A method for transmission tower sensor layout based on a dung beetle optimization algorithm

Abstract

The application discloses a kind of based on scarab optimization algorithm transmission tower sensor layout method.The method is as follows: establish transmission tower finite element model;Modal analysis is carried out on transmission tower finite element model, and the modal vibration mode vector corresponding to each modal order of transmission tower finite element model is obtained;ROC value varying with modal order is calculated based on Fisher information matrix 2-norm method, and modal order is selected;According to the modal vibration mode vector under the selected modal order, different numbers of sensors are respectively arranged using the scarab optimization algorithm;The arrangement effect of different numbers of sensors is compared, and the number of sensors is determined while the sensor arrangement scheme is given.The application can efficiently solve the problem of transmission tower sensor optimization arrangement, and provides a scientific and systematic decision support tool for power grid transmission tower state monitoring, which is beneficial to save monitoring cost, avoid data collection redundancy problem, and thus bring good social and economic benefits.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of sensor optimization arrangement, and particularly relates to a power transmission tower sensor layout method based on a harvester optimization algorithm. BACKGROUND

[0002] With the rapid development of new power system construction, overhead transmission lines as long-distance power transmission channels connecting power load centers, their importance cannot be underestimated. Once abnormal conditions occur, it will cause huge economic losses and directly affect the safety and reliability of the power grid. Landslides not only occur frequently in mountainous and hilly areas, but also increase in frequency and intensity with climate change and human activities. In addition, the prevention and treatment of basic landslides often lack experience, making it difficult to effectively judge and control. How to economically and efficiently monitor and maintain the state of the tower has become a problem to be solved. At the same time, extreme weather events and complex and variable natural environments also bring more challenges to tower state monitoring and safety assessment. Vibration monitoring of transmission towers is one of the important methods to study the state characteristics of tower structures. The first problem to be solved in tower vibration monitoring is sensor optimization arrangement. In order to reduce costs and improve monitoring efficiency, it is necessary to study how to find the reasonable position of the sensor installation on the transmission tower and how to measure more effective structural state information with as few sensors as possible. Therefore, it is of great engineering significance to study the sensor optimization arrangement of the transmission tower and explore the sensor arrangement point and the number of sensors (Wang Jian. Transmission tower vibration monitoring sensor optimization arrangement and structural state parameter analysis[D]. North China Electric Power University (Beijing), 2017).

[0003] Mathematically, the optimal sensor placement is a statistical optimal experimental design problem. The existing methods mainly include the effective independence method, the modal kinetic energy method, and the effective independent driving point residual method, which are classical algorithms for solving such problems in the field of structural dynamics. They have strict theoretical basis and good computational stability, but they are highly dependent on grid division and tend to ignore the spatial structural characteristics of the transmission tower. Heuristic algorithms such as genetic algorithm and particle swarm algorithm iteratively seek optimal solutions by simulating certain natural or human social behaviors, and are widely used to solve various complex problems due to their good robustness and applicability. However, their solutions have certain instability. In the prior art, the particle swarm algorithm is used for optimization tasks when performing sensor optimization tasks (acceleration sensor placement method, device and medium based on particle swarm algorithm (CN116522710A)). However, the particle swarm algorithm tends to quickly approach the global optimal solution. This approach may lead to convergence to a local optimum when there are multiple local optimal solutions in the search space of the problem. Therefore, the particle swarm algorithm usually needs to introduce other mechanisms (such as mutation operation) to enhance the ability to escape from local optima. At the same time, the performance of the particle swarm algorithm depends on the balance between multiple parameters (such as inertia weight, cognitive coefficient, and social coefficient). The tuning of these parameters is often a complex process, especially for different types of problems, which often need to be readjusted. SUMMARY

[0004] The purpose of the present application is to propose a dung beetle optimization algorithm-based transmission tower sensor layout method to solve the problem of how to effectively improve the layout effect while reducing the cost of transmission tower state monitoring under the premise of ensuring computational efficiency.

[0005] The present application is based on the problem of optimal placement of acceleration sensors on transmission towers, and uses the dung beetle optimization algorithm (DBO) as the basic theoretical tool. A dung beetle optimization algorithm-based transmission tower sensor layout method is proposed, which can effectively improve the layout effect and reduce the cost of transmission tower state monitoring under the premise of ensuring computational efficiency, and solve the problems of traditional methods such as difficulty in handling complex constraints, poor computational efficiency, and inapplicability to dynamic systems.

[0006] The purpose of the present application is achieved at least by one of the following technical solutions.

[0007] A dung beetle optimization algorithm-based transmission tower sensor layout method, comprising the following steps:

[0008] S1, establishing a finite element model of a transmission tower;

[0009] S2, performing modal analysis on the finite element model of the transmission tower to obtain modal shape vectors corresponding to each modal order of the finite element model of the transmission tower;

[0010] S3, calculate the ROC value changing with the modal order based on the Fisher information matrix 2-norm method, and select the modal order;

[0011] S4, according to the modal shape vector under the selected modal order, use the Scarabaeus optimization algorithm to optimize the arrangement of different numbers of sensors respectively;

[0012] S5, compare the arrangement effects of different numbers of sensors to determine the number of sensors and give the sensor arrangement scheme.

[0013] Further, in step S1, in the workbench module of the finite element analysis technology software ANSYS, 1:1 scale modeling is performed on the power transmission tower, four tower feet are fixedly constrained, and tower head is applied with power transmission line load, so as to obtain the finite element model of the power transmission tower.

[0014] Further, in step S2, all positions for setting sensors in the power transmission tower are defined as nodes, and the finite element model of the power transmission tower is analyzed by APDL of ANSYS software, so as to obtain the modal shape vector corresponding to each node under each modal, the modal shape vector is used to represent the modal information of each node in the power transmission tower, and then the modal shape vector corresponding to each modal is obtained.

[0015] Further, in step S3, the Fisher information matrix Q i of the i-th modal is expressed as:

[0016]

[0017] In the formula, φ i represents the modal shape vector of the i-th modal, which is specifically as follows:

[0018] φ i = [φ i1 , φ i2 ,..., φ in ,..., φ iN ] T

[0019] Wherein, φ in is the modal shape vector corresponding to the n-th node under the i-th modal, and N is the number of nodes included in the power transmission tower;

[0020] The rate of change (ROC) ROC i of the 2-norm of the i-th modal is calculated by the following formula:

[0021]

[0022] In the formula, Qi Fisher information matrix representing the i-th modal, ||Q i ||2 represents the 2-norm of Q i ; as the modal order i increases, the ROC i value will change, when the ROC i value is less than 0.1, it can be considered that the first i modal shape vectors can basically cover all modal information, and the next i modal shape vectors can be analyzed.

[0023] Further, in step S4, the following steps are included:

[0024] S4.1, parameter initialization is performed:

[0025] Different dimension parameters D are set according to different numbers of sensors, the value of the dimension parameter D is consistent with the number of sensors, so as to fully characterize the acceleration sensor, and facilitate subsequent steps of initializing the information of the scarab population;

[0026] S4.2, population initialization is performed;

[0027] S4.3, the scarab optimization algorithm is iteratively executed, the position of each scarab is updated, the maximum number of iterations is reached, and the global optimal solution corresponding to the current dimension parameter D and the fitness value thereof are output;

[0028] S4.4, after completing the global optimal solution calculation corresponding to the number of sensors each time, the number of sensors is modified, the dimension parameter D is changed according to the number of sensors, and step S4.2 is returned to be re-executed, until the global optimal solution calculation corresponding to all numbers of sensors is completed.

[0029] Further, in step S4.1, the parameter initialization is as follows:

[0030] The dimension, the maximum number of iterations, the population size, the proportion of rolling scarabs, the proportion of breeding scarabs, the proportion of stealing scarabs, the reference history weight, the reference optimal position weight, and the scaling factor, the search upper and lower bounds are set;

[0031] Further, in step S4.2, the population initialization is as follows:

[0032] Each dung beetle individual is randomly initialized in the search upper and lower bounds, each corresponding to a layout scheme, that is, each dung beetle individual randomly selects D nodes as initial positions, D being a dimension parameter, then calculates the MAC matrix according to the modal shape vectors corresponding to the nodes included in each layout scheme, and then calculates the fitness value of each initial position of each dung beetle individual using the largest element in the MAC matrix, and sorts the fitness values to obtain the current global best position, the global worst position and the local best position of each dung beetle.

[0033] Further, the fitness corresponding to each dung beetle is calculated based on the modal assurance criterion; the modal assurance criterion refers to a method in the related art for determining the MAC modal matrix through the modal shape vector, thereby determining the optimal position; the fitness is used to guide the optimal arrangement of the sensors of the power transmission tower, and the entire sensor optimal arrangement model is optimized towards the goal of the highest arrangement effect; the calculation method of the MAC matrix is as follows:

[0034]

[0035] wherein, MAC ij is the corresponding value of the i-th row and j-th column of the MAC modal matrix; respectively represent the modal shape vectors of the i-th and j-th order modes corresponding to the specific layout scheme, and are specifically as follows:

[0036]

[0037] wherein, is the modal shape vector corresponding to the m-th node under the i-th order mode corresponding to the specific layout scheme, and N is the number of nodes included in the specific layout scheme, is obtained by re-encoding the modal shape vectors corresponding to the nodes included in the specific layout scheme;

[0038] The calculation method of the fitness f is as follows:

[0039] f = 1 - max(|MAC ij |) / c, i≠j;

[0040] wherein, |MAC ij | is the absolute value of the corresponding value of the i-th row and j-th column of the MAC modal matrix, and c is a constant.

[0041] Further, in step S4.3, each dung beetle population is divided into rolling dung beetle, breeding dung beetle, small dung beetle, and stealing dung beetle, and each type of dung beetle has a different position updating method (Xue, Jiankai, Shen, et al. Dung beetle optimizer: A new meta-heuristic algorithm for global optimization [J]. The Journal of Supercomputing, 2023, 79(7): 7305-7336.).

[0042] In the iteration process of the dung beetle optimization algorithm, each dung beetle calculates the fitness function value according to its current position and records its optimal fitness and position. The optimal fitness of the dung beetle is the local optimal fitness. If the fitness of the current position is better than the previously recorded local optimal fitness, the current position is updated to the current local optimal position.

[0043] The position update of the rolling dung beetle can be calculated by the following formula:

[0044]

[0045] where t represents the iteration number, X a (t) represents the position information of the a-th rolling dung beetle at the t-th iteration; k ∈ {0, 1}, which divides the rolling behavior into obstacle mode and non-obstacle mode. When k = 1, it represents non-obstacle mode, and when k = 0, it represents obstacle mode. b is a constant value, b ∈ (0, 1). β is a constant value, β ∈ (0, 0.2). α is a natural coefficient, which is 1 or -1. α = -1 represents deviation from the original direction, and α = 1 represents no deviation. θ is a randomly generated number in the uniform distribution within [0, π], representing the deflection angle of the rolling dung beetle. X w is the current global worst position, which is the worst solution found in the entire population.

[0046] The position update of the breeding dung beetle can be calculated by the following formula:

[0047]

[0048] where X * is the current local optimal position. For each dung beetle, the current local optimal position is updated according to its fitness value. Lb and Ub represent the lower and upper bounds of the search, respectively. Lb * and Ub * are the lower and upper bounds of the oviposition area, respectively. R = 1-t / T max , T max represents the maximum number of iterations; B q(t) is the position information of the qth egg ball at the tth iteration, b1 and b2 represent two independent random vectors with a size of 1 x D, and D represents dimension information;

[0049] The position update of the small dung beetle can be calculated by the following formula:

[0050]

[0051] Wherein, X b represents the current global best foraging position, i.e., the current global best position, and the global best position refers to the best solution found in the entire population; Lb b and Ub b are the lower bound and upper bound of the optimal foraging area, respectively; x A (t) represents the position information of the A small dung beetle at the tth iteration, C1 represents a random number subject to normal distribution, and C2 represents a random vector belonging to (0, 1);

[0052] The position update of the thief dung beetle can be calculated by the following formula:

[0053] T V (t+1) = X b +S x g x (|T V (t)-X * |+|T V (t)-X b |);

[0054] Wherein, T V (t) represents the position information of the Vth thief dung beetle at the tth iteration; g is a random vector with a size of 1 x D, subject to normal distribution; and S represents a constant value;

[0055] After each iteration calculation, it is judged whether the position of each dung beetle exceeds the boundary, and if it exceeds the boundary, the current position of the dung beetle is reset to the boundary value, then by comparing the fitness values of all dung beetle individuals, the position of the dung beetle individual with the highest fitness value is selected to update the current global best position; the position of the dung beetle individual with the lowest fitness value is selected to update the current global worst position; each dung beetle individual updates its corresponding local best position;

[0056] The position of each dung beetle is repeatedly updated until the maximum number of iterations is reached, and when the predetermined maximum number of iterations is reached, the global optimal solution corresponding to the current dimension parameter D is output, i.e., the global best position and its fitness value obtained by the last iteration calculation.

[0057] Further, in step S5, the fitness values of the global optimal solutions obtained by the dung beetle optimization algorithm running under each dimension are compared. max, according to the formula maxMAC = 1-f max The arrangement effect value maxMAC corresponding to the global optimal solution of each dimension is calculated.

[0058] The sensor arrangement scheme with the least number of sensors under the premise that the arrangement effect value maxMAC is less than 0.25 is selected as the optimal arrangement scheme.

[0059] The beneficial effects brought by the technical scheme of the present application are as follows:

[0060] (1) Theoretical innovation. The present application first proposes a sensor optimization arrangement method based on the algorithm of the dung beetle, which simulates the natural behavior of the dung beetle to solve the optimization, effectively solves the problems such as poor adaptability and low global search capability of other algorithms, and realizes efficient solution of the model while ensuring excellent fitness value.

[0061] (2) Social and economic benefits. The present application can efficiently solve the problem of optimization arrangement of the sensor of the power transmission tower, and provides a scientific and systematic decision support tool for the state monitoring of the power transmission tower of the power grid, which is beneficial to save monitoring cost and avoid data collection redundancy, thereby bringing good social and economic benefits.

[0062] Compared with the prior art, the present application has the following advantages:

[0063] The present application proposes a layout method based on the dung beetle optimization algorithm for the problem of sensor optimization arrangement, and the researched content is closely related to the actual demand, and its importance is self-evident. Compared with the existing sensor optimization arrangement method, the present application has the following advantages: starting from the dung beetle optimization algorithm, the present application adopts a probability model to describe the uncertainty of the objective function, and optimizes through dynamic sampling and updating of the model, which can better find the optimal arrangement scheme in the global range and avoid falling into local optimum; the objective function does not need to have a specific form, and multiple objectives can be considered at the same time through the design of a multi-objective optimization strategy, which is particularly suitable for complex scenes where the dynamic system or the objective function is difficult to describe. BRIEF DESCRIPTION OF DRAWINGS

[0064] Figure 1 The step flow chart of the power transmission tower sensor layout method based on the dung beetle optimization algorithm in the embodiment of the present application.

[0065] Figure 2 The algorithm flow chart of the power transmission tower sensor layout method based on the dung beetle optimization algorithm in the embodiment of the present application.

[0066] Figure 3 The program flow chart constructed based on the algorithm in the embodiment of the present application. Figure 2 ​

[0067] Figure 4 A schematic diagram of a finite element model of a power transmission tower established in an embodiment of the present application.

[0068] Figure 5 A schematic diagram of a layout effect value calculation result in an embodiment of the present application.

[0069] Figure 6 A schematic diagram of a layout scheme result in an embodiment of the present application. DETAILED DESCRIPTION

[0070] The specific implementation of the present application is further described below in combination with the drawings and embodiments. In the description of the present application, the same or similar symbols and notations represent the same or similar physical meanings or have the same or similar functions, and the legends used in the present application are only for better explanation of the present application, and the applicability of the present application is not limited thereto.

[0071] Embodiment:

[0072] A power transmission tower sensor layout method based on a dung beetle optimization algorithm, as shown in the figure, comprises the following steps: Figure 1

[0073] S1, a finite element model of a power transmission tower is established;

[0074] In an embodiment, in the workbench module of the finite element analysis technology software ANSYS, a 1:1 scale modeling is performed on the power transmission tower, four tower feet are fixedly constrained, and a power transmission line load is applied to the tower head, so as to obtain a finite element model of the power transmission tower.

[0075] S2, modal analysis is performed on the finite element model of the power transmission tower, and modal shape vectors corresponding to each modal order of the finite element model of the power transmission tower are obtained;

[0076] All positions for setting sensors in the power transmission tower are defined as nodes, modal analysis is performed on the finite element model of the power transmission tower by APDL of the ANSYS software, so as to obtain modal shape vectors corresponding to each node under each modal order, the modal shape vectors are used to represent modal information of each node in the power transmission tower, and then modal shape vectors corresponding to each modal order are obtained.

[0077] S3, ROC values varying with modal orders are calculated based on a Fisher information matrix 2-norm method, and a modal order is selected;

[0078] The expression of the Fisher information matrix Q i of the i-th modal order is:

[0079]

[0080] ​wherein φ i represents the modal shape vector of the i-th modal, and is specifically as follows:

[0081] φ i i1 i2 in iN T

[0082] wherein φ in is the modal shape vector corresponding to the n-th node under the i-th modal, and N is the number of nodes included in the power transmission tower;

[0083] The 2-norm change rate (ROC) ROC i of the i-th modal is calculated by the following formula:

[0084]

[0085] wherein Q i represents the Fisher information matrix of the i-th modal, and ||Q i ||2 represents the 2-norm of Q i ; as the modal order i increases, the ROC i value will change, and when the ROC i value is less than 0.1, it can be considered that the first i modal shape vectors can basically cover all modal information, and the following analysis can be performed for the first i modal.

[0086] S4, according to the modal shape vector under the selected modal order, the dung beetle optimization algorithm is used to optimize the arrangement of sensors of different numbers, including the following steps:

[0087] S4.1, parameter initialization is performed:

[0088] Different dimension parameters D are set according to different numbers of sensors, and the value of the dimension parameter D is consistent with the number of sensors, so as to fully represent the acceleration sensor and facilitate the initialization of the dung beetle population information in the subsequent steps;

[0089] The parameter initialization is specifically as follows:

[0090] The dimension, the maximum number of iterations, the population size, the proportion of rolling dung beetles, the proportion of breeding dung beetles, the proportion of stealing dung beetles, the reference history weight, the reference optimal position weight, and the scaling factor, the search upper and lower bounds are set;

[0091] ​​​​​In an embodiment, taking a dry letter type tower as an example, the population quantity is set to 30, the maximum iteration quantity is set to 200, the Atta ratio is 0.2, the larva rearing Atta ratio is 0.2, the small Atta ratio is 0.2, the stealing Atta ratio is 0.4, the reference history weight is 0.1, the reference optimal position weight is 0.3, the scaling factor is 0.5, the search upper limit is 1.0, and the search lower limit is 0.001.

[0092] S4.2, population initialization is performed, specifically as follows:

[0093] Each Atta individual is randomly initialized within the search upper and lower limits, each Atta individual corresponds to a layout scheme, that is, each Atta individual randomly selects D nodes as initial positions, D being a dimension parameter, then calculates a MAC matrix according to the modal shape vectors corresponding to the nodes included in the layout scheme corresponding to each Atta individual, and then calculates the fitness value of each initial position of each Atta individual using the largest element in the MAC matrix and sorts the fitness values to obtain the global best position, the global worst position, and the local best position of each Atta; wherein the global best position refers to the best solution found in the entire population, that is, the position with the highest fitness value, the global worst position refers to the worst solution found in the entire population, that is, the position with the lowest fitness value, and the local best position of each Atta refers to the best solution among all positions experienced by each Atta individual.

[0094] The fitness corresponding to each Atta is calculated based on the modal assurance criterion; the modal assurance criterion refers to a method in the related art for determining a MAC modal matrix through a modal shape vector, thereby determining an optimal position; the fitness is used to guide the optimal arrangement of sensors for a power transmission tower, and the entire sensor optimal arrangement model is optimized towards the goal of the highest arrangement effect; the calculation method of the MAC matrix is as follows:

[0095]

[0096] MAC ij is the corresponding value of the i-th row and j-th column in the MAC modal matrix; respectively represent the modal shape vectors of the i-th and j-th modes corresponding to a specific layout scheme, specifically as follows:

[0097]

[0098] wherein, is the modal shape vector of the m-th node corresponding to the i-th mode of a specific layout scheme, and N is the number of nodes included in the specific layout scheme, is obtained by re-encoding the modal shape vectors corresponding to the nodes included in the specific layout scheme;

[0099] The calculation method of the fitness f is as follows:

[0100] f = 1 - max(|MAC ij |) / c, i≠j;

[0101] wherein |MAC ij | is the absolute value of the corresponding value of the i-th row and j-th column in the MAC modal matrix, and c is a constant, and the value of the embodiment is 1.

[0102] S4.3, iteratively performing the algorithm, updating the position of each scarab, reaching the maximum number of iterations, and outputting the global optimal solution corresponding to the current dimension parameter D and the fitness value thereof;

[0103] Each scarab population is divided into rolling scarabs, breeding scarabs, small scarabs, and stealing scarabs, and the position updating methods of each scarab are different.

[0104] In the iteration process of the scarab optimization algorithm, each scarab will calculate the fitness function value according to its current position, and record its optimal fitness and position, and the optimal fitness of itself is the local optimal fitness. If the fitness of the current position is better than the local optimal fitness recorded before, the current position is updated to the current local optimal position.

[0105] The position updating of the rolling scarab can be calculated by the following formula:

[0106]

[0107] wherein t represents the iteration number, X a (t) represents the position information of the a-th rolling scarab at the t-th iteration; k∈{0,1}, the rolling behavior is divided into an obstacle mode and a non-obstacle mode, k=1 represents the non-obstacle mode, and k=0 represents the obstacle mode; b is a constant value, b∈(0,1); β is a constant value, β∈(0,0.2); α is a natural coefficient, which is 1 or -1, α=-1 represents deviation from the original direction, and α=1 represents no deviation; θ is a randomly generated number in the uniform distribution in the range of [0, π], representing the deflection angle of the rolling scarab; X w is the current global worst position, and the global worst position refers to the worst solution found in the entire population;

[0108] The position updating of the breeding scarab can be calculated by the following formula:

[0109]

[0110] wherein X * is the current local optimal position. For each scarab, the current local optimal position will be updated according to its fitness value; Lb and Ub represent the search lower bound and the search upper bound, respectively, Lb * and Ub* Lower and upper bounds of the laying area, respectively; R = 1 - t / T max , T max represents the maximum number of iterations; B q (t) is the position information of the qth egg ball at the tth iteration, b1 and b2 represent two independent random vectors with a size of 1 x D, and D represents the dimension information;

[0111] The position update of the small dung beetle can be calculated by the following formula:

[0112]

[0113] Wherein, X b represents the current global best foraging position, i.e. the current global best position, and the global best position refers to the best solution found in the entire population; Lb b and Ub b are the lower and upper bounds of the optimal foraging area, respectively; x A (t) represents the position information of the A small dung beetle at the tth iteration, C1 represents a random number subject to normal distribution, and C2 represents a random vector belonging to (0, 1);

[0114] The position update of the thief dung beetle can be calculated by the following formula:

[0115] T V (t+1) = X b +S x g x (|T V (t)-X * |+|T V (t)-X b |);

[0116] Wherein, T V (t) represents the position information of the Vth thief dung beetle at the tth iteration; g is a random vector with a size of 1 x D, subject to normal distribution; S represents a constant value;

[0117] After each iteration calculation, it is judged whether the position of each dung beetle exceeds the boundary, and if it exceeds the boundary, the current position of the dung beetle is reset to the boundary value, then by comparing the fitness values of all dung beetle individuals, the position of the dung beetle individual with the highest fitness value is selected to update the current global best position; the position of the dung beetle individual with the lowest fitness value is selected to update the current global worst position; each dung beetle individual updates its corresponding local best position;

[0118] Repeat the position update of each dung beetle until the maximum number of iterations is reached, and when the predetermined maximum number of iterations is reached, output the global optimal solution corresponding to the current dimension parameter D, i.e. the global best position and its fitness value obtained by the last iteration calculation.

[0119] S4.4, after each global optimal solution corresponding to the number of sensors is calculated, the number of sensors is modified, and the dimension parameter D is changed according to the number of sensors, and step S4.2 is returned to be re-executed until the global optimal solution corresponding to all the numbers of sensors is calculated.

[0120] S5, the arrangement effect of different numbers of sensors is compared, and the number of sensors is determined, and a sensor arrangement scheme is given;

[0121] The fitness value f corresponding to the global optimal solution obtained by running the scarab optimization algorithm under each dimension is compared max The arrangement effect value maxMAC corresponding to the global optimal solution of each dimension is calculated according to the formula maxMAC = 1-f max

[0122] The sensor arrangement scheme with the least number of sensors is selected as the optimal arrangement scheme under the premise that the arrangement effect value maxMAC is less than 0.25.

[0123] In an embodiment, the steps according to the present application construct an algorithm as shown in Figure 2 and a program as shown in Figure 3 is constructed according to the algorithm;

[0124] In an embodiment, the established finite element model of the power transmission tower is as shown in Figure 4 The program as shown in Figure 3 is run to obtain the arrangement effect value calculation results under the conditions that the number of sensors is 3, 4, 5, 6, 7, 8, 9, and 10, as shown in Figure 5

[0125] As shown in Figure 5 , the running results under different numbers of sensors are shown, and it can be seen from the figure that the index is the best when the number of sensors is 8, that is, the arrangement effect is the best. According to the measuring point positions given by the running results under the preset number, a specific arrangement scheme is given, as shown in Figure 6 , that is, the sensors are arranged at nodes with serial numbers 28, 49, 69, 96, 120, 187, 288, and 321.

[0126] The preferred embodiments of the present application disclosed above are only used to help explain the present application. The preferred embodiments do not describe all the details, and the present application is not limited to the specific embodiments described. Obviously, many modifications and changes can be made according to the content of the present application. The embodiments are selected and described in detail in order to better explain the principles and practical applications of the present application, so that those skilled in the art can well understand and use the present application. The present application is limited by the claims and their entire scope and equivalents.​​

Claims

1. A method for sensor layout on power transmission towers based on a dung beetle optimization algorithm, characterized in that, Includes the following steps: S1. Establish a finite element model of the transmission tower; In the workbench module of the finite element analysis software ANSYS, the transmission tower is modeled at a 1:1 scale. The four tower legs are fixed and the transmission line load is applied to the tower head, thus obtaining the finite element model of the transmission tower. S2. Modal analysis is performed on the finite element model of the transmission tower to obtain the mode shape vectors corresponding to each modal order of the finite element model of the transmission tower. All locations in the transmission tower used to install sensors are defined as nodes. Modal analysis is performed on the finite element model of the transmission tower using APDL of ANSYS software to obtain the mode shape vectors corresponding to each node under each mode. The mode shape vectors are used to characterize the modal information of each node in the transmission tower, thereby obtaining the mode shape vectors corresponding to each mode. S3. Calculate the ROC value as a function of modal order based on the Fisher information matrix 2-norm method, and select the modal order; S4. Based on the mode shape vectors at the selected modal order, the dung beetle optimization algorithm is used to optimize the arrangement of different numbers of sensors; specifically including: S4.1, Execution parameter initialization: Different dimensional parameters D are set according to different numbers of sensors. The value of the dimensional parameter D is consistent with the number of sensors, so as to fully characterize the acceleration sensor and facilitate the initialization of dung beetle population information in subsequent steps. S4.2, Perform population initialization; S4.3 Iteratively execute the dung beetle optimization algorithm, update the position of each dung beetle, reach the maximum number of iterations, and output the global optimal solution and its fitness value corresponding to the current dimension parameter D; S4.4 After calculating the global optimal solution for each corresponding number of sensors, modify the number of sensors and change the dimension parameter D according to the number of sensors. Then return to re-execute step S4.2 until the global optimal solution for all numbers of sensors is calculated. S5. Compare the effects of different numbers of sensors, determine the number of sensors, and provide a sensor arrangement plan.

2. The method for sensor layout of transmission towers based on dung beetle optimization algorithm according to claim 1, characterized in that, In step S3, the Fisher information matrix Q of the i-th mode... i The expression is: In the formula, φ i The mode shape vector representing the i-th mode is as follows: f i =[φ i1 ,f i2 ,...,f in ,...,f iN ] T Where, φ in Let N be the mode shape vector corresponding to the nth node in the i-th mode, and N be the number of nodes included in the transmission tower. The 2-norm rate of change (ROC) of the i-th mode i Calculated using the following formula: In the formula, Q i Let ||Q| represent the Fisher information matrix of the i-th mode. i ||2 represents Q i The 2-norm; as the modal order i increases, the ROC... i The value will change when ROC i When the value is less than 0.1, it can be considered that the mode shape vectors of the first i-th order can basically cover all modal information, and then the analysis can be carried out on the first i-th order modes.

3. The method for sensor layout of transmission towers based on dung beetle optimization algorithm according to claim 1, characterized in that, In step S4.1, the parameter initialization is as follows: Configure dimensions, maximum number of iterations, population size, percentage of rolling dung beetles, percentage of brooding dung beetles, percentage of thieving dung beetles, historical reference weights, reference optimal position weights, scaling factors, and upper and lower bounds for the search.

4. The method for sensor layout of transmission towers based on dung beetle optimization algorithm according to claim 1, characterized in that, In step S4.2, the population is initialized, as follows: Within the upper and lower bounds of the search, each dung beetle individual is randomly initialized, and each dung beetle individual corresponds to a layout scheme, that is, each dung beetle individual randomly selects D nodes as initial positions, where D is the dimension parameter. Then, the MAC matrix is ​​calculated based on the mode shape vectors of the nodes included in the layout scheme of each dung beetle individual. Then, the fitness value of each dung beetle individual at each initial position is calculated using the element with the largest absolute value in the MAC matrix and sorted to obtain the current global best position, global worst position, and each dung beetle's own local best position. Among them, the global best position is the best solution found in the entire population, that is, the position with the highest fitness value; the global worst position is the worst solution found in the entire population, that is, the position with the lowest fitness value; and each dung beetle's own local best position is the best solution among all positions experienced by each dung beetle individual.

5. A method for sensor layout of transmission towers based on dung beetle optimization algorithm according to claim 4, characterized in that, The fitness of each dung beetle is calculated based on the modal guarantee criterion. The modal guarantee criterion refers to a method in related technologies that determines the MAC mode matrix by using mode shape vectors, thereby determining the optimal position. The fitness is used to guide the optimized placement of sensors on transmission towers, and the entire sensor optimization placement model is optimized towards the goal of maximizing the placement effect. The calculation method of the MAC matrix is ​​as follows: Among them, MAC ij This represents the corresponding value in the i-th row and j-th column of the MAC mode matrix; These represent the mode shape vectors of the i-th and j-th modes corresponding to the specific arrangement scheme, as follows: in, Let M be the mode shape vector corresponding to the m-th node in the i-th mode of the specific layout scheme, where M is the number of nodes included in the specific layout scheme. It is obtained by re-encoding the modal shape vectors corresponding to the nodes included in the specific layout scheme; The fitness f is calculated as follows: f=1-max(|MAC ij |) / c,i≠j; Among them, |MAC ij | represents the absolute value of the corresponding value in the i-th row and j-th column of the MAC mode matrix, and c is a constant.

6. The method for sensor layout of transmission towers based on dung beetle optimization algorithm according to claim 1, characterized in that, In step S4.3, each dung beetle population is divided into rolling dung beetle, brooding dung beetle, small dung beetle, and thieving dung beetle, and the location update method for each type of dung beetle is different; During the iterative process of the dung beetle optimization algorithm, each dung beetle calculates its fitness function value based on its current position and records its own optimal fitness and position. Its own best fitness is the local best fitness. If the fitness of the current position is better than the previously recorded local best fitness, then the current position is updated to the current local best position. The position update of the rolling dung beetle can be calculated using the following formula: Where t represents the number of iterations, X a (t) represents the position information of the a-th dung beetle in the t-th iteration; k∈{0,1}, classifying the rolling behavior into obstacle-prone and obstacle-free modes, k=1 represents the obstacle-free mode, and k=0 represents the obstacle-prone mode; b is a constant value, b∈(0,1); β is a constant value, β∈(0,0.2); α is the natural coefficient, taking the value 1 or -1, α=-1 indicates deviation from the original direction, and α=1 indicates no deviation; θ is a randomly generated number in a uniform distribution within the range [0,π], representing the deflection angle of the dung beetle; X w It is the current global worst position, which refers to the worst solution found in the entire population; The location update of brooding dung beetles can be calculated using the following formula: Among them, X * This represents the current local best position; for each dung beetle, the current local best position is updated based on its fitness value; Lb and Ub represent the lower and upper bounds of the search, respectively. * and Ub * These are the lower and upper limits of the spawning area, respectively; R = 1 - t / T max T max B represents the maximum number of iterations. q (t) represents the position information of the q-th egg in the t-th iteration, and b1 and b2 represent two independent random vectors of size 1×D, where D represents the dimension information; The location update of small dung beetles can be calculated using the following formula: Among them, X b This represents the current globally optimal feeding position, which is the best solution found in the entire population; Lb b and Ub b These are the lower and upper bounds of the optimal foraging region, respectively; x A (t) represents the location information of the Ath small dung beetle at the t-th iteration, C1 represents a random number that follows a normal distribution, and C2 represents a random vector belonging to (0,1); The location update of the dung beetle can be calculated using the following formula: T V (t+1)=X b +S×g×(|T V (t)-X * |+|T V (t)-X b |); Among them, T V (t) represents the position information of the Vth dung beetle at the tth iteration; g is a 1×D random vector that follows a normal distribution; S represents a constant value; After each iteration, it is determined whether the position of each dung beetle exceeds the boundary. If it does, the current position of the dung beetle is reset to the boundary value. Then, by comparing the fitness of all dung beetle individuals, the position of the dung beetle individual with the highest fitness value is selected and updated as the current global best position; the position of the dung beetle individual with the lowest fitness value is selected and updated as the current global worst position; and each dung beetle individual updates its corresponding local best position. The position of each dung beetle is repeatedly updated until the maximum number of iterations is reached. When the predetermined maximum number of iterations is reached, the global optimal solution corresponding to the current dimension parameter D is output, which is the global best position and its fitness value obtained in the last iteration calculation.

7. A method for sensor layout of transmission towers based on dung beetle optimization algorithm according to claim 1, characterized in that, In step S5, the fitness value f corresponding to the global optimal solution obtained by the dung beetle optimization algorithm under each dimension is compared. max According to the formula maxMAC=1-f max The maximum MAC value corresponding to the global optimal solution for each dimension is calculated. The optimal sensor layout is the one with the fewest number of sensors, provided that the maximum MAC value is less than 0.25.

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