Estimation method of plume boundary expansion rate in deep-sea polymetallic nodule mining area combined with vortex structure evolution

Abstract

The present application relates to the technical field of environmental monitoring, and more particularly to a method for estimating the boundary expansion rate of a plume in a deep-sea polymetallic nodule mining area combined with vortex structure evolution, comprising the following steps: S1, collecting perturbation flow field data and seabed topographic atlas, constructing a structure intermittent marker area and identifying a topographic trigger point based on the perturbation intensity change rate and its spatial adjacency relationship with the topographic protrusions; S2, tracking the vortex evolution stage and interference characteristics in the marker area, extracting boundary jump key factors and generating a jump event set; S3, mapping the jump events to the boundary trajectory, generating a non-continuous expansion rate map combined with the topographic trigger weight, and outputting a non-linear advancing trend. The present application realizes accurate modeling and dynamic estimation of the non-linear advancing trend of the plume boundary by constructing a perturbation-topographic coupling marker area, extracting vortex structure evolution information and boundary jump events, and generating a non-continuous expansion rate distribution map combined with the topographic trigger weight.

Description

Technical Field

[0001] This invention relates to the field of environmental monitoring technology, and in particular to a method for estimating the boundary expansion rate of plumes in deep-sea polymetallic nodule mining areas by incorporating vortex structure evolution. Background Technology

[0002] In the development of deep-sea polymetallic nodule resources, the plume phenomenon caused by the interaction between mechanical disturbance and topographic boundary has a significant impact on the diffusion of environmental disturbance and sediment redistribution in the mining area. The advancing behavior of the plume boundary not only affects the disturbance control strategy in the mining area, but also directly relates to the accuracy of ecological impact assessment and environmental restoration planning. Therefore, constructing an expansion rate estimation method for the dynamic evolution of the plume boundary has become an important technical issue in the field of deep-sea resource and environmental research.

[0003] Existing technologies mostly use simplified velocity profiles or fixed disturbance boundary models to simulate the expansion process of plumes. This makes it difficult to reveal the intrinsic mechanism of the nonlinear transition process at the boundary under the combined effects of vortex interference and micro-topography. Furthermore, the identification of boundary abrupt behavior relies on empirical rules and lacks structured modeling and quantitative analysis of the driving factors of disturbance evolution. This results in poor stability and insufficient spatial resolution of the velocity estimation results, which cannot meet the needs of plume prediction and control in complex deep-sea environments. Summary of the Invention

[0004] This invention provides a method for estimating the boundary expansion rate of plumes in deep-sea polymetallic nodule mining areas by combining vortex structure evolution. By constructing intermittent structural marker zones to identify key topographic trigger points, extracting vortex coupling factors within the disturbance cycle and generating a boundary jump event set, and further combining jump behavior with topographic distribution weights to construct a discontinuous expansion rate map, a precise characterization of the boundary advancement trend can be achieved, providing effective support for environmental disturbance evolution modeling and dynamic management in deep-sea polymetallic nodule mining areas.

[0005] A method for estimating the boundary expansion rate of plumes in deep-sea polymetallic nodule mining areas, incorporating vortex structure evolution, includes the following steps:

[0006] S1. Collect real-time disturbance flow field data and seabed micro-topographic structure map of the plume formation area. Based on the condition that the change amplitude of disturbance intensity exceeds the threshold of disturbance intensity change rate and that its change center is spatially adjacent to the topographic protrusion area, construct a structural intermittent marker area for judging the intermittent evolution behavior of the boundary and identify the topographic trigger point that causes the plume boundary to turn back or change abruptly.

[0007] S2, based on the intermittently marked region of the structure, track the evolution stage of the vortex structure and its local overlapping interference characteristics during the disturbance, extract the vortex coupling factor sequence that induces boundary jump behavior within the disturbance period when the change in disturbance intensity exceeds the disturbance period identification threshold, and construct a boundary jump event set including the expansion mutation time, jump direction and amplitude.

[0008] S3, map the boundary jump event set to the evolution trajectory of the feather flow boundary, and combine the distribution weight of the terrain trigger points to generate a local discontinuous expansion rate distribution map, which is used to dynamically depict the nonlinear propagation trend of the feather flow boundary under the action of vortex interference, and output it as the rate estimation result.

[0009] Optionally, S1 includes:

[0010] S11, collect real-time disturbance flow field data and seabed micro-topographic structure map of the plume formation area. The disturbance flow field data includes local velocity vectors, disturbance energy density and direction offset information at multiple time scales. The micro-topographic structure map is constructed based on multibeam bathymetry or side-scan sonar data and includes topographic slope, concave-convex distribution and protrusion volume characteristics. By continuously calculating the change amplitude of disturbance intensity in the disturbance flow field per unit time and setting a threshold for the rate of change of disturbance intensity, it is used to identify the central region of the flow field with violent disturbance fluctuations.

[0011] S12, spatially match the identified flow field center region with the micro-topographic structure map, extract the coupling unit that meets the disturbance triggering condition based on its adjacency relationship with the topographic protrusion region in three-dimensional space, and delineate the coupling unit as the structural intermittent marker area. Within the structural intermittent marker area, identify the topographic unit with local slope abrupt change, closed shape or structural spiral as potential topographic trigger points.

[0012] Optionally, S11 includes:

[0013] S111, deploying an underwater Doppler acoustic velocimeter (ADCP), a seabed vortex detection buoy, and a vortex profiler in the deep-sea polymetallic nodule mining area to collect disturbance velocity vector data in the plume formation region, with a sampling period set to [missing information]. The collected data includes each observation point at different timestamps. The local three-dimensional velocity vector V is shown below.

[0014] S112, using three-dimensional velocity vectors to calculate the perturbation kinetic energy density and instantaneous offset angle, forming the perturbation characteristic tensor;

[0015] S113 uses a multibeam echo sounder (MBES) and side-scan sonar to acquire seabed topographic data, and combines it with a three-dimensional inversion algorithm to construct a seabed micro-topographic structure map, including topographic slope, curvature field, and topographic uplift volume;

[0016] S114, by performing unit-time difference on the disturbance kinetic energy density at consecutive sampling times, calculates the rate of change of disturbance intensity. ;

[0017] S115, Set the threshold for the rate of change of disturbance intensity. , will satisfy The point is identified as the central region of the flow field with violent fluctuations.

[0018] Optionally, S113 includes:

[0019] S1131, using a multibeam echo sounder (MBES) to acquire water depth point cloud data. Simultaneously, it combines side-scan sonar equipment to obtain images of seabed reflectivity. To enhance the ability to distinguish uneven textures, and to represent them in spatial coordinate rasterization, an initial terrain elevation raster is formed;

[0020] S1132, calculates the terrain slope of each cell based on the neighborhood difference in the regular grid. ;

[0021] S1133 uses the second derivative approximation to calculate the curvature field. This reflects the local tendency of depression or bulge;

[0022] S1134, extracting continuously satisfied parameters from the curvature field. Connected regions serve as topographic protrusion structural units ,in, The curvature threshold of the protruding structure is used, and the volume of the terrain protrusion is estimated based on grid summation. .

[0023] Optionally, S12 includes:

[0024] S121, the set of all grid points whose disturbance intensity change rate exceeds the disturbance intensity change rate threshold is denoted as the set of the central region of the flow field with violent disturbance fluctuations. ;

[0025] S122, satisfying the curvature field All grid combinations form a set of protruding structures. ;

[0026] S123, Calculate the three-dimensional Euclidean distance between each disturbance point and each protrusion point. If satisfied Then it is believed and A spatial adjacency relationship exists, denoted as a disturbance-terrain coupled unit. ,in, This is the spatial adjacency threshold. Let i be the spatial center point of the i-th region of intense disturbance. Let j be the center point of the j-th topographic protrusion. This is the set of all perturbation-terrain coupling units that satisfy the spatial adjacency condition;

[0027] S124, the coupling point pairs that satisfy the spatial coupling condition. Corresponding terrain area Expanded into a set of structural intermittent marked regions ;

[0028] S125, for each structural intermittently marked region Extract grid points that satisfy the characteristics of abrupt slope changes, closed shapes, or spiral structures to construct potential terrain trigger points. .

[0029] Optionally, S2 includes:

[0030] S21, within the intermittently marked area of ​​the structure, based on the time series data of the perturbation flow field, the formation, evolution and disappearance process of the vortex structure are tracked, and the core position, rotation direction and stability index of the vortex at each moment are extracted. By analyzing the spatial overlap and rotation direction difference of adjacent vortices in continuous time periods, their evolution stages (generation, turning, merging, decay) and interference types (attraction, displacement, enhancement) are marked, forming vortex structure evolution information to describe the characteristics of perturbation evolution;

[0031] S22, based on vortex structure evolution information, identifies effective disturbance cycles in which the rate of change of disturbance intensity exceeds the disturbance cycle identification threshold within a continuous time period. It then extracts key factor sequences that cause spatial jumps at the feather boundary within the effective disturbance cycle as vortex coupling factor sequences. Each set of factors includes the vortex intensity, core position change, interference mode type, and disturbance direction deflection characteristics of the corresponding region at the time of action. Combined with the change trajectory of the boundary position before and after the jump, it records the occurrence time, spatial jump direction, and abrupt change amplitude of the jump behavior, and constructs a boundary jump event set.

[0032] Optionally, S21 includes:

[0033] S211, Acquire a continuous-time series of three-dimensional perturbation velocity fields in the intermittently marked region of the structure. It is discretized into a two-dimensional profile tensor sequence for vortex identification;

[0034] S212 uses a two-dimensional curl formula to identify vortex regions in the flow field of each frame. The rotation direction is determined by calculating the curl value, where a positive curl value indicates counterclockwise rotation and a negative curl value indicates clockwise rotation. The absolute value of the curl is also extracted. Exceeding the set threshold The region serves as the local vortex core;

[0035] S213 involves spatial registration of the vortex core region in consecutive frames to form the vortex trajectory and defining stability indices. ;

[0036] S214, in any two consecutively existing vortices , Between them, calculate their spatial overlap and rotation direction differences;

[0037] S215, based on the formation-destruction process of each vortex, labels its stages as generation, enhancement, reversal, merging, or decay, combined with the relationships between adjacent vortices. and The type of interference is determined, including attractive interference, offset interference, and enhancement interference, ultimately forming a set of information on the evolution of the vortex structure. .

[0038] Optionally, S215 includes:

[0039] S2151, based on the tracked trajectory of the r-th vortex core. Statistics on its life cycle And calculate the average curl variation trend of the vortex in consecutive frames. Used to determine evolutionary stages, specifically including:

[0040] like Marked as enhanced;

[0041] like Marked as attenuation;

[0042] If the displacement amplitude of the vortex core is greater than the spatial threshold Marked as a turn;

[0043] If it is the start or end frame of the lifecycle, mark it as generated or destroyed, respectively.

[0044] in, Let be the timestamp of the end frame of the r-th vortex. Let r be the timestamp of the starting frame of the r-th vortex. Let be the average curl of the r-th vortex at time t. To identify the threshold for the curl enhancement stage, Identify thresholds for the curl decay phase;

[0045] S2152, combined with spatial overlap rate Relationship with rotation direction Determining the type of interference specifically includes:

[0046] when and This indicates attractive interference;

[0047] when and This indicates offset interference;

[0048] when and , indicating enhanced interference;

[0049] in, , , This is an empirical threshold;

[0050] S2153, the trajectory of each vortex ,life cycle Stage tags And its interference type with adjacent vortices in the same frame. Unified encapsulation to form structured evolutionary record units Ultimately, a global vortex structure evolution information set is obtained. .

[0051] Optionally, S22 includes:

[0052] S221, Calculate the rate of change of disturbance intensity in a continuous time series. ,like Within a continuous window of at least the minimum disturbance duration The disturbance period consistently exceeds the threshold for identification within a time period of 5 sampling steps. Then this time period is considered an effective disturbance period. ;

[0053] S222, for each effective disturbance period Combining information on vortex structure evolution Extract the rate of change of boundary position Exceeding the preset rate of change threshold The time points are used as critical moments when the boundary undergoes a sudden leap, and key factors are recorded to form a sequence of vortex coupling factors. ;

[0054] S223, in the vortex coupling factor sequence In the process of changing the boundary trajectory of the plume, identify the abrupt boundary jump points and record the boundary jump event set. ,in, Let j be the time point in time when the jump event occurs. The spatial direction vector for the boundary jump. The magnitude of the boundary jump.

[0055] Optionally, S3 includes:

[0056] S31, Based on Boundary Jump Event Set Each jump event is located on the time axis at the boundary trajectory of the feather flow. Corresponding time in the middle And based on the jump direction vector With jump amplitude For boundary points Calculate the updated boundary position ;

[0057] S32, Calculate each boundary jump event point based on the set of terrain trigger points extracted within the marked area. Terrain trigger point Distance between ,like Then the topographic point is identified. For boundary points There is a triggering effect; set the trigger weight for this point. The sum of the weighted contributions of all trigger points that meet the conditions to the jump event is: ,in, The threshold for terrain-triggered action distance;

[0058] S33, based on the timing, amplitude, and trigger weight of all jump events. Constructing a locally discontinuous expansion rate field The boundary advance rate affected by all jump events per unit time is statistically calculated using spatial grids.

[0059] The beneficial effects of this invention are:

[0060] This invention collects high-precision data on disturbed flow fields and seabed micro-topography structures in the plume formation region, and introduces dual criteria of disturbance intensity change rate and topographic spatial adjacency to construct intermittent structural marker areas. This effectively identifies local disturbance-topography coupling units closely related to boundary abrupt change behavior. Compared with traditional methods that rely solely on flow field abrupt change or boundary trajectory analysis, this approach achieves coupled identification of disturbance sources and topographic factors, enhances the explanatory power of the intermittent propagation mechanism of plume boundaries, and improves the ability to accurately locate disturbance trigger points.

[0061] This invention constructs a vortex structure evolution information set, systematically tracks the vortex's life cycle, rotation direction, stability index, and interference mode, and combines a dynamic event detection mechanism that detects events where the rate of change of disturbance intensity exceeds the period threshold. It extracts key vortex coupling factors that induce boundary jumps and records the jump time, jump direction, and amplitude to form a boundary jump event set. This mechanism achieves accurate spatiotemporal mapping of boundary behavior under disturbance period, overcomes the limitation of existing models in capturing discontinuous expansion behavior, and effectively models the dynamic mechanism of boundary nonlinear response.

[0062] This invention maps the boundary jump event set to the evolution trajectory of the plume boundary, combines the distribution weights of terrain trigger points to construct a local discontinuous expansion rate field, and introduces multi-factor weights such as jump amplitude, trigger intensity, and event density to generate a rate distribution map. This enables a dynamic characterization of the nonlinear propagation trend of the plume boundary under the action of vortex interference and terrain coupling, and can reflect the driving mechanism and influence range of abrupt expansion in local areas. Compared with traditional continuous modeling methods, it has greater responsiveness and physical interpretability, and significantly improves the estimation accuracy and risk warning capability of boundary propagation behavior. Attached Figure Description

[0063] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only for this invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0064] Figure 1 This is a schematic diagram of the estimation method according to an embodiment of the present invention;

[0065] Figure 2 This is a schematic diagram illustrating the spatial matching relationship between the area of ​​severe disturbance and the micro-topographic structure in an embodiment of the present invention. Detailed Implementation

[0066] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. Those skilled in the art may employ other alternative methods to implement some well-known technologies; moreover, the accompanying drawings are only for more specific description of the embodiments and are not intended to specifically limit the present invention.

[0067] like Figures 1-2 As shown, the method for estimating the boundary expansion rate of plumes in deep-sea polymetallic nodule mining areas, which incorporates vortex structure evolution, includes the following steps:

[0068] S1. Collect real-time disturbance flow field data and seabed micro-topographic structure map of the plume formation area. Based on the condition that the change amplitude of disturbance intensity exceeds the threshold of disturbance intensity change rate and that its change center is spatially adjacent to the topographic protrusion area, construct a structural intermittent marker area for judging the intermittent evolution behavior of the boundary and identify the topographic trigger point that causes the plume boundary to turn back or change abruptly.

[0069] S2, based on the structural intermittent marker region, tracks the evolution stage of the vortex structure and its local overlapping interference characteristics during the disturbance, extracts the vortex coupling factor sequence that induces boundary jump behavior within the disturbance period when the change in disturbance intensity exceeds the disturbance period identification threshold, and constructs a boundary jump event set including the expansion mutation time, jump direction and amplitude.

[0070] S3 maps the boundary jump event set to the evolution trajectory of the feather flow boundary and combines the distribution weight of the terrain trigger points to generate a local discontinuous expansion rate distribution map, which is used to dynamically characterize the nonlinear propagation trend of the feather flow boundary under the action of vortex interference and outputs the rate estimation result.

[0071] S1 includes:

[0072] S11: Collect real-time disturbance flow field data and seabed micro-topographic structure map of the plume formation area. The disturbance flow field data includes local velocity vectors, disturbance energy density and direction offset information at multiple time scales. The micro-topographic structure map is constructed based on multibeam bathymetry or side-scan sonar data, including topographic slope, concave-convex distribution and protrusion volume characteristics. By continuously calculating the change amplitude of disturbance intensity in the disturbance flow field per unit time and setting a threshold for the rate of change of disturbance intensity, it is used to identify the central region of the flow field with violent disturbance fluctuations.

[0073] S12, spatially match the identified flow field center region with the micro-topographic structure map, extract the coupling unit that meets the disturbance triggering condition based on its adjacency relationship with the topographic protrusion region in three-dimensional space, and delineate the coupling unit as the structural intermittent marker area. Within the structural intermittent marker area, identify the topographic unit with local slope abrupt change, closed shape or structural spiral as potential topographic trigger points.

[0074] S11 includes:

[0075] S111, deploying an underwater Doppler acoustic velocimeter (ADCP), a seabed vortex detection buoy, and a vortex profiler in the deep-sea polymetallic nodule mining area to collect disturbance velocity vector data in the plume formation region, with a sampling period set to [missing information]. To meet the requirements for responding to rapid disturbance events, the collected data includes each observation point at different timestamps. The local three-dimensional velocity vector V is expressed as:

[0076] ;

[0077] Where u, v, and w are the velocity components in the horizontal and vertical directions, respectively. The spatial coordinates of the observation point;

[0078] S112, using the three-dimensional velocity vector, calculates the disturbance kinetic energy density and instantaneous offset angle, forming the disturbance characteristic tensor, expressed as:

[0079] ;

[0080] ;

[0081] in, Let K be the local perturbation kinetic energy density at time k. The density of seawater, The angle between the direction of the flow velocity at the current moment and the direction at the previous moment;

[0082] S113 uses a multibeam echo sounder (MBES) and side-scan sonar to acquire seabed topographic data, and combines it with a three-dimensional inversion algorithm to construct a seabed micro-topographic structure map, including topographic slope, curvature field, and topographic uplift volume;

[0083] S114, by performing unit-time difference on the disturbance kinetic energy density at consecutive sampling times, calculates the rate of change of disturbance intensity. , represented as:

[0084] ;

[0085] in, , These are the disturbance kinetic energy densities at the current and previous moments, respectively. The sampling time interval;

[0086] S115, Set the threshold for the rate of change of disturbance intensity. , will satisfy The points were identified as the central region of the flow field with violent fluctuations.

[0087] Disturbance intensity change rate threshold The statistical method based on sliding time windows is defined as follows:

[0088] ;

[0089] in, This represents the average rate of change of disturbance intensity within the sliding window. The standard deviation of the rate of change of disturbance intensity within the sliding window. This is the outlier amplification factor.

[0090] S113 includes:

[0091] S1131, using a multibeam echo sounder (MBES) to acquire water depth point cloud data. Simultaneously, it combines side-scan sonar equipment to obtain images of seabed reflectivity. To enhance the ability to distinguish uneven textures, and to represent them using spatial coordinate rasterization, an initial terrain elevation raster is constructed, represented as follows:

[0092] ;

[0093] in, Let m and n be the terrain elevation values ​​of the grid cells. For two-dimensional geographic coordinate grid points The seabed elevation value collected by a multibeam echo sounder at that location;

[0094] S1132, calculates the terrain slope of each cell based on the neighborhood difference in the regular grid. , represented as:

[0095] ;

[0096] in, , , , These are respectively related to the current grid. The topographic elevation values ​​in the four adjacent directions (east, west, south, and north). , These represent the spatial distances between adjacent grid cells in the horizontal and vertical directions, respectively.

[0097] S1133 uses the second derivative approximation to calculate the curvature field. This reflects a localized depression or bulge trend, and is represented as:

[0098] ;

[0099] in, For curvature field, positive values ​​represent convex regions, negative values ​​represent concave regions, and the larger the absolute value, the more severe the local undulations.

[0100] S1134, extracting continuously satisfied parameters from the curvature field. Connected regions serve as topographic protrusion structural units ,in, The curvature threshold of the protruding structure is used, and the volume of the terrain protrusion is estimated based on grid summation. , represented as:

[0101] ;

[0102] in, Let q be the volume of the q-th terrain protrusion. The reference elevation for the bottom of the protrusion is (the minimum elevation at the edge of the area).

[0103] Curvature threshold of protrusion structure Represented as:

[0104] ;

[0105] in, This represents the average curvature field within the current sliding region. The standard deviation of curvature within the current sliding region. This is the curvature significance amplification factor.

[0106] S12 includes:

[0107] S121, the set of all grid points whose disturbance intensity change rate exceeds the disturbance intensity change rate threshold is denoted as the set of the central region of the flow field with violent disturbance fluctuations. The three-dimensional coordinates of each point are ,in, Let i be the three-dimensional coordinates of the i-th disturbance point. The depth of the disturbance center in the seawater layer;

[0108] S122, satisfying the curvature field All grid combinations form a set of protruding structures. Its three-dimensional coordinates are ,in, For the corresponding terrain elevation;

[0109] S123, Calculate the three-dimensional Euclidean distance between each disturbance point and each protrusion point. If satisfied Then it is believed and A spatial adjacency relationship exists, denoted as a disturbance-terrain coupled unit. ,in, This is the spatial adjacency threshold. Let i be the spatial center point of the i-th region of intense disturbance. Let j be the center point of the j-th topographic protrusion. The set of all perturbation-terrain coupling units that satisfy the spatial adjacency condition is represented as:

[0110] ;

[0111] in, , Let x and y be the coordinates of the spatial center point of the i-th severely disturbed region in the x and y directions, respectively. Let be the spatial center point of the i-th severely disturbed region in the vertical direction. , These are the coordinates of the center point of the j-th terrain protrusion in the x and y directions, respectively.

[0112] ;

[0113] in, The attenuation radius is affected by the disturbance. The response range for terrain protrusions. As the dominant weighting factor for disturbances, Terrain is the dominant weighting factor;

[0114] S124, the coupling point pairs that satisfy the spatial coupling condition. Corresponding terrain area Expanded into a set of structural intermittent marked regions The region boundary is obtained by expanding a 3×3 or 5×5 grid around the protrusion point;

[0115] S125, for each structural intermittently marked region Extract grid points that satisfy the characteristics of abrupt slope changes, closed shapes, or spiral structures to construct potential terrain trigger points. ,in;

[0116] Grid points with abrupt slope changes satisfy This is the slope value. , These represent the mean and standard deviation of the slope within the marked area, respectively. This is the threshold coefficient;

[0117] A closed grid point is considered a local depression when the elevations of its eight neighboring areas are all higher than that point.

[0118] The grid point of the structure's rotation is the curvature of the region where that point is located. , For threshold coefficient, This represents the mean curvature within the region.

[0119] S2 includes:

[0120] S21, within the intermittently marked area of ​​the structure, based on the time series data of the perturbation flow field, the formation, evolution and disappearance process of the vortex structure are tracked, and the core position, rotation direction and stability index of the vortex at each moment are extracted. By analyzing the spatial overlap and rotation direction difference of adjacent vortices in continuous time periods, their evolution stages (generation, turning, merging, decay) and interference types (attraction, displacement, enhancement) are marked, forming vortex structure evolution information to describe the characteristics of perturbation evolution;

[0121] S22, based on vortex structure evolution information, identifies effective disturbance cycles in which the rate of change of disturbance intensity exceeds the disturbance cycle identification threshold within a continuous time period. It then extracts key factor sequences that cause spatial jumps at the feather boundary within the effective disturbance cycle as vortex coupling factor sequences. Each set of factors includes the vortex intensity, core position change, interference mode type, and disturbance direction deflection characteristics of the corresponding region at the time of action. Combined with the change trajectory of the boundary position before and after the jump, it records the occurrence time, spatial jump direction, and abrupt change amplitude of the jump behavior, and constructs a boundary jump event set.

[0122] S21 includes:

[0123] S211, Acquire a continuous-time series of three-dimensional perturbation velocity fields in the intermittently marked region of the structure. It is discretized into a two-dimensional profile tensor sequence for vortex identification, represented as:

[0124] ;

[0125] in, Let be the two-dimensional horizontal flow field tensor at time l. , For grid points At any moment The horizontal flow velocity component, where L is the total number of sampling frames. This is the timestamp of the l-th frame;

[0126] S212 uses a two-dimensional curl formula to identify vortex regions in the flow field of each frame. The rotation direction is determined by calculating the curl value, where a positive curl value indicates counterclockwise rotation and a negative curl value indicates clockwise rotation. The absolute value of the curl is also extracted. Exceeding the set threshold The region, taken as the local vortex core, is represented as:

[0127] ;

[0128] in, The midpoint of frame l The curl value;

[0129] ;

[0130] in, This represents the mean curl of all grid points in the current perturbed flow field. The standard deviation of the current curl distribution. This is the threshold adjustment coefficient;

[0131] S213 involves spatial registration of the vortex core region in consecutive frames to form the vortex trajectory and defining stability indices. , represented as:

[0132] ;

[0133] ;

[0134] in, Let r be the trajectory of the center position of the r-th vortex. , These are the start and end frames for the continuation of the vortex. is the average curl of the r-th vortex core region within the l-th frame;

[0135] S214, in any two consecutively existing vortices , Between them, calculate their spatial overlap and rotation direction difference, expressed as:

[0136] ;

[0137] ;

[0138] in, , This refers to the spatial region of the two vortices in the l-th frame. The overlap rate, -1 indicates rotation in the same direction, and -1 indicates rotation in the opposite direction.

[0139] S215, based on the formation-destruction process of each vortex, labels its stages as generation, enhancement, reversal, merging, or decay, combined with the relationships between adjacent vortices. and The type of interference is determined, including attractive interference, offset interference, and enhancement interference, ultimately forming a set of information on the evolution of the vortex structure. .

[0140] S215 includes:

[0141] S2151, based on the tracked trajectory of the r-th vortex core. Statistics on its life cycle And calculate the average curl variation trend of the vortex in consecutive frames. Used to determine evolutionary stages, specifically including:

[0142] like Marked as enhanced;

[0143] like Marked as attenuation;

[0144] If the displacement amplitude of the vortex core is greater than the spatial threshold Marked as a turn;

[0145] If it is the start or end frame of the lifecycle, mark it as generated or destroyed, respectively.

[0146] in, Let be the timestamp of the end frame of the r-th vortex. Let r be the timestamp of the starting frame of the r-th vortex. Let be the average curl of the r-th vortex at time t. To identify the threshold for the curl enhancement stage, Identify thresholds for the curl decay phase;

[0147] ;

[0148] ;

[0149] in, The mean rate of change of curl. The standard deviation of the rate of change of curl. , This is a threshold adjustment factor;

[0150] ;

[0151] in, For displacement sensitivity coefficient, The average vortex radius for the region;

[0152] S2152, combined with spatial overlap rate Relationship with rotation direction Determining the type of interference specifically includes:

[0153] when and This indicates attractive interference;

[0154] when and This indicates offset interference;

[0155] when and , indicating enhanced interference;

[0156] in, =0.6、 =0.2、 =0.4 is the empirical threshold;

[0157] S2153, the trajectory of each vortex ,life cycle Stage tags And its interference type with adjacent vortices in the same frame. Unified encapsulation to form structured evolutionary record units Ultimately, a global vortex structure evolution information set is obtained. .

[0158] S22 includes:

[0159] S221, Calculate the rate of change of disturbance intensity in a continuous time series. ,like Within a continuous window of at least the minimum disturbance duration The disturbance period consistently exceeds the threshold for identification within a time period of 5 sampling steps. Then this time period is considered an effective disturbance period. , represented as:

[0160] ;

[0161] in, This is the original perturbation time series;

[0162] ;

[0163] ;

[0164] ;

[0165] in, Let t be time. The sampling time interval for disturbance intensity. This is the average curl value (normalized) of all identified vortices in the current frame. This represents the number of local vortex cores in the current frame (after normalization). This represents the perturbation energy density or kinetic energy fluctuation intensity (after normalization). , , These are the normalized weighting coefficients. To set a time window The mean of the rate of change of disturbance intensity within, Let be the standard deviation of the rate of change of disturbance intensity within the time window. To adjust the parameters;

[0166] S222, for each effective disturbance period Combining information on vortex structure evolution Extract the rate of change of boundary position Exceeding the preset rate of change threshold The time points are used as critical moments when the boundary undergoes a sudden leap, and key factors are recorded to form a sequence of vortex coupling factors. ;

[0167] The key factor is in quadruple form, represented as:

[0168] ;

[0169] in, Let be the vortex intensity in the i-th frame during the k-th disturbance period. This represents the magnitude of the spatial position change of the vortex core between adjacent frames. The perturbation direction is the deflection angle of the main direction within this frame;

[0170] ;

[0171] ;

[0172] ;

[0173] in, , They are time points , The boundary location index value, where N is the number of boundary points. , For the i-th boundary point at time... coordinates , For the set of boundary points at time... The geometric centroid, The mean of the boundary rate of change, The standard deviation of the boundary rate of change This is the adjustment coefficient;

[0174] ;

[0175] in, Let be the area of ​​the vortex region identified in the i-th frame. Let be the velocity vector of the perturbation flow field in the i-th frame. This represents the two-dimensional curl of the velocity field in that frame.

[0176] ;

[0177] in, This represents the location of the vortex core identified in the i-th frame;

[0178] ;

[0179] in, , These are the unit vectors of the main perturbation direction in the i-th frame and the (i-1)-th frame, respectively;

[0180] S223, in the vortex coupling factor sequence In the process of changing the boundary trajectory of the plume, identify the abrupt boundary jump points and record the boundary jump event set. ,in, Let j be the time point in time when the jump event occurs. The spatial direction vector for the boundary jump. The magnitude of the boundary jump;

[0181] ;

[0182] ;

[0183] in, , They are time points , The boundary position index value.

[0184] S3 includes:

[0185] S31, Based on Boundary Jump Event Set Each jump event is located on the time axis at the boundary trajectory of the feather flow. Corresponding time in the middle And based on the jump direction vector With jump amplitude For boundary points Calculate the updated boundary position , represented as:

[0186] ;

[0187] in, This is the normalized jump direction vector;

[0188] S32, Calculate each boundary jump event point based on the set of terrain trigger points extracted within the marked area. Terrain trigger point Distance between ,like Then the topographic point is identified. For boundary points There is a triggering effect; set the trigger weight for this point. The sum of the weighted contributions of all trigger points that meet the conditions to the jump event is: ,in, The terrain-triggered effect distance threshold is expressed as:

[0189] ;

[0190] ;

[0191] ;

[0192] in, To control the scale parameter of distance attenuation;

[0193] ;

[0194] in, The average spatial scale of all vortex cores during the perturbation period. The standard deviation of the spatial scale of the vortex core. These are adjustable parameters;

[0195] S33, based on the timing, amplitude, and trigger weight of all jump events. Constructing a locally discontinuous expansion rate field The boundary advance rate affected by all jump events per unit time, calculated using the spatial grid, is expressed as:

[0196] ;

[0197] Among them, when Falling into coordinates In the corresponding grid, Otherwise, it is 0. This represents the time width of the sliding window.

[0198] This invention encompasses any substitutions, modifications, equivalent methods, and solutions made within the spirit and scope of this invention. To provide the public with a thorough understanding of this invention, specific details are described in detail in the following preferred embodiments; however, those skilled in the art will fully understand the invention even without these details. Furthermore, to avoid unnecessary misunderstanding of the essence of this invention, well-known methods, processes, procedures, components, and circuits are not described in detail.

[0199] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for estimating the boundary expansion rate of plumes in deep-sea polymetallic nodule mining areas, incorporating vortex structure evolution, characterized in that... Includes the following steps: S1. Collect real-time disturbance flow field data and seabed micro-topographic structure map of the plume formation area. Based on the condition that the change amplitude of disturbance intensity exceeds the threshold of disturbance intensity change rate and that its change center is spatially adjacent to the topographic protrusion area, construct a structural intermittent marker area for judging the intermittent evolution behavior of the boundary and identify the topographic trigger point that causes the plume boundary to turn back or change abruptly. S2, based on the intermittently marked region of the structure, track the evolution stage of the vortex structure and its local overlapping interference characteristics during the disturbance, extract the vortex coupling factor sequence that induces boundary jump behavior within the disturbance period when the change in disturbance intensity exceeds the disturbance period identification threshold, and construct a boundary jump event set including the expansion mutation time, jump direction and amplitude. S3, map the boundary jump event set to the evolution trajectory of the feather flow boundary, and combine the distribution weight of the terrain trigger points to generate a local discontinuous expansion rate distribution map, which is used to dynamically depict the nonlinear propagation trend of the feather flow boundary under the action of vortex interference, and output it as the rate estimation result.

2. The method for estimating the boundary expansion rate of plumes in deep-sea polymetallic nodule mining areas, combining vortex structure evolution as described in claim 1, is characterized in that... S1 includes: S11, collect real-time disturbance flow field data and seabed micro-topographic structure map of the plume formation area. The disturbance flow field data includes local velocity vectors, disturbance energy density and direction offset information at multiple time scales. The micro-topographic structure map is constructed based on multibeam bathymetry or side-scan sonar data and includes topographic slope, concave-convex distribution and protrusion volume characteristics. By continuously calculating the change amplitude of disturbance intensity in the disturbance flow field per unit time and setting a threshold for the rate of change of disturbance intensity, it is used to identify the central region of the flow field with violent disturbance fluctuations. S12, spatially match the identified flow field center region with the micro-topographic structure map, extract the coupling unit that meets the disturbance triggering condition based on its adjacency relationship with the topographic protrusion region in three-dimensional space, and delineate the coupling unit as the structural intermittent marker area. Within the structural intermittent marker area, identify the topographic unit with local slope abrupt change, closed shape or structural spiral as potential topographic trigger points.

3. The method for estimating the boundary expansion rate of plumes in deep-sea polymetallic nodule mining areas, combining vortex structure evolution as described in claim 2, is characterized in that... S11 includes: S111: Deploy underwater Doppler acoustic velocimeters, seabed vortex detection buoys, and vorticity profilers in the deep-sea polymetallic nodule mining area to collect disturbance velocity vector data in the plume formation region. The sampling period is set to... The collected data includes each observation point at different timestamps. The local three-dimensional velocity vector V; S112, using three-dimensional velocity vectors to calculate the perturbation kinetic energy density and instantaneous offset angle, forming the perturbation characteristic tensor; S113 uses a multibeam echo sounder and side-scan sonar to acquire seabed topographic data, and combines it with a three-dimensional inversion algorithm to construct a seabed micro-topographic structure map, including topographic slope, curvature field, and topographic protrusion volume; S114, by performing unit-time difference on the disturbance kinetic energy density at consecutive sampling times, calculates the rate of change of disturbance intensity. ; S115, Set the threshold for the rate of change of disturbance intensity. , will satisfy The point is identified as the central region of the flow field with violent fluctuations.

4. The method for estimating the boundary expansion rate of plumes in deep-sea polymetallic nodule mining areas, combining vortex structure evolution as described in claim 3, is characterized in that... S113 includes: S1131, using a multibeam echo sounder to acquire water depth point cloud data. Simultaneously, it combines side-scan sonar equipment to acquire images of seabed reflectivity. To enhance the ability to distinguish uneven textures, and to represent them in spatial coordinate rasterization, an initial terrain elevation raster is formed; S1132, calculates the terrain slope of each cell based on the neighborhood difference in the regular grid. ; S1133 uses the second derivative approximation to calculate the curvature field. This reflects the local tendency of depression or bulge; S1134, extracting continuously satisfied parameters from the curvature field. Connected regions serve as topographic protrusion structural units ,in, The curvature threshold of the protruding structure is used, and the volume of the terrain protrusion is estimated based on grid summation. .

5. The method for estimating the boundary expansion rate of plumes in deep-sea polymetallic nodule mining areas, combining vortex structure evolution as described in claim 4, is characterized in that... S12 includes: S121, the set of all grid points whose disturbance intensity change rate exceeds the disturbance intensity change rate threshold is denoted as the set of the central region of the flow field with violent disturbance fluctuations. ; S122, satisfying the curvature field All grid combinations form a set of protruding structures. ; S123, Calculate the three-dimensional Euclidean distance between each disturbance point and each protrusion point. If satisfied Then it is believed and A spatial adjacency relationship exists, denoted as a disturbance-terrain coupled unit. ,in, This is the spatial adjacency threshold. Let i be the spatial center point of the i-th region of intense disturbance. Let j be the center point of the j-th topographic protrusion. This is the set of all perturbation-terrain coupling units that satisfy the spatial adjacency condition; S124, the coupling point pairs that satisfy the spatial coupling condition. Corresponding terrain area Expanded into a set of structural intermittent marked regions ; S125, for each structural intermittently marked region Extract grid points that satisfy the characteristics of abrupt slope changes, closed shapes, or spiral structures to construct potential terrain trigger points. .

6. The method for estimating the boundary expansion rate of plumes in deep-sea polymetallic nodule mining areas, combining vortex structure evolution as described in claim 5, is characterized in that... S2 includes: S21. Within the intermittently marked area of ​​the structure, the formation, evolution and disappearance of the vortex structure are tracked based on the time series data of the perturbation flow field. The core position, rotation direction and stability index of the vortex at each moment are extracted. By analyzing the spatial overlap and rotation direction difference of adjacent vortices in continuous time periods, their evolution stages and interference types are marked, forming vortex structure evolution information to describe the characteristics of perturbation evolution. S22, based on vortex structure evolution information, identifies effective disturbance cycles in which the rate of change of disturbance intensity exceeds the disturbance cycle identification threshold within a continuous time period. It then extracts key factor sequences that lead to spatial jumps at the feather boundary within the effective disturbance cycle as vortex coupling factor sequences. Each set of factors includes the vortex intensity, core position change, interference mode type, and disturbance direction deflection characteristics of the corresponding region at the time of action. Combined with the change trajectory of the boundary position before and after the jump, it records the occurrence time, spatial jump direction, and abrupt change amplitude of the jump behavior, and constructs a boundary jump event set.

7. The method for estimating the boundary expansion rate of plumes in deep-sea polymetallic nodule mining areas, combining vortex structure evolution as described in claim 6, is characterized in that... S21 includes: S211, Acquire a continuous-time series of three-dimensional perturbation velocity fields in the intermittently marked region of the structure. It is discretized into a two-dimensional profile tensor sequence for vortex identification; S212 uses a two-dimensional curl formula to identify vortex regions in the flow field of each frame. The rotation direction is determined by calculating the curl value, where a positive curl value indicates counterclockwise rotation and a negative curl value indicates clockwise rotation. The absolute value of the curl is also extracted. Exceeding the set threshold The region serves as the local vortex core; S213 involves spatial registration of the vortex core region in consecutive frames to form the vortex trajectory and defining stability indices. ; S214, in any two consecutively existing vortices , Between them, calculate their spatial overlap and rotation direction differences; S215, based on the formation-destruction process of each vortex, labels its stages as generation, enhancement, reversal, merging, or decay, combined with the relationships between adjacent vortices. and The type of interference is determined, including attractive interference, offset interference, and enhancement interference, ultimately forming a set of information on the evolution of the vortex structure. .

8. The method for estimating the boundary expansion rate of plumes in deep-sea polymetallic nodule mining areas, combining vortex structure evolution as described in claim 7, is characterized in that... S215 includes: S2151, based on the tracked trajectory of the r-th vortex core. Statistics on its life cycle And calculate the average curl variation trend of the vortex in consecutive frames. Used to determine evolutionary stages, specifically including: like Marked as enhanced; like Marked as attenuation; If the displacement amplitude of the vortex core is greater than the spatial threshold Marked as a turn; If it is the start or end frame of the lifecycle, mark it as generated or destroyed, respectively. in, Let be the timestamp of the end frame of the r-th vortex. Let r be the timestamp of the starting frame of the r-th vortex. Let be the average curl of the r-th vortex at time t. To identify the threshold for the curl enhancement stage, Identify thresholds for the curl decay phase; S2152, combined with spatial overlap rate Relationship with rotation direction Determining the type of interference specifically includes: when and This indicates attractive interference; when and This indicates offset interference; when and , indicating enhanced interference; in, , , This is an empirical threshold; S2153, the trajectory of each vortex ,life cycle Stage tags And its interference type with adjacent vortices in the same frame. Unified encapsulation to form structured evolutionary record units Finally, a global vortex structure evolution information set is obtained. .

9. The method for estimating the boundary expansion rate of plumes in deep-sea polymetallic nodule mining areas, combining vortex structure evolution as described in claim 8, is characterized in that... S22 includes: S221, Calculate the rate of change of disturbance intensity in a continuous time series. ,like Within a continuous window of at least the minimum disturbance duration The disturbance period continues to exceed the identification threshold within a certain time period. Then this time period is considered an effective disturbance period. ; S222, for each effective disturbance period Combining information on vortex structure evolution Extract the rate of change of boundary position Exceeding the preset rate of change threshold The time points are used as critical moments when the boundary undergoes a sudden leap, and key factors are recorded to form a sequence of vortex coupling factors. ; S223, in the vortex coupling factor sequence In the process of changing the boundary trajectory of the plume, identify the abrupt boundary jump points and record the boundary jump event set. ,in, Let j be the time point in time when the jump event occurs. The spatial direction vector for the boundary jump. The magnitude of the boundary jump.

10. The method for estimating the boundary expansion rate of plumes in deep-sea polymetallic nodule mining areas, combining vortex structure evolution as described in claim 9, is characterized in that... S3 includes: S31, Based on Boundary Jump Event Set Each jump event is located on the time axis at the boundary trajectory of the feather flow. Corresponding time in the middle And based on the jump direction vector With jump amplitude For boundary points Calculate the updated boundary position ; S32, Calculate each boundary jump event point based on the set of terrain trigger points extracted within the marked area. Terrain trigger point Distance between ,like Then the topographic point is identified. For boundary points There is a triggering effect; set the trigger weight for this point. The sum of the weighted contributions of all trigger points that meet the conditions to the jump event is: ,in, The threshold for terrain-triggered action distance; S33, based on the timing, amplitude, and trigger weight of all jump events. Constructing a locally discontinuous expansion rate field The boundary advance rate affected by all jump events per unit time is statistically calculated using spatial grids.

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