Bridge sensor multi-objective optimization arrangement method and system based on modal information driving

Abstract

The application discloses a bridge sensor multi-objective optimization arrangement method and system based on modal information driving, and the method comprises the following steps: establishing a finite element model based on bridge structure parameters and performing modal analysis to obtain modal vibration mode vectors and a candidate measuring point set; a multi-objective function containing a modal confidence criterion index, a modal kinetic energy index and a singular value decomposition index is constructed; an improved multi-objective snake optimization algorithm is used to solve the function, the algorithm initializes a population through chaotic mapping, introduces sparse coding constraints to match the essence of discrete combination optimization, realizes adaptive switching of global exploration and local development based on food quantity and temperature parameters, combines deductive non-dominated sorting and elite elimination strategies, and efficiently searches for a uniformly distributed Pareto optimal solution set; the application effectively overcomes the problems that the traditional method is easy to fall into local optimization and slow convergence, and can provide a group of feasible schemes for bridge sensor arrangement which are balanced and optimized among multiple objectives.

Description

Technical Field

[0001] This invention relates to the field of structural health monitoring technology, and in particular to a method and system for multi-objective optimization of bridge sensor layout based on modal information. Background Technology

[0002] In large-scale engineering structural health monitoring systems, the sensor subsystem deployment scheme is a crucial factor determining monitoring efficiency and data quality. Sensor arrangement directly affects the acquisition of overall structural dynamic response information and modal parameter identification. Traditional sensor optimization deployment methods are mostly based on continuous beam bridge structural design. Their optimization criteria and search strategies are difficult to effectively adapt to the modal localization effects and strong spatial coupling vibration characteristics of different types of bridge structures. This can easily lead to the omission of key modal information and insufficient measurement signal-to-noise ratio, resulting in "blind spots" or a large amount of redundant information in the monitoring system, thus reducing the accuracy of the monitoring system.

[0003] The sensor placement optimization problem is mathematically a high-dimensional, nonlinear, and discrete combinatorial optimization problem, exhibiting significant NP-hard characteristics. Existing optimization methods are mainly divided into two categories: sequential methods and intelligent optimization algorithms. Sequential methods have high computational efficiency, but the greedy search strategy they employ can easily lead to solutions getting trapped in local optima, limiting their global optimization capabilities. Intelligent optimization algorithms, represented by genetic algorithms and particle swarm optimization, have improved global search capabilities, but their population update mechanisms often rely on random operations. When faced with the large number of candidate measurement points in structural health monitoring, resulting in a high-dimensional solution space, they suffer from slow convergence, premature convergence, and premature convergence, making it difficult to efficiently approximate the true Pareto optimal front under multi-objective trade-offs. Furthermore, existing technologies partially focus on single optimization objectives, such as modal confidence criteria or Fisher information matrix determinants, making it difficult to systematically coordinate and balance multi-dimensional engineering requirements such as modal identifiability, signal measurement quality, and information completeness, thus limiting the overall effectiveness of the placement scheme.

[0004] In view of this, the present invention proposes a method and system for multi-objective optimization of bridge sensor placement based on modal information. Summary of the Invention

[0005] In view of the shortcomings of the prior art, the present invention provides a method and system for multi-objective optimization of bridge sensor layout based on modal information driving, which overcomes the limitations of existing methods such as poor adaptability to complex bridge structures, low optimization efficiency and single optimization objective, thereby providing a reliable solution for the scientific deployment of sensors.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] In a first aspect, the present invention provides a method for multi-objective optimization of bridge sensor placement based on modal information, comprising:

[0008] A finite element model of the bridge was established based on its structural parameters.

[0009] Modal analysis was performed on the finite element model of the bridge to obtain the mode shape vectors of each order of the bridge and to determine the candidate measurement point set of the bridge sensor.

[0010] Based on the mode shape vectors of each order and the candidate measurement point set, a multi-objective function is constructed to optimize the sensor arrangement.

[0011] An improved snake multi-objective optimization algorithm is used to solve the multi-objective function to obtain the Pareto optimal solution set for the sensor arrangement.

[0012] In an optional implementation, the method further includes:

[0013] Based on the specific monitoring requirements of the bridge, the final sensor layout scheme is selected from the Pareto optimal solution set.

[0014] In an optional implementation, the construction steps of the multi-objective function include:

[0015] With minimizing the modal confidence criterion index as the optimization objective, a first objective function is established to reduce the correlation between different modal modes.

[0016] With minimizing the modal kinetic energy index as the optimization objective, a second objective function is established to improve the signal energy of the selected measurement points in the candidate measurement point set;

[0017] With minimizing the singular value decomposition index as the optimization objective, a third objective function is established to enhance the information completeness of the modal information matrix of the selected measurement points in the candidate measurement point set.

[0018] The multi-objective function is obtained based on the first objective function, the second objective function, and the third objective function.

[0019] In an optional implementation, the step of using an improved snake multi-objective optimization algorithm to optimize and solve the multi-objective function to obtain the Pareto optimal solution set for the sensor arrangement specifically includes the following steps:

[0020] A1. Establish an initial snake optimization algorithm, and introduce a chaotic mapping mechanism, a sparse coding constraint strategy, and a deductive non-dominated sorting method into the initial snake optimization algorithm to construct an improved snake multi-objective optimization algorithm;

[0021] A2. Generate an initial snake group based on a chaotic mapping mechanism, and group the individuals in the initial snake group by gender.

[0022] A3. Use a sparse coding strategy to represent the sensor layout scheme and initialize the global non-dominated solution set;

[0023] A4. Based on the current iteration number, calculate the current food quantity and temperature value of the snake group;

[0024] A5. Based on the comparison result between the amount of food and the first preset threshold, select to enter the exploration stage or the development stage, and update the position of male and female individuals respectively according to the individual's gender using the corresponding update strategy.

[0025] A6. Apply sparse constraints to each individual in the snake group after the position is updated to meet the preset number of sensors, and calculate the multi-objective function value of the individual after sparse constraints.

[0026] A7. Based on the deductive non-dominated sorting method, perform Pareto classification on the current snake group and update the global non-dominated solution set;

[0027] A8. Repeat steps A4 to A7 until the preset iteration termination condition is met;

[0028] A9. Output the final globally non-dominated solution set as the Pareto optimal solution set for sensor placement.

[0029] In an optional implementation, step A5 specifically includes the following steps:

[0030] A501. Based on the comparison result between the amount of food and the first preset threshold, select to enter the exploration stage or the development stage:

[0031] If the amount of food is less than the first preset threshold, then enter the exploration phase and execute step A502;

[0032] If the amount of food is greater than or equal to the first preset threshold, then the development phase begins and step A503 is executed.

[0033] A502. For each individual in the snake group to be updated, the first update strategy and the second update strategy are adopted respectively to generate two candidate new positions, and the position with the better multi-objective function value is selected from the candidate new positions as the updated individual position.

[0034] The first update strategy is to update the current individual position based on the proportion of randomly selected heterosexual individual positions and their multi-objective function values;

[0035] The second update strategy is to update the current individual position based on a search boundary that decays non-linearly with the number of iterations.

[0036] A503. Based on the comparison result between the temperature value and the second preset threshold, select the position update mode:

[0037] If the temperature value is greater than the second preset threshold, all individuals in the snake group will adopt the third update strategy to move towards the male and female individuals with the best multi-objective function values ​​in the current snake group, respectively.

[0038] If the temperature value is less than or equal to the second preset threshold, the position is updated randomly using either combat mode or mating mode;

[0039] The combat mode is that individuals move towards the direction of the most outstanding individual based on the multi-objective function value of the current most outstanding individual;

[0040] The mating mode involves individuals interacting with opposite-sex individuals based on their own mating abilities to generate new individuals, and an elite elimination strategy is activated based on a preset probability in the mating mode.

[0041] In one optional implementation, the elite elimination strategy includes

[0042] The current snake population is sorted according to fitness, and divided into elite subpopulations and non-elite subpopulations based on a preset elite threshold.

[0043] For individuals in the elite subpopulation, the fourth update strategy is used to update their positions;

[0044] For individuals in the non-elite subpopulation, the fifth or sixth update strategy is randomly applied to update their positions.

[0045] The function expression for the fourth update strategy is:

[0046]

[0047] In the formula, X good For individuals in the elite subpopulation awaiting renewal; X rand,1 and X rand,2 These represent different individuals randomly selected from the elite subpopulation; Dim is the dimension of the individual vector; X food The optimal position for the individual snake; t is the current loop number; T is the maximum number of iterations; This is the rounding parameter; rand is a random number between 0 and 1.

[0048] The function expression for the fifth update strategy is:

[0049]

[0050] In the formula, X bad (t+1) represents the individual to be updated in the non-elite subpopulation; sign is the sign function; and These represent the upper and lower boundaries of the problem to be solved;

[0051] The function expression for the sixth update strategy is:

[0052]

[0053] In the formula, and These represent the upper and lower boundaries after nonlinear decay.

[0054] In an optional implementation, step A7 specifically includes the following steps:

[0055] A701. Based on the unsorted solution set of the current snake group, construct a label set with the same size as the unsorted solution set, and initialize each element in the label set to a first label value representing the undominated state;

[0056] A702. Traverse each solution in the unsorted solution set and compare it with other solutions in the unsorted solution set whose index follows that of the solution;

[0057] If the current solution is dominated by any subsequent solution, the element value at the corresponding position in the label set is updated to the second label value representing the dominated state, and the comparison between the current solution and subsequent solutions is stopped.

[0058] If the current solution is not dominated by any other solution, the element value at the corresponding position in the label set remains the first label value;

[0059] A703. Repeat step A702. After completing the comparison between all solutions in the unsorted solution set, extract the solutions corresponding to all first label values ​​from the unsorted solution set based on all first label values ​​in the label set, and use them as the first Pareto front.

[0060] A704, add the solutions in the first Pareto front obtained in this iteration to the global non-dominated solution set, and remove the solutions that are therefore dominated, thereby completing the update of the global non-dominated solution set;

[0061] A705. Based on the solutions that have not been extracted from the unsorted solution set, form a new unsorted solution set and return to step A701 until all solutions are assigned to the corresponding Pareto front.

[0062] Secondly, the present invention provides a bridge sensor multi-objective optimization layout system based on modal information driving, comprising:

[0063] The model building module is used to obtain the structural parameters of the bridge and establish the finite element model of the bridge.

[0064] The modal analysis module is used to perform modal analysis on the finite element model of the bridge to obtain the mode shape vectors of each order of the bridge and determine the candidate measurement point set of the bridge sensors.

[0065] The function construction module is used to construct a multi-objective function for optimizing the sensor arrangement based on the mode shape vectors of each order and the candidate measurement point set;

[0066] The optimization solution module is used to solve the multi-objective function using an improved snake multi-objective optimization algorithm to obtain the Pareto optimal solution set of the sensor arrangement.

[0067] In an optional implementation, it further includes:

[0068] The decision output module is used to select the final sensor layout scheme from the Pareto optimal solution set according to the specific monitoring requirements of the bridge.

[0069] Thirdly, the present invention provides an electronic device, comprising:

[0070] At least one processor;

[0071] At least one memory storing computer-executable instructions, wherein, when executed by the at least one processor, the at least one processor causes the at least one processor to perform the modal information-driven multi-objective optimization arrangement method for bridge sensors as described above.

[0072] The beneficial effects of the embodiments provided by the present invention include:

[0073] This invention improves the snake optimization algorithm by integrating chaotic mapping initialization, sparse coding constraints, and deductive non-dominated sorting mechanism. It effectively overcomes the shortcomings of traditional sequence optimization methods that are prone to getting trapped in local optima, and significantly improves the shortcomings of existing algorithms in dealing with high-dimensional discrete combinatorial optimization problems, such as slow convergence speed and premature convergence. This algorithm is particularly suitable for complex structures such as long-span bridges, and can significantly improve the uniformity of Pareto solution set distribution and convergence efficiency while maintaining strong global search capabilities.

[0074] The improved multi-objective snake optimization algorithm in this invention introduces a two-stage adaptive behavior switching mechanism with food quantity and temperature as decision parameters, which realizes the adaptive and smooth transition between global exploration and local development. Combined with strategies such as elite elimination, the algorithm can not only widely explore potential optimal solutions in the high-dimensional discrete solution space, but also perform fine search on the advantageous regions, thereby efficiently approximating the widely distributed and well-covered real Pareto front.

[0075] This invention establishes a multi-objective function that includes modal confidence criteria, modal kinetic energy, and singular value decomposition indices. It systematically evaluates and optimizes sensor placement schemes from three dimensions: modal identifiability, signal energy, and information completeness. This overcomes the limitations of suboptimal solutions caused by traditional step-by-step optimization or single-objective optimization. Finally, it outputs a set of Pareto optimal solutions that achieve the best trade-off among multiple objectives, providing a scientific and comprehensive basis for selecting placement schemes in engineering decisions. Attached Figure Description

[0076] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other embodiments can be obtained based on these drawings.

[0077] Figure 1 A flowchart of a multi-objective optimization arrangement method for bridge sensors based on modal information driving, as illustrated in an embodiment of this specification, is shown.

[0078] Figure 2 A flowchart illustrating the improved snake multi-objective optimization algorithm in the embodiments of this specification is shown;

[0079] Figure 3 A structural block diagram of a bridge sensor multi-objective optimization layout system based on modal information driven in an embodiment of this specification is shown. Detailed Implementation

[0080] The features and exemplary embodiments of various aspects of the present invention will now be described in detail. In the following detailed description, numerous specific details are set forth in order to provide a thorough understanding of the invention. However, it will be apparent to those skilled in the art that the invention may be practiced without requiring some of these specific details. The following description of embodiments is merely intended to provide a better understanding of the invention by illustrating examples of the invention.

[0081] In some of the processes described in the specification, claims, and accompanying drawings of this invention, multiple operations appear in a specific order. However, it should be clearly understood that these operations may not be performed in the order they appear herein, or they may be performed in parallel. The operation numbers, such as S1, S2, etc., are merely used to distinguish different operations and do not themselves represent any execution order. Furthermore, these processes may include more or fewer operations, and these operations may be performed sequentially or in parallel.

[0082] Example 1

[0083] like Figure 1As shown, this embodiment provides a multi-objective optimization arrangement method for bridge sensors based on modal information, including:

[0084] S1. Based on the structural parameters of the bridge, establish a finite element model of the bridge;

[0085] For example, step S1 specifically includes the following steps:

[0086] S101. Based on the structural parameters of the bridge, a finite element model of the bridge is established using professional finite element analysis software.

[0087] S102. Assign the correct material property parameters to each component of the bridge;

[0088] S103. Through spring elements, coupling constraints, or contact relationships, accurately simulate the connection between supports, piers, and foundations, as well as the anchorage of cables and beams, so that the boundary conditions are as close to reality as possible.

[0089] S104. Mesh the finite element model and perform static verification on the meshed finite element model to calculate the displacement and internal force of the finite element model under its own weight or simple load, and compare it with the set value to calibrate the finite element model.

[0090] In some embodiments, the finite element model of a bridge can be described by the structural dynamics differential equations of a multi-degree-of-freedom system.

[0091] Specifically, the functional expression of the finite element model of the bridge is:

[0092]

[0093] In the formula, K is the overall structural stiffness matrix; M is the overall structural mass matrix; and C is the overall structural damping matrix. is the Laplace transform factor, where The imaginary unit, Angular frequency; and These are the displacement vector and the force vector, respectively.

[0094] In this embodiment, the structural parameters of the bridge include, but are not limited to, the bridge's geometric dimensions, material properties, connection conditions, and boundary support conditions.

[0095] The methods for obtaining bridge structural parameters include, but are not limited to, design drawings, technical specifications, and on-site measurement data.

[0096] S2. Perform modal analysis on the finite element model of the bridge to obtain the mode shape vectors of each order of the bridge and determine the candidate measurement point set of the bridge sensor.

[0097] In this embodiment, modal analysis is performed on the bridge finite element model to obtain a modal analysis result file; the finite element mass matrix and modal matrix are extracted from the result file, and the modal coordinates of all accessible nodes are further extracted to form a complete modal shape matrix; the candidate measurement point set of the sensor is determined based on the modal shape matrix.

[0098] Specifically, based on the theory of modal superposition, the dynamic response at any point in a linear time-invariant system can be expressed as a linear combination of modes of all orders. The relationship between the displacement vector in the frequency domain and the mode shape matrix and modal coordinate vector can be expressed as:

[0099]

[0100]

[0101]

[0102] In the formula, The modal shape matrix; Let be the nth mode shape vector; n is the total number of modes; m is the number of differential equations; G is the modal coordinate vector;

[0103] S3. Based on the mode shape vectors of each order and the candidate measurement point set, construct a multi-objective function for optimizing the sensor arrangement;

[0104] For example, the steps for constructing a multi-objective function include:

[0105] S301. With minimizing the modal confidence criterion index as the optimization objective, establish the first objective function to reduce the correlation between different modal modes.

[0106] Specifically, the first objective function is the modal confidence criterion index function, and its expression is:

[0107]

[0108]

[0109] In the formula, Here is the modal confidence matrix; and These represent the mode shape vectors of the i-th and j-th orders, respectively.

[0110] The modal confidence matrix is ​​essentially the square of the cosine of the angle between the two mode shape vectors. The smaller the value, the better the independence between the different mode shape vectors corresponding to the selected measurement points in the sensor layout scheme. The first objective function minimizes the maximum value of the modal confidence matrix, thereby ensuring that the mode shape vectors corresponding to the selected measurement points maintain good independence and effectively avoids the overlap and interference of different mode shape information.

[0111] S302. With minimizing the modal kinetic energy index as the optimization objective, a second objective function is established to improve the signal energy of the selected measurement points in the candidate measurement point set.

[0112] Specifically, the second objective function is the modal kinetic energy index function, and its expression is:

[0113]

[0114]

[0115] In the formula, Let be the modal kinetic energy of the m-th mode at the p-th measurement point; s be the selected candidate measurement point positions, where m = 1, 2, ..., n; r be the selected modal order, where r = 1, 2, ..., p;

[0116] Modal kinetic energy is used to measure the signal energy of selected measurement points in the candidate measurement point set. By minimizing the second objective function, its denominator is maximized, that is, the total modal kinetic energy of all selected measurement points and modes is maximized. Subsequently, sensors can be deployed at locations with larger total modal kinetic energy so that the selected deployment scheme can obtain data with a high signal-to-noise ratio during measurement.

[0117] S303. With minimizing the singular value decomposition index as the optimization objective, a third objective function is established to enhance the information completeness of the modal information matrix of the selected measurement points in the candidate measurement point set.

[0118] Specifically, the third objective function is the singular value decomposition index function, and its expression is:

[0119]

[0120] In the formula, This is the determinant of the original information matrix; is the determinant of the remaining measurement point information matrix; nd represents the number of measurement points deleted.

[0121] The third objective function is a measure of the relative change in the determinant of the information matrix. Its value represents the modal information loss rate caused by removing a specific sensor from the candidate measurement points. By minimizing the third objective function, the information completeness of the modal information matrix of the selected measurement points in the candidate measurement point set can be directly enhanced, and the degree to which the measurement point combination retains the overall information can be improved.

[0122] S304. Based on the first objective function, the second objective function, and the third objective function, the multi-objective function is obtained.

[0123] Specifically, the expression for the multi-objective function for optimal sensor placement is:

[0124]

[0125] In the formula, It is a multi-objective function; Let this be the first objective function; The second objective function; The third objective function; Let the location number of the i-th sensor be denoted as , where Selected from the candidate measurement point set; d is the total number of sensors;

[0126] In this embodiment, a comprehensive evaluation system containing three objective functions is constructed, taking into account the independence of mode shapes, the maximization of modal energy, and the optimality of the Fisher information matrix, thereby providing a complete mathematical model foundation for subsequent multi-objective optimization algorithms to solve the Pareto optimal solution set.

[0127] S4. Construct an improved snake multi-objective optimization algorithm, and use the improved snake multi-objective optimization algorithm to optimize and solve the multi-objective function to obtain the Pareto optimal solution set for sensor arrangement.

[0128] For example, step S4 specifically includes the following steps:

[0129] S401. Establish an initial snake optimization algorithm, and introduce a chaotic mapping mechanism, a sparse coding constraint strategy and a deductive non-dominated sorting method into the initial snake optimization algorithm to construct an improved snake multi-objective optimization algorithm.

[0130] S402. Generate an initial snake group based on a chaotic mapping mechanism, and group the individuals in the initial snake group by gender.

[0131] Specifically, the initial snake swarm is generated by combining logical chaotic mapping and sinusoidal chaotic mapping, and the individuals are divided into roughly equal numbers of males and females;

[0132] The functional expression for the position of an individual in the initial snake swarm is:

[0133]

[0134] In the formula, It refers to an individual's location; It is a constant; and These are the upper and lower boundaries of the problem to be solved; and These are logical chaotic mapping and sinusoidal chaotic mapping, respectively.

[0135] S403. Use a sparse coding strategy to represent the sensor layout scheme and initialize the global non-dominated solution set;

[0136] Specifically, to meet the constraint of the number of sensors, a sparse constraint strategy is adopted to control the position vector representing the arrangement scheme. This strategy limits the number of sensors by strictly adjusting the ratio of positive and negative values ​​in the position vector.

[0137] Assuming the number of sensors to be deployed is sp, after one update, the set of locations where the position vector is greater than zero is denoted as x. + The set of positions whose position vectors are less than or equal to zero is denoted as x. − If x + >sp, then the update method in the improved snake multi-objective optimization algorithm is adopted, in set x + Randomly select (x) + Update at -sp) positions; if x + If ≤sp, then in set x − Random selection (sp-x) − The number of effective sensors is updated at each location so that the final number of sensors equals the number of sensors that need to be deployed.

[0138] In addition, a threshold for the number of updates is set. If the quantity constraint is still not met after the iteration exceeds the threshold, the sign of some position vectors is randomly changed until the updated vector meets the arrangement quantity requirements.

[0139] S404. Based on the current iteration number, calculate the current food quantity and temperature value of the snake group;

[0140] Specifically, the current food requirement for the snake swarm is expressed as the function:

[0141]

[0142] In the formula, t is the amount of food; t is the current loop number; T is the maximum number of iterations; c1 is a constant.

[0143] Specifically, the current temperature value of the snake swarm is expressed as a function:

[0144]

[0145] In the formula, Temp represents temperature;

[0146] S405. Based on the comparison result between the amount of food and the first preset threshold, select to enter the exploration stage or the development stage, and update the position of male and female individuals respectively according to the individual's gender using the corresponding update strategy.

[0147] Specifically, step S405 includes the following steps:

[0148] S4051. Based on the comparison result between the amount of food and the first preset threshold, select to enter the exploration stage or the development stage:

[0149] If the amount of food is less than the first preset threshold, then the exploration phase is entered and step S4052 is executed;

[0150] If the amount of food is greater than or equal to the first preset threshold, then the development phase begins and step S4053 is executed.

[0151] S4052. For each individual in the snake group to be updated, the first update strategy and the second update strategy are adopted respectively to generate two candidate new positions, and the position with the better multi-objective function value is selected from the candidate new positions as the updated individual position.

[0152] Specifically, the first update strategy is to update the current individual position based on the proportion of randomly selected heterosexual individual positions and their multi-objective function values;

[0153] The function expression for the first update strategy is:

[0154]

[0155]

[0156] In the formula, X i,m (t+1) and X i,f (t+1) represents the positions of the male and female individuals that need to be updated, respectively; rand is a random number between 0 and 1; X rand,m (t) and X rand,f (t) represents the positions of randomly selected male and female individuals, respectively; f rand,m The location X of a randomly selected male rand,m The objective function value; f i,m Male position X i,m The objective function value; f rand,f The location X of a randomly selected female rand,f The objective function value; f i,fFemale position X i,f The objective function value; and Here, c represents the upper and lower boundaries of the problem to be solved; c2 is a constant.

[0157] Specifically, the second update strategy is to perform deterministic boundary updates on the current individual position based on the search boundary that decays linearly with the number of iterations.

[0158]

[0159]

[0160]

[0161]

[0162] In the formula, and These are the upper and lower boundaries, respectively, after nonlinear decay with increasing iteration number; This is the best position for the female snake;

[0163] S4053. Based on the comparison result between the temperature value and the second preset threshold, select the position update mode:

[0164] If the temperature value is greater than the second preset threshold, then all individuals in the snake group adopt the third update strategy to move towards the male and female individuals with the best multi-objective function values ​​in the current snake group, respectively.

[0165]

[0166] In the formula, X i,j (t+1) represents the position of the individual that needs to be updated; c3 is a constant; X food The optimal position for the individual snake;

[0167] If the temperature value is less than or equal to the second preset threshold, the position is updated randomly using either combat mode or mating mode;

[0168] Preferably, the first preset threshold can be set to 0.25, and the second preset threshold can be set to 0.6;

[0169] Specifically, the combat mode involves individuals moving towards the direction of the currently best individual based on the multi-objective function value of that individual.

[0170] The function expression for the combat mode is:

[0171]

[0172]

[0173] In the formula, f best,m The location X of a randomly selected male best,m The objective function value; X best,m The best position for the male snake; f best,f The location X of a randomly selected female best,f The objective function value.

[0174] Specifically, the mating mode involves individuals interacting with the opposite sex based on their own mating abilities to generate new individuals, and in this mode, an elite elimination strategy is activated according to a preset probability.

[0175] The functional expression for the mating pattern is:

[0176]

[0177]

[0178]

[0179]

[0180] In the formula, For male mating ability; For female mating ability;

[0181] In some embodiments, the elite elimination strategy includes:

[0182] The current snake population is sorted according to fitness, and divided into elite subpopulations and non-elite subpopulations based on a preset elite threshold.

[0183] In this embodiment, the top 20% of snake populations are classified as elite subpopulations, and the bottom 80% of snake populations are classified as non-elite subpopulations.

[0184] For individuals in the elite subpopulation, the fourth update strategy is used to update their positions;

[0185] Specifically, the function expression for the fourth update strategy is:

[0186]

[0187] In the formula, X good For individuals in the elite subpopulation awaiting renewal; X rand,1 and X rand,2 These represent different individuals randomly selected from the elite subpopulation; Dim is the dimension of the individual vector; t is the current loop number; T is the maximum number of iterations. For rounding parameters, For the expression The value obtained after performing the rounding operation;

[0188] in, The expression for a composite random function that incorporates two chaotic maps is:

[0189]

[0190] In the formula, f1(4,z) is a constant. i f2(4,z) and f2(4,z) i These are logical chaotic mapping and sinusoidal chaotic mapping, respectively.

[0191] For individuals in the non-elite subpopulation, the fifth or sixth update strategy is randomly applied to update their positions.

[0192] Specifically, the function expression for the fifth update strategy is:

[0193]

[0194] The function expression for the sixth update strategy is:

[0195]

[0196] In the formula, X bad is the individual to be updated in the non-elite subpopulation; sign is the sign function.

[0197] S406. Apply sparse constraints to each individual in the snake group after the position is updated to meet the preset number of sensors, and calculate the multi-objective function value of the individual after sparse constraints.

[0198] S407. Based on the deductive non-dominated sorting method, perform Pareto classification on the current snake group and update the global non-dominated solution set;

[0199] Specifically, step S407 includes the following steps:

[0200] S4071. Based on the unsorted solution set X=(x1,x2…x) of the current snake group n Construct a label set D=(0,0…0) with the same size as the solution set to be sorted, and initialize each element in the label set to the first label value 0, which represents the undominated state;

[0201] S4072, Traverse each solution x in the unsorted solution set. i (i=1,2…n), and other solutions x whose index follows in the unsorted solution set. j (j=i+1,i+2…n) are compared;

[0202] If the current solution x i The subsequent solution x j If the state is dominated, the element value at position i in the tag set D will be updated to the second tag value 1, which represents the dominated state, and the comparison between the current solution and subsequent solutions will be stopped.

[0203] If the current solution x i Not by any other solution x j If the element at position i in the mark set is dominant, then the value of the element at position i in the mark set remains the first mark value 0;

[0204] S4073. Repeat step S4072. After completing the comparison between all solutions in the unsorted solution set, extract the solutions corresponding to all first label values ​​from the unsorted solution set according to all first label values ​​in the label set, and use them as the first Pareto front f1.

[0205] S4074, add the solutions in the first Pareto front f1 obtained in this iteration to the global non-dominated solution set F, and remove the solutions that are therefore dominated, thereby completing the update of the global non-dominated solution set;

[0206] S4075. Based on the solutions that have not been extracted from the unsorted solution set, form a new unsorted solution set X. rest Then return to step S4071 to begin the next round of decomposition until all solutions are assigned to the corresponding Pareto front.

[0207] S408. Repeat steps S404 to S407 until the current iteration number t reaches the preset termination iteration number T, then stop the iterative optimization.

[0208] S409. The final globally non-dominated solution set F = (f1, f1…f m ) is the Pareto optimal solution set output for the sensor arrangement; where m is the number of Pareto fronts.

[0209] In this embodiment, the chaotic mapping mechanism enhances the ergodicity and diversity of the initial population in the complex solution space, reducing the risk of getting trapped in local optima from the source. The sparse coding constraint fixes the number of sensors, effectively avoiding illegal solutions generated by traditional continuous optimization algorithms, ensuring that iterative search always takes place within an effective discrete combination space, fundamentally improving optimization efficiency. The deductive non-dominated sorting mechanism reduces the computational complexity of comparing individual merits and improves the efficiency of Pareto ranking. Through these mechanisms, the improved snake multi-objective optimization algorithm has a faster convergence speed and more stable solution performance when facing high-dimensional bridge optimization problems.

[0210] S5. Based on the specific monitoring requirements of the bridge, select the final sensor layout scheme from the Pareto optimal solution set.

[0211] In this embodiment, the Pareto optimal solution set includes various sensor deployment schemes. In practical engineering applications, the final sensor deployment scheme can be determined from the Pareto optimal solution set according to specific monitoring requirements. For example, according to the priority of different optimization objectives in the multi-objective function, if improving modal discriminability is the primary objective, the scheme with the optimal value of the first objective function can be selected; if it is necessary to prioritize ensuring the response strength of key modes, the scheme with the optimal value of the second objective function can be selected.

[0212] Example 2

[0213] This embodiment provides a bridge sensor multi-objective optimization layout system 100 driven by modal information, including:

[0214] Model building module 101 is used to obtain the structural parameters of the bridge and establish the finite element model of the bridge.

[0215] Modal analysis module 102 is used to perform modal analysis on the bridge finite element model to obtain the mode shape vectors of each order of the bridge and determine the candidate measurement point set of the bridge sensor.

[0216] The function construction module 103 is used to construct a multi-objective function for optimizing the sensor arrangement based on the mode shape vectors of each order and the candidate measurement point set;

[0217] The optimization solution module 104 is used to solve the multi-objective function using an improved snake multi-objective optimization algorithm to obtain the Pareto optimal solution set of the sensor arrangement.

[0218] Some implementation examples also include:

[0219] The decision output module 105 is used to select the final sensor layout scheme from the Pareto optimal solution set according to the specific monitoring requirements of the bridge.

[0220] Example 3

[0221] This embodiment provides an electronic device, including at least one control processor and a memory for communicatively connecting to the at least one control processor;

[0222] Memory, as a non-transitory computer-readable storage medium, can be used to store non-transitory software programs and non-transitory computer-executable programs. Furthermore, memory may include high-speed random access memory, and may also include non-transitory memory, such as at least one disk storage device, flash memory device, or other non-transitory solid-state storage device. In some embodiments, memory may optionally include memory remotely located relative to the processor, and these remote memories can be connected to the processor via a network. Examples of such networks include, but are not limited to, the Internet, intranets, local area networks, mobile communication networks, and combinations thereof.

[0223] The non-transient software program and instructions required to implement the modal information-driven multi-objective optimization layout system method for bridge sensors in the above embodiments are stored in memory. When executed by the processor, the modal information-driven multi-objective optimization layout system method for bridge sensors in the above embodiments is executed, for example, the method described above is executed. Figure 1 Method steps S1 to S5;

[0224] The system embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0225] Example 4

[0226] This embodiment provides a computer-readable storage medium storing computer-executable instructions for causing a computer to execute a method for a bridge sensor multi-objective optimization layout system based on modal information driven as described in Embodiment 1.

[0227] It should be noted that the computer-readable storage medium in this embodiment may be a computer-readable signal medium or a computer-readable storage medium, or any combination thereof. The computer-readable storage medium may be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination thereof.

[0228] More specific examples of computer-readable storage media may include, but are not limited to: electrical connections having one or more wires, portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination of the foregoing.

[0229] In this embodiment, the computer-readable storage medium can be any tangible medium containing or storing a program that can be used by or in conjunction with an instruction execution system, apparatus, or device. In this embodiment, the computer-readable signal medium can include a data signal propagated in baseband or as part of a carrier wave, carrying a computer-readable program. Such propagated data signals can take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof.

[0230] The computer-readable signal medium may also be any computer-readable storage medium other than a computer-readable storage medium, which can send, propagate or transmit a program for use by or in connection with an instruction execution system, apparatus or device.

[0231] Computer programs contained on a computer-readable storage medium can be transmitted using any suitable medium, including but not limited to: wires, optical fibers, RF (radio frequency), etc., or any suitable combination thereof.

[0232] In summary, this embodiment systematically improves the snake optimization algorithm by integrating chaotic mapping initialization, sparse coding constraints, and deductive non-dominated sorting mechanisms to construct an improved multi-objective snake optimization algorithm. This effectively overcomes the shortcomings of traditional sequence methods, which are prone to getting trapped in local optima. Simultaneously, it significantly improves upon the slow convergence speed and premature convergence problems commonly encountered by genetic algorithms and particle swarm optimization algorithms when dealing with high-dimensional discrete combinatorial optimization problems such as bridge sensor placement. It is particularly suitable for the complex solution spaces of long-span bridge structures, significantly improving the distribution and convergence efficiency of the Pareto solution set while ensuring global search capabilities.

[0233] This embodiment improves the multi-objective snake optimization algorithm by introducing a two-stage adaptive behavior switching mechanism with food quantity and temperature as decision parameters. This mechanism enables the algorithm to adaptively transition between the global exploration phase and the local development phase. Furthermore, by combining strategies such as elite elimination, the algorithm can not only extensively explore potential high-quality solution regions when searching in high-dimensional discrete space, but also finely mine the discovered advantageous regions, thereby efficiently approximating the true Pareto optimal front with uniform distribution and good coverage.

[0234] This embodiment constructs a multi-objective function that includes modal confidence criteria, modal kinetic energy, and singular value decomposition indices to systematically evaluate and optimize sensor placement schemes from three dimensions: modal identifiability, signal quality, and information completeness. This overcomes the suboptimal solution problem caused by traditional step-by-step optimization or single-objective optimization, and provides a set of Pareto optimal solutions that achieve the best trade-off among multiple objectives for the final engineering decision.

[0235] The above description is merely a preferred embodiment of the present invention. It will be apparent to those skilled in the art that the present invention is not limited to the details of the above exemplary embodiments, and that the present invention can be implemented in other specific forms without departing from the spirit or essential characteristics of the invention. Therefore, the embodiments should be considered exemplary and non-limiting in all respects. The scope of the present invention is defined by the appended claims rather than the foregoing description, and thus all variations falling within the meaning and scope of the equivalents of the claims are intended to be included within the present invention.

Claims

1. A method for multi-objective optimization of bridge sensor placement based on modal information, characterized in that, include: A finite element model of the bridge was established based on its structural parameters. Modal analysis was performed on the finite element model of the bridge to obtain the mode shape vectors of each order of the bridge and to determine the candidate measurement point set of the bridge sensor. Based on the mode shape vectors of each order and the candidate measurement point set, a multi-objective function is constructed to optimize the sensor arrangement. An improved snake multi-objective optimization algorithm is used to solve the multi-objective function to obtain the Pareto optimal solution set for the sensor arrangement.

2. The method according to claim 1, characterized in that, The method further includes: Based on the specific monitoring requirements of the bridge, the final sensor layout scheme is selected from the Pareto optimal solution set.

3. The method according to claim 1, characterized in that, The steps for constructing the multi-objective function include: With minimizing the modal confidence criterion index as the optimization objective, a first objective function is established to reduce the correlation between different modal modes. With minimizing the modal kinetic energy index as the optimization objective, a second objective function is established to improve the signal energy of the selected measurement points in the candidate measurement point set; With minimizing the singular value decomposition index as the optimization objective, a third objective function is established to enhance the information completeness of the modal information matrix of the selected measurement points in the candidate measurement point set. The multi-objective function is obtained based on the first objective function, the second objective function, and the third objective function.

4. The method according to claim 1, characterized in that, The step of using an improved snake multi-objective optimization algorithm to optimize and solve the multi-objective function to obtain the Pareto optimal solution set for the sensor deployment specifically includes the following steps: A1. Establish an initial snake optimization algorithm, and introduce a chaotic mapping mechanism, a sparse coding constraint strategy, and a deductive non-dominated sorting method into the initial snake optimization algorithm to construct an improved snake multi-objective optimization algorithm; A2. Generate an initial snake group based on a chaotic mapping mechanism, and group the individuals in the initial snake group by gender. A3. Use a sparse coding strategy to represent the sensor layout scheme and initialize the global non-dominated solution set; A4. Based on the current iteration number, calculate the current food quantity and temperature value of the snake group; A5. Based on the comparison result between the amount of food and the first preset threshold, select to enter the exploration stage or the development stage, and update the position of male and female individuals respectively according to the individual's gender using the corresponding update strategy. A6. Apply sparse constraints to each individual in the snake group after the position is updated to meet the preset number of sensors, and calculate the multi-objective function value of the individual after sparse constraints. A7. Based on the deductive non-dominated sorting method, perform Pareto classification on the current snake group and update the global non-dominated solution set; A8. Repeat steps A4 to A7 until the preset iteration termination condition is met; A9. Output the final globally non-dominated solution set as the Pareto optimal solution set for sensor placement.

5. The method according to claim 4, characterized in that, Step A5 specifically includes the following steps: A501. Based on the comparison result between the amount of food and the first preset threshold, select to enter the exploration stage or the development stage: If the amount of food is less than the first preset threshold, then enter the exploration phase and execute step A502; If the amount of food is greater than or equal to the first preset threshold, then the development phase begins and step A503 is executed. A502. For each individual in the snake group to be updated, the first update strategy and the second update strategy are adopted respectively to generate two candidate new positions, and the position with the better multi-objective function value is selected from the candidate new positions as the updated individual position. The first update strategy is to update the current individual position based on the proportion of randomly selected heterosexual individual positions and their multi-objective function values; The second update strategy is to update the current individual position based on a search boundary that decays non-linearly with the number of iterations. A503. Based on the comparison result between the temperature value and the second preset threshold, select the position update mode: If the temperature value is greater than the second preset threshold, all individuals in the snake group will adopt the third update strategy to move towards the male and female individuals with the best multi-objective function values ​​in the current snake group, respectively. If the temperature value is less than or equal to the second preset threshold, the position is updated randomly using either combat mode or mating mode; The combat mode is that individuals move towards the direction of the most outstanding individual based on the multi-objective function value of the current most outstanding individual; The mating mode involves individuals interacting with opposite-sex individuals based on their own mating abilities to generate new individuals, and an elite elimination strategy is activated based on a preset probability in the mating mode.

6. The method according to claim 5, characterized in that, The elite elimination strategy includes The current snake population is sorted according to fitness, and divided into elite subpopulations and non-elite subpopulations based on a preset elite threshold. For individuals in the elite subpopulation, the fourth update strategy is used to update their positions; For individuals in the non-elite subpopulation, the fifth or sixth update strategy is randomly applied to update their positions. The function expression for the fourth update strategy is: ； In the formula, X good For individuals in the elite subpopulation awaiting renewal; X rand,1 and X rand,2 These represent different individuals randomly selected from the elite subpopulation; Dim is the dimension of the individual vector; X food The optimal position for the individual snake; t is the current loop number; T is the maximum number of iterations; This is the rounding parameter; rand is a random number between 0 and 1. The function expression for the fifth update strategy is: ； In the formula, X bad (t+1) represents the individual to be updated in the non-elite subpopulation; sign is the sign function; and These represent the upper and lower boundaries of the problem to be solved; The function expression for the sixth update strategy is: ； In the formula, and These represent the upper and lower boundaries after nonlinear decay.

7. The method according to claim 4, characterized in that, Step A7 specifically includes the following steps: A701. Based on the unsorted solution set of the current snake group, construct a label set with the same size as the unsorted solution set, and initialize each element in the label set to a first label value representing the undominated state; A702. Traverse each solution in the unsorted solution set and compare it with other solutions in the unsorted solution set whose index follows that of the solution; If the current solution is dominated by any subsequent solution, the element value at the corresponding position in the label set is updated to the second label value representing the dominated state, and the comparison between the current solution and subsequent solutions is stopped. If the current solution is not dominated by any other solution, the element value at the corresponding position in the label set remains the first label value; A703. Repeat step A702. After completing the comparison between all solutions in the unsorted solution set, extract the solutions corresponding to all first label values ​​from the unsorted solution set based on all first label values ​​in the label set, and use them as the first Pareto front. A704. Add the solutions in the first Pareto front obtained in this iteration to the global non-dominated solution set, and remove the solutions that are therefore dominated, thereby completing the update of the global non-dominated solution set. A705. Based on the solutions that have not been extracted from the unsorted solution set, form a new unsorted solution set and return to step A701 until all solutions are assigned to the corresponding Pareto front.

8. A bridge sensor multi-objective optimization layout system based on modal information driving, characterized in that, include: The model building module is used to obtain the structural parameters of the bridge and establish the finite element model of the bridge. The modal analysis module is used to perform modal analysis on the finite element model of the bridge to obtain the mode shape vectors of each order of the bridge and determine the candidate measurement point set of the bridge sensors. The function construction module is used to construct a multi-objective function for optimizing the sensor arrangement based on the mode shape vectors of each order and the candidate measurement point set; The optimization solution module is used to solve the multi-objective function using an improved snake multi-objective optimization algorithm to obtain the Pareto optimal solution set of the sensor arrangement.

9. The system according to claim 8, characterized in that, Also includes: The decision output module is used to select the final sensor layout scheme from the Pareto optimal solution set according to the specific monitoring requirements of the bridge.

10. An electronic device, characterized in that, include: At least one processor; At least one memory storing computer-executable instructions, wherein, when executed by the at least one processor, the computer-executable instructions cause the at least one processor to perform the modal information-driven multi-objective optimization arrangement method for bridge sensors as described in any one of claims 1 to 7.

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