Physical field modeling and hybrid optimization collaborative vibration sensor intelligent layout method

Abstract

The invention discloses an intelligent vibration sensor layout method based on cooperation of physical field modeling and hybrid optimization. The method comprises the steps that a geometric model of a target mechanical structure is acquired, and a material parameter set is extracted; the curvature and stress of the surface of the mechanical structure are calculated, and a high-sensitivity area is recognized in combination with a vibration transmission efficiency matrix; curvature self-adaptive sampling is executed in the high-sensitivity area, a candidate point set is generated based on an improved greedy algorithm, and redundant candidate points are eliminated to obtain an effective candidate point set; calculating coverage weights of the effective candidate points; adding the candidate point with the maximum coverage weight selected through bubble sorting into a sensor set, and calculating the total coverage rate once when each effective candidate point is added until the coverage rate reaches a preset value; performing global optimization based on a simulated annealing algorithm, and performing crossover and mutation operation on the selected sensor individuals; calculating the contribution degree of each sensor, and removing low-efficiency sensors until the maximum iteration value is reached. According to the invention, efficient calculation and resource configuration optimization are realized.

Description

Technical Field

[0001] This invention relates to the field of mechanical structure health monitoring technology, specifically to a method for intelligent placement of vibration sensors that combines physical field modeling and hybrid optimization. Background Technology

[0002] With the continuous development of mechanical structure health monitoring technology, vibration sensors are increasingly widely used in industrial equipment, aerospace, civil engineering and other fields. The optimization of the layout of vibration sensors is a key link to ensure the performance of the monitoring system, which directly affects the accuracy, efficiency and cost of structural health monitoring.

[0003] Current sensor placement optimization methods mostly rely on a single optimization algorithm, such as greedy algorithms, genetic algorithms, or simulated annealing. While these algorithms demonstrate some effectiveness in specific scenarios, they often struggle to balance global search capability with local optimization accuracy. For example, greedy algorithms, although computationally efficient, are prone to getting trapped in local optima; and simulated annealing, while possessing global search capabilities, suffers from low computational efficiency in complex structures. Furthermore, existing sensor placement optimization methods typically neglect the physical characteristics of the target structure, such as vibration attenuation characteristics, curvature distribution, and stress distribution. These characteristics significantly impact vibration signal propagation and sensor sensitivity, but current methods fail to fully utilize this information, leading to optimization results that are out of touch with real-world applications. Summary of the Invention

[0004] The purpose of this invention is to provide a smart layout method for vibration sensors that combines physical field modeling and hybrid optimization, so as to more accurately identify high-sensitivity monitoring areas, achieve a balance between global search capability and local optimization accuracy, and improve the efficiency and economy of optimization results.

[0005] The technical solution to achieve the purpose of this invention is as follows:

[0006] A method for intelligent placement of vibration sensors that combines physical field modeling and hybrid optimization includes:

[0007] Obtain the geometric model of the target mechanical structure and extract the material parameter set;

[0008] Calculate the curvature and stress of the surface of the mechanical structure, and identify high-sensitivity areas by combining the vibration transmission efficiency matrix;

[0009] Curvature adaptive sampling is performed within a high-sensitivity region, and a candidate point set is generated based on an improved greedy algorithm.

[0010] Eliminate redundant candidate points to obtain a set of valid candidate points;

[0011] Calculate the coverage weights of valid candidate points;

[0012] Candidate points with the highest coverage weight are selected by bubble sort and added to the sensor set S. The overall coverage rate is calculated once for each valid candidate point added, until the coverage rate reaches the preset value.

[0013] Global optimization is performed based on the simulated annealing algorithm, and crossover and mutation operations are performed on the selected individual sensors.

[0014] Calculate the contribution of each sensor and remove inefficient sensors until the maximum iteration value is reached.

[0015] The significant advantages of this invention compared to existing technologies are:

[0016] (1) By integrating material properties, this invention constructs a vibration transmission efficiency matrix and accurately quantifies signal attenuation characteristics, making the layout scheme more suitable for actual application scenarios.

[0017] (2) This invention avoids problems such as iterative local convergence, early convergence, and divergence by optimizing in multiple stages and dynamically adjusting the crossover probability and mutation intensity. It can also obtain an approximate theoretical optimal solution in a relatively short time.

[0018] (3) This invention solves the geodesic distance by using the anisotropic wave velocity equation. Compared with the classical Euclidean geometric algorithm, the computational efficiency is greatly improved. By dynamically removing redundant sensors, efficient computation and resource allocation optimization are achieved. Attached Figure Description

[0019] Figure 1 This is a flowchart illustrating the working principle of the method of the present invention;

[0020] Figure 2 This is a diagram illustrating the implementation steps of the method of the present invention;

[0021] Figure 3 This diagram illustrates the execution steps of the multi-stage hybrid optimization strategy in the method of this invention. Detailed Implementation

[0022] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0023] Please see Figure 1-3 This embodiment of a method for intelligent placement of vibration sensors that combines physical field modeling and hybrid optimization includes the following steps:

[0024] S1. Obtain the geometric model of the target mechanical structure through three-dimensional laser scanning and extract the material parameter set;

[0025] The expression for the material parameter set is:

[0026] M = {ρ, E, ζ}

[0027] In the expression, M represents the material parameter set, ρ represents density, E represents elastic modulus, and ζ represents vibration damping coefficient.

[0028] The method for obtaining the geometric model of the target mechanical structure is as follows:

[0029] Extract the vertex coordinate set and surface topological relationships of the target mechanical structure, and reconstruct the discretized geometric model of the target mechanical structure. The expression for the vertex coordinate set is:

[0030] V = {v1, v2, ..., v} n}

[0031] In the expression, V represents the set of vertex coordinates, v1 represents the coordinates of the first vertex, and v n Represents the coordinates of the nth vertex;

[0032] By acquiring the geometric model of the target mechanical structure and extracting the material parameter set through 3D laser scanning, the geometric features and physical properties of the structure can be accurately captured, providing high-precision basic data for subsequent curvature calculation, stress analysis and vibration transmission efficiency assessment. This ensures that the identification of high-sensitivity areas is closer to the actual working conditions, while providing reliable input for multi-stage hybrid optimization strategies, ultimately improving the scientific nature and optimization effect of vibration sensor layout.

[0033] S2. Calculate the curvature and stress of the mechanical structure surface, and identify high-sensitivity areas using the vibration transmission efficiency matrix; the formula for calculating curvature is:

[0034]

[0035] In the formula, k (x) R represents the curvature of the x-th vertex in the set of vertex coordinates. (x) The principal radius of curvature representing the coordinates of the x-th vertex;

[0036] The formula for calculating stress is:

[0037] σ (x) =E*k (x) *c

[0038] In the formula, σ (x) represents the stress at the x-th vertex in the set of vertex coordinates, and c represents the perpendicular distance from the x-th point to the neutral axis.

[0039] The expression for constructing the vibration transmission efficiency matrix is:

[0040]

[0041] In the expression, T ij The element in the i-th row and j-th column of the vibration transmission efficiency matrix representing the relationship between the i-th and j-th vertex coordinates in the vertex coordinate set, d ij E represents the geodesic distance between the coordinates of the i-th vertex and the j-th vertex. i E represents the elastic modulus of the i-th vertex. j This represents the elastic modulus of the j-th vertex;

[0042] d ij The solution method is to calculate the anisotropic wave velocity equation using the fast travel method. The specific calculation formula is as follows:

[0043]

[0044] In the formula, Represents the gradient. Represents geodesic distance d ij The gradient, i.e., the path direction from the coordinates of the i-th vertex to the j-th vertex, v i Let n represent the wave velocity vector at the i-th vertex. i ρ represents the normal vector of the i-th vertex. i E represents the density of the i-th vertex. i Represents the elastic modulus of the i-th vertex;

[0045] The formula for defining the high-sensitivity region is:

[0046] Ω high ={x|k (x) >k th ∪σ (x) >σ th}

[0047] In the formula, Ω high Represents the high-sensitivity region, k th Represents the preset threshold for curvature, σ th This represents a preset stress threshold.

[0048] The region or T that satisfies the definition formula of the high sensitivity region ij ≥T th The region was identified as the high-sensitivity region, where T th A threshold representing vibration transmission efficiency;

[0049] By calculating the curvature and stress of the structural surface and combining it with the vibration transmission efficiency matrix to identify high-sensitivity areas, it is possible to accurately locate the parts of the mechanical structure that are most sensitive to vibration response. This provides a scientific basis for sensor layout, ensuring that sensors are concentrated at key monitoring points, improving the reliability and effectiveness of the monitoring system, while avoiding redundant layout and optimizing resource allocation.

[0050] A multi-stage hybrid optimization strategy is implemented to provide a set of multi-objective optimization solutions for sensor layout, specifically including the following steps:

[0051] S3. Perform curvature adaptive sampling within the high-sensitivity region, and generate a candidate point set C based on an improved greedy algorithm. The specific method is as follows:

[0052] S3.1 Calculate the curvature of each vertex of the structure surface;

[0053] S3.2 Set a curvature threshold, classify vertices above the curvature threshold as high curvature regions, and classify vertices equal to or below the curvature threshold as low curvature regions;

[0054] S3.3. Set the acquisition density for high curvature and low curvature regions. The formula for calculating the acquisition density for high curvature regions is:

[0055] D high =n*D low

[0056] In the formula, D high D represents the sampling density in the high curvature region, n represents the ratio coefficient between the sampling density in the high curvature region and the sampling density in the low curvature region. low The sampling density is set for regions with low curvature. The formula for calculating the sampling density for low curvature regions is as follows:

[0057]

[0058] In the formula, The total sampling density of low-curvature regions representing historical cases, m α The sampling density of the low curvature region represents the α-th historical case, and N represents the number of historical cases;

[0059] S3.4. Calculate the upper limit of the number of sensors in each region based on the sampling density in high-curvature areas and low-curvature areas. The formula for calculating the upper limit of sensors is:

[0060]

[0061]

[0062]

[0063] in the formula This represents the upper limit of the number of sensors in the p-th high curvature region. This represents the area of ​​the p-th high curvature region. The coverage area of ​​the sensor represents the high curvature region;

[0064] This represents the upper limit of the number of sensors in the q-th low curvature region. This represents the area of ​​the q-th low-curvature region. The coverage area of ​​the sensor represents the low curvature region;

[0065] A eit x represents the area of ​​either the high-curvature region or the low-curvature region, M represents the number of vertices in either the high-curvature region or the low-curvature region, and x represents the area of ​​either region. j y j x represents the area of ​​a region with high curvature or the coordinates of the j-th vertex in a region with low curvature. j+1 y j+1 Represents the area of ​​a high-curvature region or the coordinates of the (j+1)th vertex of a low-curvature region;

[0066] S3.5. Generate candidate point set C based on an improved greedy algorithm. The specific method is as follows:

[0067] Using a greedy rule to select in high curvature regions These points are selected as the candidate point set for the high curvature region. The points are evenly distributed among them;

[0068] Select using a greedy rule in the low curvature region. These points are selected as the candidate point set for the low curvature region. The points are evenly distributed among them;

[0069] extract points and The coordinates of each point are summarized to generate a candidate point set C;

[0070] C = C high ∪C low ={P1, P2, ..., P β(Dhigh) Q1, Q2, ..., Q β(Dlow)}

[0071] Among them, C high The candidate point set representing the high curvature region, P1~P α(high) Representing the first to the second in the high curvature region There are candidate points, where P represents the two-dimensional coordinates of the corresponding candidate point in the high curvature region;

[0072] C low The candidate point set representing the low curvature region, Q1~Qβ(low) Represents the first to the second in the low curvature region There are 1 candidate points, where Q represents the two-dimensional coordinates of the corresponding candidate point in the low curvature region;

[0073] By using curvature adaptive sampling and generating candidate point sets based on an improved greedy algorithm, the sampling density can be dynamically adjusted according to the curvature distribution of the structural surface. Candidate points are densely arranged in high curvature areas to capture complex geometric features, while sampling is reasonably sparse in low curvature areas. This ensures that the sensor layout covers key areas while avoiding redundancy, thereby improving monitoring accuracy and resource utilization, and providing a high-quality initial solution set for subsequent multi-objective optimization.

[0074] S4. Eliminate candidate points with a spacing smaller than [missing information]. Redundant candidate points are used to avoid over-concentration of sensors leading to monitoring overlap, where r is the sensor detection radius. To set coefficients;

[0075] S5. Calculate the coverage weight of candidate points, and use bubble sort to prioritize points that contribute significantly to the coverage of the target area. The formula for calculating the coverage weight is:

[0076]

[0077] In the calculation formula, ω z N represents the coverage weight of candidate point z. (ci) x represents the set of other candidate points within the detection radius of the candidate point (the valid candidate points remaining after S4 redundancy removal), that is, all other candidate points within the sensor's detection radius centered on the candidate point ci. j Represents N (ci) A specific candidate point, k(x) j ) represents x j The basic weights, σ(x) j ) represents x j Additional weights.

[0078] S6. Stepwise select effective candidate points and add them to the sensor set S. The process is as follows: Add the candidate points with the largest coverage weight selected by bubble sort in step S5 to the sensor set S. Calculate the overall coverage rate once for each effective candidate point added. Repeat this process until the coverage rate reaches a preset value. This process can maximize the monitoring range with the fewest number of sensors, improve layout efficiency and monitoring reliability, and avoid resource waste. The coverage rate calculation formula is:

[0079]

[0080] In the calculation formula, N totalS represents the total number of candidate points (the valid candidate points remaining after redundancy removal in S4), and S represents the set of candidate sensors, containing all individual sensors to be evaluated, S = s1, s2, ..., s i ,···,s n , where s i Let N(s) represent the i-th sensor. i ) represents the i-th sensor s i The set of other candidate points within the detection radius, U si∈s N(si) represents the union of all sensor-covered nodes, that is, the total set of nodes covered by at least one sensor;

[0081] S7. Global optimization based on simulated annealing algorithm, specifically:

[0082] f(S)=γ·|S|+δ·(1-C(S))+ε·σ(S)

[0083] Where f(S) represents the objective function for global optimization, |S| represents the number of sensors, C(S) represents the coverage of the sensor set, σ(S) represents the signal strength variance of the sensor set, and γ, δ, and ε all represent weights that need to be set manually.

[0084] Global optimization based on simulated annealing algorithm constructs a comprehensive objective function that includes the number of sensors, coverage, and signal strength variance. It can balance resource consumption and monitoring performance in multi-objective conflicts, and probabilistically search to escape local optima, thereby generating a sensor layout scheme that is efficient, reliable, and stable, and improving the overall performance of the monitoring system.

[0085] S8. Perform cross-operations on the selected individual sensors;

[0086] S9. Perform mutation operation on the newly generated sensor individuals;

[0087] S10. Dynamically adjust the crossover probability so that it decays exponentially with the number of generations and temperature. The formula for calculating the crossover probability is:

[0088]

[0089] In the formula, P c (t, T) represents the dynamic crossover probability, P cO τ1 and τ2 represent the initial crossover probability, t represents the number of generations, T represents the temperature exponent, 1-D represents the complement of population diversity, D represents population diversity, and τ1 and τ2 represent the decay coefficients.

[0090] S11, Dynamically adjust the intensity of variation;

[0091]

[0092] In the formula, η m (t, T) represents the intensity of dynamic variation, η mo Represents the initial mutation intensity. Represents the attenuation coefficient;

[0093] By dynamically adjusting the crossover probability and mutation intensity, which decay with the number of generations and temperature exponential and are negatively correlated with population diversity, the genetic algorithm can adaptively balance exploration and development capabilities during optimization: retaining a high crossover probability in the early stage to promote global search, and reducing it in the later stage to avoid destroying excellent individuals; the mutation intensity is dynamically adjusted according to population diversity, suppressing mutation to prevent disturbance when diversity is high, and enhancing mutation to escape local optima when diversity is low, thereby improving the efficiency and quality of sensor layout optimization.

[0094] S12. Calculate the contribution of each sensor and remove inefficient sensors. The formula for calculating the sensor contribution is:

[0095]

[0096] In the formula, C i Represents the contribution of the i-th sensor, C(S{s i}) represents removing the i-th sensor s i Total coverage after;

[0097] The rules for removing inefficient sensors are as follows:

[0098] C i <θ·C(S)

[0099] Where θ represents the dynamic removal threshold coefficient, and its definition rule is as follows:

[0100]

[0101] Where, θ min θ is the minimum value within the preset removal threshold range. max C is the maximum value within the preset removal threshold range. min λ is the minimum preset coverage rate, and λ is the non-linear adjustment coefficient.

[0102] S13. Repeat steps S4 to S12 until the maximum iteration value (number of repetitions) is reached;

[0103] By calculating the contribution of each sensor and dynamically removing inefficient sensors, redundant sensors that contribute little to improving coverage can be accurately identified and eliminated. Combined with a non-linearly adjusted dynamic threshold coefficient, the removal criteria are adaptively adjusted during the optimization process, thereby minimizing the number of sensors, reducing resource consumption, and improving the economy and practicality of the layout while ensuring monitoring performance.

[0104] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for intelligent placement of vibration sensors that combines physical field modeling and hybrid optimization, characterized in that, include: Obtain the geometric model of the target mechanical structure and extract the material parameter set; Calculate the curvature and stress of the surface of the mechanical structure, and identify high-sensitivity areas by combining the vibration transmission efficiency matrix; Curvature adaptive sampling is performed within a high-sensitivity region, and a candidate point set is generated based on an improved greedy algorithm. Eliminate redundant candidate points to obtain a set of valid candidate points; Calculate the coverage weights of valid candidate points; Candidate points with the highest coverage weight are selected by bubble sort and added to the sensor set S. The overall coverage rate is calculated once for each valid candidate point added, until the coverage rate reaches the preset value. Global optimization is performed based on the simulated annealing algorithm, and crossover and mutation operations are performed on the selected individual sensors. Calculate the contribution of each sensor and remove inefficient sensors until the maximum iteration value is reached.

2. The intelligent layout method for vibration sensors based on physical field modeling and hybrid optimization as described in claim 1, characterized in that, The region or T that satisfies the definition formula of the high sensitivity region ij ≥T th The region is defined as the high-sensitivity region, and the formula for defining the high-sensitivity region is: Oh high ={x|k (x) >k th ∪σ (x) >s th } Ω high Represents the high-sensitivity region, k (x) k represents the curvature of the x-th vertex in the set of vertex coordinates. th Represents the preset threshold for curvature, σ (x) σ represents the stress at the x-th vertex in the set of vertex coordinates. th This represents a preset stress threshold. T ij The element in the i-th row and j-th column of the vibration transmission efficiency matrix representing the relationship between the i-th and j-th vertex coordinates in the vertex coordinate set: d ij E represents the geodesic distance between the coordinates of the i-th vertex and the j-th vertex. i E represents the elastic modulus of the i-th vertex. j ρ represents the elastic modulus of the j-th vertex, and ρ represents the material density.

3. The intelligent layout method for vibration sensors based on physical field modeling and hybrid optimization as described in claim 1, characterized in that, The candidate point set is generated based on an improved greedy algorithm. The specific method is as follows: Calculate the curvature of each vertex, classify vertices above the curvature threshold as high curvature regions, and classify vertices equal to or below the curvature threshold as low curvature regions; Set the sampling density for high curvature and low curvature regions: The sampling density in the high curvature region is: D high =n*D low The density of the low curvature region set is: n represents the ratio of the sampling density in high curvature areas to the sampling density in low curvature areas, and m represents the ratio of the sampling density in high curvature areas to the sampling density in low curvature areas. α The sampling density of the low curvature region represents the α-th historical case, and N represents the number of historical cases; The upper limit of the number of sensors in each region is calculated based on the acquisition density in high curvature regions and low curvature regions: This represents the upper limit of the number of sensors in the p-th high curvature region. This represents the area of ​​the p-th high curvature region. The coverage area of ​​the sensor represents the high curvature region; This represents the upper limit of the number of sensors in the q-th low curvature region. This represents the area of ​​the q-th low-curvature region. The coverage area of ​​the sensor in the low curvature region; Use a greedy rule to select in high curvature regions. These points are selected as the candidate point set for the high curvature region. The points are evenly distributed; a greedy rule is used to select points in the low curvature region. These points are selected as the candidate point set for the low curvature region. The points are evenly distributed among themselves; extraction points and The coordinates of each point are summarized to generate a candidate point set.

4. The intelligent placement method for vibration sensors based on physical field modeling and hybrid optimization as described in claim 1, characterized in that, The formula for calculating coverage weight is: oh z =∑x j ∈N (ci )(T ij *(k(x j )+σ(x j ))) ω z N represents the coverage weight of candidate point z. (ci) x represents the set of valid candidate points within the candidate point detection radius. j Represents N (ci) A specific candidate point, k(x) j ) represents x j The basic weights, σ(x) j ) represents x j Additional weights. The formula for calculating coverage is: N total S represents the total number of valid candidate points, and S represents the set of candidate sensors. i Let represent the i-th sensor, and N(si) represent the i-th sensor s. i The set of other candidate points within the detection radius.

5. The intelligent placement method for vibration sensors based on physical field modeling and hybrid optimization as described in claim 1, characterized in that, Global optimization is performed based on the simulated annealing algorithm, specifically as follows: f(S)=γ·|S|+δ·(1-C(S))+ε·σ(S) Where f(S) represents the objective function for global optimization, |S| represents the number of sensors, C(S) represents the coverage of the sensor set, σ(S) represents the signal strength variance of the sensor set, and γ, δ, and ε all represent weights.

6. The intelligent placement method for vibration sensors based on physical field modeling and hybrid optimization as described in claim 1, characterized in that, Dynamically adjust the crossover probability during crossover operations: P c (t, T) represents the dynamic crossover probability, P cO τ represents the initial crossover probability, t represents the number of generations, T represents the temperature index, D represents the population diversity, and τ1 and τ2 represent the decay coefficients.

7. The intelligent placement method for vibration sensors based on physical field modeling and hybrid optimization as described in claim 1, characterized in that, Dynamically adjust the mutation intensity during mutation operations: η m (t, T) represents the intensity of dynamic variation, η mo denoted by , where t represents the initial variation intensity, t represents the generation number, T represents the temperature index, and D represents population diversity. This represents the attenuation coefficient.

8. The intelligent placement method for vibration sensors based on physical field modeling and hybrid optimization as described in claim 1, characterized in that, The formula for calculating the sensor's contribution is: C i C(S) represents the contribution of the i-th sensor, and C(S{s}) represents the coverage rate. i }) represents removing the i-th sensor s i Total coverage after; The rules for removing inefficient sensors are as follows: C i <θ·C(S) Where θ represents the dynamic removal threshold coefficient, and its definition rule is as follows: Where, θ min θ is the minimum value within the preset removal threshold range. max C is the maximum value within the preset removal threshold range. min λ is the minimum preset coverage rate, and λ is the non-linear adjustment coefficient.

9. The intelligent placement method for vibration sensors based on physical field modeling and hybrid optimization as described in claim 1, characterized in that, Eliminate candidate points with a spacing smaller than The redundant candidate points, where r is the sensor detection radius. To set the coefficients.

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