A method and system for optimizing the layout of spatially constrained sensor mounting points

Abstract

The application discloses a kind of space constrained sensor installation point optimization layout method and system.The method will allow installation area to be divided into installation subarea with fixed number, establish initial installation point, adjustable coordinate range and attitude range;Based on space occlusion, distance and incident attitude, calculate coverage contribution and measurement reliability, and form effective coverage criterion;According to the constraint satisfaction state of candidate scheme, construct constraint coupling matrix and joint violation penalty term;Length coding containing activation, installation coordinates and installation attitude is used for particle swarm search, and when group dispersion and target improvement rate are simultaneously lower than threshold value, difference mutation and crossover are executed;Finally, according to marginal contribution, redundant points are deleted, and installation point coordinates, attitude and installation order are output.The application is suitable for sensor layout with obstacles, forbidden installation area, installation spacing, measurement accuracy and cost constraints.

Description

Technical Field

[0001] This invention relates to the fields of spatial measurement, sensor deployment and intelligent optimization technology, and in particular to a method and system for optimizing the deployment of sensor installation points under spatial constraints. Background Technology

[0002] With the increasing demand for digital monitoring in industrial plants, large equipment, bridges and tunnels, energy facilities, and complex buildings, it is necessary to install temperature, vibration, stress, displacement, gas, or image sensors in confined spaces to collect status information of the structure under test. The sensor installation location and orientation directly affect the coverage of the measured surface, measurement accuracy, and data stability. In actual deployment, installation points are also limited by conditions such as permitted installation areas, prohibited areas, obstacles, maintenance access, bracket dimensions, cable routing, and construction accessibility.

[0003] Existing technologies typically first generate discrete candidate installation points based on a 3D model, permissible mounting components, or a uniform mesh. Then, using particle swarm optimization, genetic algorithms, or multi-objective evolutionary algorithms, the candidate installation points are selected based on objectives such as coverage of the area to be measured, number of sensors, or deployment cost. Some schemes also determine the visual relationship between the installation point and the surface to be measured through ray intersection or field of view judgment, and use penalty functions to handle constraints such as intrusion into prohibited areas, insufficient installation spacing, exceeding measurement distance limits, and non-compliant installation posture, ultimately outputting the selected sensor installation location.

[0004] However, fixed candidate points make it difficult to continuously adjust the actual installation coordinates and attitude locally, while using a set of coordinates with variable numbers and order results in a lack of stable point correspondences between different candidate schemes. Existing coverage evaluations are mostly based on visibility or the number of coverage events, failing to fully reflect the combined impact of measurement distance, incident attitude, and sensor quality on effective measurement results. Furthermore, some intermediate coverage contributions are not clearly linked to the final effective coverage criteria. In addition, multiple spatial constraints are often penalized independently, making it difficult to reflect the correlation of common constraint violations. The optimization results may also retain redundant installation points with low contributions, making it difficult to balance the number of installations, construction costs, and measurement reliability.

[0005] Therefore, there is a need for a spatial constraint optimization deployment scheme that can maintain the correspondence between candidate scheme points, jointly optimize the activation status, coordinates and attitude of sensor installation points, effectively integrate coverage contribution into effective coverage judgment, and form coupling penalty based on the constraints in the search samples that are jointly satisfied or jointly violated. Summary of the Invention

[0006] The purpose of this invention is to provide a spatially constrained sensor installation point optimization layout method and system to solve the problems of lack of local adjustability of fixed candidate points in complex spaces, difficulty in corresponding to variable length schemes, disconnect between coverage evaluation and final target, difficulty in characterizing multiple constraints in common violation, and the existence of redundant installation points after optimization.

[0007] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows: A method for optimizing the layout of sensor mounting points under spatial constraints includes the following steps: S1. Obtain the three-dimensional geometric model of the space to be measured, the surface to be measured, the allowed installation area, the prohibited installation area, obstacles, sensor parameters and layout constraints. Discretize the surface to be measured into multiple surface units, divide the allowed installation area into multiple installation sub-regions with unique numbers, and determine the initial installation point, adjustable coordinate range and adjustable attitude range for each installation sub-region. S2, for the candidate deployment scheme consisting of sensor mounting points in the activated installation sub-region, perform visibility detection from the mounting points to each surface unit, combine visibility, distance between the mounting points and surface units and incident attitude, calculate coverage contribution and measurement reliability, and determine effective coverage status based on the cumulative coverage and aggregate reliability of each surface unit. S3, count the satisfaction status of multiple candidate layout schemes for each layout constraint, construct a constraint coupling matrix based on the occurrence of the common satisfaction, common violation and single violation of any two layout constraints, and form a constraint penalty term based on the constraint coupling matrix that simultaneously represents the single constraint violation and the common violation of coupled constraints. S4. A candidate deployment scheme is constructed using a fixed-length code consisting of the activation degree of each installation sub-region, the coordinates of the sensor installation point, and the installation attitude. The particle swarm optimization is performed with effective coverage, measurement reliability, deployment cost, and the constraint penalty term as the optimization objectives. When the population dispersion and the optimal objective improvement rate are both lower than their respective thresholds, differential mutation and crossover are performed on the candidate deployment schemes, and boundary projection and constraint repair are performed on the activation degree, coordinates, and installation attitude after mutation and crossover. S5 calculates the effective coverage loss, measurement reliability loss, and cost savings of each sensor installation point before and after deletion for the obtained candidate optimal deployment scheme. Based on this, the marginal contribution is determined and redundant sensor installation points with low marginal contribution are deleted in sequence. After each deletion, the effective coverage and deployment constraint verification is re-executed, and the coordinates, installation posture, and installation sequence of the sensor installation points that pass the verification are output.

[0008] Preferably, the surface unit is a triangular surface element obtained by triangulation of the surface to be measured, the first... j Each surface unit has at least a center point. c j ,areaa j Unit normal vector n j And importance weight w j ;No. i Each installation sub-area is denoted as Oh i The corresponding sensor installation point coordinates p i satisfy p i ∈ Oh i Installation posture f i Located within a preset posture range; the visibility detection includes from p i Towards c j The detection line segment is emitted when the detection line segment does not coincide with the obstacle model prior to... c j When the intersection occurs and the incident attitude satisfies the sensor's field of view conditions, the visibility marker will be displayed. v ij Set to 1 otherwise set to 0.

[0009] As a preferred option, the first i The sensor installation point is related to the first j Coverage contribution of each surface unit g ij Calculate using the following formula:

[0010] in: d ij =‖ p i - c j ‖2 represents the distance between the sensor mounting point and the center point of the surface unit; d 0 is the preferred measurement distance; s d The distance attenuation scale; i ij This is the angle of deviation between the measurement direction and the unit normal vector; i 0 represents the allowable deviation from the angular scale, and 0 < i 0< π / 2.

[0011] As a preferred option, the first i The sensor installation point is related to the firstj Measurement reliability of individual surface units r ij Calculate using the following formula:

[0012]

[0013] in: q i ∈[0,1] is the first i The calibration quality coefficient of each sensor; d min and d max These are the lower and upper limits of the allowed measurement distance, respectively. d min < d 0< d max； i max To allow for the upper limit of the deviation angle; To effectively measure operating conditions; The interval truncation operator is defined as:

[0014] Used to limit the corresponding distance attenuation factor and angle attenuation factor to the interval [0,1].

[0015] As a preferred option, let z i ∈{0,1} represents the first... i Whether each installation sub-region is activated, the normalized coverage contribution is... c ij = g ij / a j , No. j Cumulative coverage of each surface unit C j(P) Aggregate reliability R j(P) and effective coverage identifier e j(P) They are respectively:

[0016]

[0017]

[0018] in: P Candidate deployment schemes; M Number of sub-regions to install; e To prevent positive numbers with a denominator of zero; t j and or j The first j Coverage threshold and reliability threshold for each surface unit; The weighted effective coverage of the candidate deployment schemes is:

[0019] As a preferred option, regarding the layout constraints p and layout constraints q Within a preset statistical window, count the number of times both conditions are met. N pq 11 Number of joint violations N pq 00 ,constraint p Satisfaction and Constraint q Number of violations N pq 10 and constraints p Violation and constraint q Number of times satisfied N pq 01 The elements in the constraint coupling matrix are:

[0020] make d p(P) Candidate deployment schemes P Constraints p If the normalized violation is zero, then the constraint penalty term is:

[0021] in, l p This is the penalty coefficient for a single constraint. m This is the penalty coefficient for coupling constraints.

[0022] As a preferred option, the first k The candidate deployment schemes adopt the following fixed-length coding:

[0023] in, r ki∈[0,1] is the first i The activation level of each installation sub-region, and when r ki ≥ t s season z ki =1, otherwise let z ki =0; Installation sub-regions with the same number in different candidate deployment schemes correspond to each other; the optimization objective is:

[0024] Where F(P) is the overall target value of the candidate deployment scheme, C(P) is the weighted effective coverage, R(P) is the weighted aggregate reliability, and K(P) is the normalized deployment cost. To constrain penalties, α C , α R , α K These are the weighting coefficients.

[0025] As is preferred, in the... t In the next iteration, let A i (t) ={ k | z ki (t) =1} indicates activation of the first i The set of candidate deployment schemes for each installation sub-region, the group dispersion D (t) and optimal target improvement rate ΔF (t) They are respectively:

[0026]

[0027] in, p _ i (t) For set A i (t) The Middle i The average coordinates of each sensor installation point. L i For installing sub-regions Oh i The characteristic length; when D (t) < t D and ΔF (t) < t F The differential mutation and crossover are triggered at the time, and Ft best and Ft-1 best are the population optimal objective values ​​for the t-th and t-1-th iterations, respectively.

[0028] Preferably, differential mutation and crossover simultaneously apply to activation, sensor mounting point coordinates, and mounting attitude. After crossover, the activation is truncated to the interval [0,1], the sensor mounting point coordinates are projected to the corresponding mounting sub-region, and the mounting attitude is projected to the corresponding attitude range. Furthermore, it corrects for violations of restricted areas, obstacle collisions, and minimum mounting spacing. For the current deployment scheme... P The first in i The marginal contribution of each sensor installation point is:

[0029] in, β C , β R and β K The weighting coefficients are for effective coverage loss, aggregate reliability loss, and cost savings, respectively. Sensor installation points are attempted to be deleted in order of increasing marginal contribution. The deletion operation is retained only if the minimum effective coverage, minimum aggregate reliability, and all hard constraints are still met after deletion. The installation order is generated based on the reachability distance between adjacent installation points.

[0030] A spatially constrained sensor mounting point optimization layout system, comprising: The spatial modeling and discretization module is used to acquire the three-dimensional geometric model and layout data of the space to be measured, discretize the surface to be measured into multiple surface units, divide the allowable installation area into multiple installation sub-regions with unique numbers, and determine the initial installation point, adjustable coordinate range and adjustable attitude range for each installation sub-region. The coverage and reliability calculation module is used to perform visibility detection from the sensor mounting point to the surface unit, and calculate coverage contribution, measurement reliability, cumulative coverage, aggregate reliability, and effective coverage status. The constraint coupling analysis module is used to statistically analyze the satisfaction status of candidate layout schemes with various layout constraints, construct the constraint coupling matrix, and generate constraint penalty terms. The hybrid optimization module is used to perform particle swarm iteration using a fixed-length code that includes activation degree, sensor mounting point coordinates and mounting attitude, and to perform differential mutation and crossover when the population dispersion and the optimal target improvement rate are both below their respective thresholds, as well as to perform boundary projection and constraint repair. The redundancy reduction and output module is used to calculate the marginal contribution of sensor installation points, sequentially attempt to delete sensor installation points with low marginal contributions, re-verify effective coverage and layout constraints, and output the coordinates, installation posture, and installation sequence of sensor installation points.

[0031] Preferably, an electronic device for performing the method and a computer-readable storage medium are also provided.

[0032] The present invention has the following beneficial effects: 1. This invention adopts a representation method of "unique numbered installation sub-region, logical point slot, activation degree and continuous coordinates within the region", which can not only ensure that the points in different candidate schemes correspond one-to-one, but also allow the actual installation points to be refined within the engineering permit range, thus avoiding mismatch between different physical points in particles or difference vectors from the data structure perspective.

[0033] 2. This invention normalizes the coverage contribution with area dimensions into a dimensionless contribution, and then sequentially forms the cumulative coverage degree of surface units, aggregate reliability, effective coverage identifier, and overall weighted effective coverage rate, so that the local contribution of the installation point and the final optimization target form a clear calculation chain, which can simultaneously exclude surface units that are "visible but at an inappropriate angle" and "coverage achieved but reliability insufficient".

[0034] 3. This invention constructs a symmetric constraint coupling matrix based on four states: common satisfaction, common violation, and two types of individual violations. The statistical meaning is clear. The coupling matrix applies joint penalties only to positively coupled and jointly violated constraint pairs, which can guide the search to avoid recurring compound infeasible regions without replacing hard constraint repair.

[0035] 4. This invention combines the rapid global search capability of particle swarm with differential mutation triggered by dual thresholds of discreteness and improvement rate. Additional perturbation is only introduced when the swarm aggregates and the target improvement is insufficient, thus balancing iteration efficiency and the ability to escape local stagnation. The boundary projection and constraint repair after mutation ensure that the installation coordinates, attitude and activation state still have clear engineering significance.

[0036] 5. After optimization, this invention determines the marginal contribution based on both performance loss and cost savings, and verifies hard constraints point by point. This can reduce redundant sensor installation points that contribute little to effective coverage and reliability, while outputting executable coordinates, orientations, and installation sequences, which helps reduce procurement, wiring, construction, and maintenance costs. Attached Figure Description

[0037] Figure 1 The overall flowchart of the five steps of the spatially constrained sensor installation point optimization layout method of the present invention; Figure 2This is a schematic diagram illustrating the spatial relationship between the space to be measured, the surface to be measured, the mounting sub-region, the sensor mounting point, obstacles, and the detection line segment in this invention. Figure 3 This is a flowchart illustrating the calculation of coverage contribution, measurement reliability, and effective coverage status in this invention. Figure 4 This is a schematic diagram illustrating the formation of four-state constraint statistics, constraint coupling matrix, and constraint penalty terms in this invention. Figure 5 This is a flowchart of particle swarm optimization using fixed-length encoding in this invention. Figure 6 This is a flowchart of the process for reducing redundant sensor installation points based on marginal contribution in this invention. Figure 7 This is a structural block diagram of the spatially constrained sensor mounting point optimization layout system of the present invention.

[0038] in: 201. Surface to be tested; 202. Permitted installation area; 203. Prohibited installation area; 204. Obstacle; 205. Installation channel; 206. Sensor mounting point; 207. Surface unit; 208. Detection line segment; 209. Installation sub-area; 301. Installation point parameter input; 302. Surface unit parameter input; 303. Visibility detection; 304. Distance calculation; 305. Deviation angle calculation; 306. Coverage contribution calculation; 307. Normalized coverage contribution; 308. Measurement reliability calculation; 309. Cumulative coverage degree; 310. Aggregate reliability; 311. Effective coverage judgment; 312. Weighted effective coverage output; 401. Candidate layout scheme; 402. Constraint satisfaction state; 403. Number of times common satisfaction is achieved; 404. Number of times common violation is achieved; 405. Number of times the first individual violation is achieved; 406. Number of times the second individual violation is achieved; 407. Constraint coupling matrix; 408. Normalized violation amount; 409. Penalty for individual violation; 410. Judgment of positive coupling common violation; 411. Penalty for joint violation; 412. Constraint penalty term; 501. Initialize fixed-length encoded population; 502. Activation state generation; 503. Particle swarm update; 504. Boundary projection; 505. Constraint repair; 506. Scheme evaluation; 507. Individual optimal update; 508. Population optimal update; 509. Population dispersion calculation; 510. Target improvement rate calculation; 511. Double threshold judgment; 512. Differential mutation; 513. Crossover and selection; 514. Termination and candidate optimal scheme output; 601. Input candidate optimal solutions; 602. Construct single-point deletion solutions; 603. Coverage loss calculation; 604. Reliability loss calculation; 605. Cost saving calculation; 606. Marginal contribution ranking; 607. Delete the lowest marginal contribution point; 608. Lowest coverage verification; 609. Lowest reliability verification; 610. Hard constraint verification; 611. Installation sequence generation; 612. Final solution output; 701. Spatial Modeling and Discretization Module; 702. Coverage and Reliability Calculation Module; 703. Constraint Coupling Analysis Module; 704. Hybrid Optimization Module; 705. Redundancy Reduction and Output Module; 706. Data Storage Module; 707. Human-Computer Interaction Module; 708. Interface Module. Detailed Implementation

[0039] The technical solutions in 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.

[0040] like Figure 1 As shown, this embodiment provides a method for optimizing the layout of sensor installation points under spatial constraints, including steps S1 to S5.

[0041] Step S1: Establish the spatial model to be tested and divide it into installation sub-regions. like Figure 2 As shown, the first step is to import a 3D model of the space to be measured. The 3D model includes at least the surface to be measured 201, the permitted installation area 202, the prohibited installation area 203, obstacles 204, and the installation channel 205. The surface to be measured 201 can be an equipment casing, building component, pipe, tank, bridge component, or other surface from which measurement data needs to be obtained; the permitted installation area 202 can be located on a wall, beam, column, bracket, track, or independent mounting bracket. The sensor mounting point 206 is the actual reference position of the sensor or sensor mounting bracket, not a sampling point on the surface to be measured.

[0042] The surface 201 to be tested is triangulated to obtain... J 207 surface units. j Each surface unit has a center point. c j ,area a j Unit normal vector n j and importance weight w jWeights can be set based on the structural criticality, expected magnitude of change, regulatory level, or historical defect distribution. For example, areas prone to deformation or leakage can be given higher weights, while areas requiring only routine inspections can be given lower weights. To avoid imbalances in evaluation results due to changes in grid density, the overall coverage rate is set at... w ja _ j As area weight.

[0043] The permitted installation area 202 is divided according to component boundaries, installation methods, adjustable range, and project spacing. M Each installation sub-area has a unique number. Oh i Each installation sub-region is assigned a unique number. i Record the initial installation point p i 0 Adjustable coordinate boundaries, attitude boundaries, sensor type, calibration quality coefficient q i Single point cost k i And attributes such as whether it must be enabled. The installation sub-regions are not required to have the same shape; they can be rectangular patches, polygonal patches, strip-shaped regions near line segments, or three-dimensional local regions defined by multiple boundary conditions.

[0044] This division is not equivalent to pre-fixing the actual installation coordinates. (Numbering) i Represents stable logical point slots, actual coordinates p i Available Oh i Internal continuous change, attitude f i The activation level can be varied within the permitted range. r i This determines whether a sensor will ultimately be installed in the logic point slot. r i ≥ t s At that time, place z i =1; when r i < t s At that time, place z i =0. In one embodiment, t s =0.5. If a certain point is a legally or process-required mandatory installation point, its activation state can be fixed at 1.

[0045] For coordinates exceeding the installation sub-region, perform nearest-point projection. For rectangular installation surfaces, the coordinates within both surfaces can be truncated separately; for polygonal installation surfaces, the out-of-bounds coordinates can be projected to the nearest point on the polygon boundary; for curved installation areas, they can be truncated within the parameter domain first, and then mapped back to the 3D surface. After projection, the bracket's outer envelope should also be considered, and installation should not be based solely on whether mathematical points are within the allowable area.

[0046] Step S2: Determine the visibility relationship and calculate the coverage contribution and measurement reliability. Visibility detection is performed for each activated sensor mounting point 206 and surface unit 207. This is based on the mounting point coordinates. p i Towards the center point of the surface unit c j Construct detection line segment 208 and use bounding box tree, octree, or other spatial indexing to determine whether the line segment intersects with obstacle 204 or a non-target surface first. If there is no intersection prior to the target center point, and the center point is within the sensor's field of view, then... v ij =1; otherwise v ij =0. To reduce edge errors caused by only detecting the center point, for surface units with an area exceeding a preset threshold, the same detection can be performed on three vertices or multiple internal sampling points, and the ratio can be determined according to the visible sampling points. v ij The face value may be further subdivided.

[0047] The sensor's measurement direction is determined by its installation orientation. f i OK. Let the unit direction vector from the mounting point to the center of the surface element be...

[0048] The calculation can be performed based on the agreed-upon direction of the sensor facing the target or the surface normal. u ij and n j The included angle or its supplementary angle is used as the deviation angle. i ij And uniformly select the time that makes the ideal normal incidence. i ij The definition of =0. If | i ij |> i max If so, the combination is considered unavailable.

[0049] Coverage contribution is calculated using the following formula:

[0050] In the above formula, d ij =‖ p i - c j ‖2, d 0 is the preferred measurement distance when the sensor achieves its best signal-to-noise ratio or spatial resolution. s d Controlling the decay rate when the distance deviates, i 0 is the deviation angle attenuation scale. sinth ij / sinth Zero is a dimensionless quantity, avoiding direct division of parameters with angular units by the sine value. When visibility is 0, the coverage contribution is necessarily 0; under the same conditions, the installation distance is close. d 0. The contribution is greater when the deviation angle is close to 0.

[0051] because g ij Area a j It cannot be directly compared with a fixed threshold. Therefore, a normalized coverage contribution is defined. c ij = g ij / a j .when a j When >0, c ij ∈[0,1]. The contributions of multiple sensors to the same surface element are added together, and the cumulative coverage is obtained by truncation through an upper limit:

[0052] Measurement reliability is calculated using the following formula:

[0053]

[0054] in, q i It can be determined by calibration error, sensor health status, environmental adaptability level, or historical statistics of the same model; d min and d max Limit the permissible measurement distance and meet the following requirements. d min < d 0< d max . what ijTo effectively measure operating conditions, values ​​are set to 0 when the allowable distance or allowable deviation angle is exceeded. The interval truncation operator is applied to the distance attenuation factor and the angle attenuation factor respectively, avoiding the generation of false positive reliability after multiplying two negative factors, and ensuring that the reliability is between 0 and 1. Reliability is not a duplicate calculation of coverage contribution: coverage contribution emphasizes the geometric coverage of an array at a certain installation point, while reliability further describes the credibility of the coverage in generating usable measurement data.

[0055] The reliability of surface element aggregation is weighted by coverage contribution:

[0056] when C j(P) ≥ t j and R j(P) ≥ or j hour, e j(P) =1, otherwise e j(P) =0. Therefore, if a surface cell is only scanned by a sensor at a distance but its reliability is insufficient, it will not be counted as effective coverage; multiple sensors with weaker contributions but acceptable orientation and distance can collectively bring the cumulative coverage to the threshold. The overall weighted effective coverage rate is:

[0057] The weighted aggregate reliability of candidate deployment schemes can be defined as:

[0058] To prevent the optimization algorithm from achieving a higher average reliability by abandoning difficult regions, a minimum effective coverage rate is set during implementation. C min It also allows setting the requirements that key elements must meet. e j(P) =1 Hard constraint. For regions requiring dual-redundancy measurements, at least two additional distinct mounting sub-regions can be added to provide constraints on the surface element that are no less than a given contribution.

[0059] Step S3: Construct the constraint coupling matrix and constraint penalty terms. Deployment constraints can be divided into hard constraints and soft constraints. Hard constraints include that installation points and brackets must not encroach on restricted areas, must not collide with obstacles, the distance between any two installation points must not be less than the construction spacing, mandatory installation points must be activated, and critical elements must be effectively covered. Soft constraints include budget deviations, insufficient coverage of general elements, excessively long installation paths, or excessively long cables. Hard constraints are primarily corrected through projection, relocation, disabling conflicting points, or reinitialization. If they cannot be corrected, the candidate solution is deemed infeasible. Soft constraints and violations that still need to be compared after correction are included in the penalty items.

[0060] For each constraint p Define normalization violation quantity d p(P) For example, for the maximum allowed value form f p(P) ≤ b p , f p(P) Let P be the function value of the p-th placement constraint for the candidate placement scheme P. b p The limit value corresponding to this constraint can be taken as follows:

[0061] For the minimum requirement form f p(P) ≥ b p It is acceptable

[0062] like d p(P) =0, then constraint p To satisfy state 1; if d p(P) If the value is greater than 0, then state 0 is violated. In the most recent... W Within a statistical window consisting of evaluated candidate solutions, constraints are considered. p and constraints q Four statistical states: both conditions must be met. N pq 11 Both violated N pq 00 , p Satisfy and q violation N pq 10 ,as well as p Violation and q satisfy N pq 01All exponents are non-negative integers, and the sum of the four is not greater than the number of valid samples in the statistical window; when each sample can determine both constraints, the sum of the four equals W .

[0063] The elements of the constraint coupling matrix are:

[0064] This definition applies to p and q Symmetry, that is h pq = h qp The 1 in the denominator is a smoothing term, used to prevent the denominator from being zero and to suppress extreme values ​​when the sample size is small. When there are many common satisfactions or common violations... h pq A positive value indicates that the two constraints tend to be consistent; when there are many violations of a single constraint, h pq A negative value indicates that the two tend to exhibit opposite states. The coupling value is generated from the current search data and updates as the statistics window scrolls; it is not interpreted as a strict causal relationship.

[0065] The constraint penalty items are:

[0066] The first item is used to handle single constraint violations; the second item only applies when... h pq An additional penalty is incurred when both constraints are violated (>0). p < q This avoids double counting of the same constraint pairs. For safety boundaries that must be strictly satisfied, the remedial or infeasibility decision is still used, and the safety requirements are not replaced by limited penalties. l p It can be set according to the importance of the constraint and adjusted according to the violation rate of several consecutive generations; m Used to control the strength of the coupling penalty relative to the single penalty.

[0067] Step S4: Perform hybrid optimization using fixed-length encoding. No. k The candidate deployment schemes are coded as follows:

[0068] Regardless of whether a particular installation sub-region is activated, its activation level, coordinates, and orientation are preserved in the encoding, thus all candidate schemes have the same dimension. Installation sub-regions with the same number represent the same engineering area in different candidate schemes, and the corresponding components in the difference vector are comparable. For inactive points, their coordinates and orientation can still be updated iteratively to provide a usable initial position immediately after the activation state changes.

[0069] During initialization, a subset of candidate solutions are generated from the initial installation point. p i 0 Random perturbations in the vicinity are generated, while another part is sampled uniformly or hierarchically within each installation sub-region. The activation degree of the mandatory points is fixed at 1; installation sub-regions where no test elements can be observed can be excluded in advance. After initialization, coordinate projection, attitude truncation, bracket collision detection, and minimum spacing repair are performed to obtain an initial feasible or near-feasible population.

[0070] The objective function is:

[0071] Wherein, K( P This can include sensor procurement costs, bracket costs, cable length, construction difficulty, and maintenance accessibility costs, and is normalized by dividing by a preset cost benchmark. The weights can be determined based on the application objectives, typically set to... α C + α R + α K =1, but this equation is not a necessary condition. For infeasible solutions with hard constraints, a lower grade than any feasible solution can be assigned directly, or a feasibility-priority comparison rule can be used outside the objective function.

[0072] The particle swarm stage updates the activation, coordinate, and attitude components separately. Continuous activations are converted into discrete selection states through a threshold, while coordinates and attitude remain continuous. Velocity updates can use inertial terms, individual optimal guidance terms, or swarm optimal guidance terms. To avoid excessive differences when the attitude angle crosses the period boundary, the azimuth angle can be represented as a pair of sine and cosines, or periodic normalization can be performed after the update.

[0073] To determine whether the group has stagnated, let A i (t) ={ k | z ki (t) =1}, calculate the mean of the coordinates in this set. p _ i (t) Installation sub-region feature lengthL i The bounding box diagonal length, equivalent diameter, or allowable movement path length can be used. The normalized population dispersion is:

[0074] The denominator above uses the actual number of activated samples involved in the statistics, therefore it will not disproportionately amplify the dispersion due to different activation frequencies in different installation sub-regions. For A i (t) For empty installation sub-regions, the corresponding mean and distance terms are not calculated. The target improvement rate is:

[0075] When D(t) < τD and ΔF(t) < τF, it indicates that the spatial location of the population has clustered and the improvement of the optimal target is insufficient, triggering differential mutation. Dual-condition triggering can avoid premature perturbation when the target is temporarily stable but the population still maintains diversity, and also avoid interrupting the effective search when the population accidentally clusters but the target continues to improve. Furthermore, it can be required that the dual conditions continuously satisfy T. s Triggering again after a generation to reduce the impact of single-generation fluctuations, T s The number of iterations in which the two thresholds are continuously satisfied before triggering differential mutation.

[0076] For the target candidate solution X k Select different schemes X from the group. r1 X r2 and X r3 This forms the mutation vector V. k =X r1 +F d (X r2 -X r3 ), where F d The difference scaling factor is used; then, according to the crossover probability C... r V k With X k The combination forms the test scheme. This operation is performed on the corresponding components of activation, coordinates, and attitude according to the same installation sub-region number, without exchanging the coordinate meanings between different numbers.

[0077] The test plan was repaired in the following order: First, the activation level was truncated to 0 to 1 and a new zi was generated; second, the coordinates were projected onto the corresponding installation sub-region; third, the attitude was projected onto the permissible range; fourth, the bracket shape was checked for intrusion into the prohibited area or obstacles. If intrusion was found, the bracket was moved along the feasible direction. If the problem could not be repaired, non-essential installation points were discontinued or resampling was performed; fifth, minimum spacing conflicts were handled according to point priority; sixth, visibility, coverage, and constraint violations were recalculated. The repaired test plan was replaced if it was superior to the original plan.

[0078] Optimization termination conditions may include reaching the maximum number of iterations, the optimal objective improvement rate being lower than the termination threshold for several consecutive generations and the solution satisfying all hard constraints, or reaching the computation time limit. Several non-dominated or high-scoring feasible solutions from the hybrid optimization phase are output for redundancy removal to avoid retaining only one solution that is overly sensitive to weight settings.

[0079] Step S5: Remove redundant sensor mounting points and generate the installation sequence. For each activated point i in the current feasible scheme P, construct a scheme P after deleting that point. {i}, recalculate coverage, reliability, and cost. The marginal contribution is:

[0080] The first two terms represent the performance loss caused by deleting a point, and the third term represents the cost savings brought by deleting a point. The smaller mi is, the lower the net contribution of that point relative to its cost; when mi < 0, the cost savings outweigh the coverage and reliability losses according to the current weights. It should be noted that the marginal contribution is only used to determine the order in which deletion attempts are made; whether a point is actually deleted is still determined by the minimum effective coverage, minimum aggregate reliability, critical element coverage, redundant measurement requirements, and other hard constraints.

[0081] Sort all points according to mi in ascending order, and attempt to delete the first point. If all hard constraints are still satisfied after deletion, confirm the deletion and recalculate the marginal contribution of the remaining points based on the new scheme; if not, restore the point and mark it as non-deletable in the current round, then try the next point. The reason for recalculating after each deletion is that two sensors may cover the same area, and deleting one will significantly increase the marginal contribution of the other.

[0082] After redundancy reduction is terminated, a graph structure is formed based on installation channel 205, construction entrance, the reachability of installation equipment, and the movement costs between points. Nodes in the graph represent the final installation point and construction entrance, and edge weights represent the reachable path length or overall construction time. The installation sequence can be generated using nearest neighbor and local exchange, dynamic programming, or other path sorting methods. The installation sequence is a construction organization output for the final set of points and does not change the aforementioned coverage and reliability calculation results.

[0083] Validation Examples of Computation on the Same Dataset To verify the feasibility of the method, a comparison was conducted on the same computational dataset. This dataset constructed an industrial plant space with a length of 120 mm, a width of 48 mm, and a height of 18 mm, containing six types of equipment surfaces to be tested, beam and column structures, two main pipelines, three restricted areas, and two construction access routes. The test surfaces were triangulated into 1860 surface units, allowing the installation area to be divided into 64 numbered installation sub-regions. The initial installation point of each sub-region was taken as the geometric center of the region, allowing continuous adjustment of coordinates within the region, with the attitude azimuth and pitch angles varying within permissible ranges.

[0084] The preferred sensor measurement distance d0 is set to 12, the allowable measurement distances dmin and dmax are set to 3 and 24 respectively, the distance attenuation scale sd is set to 7, the upper limit of the allowable deviation angle θmax is set to 60°, and the deviation angle attenuation scale θ0 is set to 35°. The coverage threshold τj for ordinary surface elements is 0.55, and the reliability threshold ηj is 0.60; for critical surface elements, these are increased to 0.65 and 0.70 respectively. The sensor calibration quality coefficients are set to 0.92, 0.95, and 0.98 according to the three quality levels. The point activation threshold τs is set to 0.5.

[0085] Deployment constraints include: the bracket envelope must not enter the restricted area; the distance from the installation point to the outer surface of the obstacle must be no less than 0.25; the construction spacing between any two installation points must be no less than 1.20; the overall weighted effective coverage rate must be no less than 0.94; the weighted aggregate reliability must be no less than 0.76; all critical surface elements must be effectively covered; the number of installation points must not exceed 42; and the final location must be accessible through the construction access road. The statistical window W takes the most recent 200 evaluated schemes, the coupling penalty coefficient μ is set to 0.35, the dispersion threshold τD is set to 0.035, and the target improvement rate threshold τF is set to 0.001. Differential mutation is triggered after both thresholds are continuously satisfied for 5 generations.

[0086] To ensure consistent comparison conditions, the aforementioned geometric model, surface mesh, installation area, sensor parameters, hard constraints, and maximum number of evaluations were used. Comparison method A involved uniformly distributing points according to the allowable area and then filtering using fixed coordinates; method B used only particle swarm optimization without differential mutation; method C used multi-objective evolutionary optimization without constraint coupling terms; and method D was the method of this invention. Each method underwent 20 independent calculations. The coverage, reliability, number of points, number of violations, and normalization time in Table 1 are the average values ​​of the feasible optimal solutions obtained from the 20 calculations. These values ​​are used to illustrate the calculation verification process and do not represent actual field measurement results.

[0087] Validation results table on the same dataset

[0088] The calculation results show that, under this dataset and parameters, method D has an average weighted effective coverage of 0.960, an average weighted aggregation reliability of 0.800, an average number of mounting points of 32, and the final solution does not retain any constraint violations. Compared with method B, which only uses particle swarm optimization, method D improves both coverage and reliability, and reduces the number of mounting points; compared with method C, method D eliminates the final constraint violation with lower normalization time. These differences are derived from the calculation conditions of this embodiment and cannot be directly extrapolated to a fixed improvement for all application scenarios.

[0089] Further examination of the intermediate process of Method D revealed that the "obstacle avoidance constraint - maximum deviation angle constraint" and the "minimum installation spacing constraint - key element coverage constraint" in the constraint coupling matrix were positively coupled in the early stages of the search. After adding a joint violation penalty, the frequency of candidate solutions simultaneously violating the corresponding constraints decreased. The hybrid optimization output consisted of 35 points; after point-by-point verification in the marginal contribution reduction stage, 3 points were deleted, ultimately retaining 32. This process demonstrates that constraint coupling is used to guide the search, while marginal contribution is used for redundancy compression within the feasible solution; their functions are different.

[0090] In actual projects, the 3D model, installation area, and sensor parameters can be replaced with engineering data, and corrected using a small number of calibration records from already installed sensors. q i , d 0、 s d , i 0 and all threshold values. If field records are lacking, initial parameters can be established within the range allowed by the equipment manual, and then updated through trial assembly measurements. Calculated verification data should not be presented as field experimental data; if it is necessary to prove a specific effect during subsequent review of the application or project implementation, traceable and authentic test records can be supplemented.

[0091] The same dataset described above can be organized into a verifiable data file. The geometry table stores the object number, object category, triangular mesh vertices, facet normals, and obstacle boundaries item by item; the installation sub-region table stores the region number, associated component, boundary vertices, initial coordinates, upper and lower attitude limits, support envelope, and single-point cost; the sensor parameter table stores the model number, preferred distance, allowable distance, field of view, calibration quality coefficient, and measurement direction definition; the constraint table stores the constraint number, constraint type, threshold, whether it is a hard constraint, and the normalization benchmark for the violation. The candidate scheme evaluation results store the activation degree, coordinates, attitude, violation amount of each constraint, coverage, reliability, cost, and target value for each logical point slot. Each data table is associated with a unique number, allowing for the reproduction of the evaluation process for a particular candidate scheme. The final output file records, line by line, the installation sub-region, 3D coordinates, azimuth, elevation, sensor model, support model, expected cable length, installation sequence number, and the key facet number covered by that point; it also outputs uncovered facets, points close to the constraint threshold, and the optimized parameter version. After construction personnel adjust a coordinate or orientation, the system uses this manual modification as a locking condition to re-execute the overwrite and constraint verification. Only versions that pass the verification are marked as buildable. To prevent misuse of the coordinate system, the output file also records the coordinate system name, origin, axis, length unit, and orientation rotation sequence, and generates corresponding point markers in the 3D model.

[0092] Taking installation sub-region 17 as an example, it is located on the installable surface of the beam on the north side of the factory building. The local allowable movement range is 1.8 along the beam length and 0.35 along the beam width, with a bracket extension length of 0.22. The azimuth range is 70° facing the equipment area, and the pitch range is -25° to 15°. If the activation degree of this region in a candidate scheme is 0.68, the corresponding point is activated. If the coordinates exceed the beam surface by 0.06 after particle swarm optimization, they are projected back to the beam surface boundary. Subsequently, the shortest distance between the bracket envelope and adjacent pipelines is detected. Only after coordinate projection, envelope obstacle avoidance, and attitude truncation are completed is the visibility, coverage contribution, and reliability of each surface unit recalculated. This process shows that the coordinates in the optimization variables are always the actual sensor installation reference points, not virtual measurement points on the surface to be measured.

[0093] Parameter calibration can be performed using a set of reference measurement records with different distances and deviation angles. Start by determining the distance range with the smallest error. d 0, then determine the rate of descent of the measured mass as it deviates from the distance. s d The mass is determined based on the rate at which the measured mass decreases with the deviation angle. i 0 and i max For sensors of the same model, a uniform attenuation parameter can be used and... q iThis indicates individual calibration differences; for sensors with different operating principles, parameter groups should be set separately. Threshold t j and or j Multiple levels can be set for key areas, rather than selecting the threshold in reverse after obtaining the optimization results. After calibration, the parameter version number and calculation results should be saved together to ensure the traceability of the calculation data.

[0094] To check whether parameter changes cause instability in the scheme, the following steps can be taken on the same dataset: s d , i 0、 t j and or j Adjust the parameters near the baseline value and record the final number of points, critical element coverage, and target value. When small parameter changes lead to a large number of point replacements, the coordinate robustness margin within the installation sub-region can be increased, or a multi-condition evaluation can be added to the objective function. During multi-condition evaluation, calculations are performed separately for normal operation, partial occlusion operation, and individual sensor failure operation. C ( P ) and R ( P The optimization is performed using the weighted average or worst-case value for each operating condition. This optional method does not change the basic processing chain of installation sub-region numbering, coverage contribution normalization, constraint coupling statistics, and marginal reduction.

[0095] In an optional review, the selection frequency of points can be statistically analyzed across multiple runs with different random seeds. Points with high selection frequency and small coordinate fluctuations can be marked as stable points, while points with lower selection frequency are designated as candidate points. If on-site construction causes stable points to become ineffective, their activation state is fixed at 0, and optimization is restarted from the candidate points to avoid redesigning all points.

[0096] VII. Other Embodiments When a critical element is invisible to all installation sub-regions, the system outputs the reason for infeasibility and related occlusion objects, instead of forcibly providing a solution by infinitely increasing penalties. Engineers can add mounting brackets, adjust the allowed installation area, or change the sensor type and then re-optimize. The system should also report input constraint conflicts when two forced-enable points violate the minimum spacing.

[0097] For mobile or track-adjustable sensors, the installation sub-region can be defined as a track segment, and the coordinate variables degenerate into a single parameter along the track. For cases where sensors can only be installed at pre-drilled holes, the installation sub-region can be reduced to a single point or a set of discrete holes. Thus, this representation method can cover different engineering scenarios such as fixed hole selection, local continuous adjustment, and track position optimization.

[0098] The exponent kernel in the coverage contribution formula can be adjusted using calibration data, but visibility, distance deviation, and attitude deviation should all participate in coverage evaluation, and the coverage contribution should be normalized by area before being included in the cumulative coverage level. Measurement reliability can also incorporate normalized quality factors such as ambient temperature, vibration, electromagnetic interference, or communication packet loss rate. When adding quality factors, their value range and their relationship with reliability calculations should be clearly defined.

[0099] The constraint coupling matrix can be updated every generation or every few generations. A statistical window that is too short will cause fluctuations in coupling values, while a window that is too long will result in a slow response to changes during the search phase. A longer window can be used during the initialization phase, and then shortened in the later stages of the search, or an exponential decay can be applied to the four types of counts. Regardless of the window method used, all four types of complete states—common satisfaction, common violation, and two individual violations—are preserved to ensure consistency in the meaning of the matrix elements.

[0100] In the system embodiment, the spatial modeling and discretization module 701 receives the 3D model and layout data; the coverage and reliability calculation module 702 generates coverage contribution, reliability, and effective coverage results; the constraint coupling analysis module 703 generates the constraint coupling matrix and penalty terms; the hybrid optimization module 704 performs fixed-length coding, particle swarm iteration, stagnation judgment, differential mutation, and constraint repair; the redundancy reduction and output module 705 generates the final point locations and installation sequence; the data storage module 706 saves the mesh, installation sub-regions, parameters, and intermediate schemes; the human-computer interaction module 707 is used to input thresholds and display results; and the interface module 708 is used to output data to the construction management or digital twin platform.

[0101] The aforementioned system modules can be implemented in software or a combination of software and hardware. When the processor executes the program in memory, it sequentially or in parallel performs spatial index construction, ray intersection detection, matrix statistics, candidate scheme evaluation, and optimization updates. For larger meshes, visibility detection of mounting points and surface elements can be performed in parallel on the graphics processor, and obstacle spatial indices that do not change with pose can be cached.

[0102] Those skilled in the art can make equivalent substitutions for the surface discretization method, spatial index structure, particle swarm parameters, differential mutation strategy, path sorting algorithm, and system deployment method without departing from the core concept of this invention. Any equivalent technical solution that establishes a fixed-length point correspondence based on a uniquely numbered installation sub-region, incorporates coverage contribution into the effective coverage criterion, and combines constraint coupling penalty and hybrid optimization to obtain the sensor installation point scheme should fall within the protection scope of this invention.

[0103] 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 optimizing the layout of sensor mounting points under spatial constraints, characterized in that, Includes the following steps: S1. Obtain the three-dimensional geometric model of the space to be measured, the surface to be measured, the allowed installation area, the prohibited installation area, obstacles, sensor parameters and layout constraints. Discretize the surface to be measured into multiple surface units, divide the allowed installation area into multiple installation sub-regions with unique numbers, and determine the initial installation point, adjustable coordinate range and adjustable attitude range for each installation sub-region. S2, for the candidate deployment scheme consisting of sensor mounting points in the activated installation sub-region, perform visibility detection from the mounting points to each surface unit, combine visibility, distance between the mounting points and surface units and incident attitude, calculate coverage contribution and measurement reliability, and determine effective coverage status based on the cumulative coverage and aggregate reliability of each surface unit. S3, count the satisfaction status of multiple candidate layout schemes for each layout constraint, construct a constraint coupling matrix based on the occurrence of the common satisfaction, common violation and single violation of any two layout constraints, and form a constraint penalty term based on the constraint coupling matrix that simultaneously represents the single constraint violation and the common violation of coupled constraints. S4. A candidate deployment scheme is constructed using a fixed-length code consisting of the activation degree of each installation sub-region, the coordinates of the sensor installation point, and the installation attitude. The particle swarm optimization is performed with effective coverage, measurement reliability, deployment cost, and the constraint penalty term as the optimization objectives. When the population dispersion and the optimal objective improvement rate are both lower than their respective thresholds, differential mutation and crossover are performed on the candidate deployment schemes, and boundary projection and constraint repair are performed on the activation degree, coordinates, and installation attitude after mutation and crossover. S5 calculates the effective coverage loss, measurement reliability loss, and cost savings of each sensor installation point before and after deletion for the obtained candidate optimal deployment scheme. Based on this, the marginal contribution is determined and redundant sensor installation points with low marginal contribution are deleted in sequence. After each deletion, the effective coverage and deployment constraint verification is re-executed, and the coordinates, installation posture, and installation sequence of the sensor installation points that pass the verification are output.

2. The method according to claim 1, characterized in that, The surface unit is a triangular surface element obtained by triangulation of the surface to be measured. The j-th surface unit has at least a center point, area, unit normal vector and importance weight. The i-th installation sub-region has corresponding sensor installation point coordinates and a preset attitude range. The sensor installation point coordinates are located within the corresponding installation sub-region, and the installation attitude is located within the preset attitude range. The installation attitude corresponds to the sensor's measurement direction. The visibility detection includes emitting a detection line segment from the sensor installation point to the center point of the surface unit. When the detection line segment does not intersect the obstacle model before the center point and the incident attitude satisfies the sensor's field of view conditions, the corresponding visibility flag is set to 1; otherwise, it is set to 0.

3. The method according to claim 2, characterized in that, The coverage contribution of the i-th sensor mounting point to the j-th surface unit is based on the product of the area of ​​the j-th surface unit and the corresponding visibility marker, and is jointly corrected by the distance attenuation factor and the attitude attenuation factor. The distance attenuation factor decreases as the deviation of the distance from the sensor mounting point to the center point of the surface unit relative to the preferred measurement distance increases, and the attitude attenuation factor decreases as the deviation angle of the measurement direction relative to the unit normal vector of the surface unit increases.

4. The method according to claim 3, characterized in that, The measurement reliability of the i-th sensor mounting point to the j-th surface unit is obtained by multiplying the corresponding visibility identifier, sensor calibration quality coefficient, effective measurement condition identifier, distance reliability factor, and angle reliability factor. When the distance from the sensor mounting point to the center point of the surface unit is within the allowable measurement distance range, and the deviation angle of the measurement direction relative to the unit normal vector of the surface unit does not exceed the upper limit of the allowable deviation angle, the effective measurement condition identifier is set to 1; otherwise, it is set to 0. The distance reliability factor is determined based on the absolute deviation of the distance relative to the preferred measurement distance, and the angle reliability factor is determined based on the absolute value of the deviation angle. Both the distance reliability factor and the angle reliability factor are limited to the range of 0 to 1.

5. The method according to claim 4, characterized in that, The coverage contribution of each sensor mounting point is normalized according to the area of ​​the corresponding surface unit. The normalized coverage contribution of each sensor mounting point in the activated mounting sub-region to the j-th surface unit is accumulated and limited to the range of 0 to 1 to obtain the cumulative coverage of the j-th surface unit. Using the normalized coverage contribution as a weight, the measurement reliability of the corresponding sensor installation points is aggregated to obtain the aggregated reliability of the j-th surface unit; when the cumulative coverage is not lower than the corresponding coverage threshold and the aggregated reliability is not lower than the corresponding reliability threshold, the j-th surface unit is determined as effective coverage; based on the importance weight and area of ​​each surface unit, the effective coverage status of each surface unit is weighted to obtain the weighted effective coverage rate of the candidate deployment scheme.

6. The method according to claim 5, characterized in that, For any two constraints, the number of times they are both satisfied, both are violated, and both are violated individually are counted within a preset statistical window. The normalized difference between the sum of the number of times they are both satisfied and the number of times they are both violated, and the sum of the number of times they are violated individually, is used as the corresponding element in the constraint coupling matrix. Based on the candidate deployment scheme, a single constraint penalty is formed for the normalized violation amount of each deployment constraint, and a joint violation penalty is formed for the constraint coupling matrix that has a positive value and is jointly violated in the candidate deployment scheme. The single constraint penalty and the joint violation penalty together constitute the constraint penalty term.

7. The method according to claim 6, characterized in that, Each candidate deployment scheme is assigned a unique number to the installation sub-region, and the activation level, sensor installation point coordinates, and installation attitude of each installation sub-region are encoded in the same order. When the activation level of an installation sub-region reaches a preset activation threshold, the installation sub-region is identified as an activated installation sub-region; otherwise, it is identified as an inactive installation sub-region. The optimization objective is to improve the weighted effective coverage and weighted aggregation reliability of the candidate deployment schemes, and to reduce the normalized deployment cost and the constraint penalty term.

8. The method according to claim 7, characterized in that In each iteration, the discreteness of sensor installation point coordinates in candidate deployment schemes activating the same installation sub-region is calculated according to the unique number of the installation sub-region, and normalized using the characteristic length of the corresponding installation sub-region to obtain the population discreteness. The optimal target improvement rate is determined based on the relative change of the optimal target value between the current iteration and the previous iteration. When the population discreteness is lower than a preset discreteness threshold and the optimal target improvement rate is lower than a preset improvement rate threshold, the differential mutation and crossover are triggered.

9. The method according to claim 8, characterized in that, The differential mutation and crossover simultaneously affect activation, sensor mounting point coordinates, and mounting attitude. After crossover, the activation is limited to the range of 0 to 1. The sensor mounting point coordinates are projected onto the corresponding mounting sub-region, and the mounting attitude is projected onto the corresponding attitude range. Intrusion into restricted areas, obstacle collisions, and violations of minimum mounting spacing are repaired. The marginal contribution of a sensor mounting point is determined based on the weighted results of the weighted effective coverage loss, weighted aggregate reliability loss, and normalized deployment cost savings before and after deleting a sensor mounting point. Sensor mounting points are attempted to be deleted in ascending order of marginal contribution. The deletion operation is retained only if the minimum effective coverage, minimum aggregate reliability, and all hard constraints are still met after deletion. The installation order is generated based on the reachability distance between adjacent mounting points.

10. A spatially constrained sensor mounting point optimization layout system, characterized in that, include: The spatial modeling and discretization module is used to acquire the three-dimensional geometric model and layout data of the space to be measured, discretize the surface to be measured into multiple surface units, divide the allowable installation area into multiple installation sub-regions with unique numbers, and determine the initial installation point, adjustable coordinate range and adjustable attitude range for each installation sub-region. The coverage and reliability calculation module is used to perform visibility detection from the sensor mounting point to the surface unit, and calculate coverage contribution, measurement reliability, cumulative coverage, aggregate reliability, and effective coverage status. The constraint coupling analysis module is used to statistically analyze the satisfaction status of candidate layout schemes with various layout constraints, construct the constraint coupling matrix, and generate constraint penalty terms. The hybrid optimization module is used to perform particle swarm iteration using a fixed-length code that includes activation degree, sensor mounting point coordinates and mounting attitude, and to perform differential mutation and crossover when the population dispersion and the optimal target improvement rate are both below their respective thresholds, as well as to perform boundary projection and constraint repair. The redundancy reduction and output module is used to calculate the marginal contribution of sensor installation points, attempt to delete sensor installation points with low marginal contribution in turn, re-verify effective coverage and layout constraints, and output the coordinates, installation posture and installation sequence of sensor installation points. Each module is configured to perform the method of claim 1.

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