sensor multi-objective optimization placement system for structural damage identification is provided. The system is configured to execute the multi-sensor multi-objective optimization placement method for structural damage identification. The system may be implemented using any hardware support and may include the following modules:

[0098] (1) a sensor position structural response data acquisition module, which is used to establish a finite element model of a preset civil structure on which multiple sensors can be deployed, and to acquire structural response data of all candidate sensor positions among the multiple sensors by inputting excitations;

[0099] (2) a multivariate data fusion damage identification index calculation module, which is used to standardize and dimensionlessly process the structural response data of the candidate sensor positions, and use a covariance function to perform multivariate data fusion and construct an index sensitive to local damage to obtain a multivariate data fusion damage identification index;

[0100] The standardization and dimensionless processing are used to convert data with different dimensions and variation characteristics; the covariance function is used to fuse multi-source heterogeneous data; the damage identification index of multivariate data fusion is used to improve the sensitivity of the damage identification index to structural damage and reduce the impact of measurement noise on damage identification;

[0101] (4) an objective function construction module, configured to perform damage sensitivity analysis and redundancy analysis using the damage identification index of the multivariate data fusion, and to establish an objective function for optimizing the placement of two sensors; wherein the first objective function corresponds to damage sensitivity, and the second objective function corresponds to data redundancy;

[0102] (5) An optimal solution solving module, used to solve the objective function of the optimal arrangement of the two sensors using a non-dominated sorting genetic algorithm, and determine the optimal number and position of each sensor.

[0103] In one embodiment, a damage identification method based on a multi-objective optimization arrangement scheme of multiple sensors is provided, and the process is as follows: Figure 5 As shown, the steps include:

[0104] (1) The structural dynamic response monitoring data of the target civil structure are acquired in real time. Based on the sensor optimization scheme obtained by the multi-objective optimization arrangement method of multiple sensors for structural damage identification, the structural dynamic indicators sensitive to structural damage are extracted from the structural dynamic response monitoring data.

[0105] (2) Based on structural dynamic indicators that are sensitive to structural damage, the damage location and extent of the target civil structure are identified.

[0106] Structural dynamic response monitoring data includes, but is not limited to, acceleration response, displacement response, and strain response. After obtaining the optimal sensor combination based on the multi-objective optimization layout method for these multiple sensors, a multi-sensor data fusion method is employed to jointly extract structural dynamic indicators sensitive to structural damage from various structural dynamic response data, such as acceleration, displacement, and strain. The different characteristics of these data types can effectively improve the quality of structural dynamic indicator data. By combining this with the finite element model of the engineering structure for structural damage identification, highly sensitive and accurate damage location and quantitative analysis can ultimately be achieved.

[0107] Taking a three-dimensional cantilever beam as an example, the results of structural damage identification using two optimized sensor layout schemes are shown in the following figure. Figure 6 shown.

[0108] In one embodiment, a damage identification system based on a multi-sensor multi-objective optimization arrangement scheme is provided, such as Figure 7 As shown, the damage identification system includes a multi-sensor multi-objective optimization arrangement system for structural damage identification, and uses a plurality of sensors with optimized arrangement to perform structural damage identification; the damage identification system includes:

[0109] (1) a structural dynamic index acquisition module, which is used to acquire structural dynamic response monitoring data of the target civil structure in real time, and to perform multi-objective optimization layout calculation of multiple sensors using the multi-objective optimization layout system for structural damage identification, and then to extract structural dynamic indicators sensitive to structural damage based on the structural dynamic response monitoring data obtained from the optimized arrangement of sensors;

[0110] (2) A damage location and extent identification module, which is used to identify the damage location and extent of the target civil structure based on the structural dynamic indicators that are sensitive to structural damage.

[0111] The above is an explanation of the multi-objective optimization arrangement scheme of multiple sensors for structural damage identification of the present invention, which is used to help understand the present invention; however, the implementation of the present invention is not limited to the above embodiments, and any changes, modifications, substitutions, combinations, and simplifications made without departing from the principles of the present invention should be equivalent replacement methods and are included in the scope of protection of the present invention.

Claims

1. A multi-objective optimization layout method for multiple sensors for structural damage identification, characterized by At the same time, a comprehensive optimization layout of multiple sensors is performed. Damage sensitivity analysis and correlation analysis of measurement data are performed using damage identification indicators based on multivariate data fusion. Then, a non-dominated sorting genetic algorithm is combined to solve the multi-objective optimization layout problem, balancing the contradiction between the sensitivity and independence of multiple sensors to local damage. The specific process includes: S1: Establish a finite element model of a preset civil structure where multiple sensors can be deployed, and obtain structural response data of all candidate sensor locations among the multiple sensors by inputting excitations; S2: normalizing and dimensionless processing the structural response data of the candidate sensor position, and using a covariance function to perform multivariate data fusion and construct an index sensitive to local damage, thereby obtaining a damage identification index fused by the multivariate data; The standardization and dimensionless processing are used to convert data with different dimensions and variation characteristics; the covariance function is used to fuse multi-source heterogeneous data; the damage identification index of multivariate data fusion is used to improve the sensitivity of the damage identification index to structural damage and reduce the impact of measurement noise on damage identification; S3: Using the damage identification index of the multivariate data fusion to perform damage sensitivity analysis and redundancy analysis, and establish a comprehensive objective function for the optimal placement of the two sensors; wherein the first objective function corresponds to damage sensitivity, and the second objective function corresponds to data redundancy; S4: Use the non-dominated sorting genetic algorithm to solve the objective function of the optimal placement of two competing sensors and obtain the optimal compromise solution, thereby determining the optimal number and location of each sensor; In S3, the comprehensive objective function for establishing the optimal arrangement of the two sensors is expressed as follows: in, F(θ) is a multi-objective function for damage sensitivity and correlation analysis based on the covariance multivariate data fusion index of the structural dynamic response, while the variable θ represents the vector of the optimal arrangement and combination of sensors; is the dimensionless objective function normalized by the maximum value, f SA is the first objective function, f CA is the second objective function; and are the lower and upper limits of the number of sensors of type i, N oi is the total number of candidate locations.

2. The multi-objective optimization arrangement method for multiple sensors for structural damage identification according to claim 1, characterized in that: The first objective function f SA The definition is as follows: The stiffness matrix of the damaged structure can be expressed mathematically as: Among them, α i ∈α is the coefficient of the stiffness matrix corresponding to the i-th unit; Δα i ∈Δα is the local stiffness change of the i-th element, ne is the total number of elements; α is the vector of stiffness matrix coefficients; Δα is the vector of local stiffness change of the damaged element; Measured damage indicators and the damage index calculated based on the finite element model of the structure in good condition The following damage identification equation is satisfied: In the formula It is the damage sensitivity, which is the partial derivative of the damage index with respect to the change in unit stiffness. It indicates the change in the damage index when the unit stiffness decreases. It is used to measure the sensitivity of the index to damage. α is a vector, and the damage sensitivity is It can be expressed in matrix form: The first objective function is taken as follows to measure the size of the sensitivity matrix S and characterize the damage sensitivity of the sensor layout scheme:

3. The multi-objective optimization arrangement method for multiple sensors for structural damage identification according to claim 2, characterized in that: The second objective function f CA The definition is as follows: in, where the vector θ represents the optimal sensor configuration; S is the sensitivity matrix; R is the correlation matrix of the selected responses; and the subscript p l ∈[p1,p s ],q k ∈[q1,q s ]; correlation coefficient r plqk It is the sensor p l and q k A scalar calculated from the logged response.

4. The multi-objective optimization arrangement method for multiple sensors for structural damage identification according to claim 3, characterized in that: In S4, the non-dominated sorting genetic algorithm is used to solve the objective function of the optimal arrangement of the two competing sensors and obtain the optimal compromise solution, including: S41: The initial sensor position is specified as between 1 and N o A random integer uniformly distributed between 1 and N; the non-dominated sorting genetic algorithm starts from the set of chromosomes of generation 0, which is between 1 and N o A string of random integers uniformly distributed between ; S42: In newly generated chromosomes or chromosomes that will subsequently undergo crossover and mutation operations, the same sensor can be placed more than once at the same position. A forced mutation mechanism is used to replace duplicate genes in each chromosome with non-repeated and uniformly distributed random integers from the difference between the set θ and the entire set of candidate sensor positions. S43: Calculate the standardized objective function of each chromosome θ, and S44: perform elite non-dominated sorting on all chromosomes of the current generation and determine the non-dominated frontier; S45: Execute genetic algorithm operations, including selection, crossover, and mutation, to generate a new population Q(θ), after which the forced mutation introduced in S42 is performed to replace duplicate genes in each chromosome, and the standardized objective function is calculated as in step S43; the old population and the new population are merged into P(θ)∪Q(θ), and the elite non-dominated sorting described in step S44 is performed to generate the next population; S46: Repeat step S45 until the maximum number of generated sensors is reached, and finally obtain the optimal solution under different optimal sensor configurations for the multi-target multi-type sensor optimization layout problem; After S46, the Pareto front obtained by the non-dominated sorting genetic algorithm includes a series of Pareto solutions, each of which has a different weight factor of the objective function and corresponds to a compromised suboptimal sensor layout scheme. An optimal solution is determined in the Pareto front by determining the utility function or selecting the inflection point scheme.

5. The multi-objective optimization arrangement method for multiple sensors for structural damage identification according to claim 4, characterized in that: The inflection point selection scheme includes: determining an optimal sensor optimization layout solution based on the inflection point of the Pareto front fitting curve, that is, fitting the Pareto solution obtained by the multi-objective optimization solution into a smooth and differentiable Pareto front curve through a spline curve function, and calculating the curvature of the curve. The inflection point of the Pareto front curve mentioned above can be obtained at the place where the curvature is maximum. This inflection point represents the optimal compromise solution to the multi-objective optimization problem.

6. The multi-objective optimization arrangement method for multiple sensors for structural damage identification according to claim 4, characterized in that: The determining of the utility function comprises: The expression that defines the utility function is as follows: Among them, I SCA (θ Pa ) is the utility function; θ Pa is the Pareto solution of the sensor optimization placement problem; w SCA is a weighting factor.

7. A multi-sensor multi-objective optimization placement system for structural damage identification, characterized by: The system is used to execute the multi-objective optimization arrangement method for multiple sensors for structural damage identification according to any one of claims 1 to 6, and includes: (1) a sensor position structural response data acquisition module, which is used to establish a finite element model of a preset civil structure on which multiple sensors can be deployed, and to acquire structural response data of all candidate sensor positions among the multiple sensors by inputting excitations; (2) a multivariate data fusion damage identification index calculation module, which is used to standardize and dimensionlessly process the structural response data of the candidate sensor positions, and use a covariance function to perform multivariate data fusion and construct an index sensitive to local damage to obtain a multivariate data fusion damage identification index; The standardization and dimensionless processing are used to convert data with different dimensions and variation characteristics; the covariance function is used to fuse multi-source heterogeneous data; the damage identification index of multivariate data fusion is used to improve the sensitivity of the damage identification index to structural damage and reduce the impact of measurement noise on damage identification; (4) an objective function construction module, configured to perform damage sensitivity analysis and redundancy analysis using the damage identification index of the multivariate data fusion, and to establish an objective function for optimizing the placement of two sensors; wherein the first objective function corresponds to damage sensitivity, and the second objective function corresponds to data redundancy; (5) An optimal solution solving module, used to solve the objective function of the optimal arrangement of the two sensors using a non-dominated sorting genetic algorithm, and determine the optimal number and position of each sensor.

8. A damage identification system based on a multi-sensor multi-objective optimization layout scheme, characterized in that: The damage identification system includes the multi-sensor multi-objective optimization arrangement system for structural damage identification according to claim 7, and uses a plurality of sensors with optimal arrangement to perform structural damage identification; The damage identification system comprises: (1) a structural dynamic index acquisition module, which is used to acquire structural dynamic response monitoring data of the target civil structure in real time, and to perform multi-objective optimization layout calculation of multiple sensors using the multi-objective optimization layout system for structural damage identification, and then to extract structural dynamic indicators sensitive to structural damage based on the structural dynamic response monitoring data obtained from the optimized arrangement of sensors; (2) A damage location and extent identification module, which is used to identify the damage location and extent of the target civil structure based on the structural dynamic indicators that are sensitive to structural damage.

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