Anomaly identification methods, devices, and electronic equipment based on seepage and displacement response

Abstract

This application provides an anomaly identification method, device, and electronic equipment based on seepage and displacement response. The method includes: acquiring seepage response data and displacement response data of an earth-rock dam under various operating conditions, and constructing a response observation vector field; embedding the response observation vector field into a structural state manifold space; constructing a structural state evolution diagram in the structural state manifold space based on the driving relationship of operating conditions, with equivalent structural states as nodes and evolutionary relationships between states as edges; inverting the evolution path of the structural state of the earth-rock dam under multiple time scales based on the structural state evolution diagram and operating condition constraints; performing forward and reverse operating condition mapping on the evolution path respectively to generate a set of state paths; determining that the earth-rock dam has undergone irreversible deterioration evolution in response to the inequivalence of the forward and reverse path sets in the structural state manifold space, and outputting the identification result. Using the above scheme can improve the reliability and accuracy of the operational safety assessment of earth-rock dams.

Description

Technical Field

[0001] This application relates to the field of hydraulic engineering safety monitoring technology, and in particular to an anomaly identification method, device and electronic equipment based on seepage and displacement response. Background Technology

[0002] Earth-rock dams are one of the most widely used dam types in reservoir engineering, and their safety is highly dependent on the seepage state and deformation response within the dam body and foundation. In current engineering practice, the dam's operational status is usually assessed using empirical thresholds or single-index exceedance criteria.

[0003] However, earth-rock dams are typical heterogeneous, porous media structures, and there is a significant physical coupling between their seepage behavior and deformation response. On the one hand, changes in the seepage field alter the effective stress distribution within the dam body, thereby inducing deformation; on the other hand, dam deformation may lead to seepage channel remodeling, causing abrupt changes in the seepage state. Relying solely on a single indicator or static threshold method makes it difficult to identify early instability risks caused by the evolution of the dam's internal structure in a timely manner.

[0004] Therefore, there is an urgent need for a new method that can comprehensively consider the coupling relationship between seepage and displacement and evaluate the operating status of earth-rock dams from the perspective of system evolution. Summary of the Invention

[0005] In view of this, this application provides an anomaly identification method, device and electronic equipment based on seepage and displacement response, which can improve the reliability and accuracy of the safety assessment of earth-rock dam operation.

[0006] In a first aspect, embodiments of this application provide an anomaly identification method based on seepage and displacement response, including:

[0007] We acquire seepage response data and displacement response data of earth-rock dams under various operating conditions, and construct a response observation vector field to characterize the coupled temporal relationship between the seepage response and displacement response of the dam body.

[0008] The response observation vector field is embedded into the structural state manifold space to obtain the equivalent structural state and its evolution position inside the earth-rock dam;

[0009] In the structural state manifold space, a structural state evolution graph is constructed based on the driving relationship of operating conditions, with equivalent structural states as nodes and the evolution relationship between states as edges;

[0010] Based on the structural state evolution diagram and operating condition constraints, the evolution path of the earth-rock dam's structural state under multiple time scales is obtained by inversion.

[0011] The evolution path is mapped to forward and reverse operating conditions respectively, generating corresponding sets of forward and reverse structural state paths;

[0012] In response to the inequivalence of the forward and reverse path sets in the structural state manifold space, the irreversible deterioration evolution of the earth-rock dam is determined, and the identification result is output.

[0013] Optionally, embedding the response observation vector field into the structural state manifold space includes:

[0014] Based on the spatiotemporal proximity between data points in the response observation vector field, a weighted adjacency graph is constructed.

[0015] Determine the symmetric normalized Laplacian matrix corresponding to the weighted adjacency graph, and solve the eigensystem of the Laplacian matrix to obtain the sequence of eigenvectors arranged in ascending order of eigenvalues;

[0016] The eigenvectors corresponding to the first k smallest non-zero eigenvalues ​​are selected, and the original high-dimensional response observation vector field is projected onto the low-dimensional space to form a coordinate representation in the structure state manifold space.

[0017] Optionally, the anomaly detection method further includes: constructing a multi-layered structural state manifold space, including:

[0018] Based on the physical structural zoning of the earth-rock dam, the dam body is divided into multiple sub-regions;

[0019] For each sub-region, the seepage response data and displacement response data are independently embedded into the structural state manifold space to generate the corresponding local structural state submanifold.

[0020] The state coordinates of all local structural state submanifolds are merged, and a second dimensionality reduction is performed to generate a multi-layer structural state manifold space.

[0021] Optionally, the step of inverting the evolution path of the structural state of the earth-rock dam at multiple time scales based on the evolution diagram and operating condition constraints includes:

[0022] Define the state coordinates corresponding to each time point in the structural state manifold space as a graph node;

[0023] Calculate the directed transfer intensity from any time node to its successor time node. This intensity is determined by the change in operating conditions within the corresponding time period and the spatial similarity between the two nodes.

[0024] Valid state transition relationships are selected based on a preset intensity threshold. The structure state evolution graph is constructed with nodes as vertices and valid directed transition relationships as edges.

[0025] Optionally, the process of inverting the evolution path of the earth-rock dam's structural state across multiple time scales based on the structural state evolution diagram and operational constraints includes:

[0026] The time series of historical operating conditions is transformed into a sequence of conditional constraints for edge selection in the structural state evolution graph;

[0027] Under the given conditional constraints, a graph search algorithm is used to search for an optimal path from the initial state node to the current state node in the evolution graph. This path must maximize the overall fit between the state sequence corresponding to the path and all observed data. The optimal path obtained is the evolution path of the inverted structural state at multiple time scales.

[0028] Optionally, the step of mapping the evolution path to forward and reverse operating conditions to generate corresponding sets of forward and reverse structural state paths includes:

[0029] Starting from the earliest historical structural state, and following the time sequence of actual operating conditions, a step-by-step state transition deduction is performed in the structural state evolution diagram to generate a deduced positive structural state sequence.

[0030] Starting from the current or specific end-of-term structural state, reverse state transition deduction is performed in the structural state evolution diagram according to the time sequence opposite to the actual operating conditions, generating the deduced reverse structural state sequence.

[0031] All state sequences obtained by performing the above deduction at different time scales or different starting points are collected to form the set of forward structural state paths and the set of reverse structural state paths, respectively.

[0032] Optionally, the determination that the earth-rock dam has undergone irreversible deterioration evolution in response to the inequivalence of the forward and reverse path sets in the structural state manifold space, and the output of the identification result, includes:

[0033] In the structural state manifold space, calculate the average distance between the paired paths and the corresponding state points at the same time between the forward path set and the corresponding reverse path set.

[0034] Calculate the curve similarity distance between the entire set of reverse paths and the set of forward paths;

[0035] If the average distance and the curve similarity distance are both not less than their respective preset equivalence thresholds, then they are determined to be unequal.

[0036] Optionally, the anomaly detection method further includes:

[0037] When irreversible degradation is determined to have occurred, the key nodes and directed edges that cause the forward and reverse paths to begin to separate significantly are located in the structural state evolution diagram.

[0038] Based on the coordinates of the key nodes in the manifold space, the response data characteristics of their main contributions are inverted and correlated to possible spatial locations within the dam body.

[0039] The degree of bifurcation of the forward and reverse paths in the manifold space, starting from the key node, is calculated as a quantitative indicator of the degree of irreversible degradation evolution.

[0040] Secondly, embodiments of this application provide an anomaly identification device based on seepage and displacement response, comprising:

[0041] The acquisition unit is configured to acquire seepage response data and displacement response data of earth-rock dams under various operating conditions, and to construct a response observation vector field to characterize the coupled temporal relationship between the seepage response and displacement response of the dam body.

[0042] The embedding unit is configured to embed the response observation vector field into the structural state manifold space to obtain a characterization of the equivalent structural state inside the earth-rock dam and its evolution position.

[0043] An evolution unit is configured to construct a structural state evolution graph in the structural state manifold space based on the driving relationship of the operating conditions, with equivalent structural states as nodes and evolutionary relationships between states as edges;

[0044] The inversion unit is configured to invert the evolution path of the earth-rock dam's structural state at multiple time scales based on the structural state evolution diagram and operating condition constraints.

[0045] The identification unit is configured to perform forward and reverse operating condition mapping on the evolution path respectively, generate corresponding forward and reverse structural state path sets, and determine that the earth-rock dam has undergone irreversible deterioration evolution in response to the inequivalence of the forward and reverse path sets in the structural state manifold space, and output the identification result.

[0046] Secondly, embodiments of this application provide an electronic device, including a memory and a processor, wherein the memory stores a computer program that can run on the processor, and when the processor runs the computer program, it executes the steps of the anomaly identification method based on seepage and displacement response as described in any of the foregoing embodiments.

[0047] Compared with the prior art, the technical solution of this application has the following advantages:

[0048] The anomaly identification method based on seepage and displacement response provided in this application acquires seepage response data and displacement response data of earth-rock dams under various operating conditions, constructs a response observation vector field characterizing the coupling relationship between the two, and embeds it into the structural state manifold space, thereby characterizing the equivalent structural state and its evolution behavior inside the earth-rock dam at the overall structural level. On this basis, by constructing a structural state evolution diagram and combining it with operating condition constraints to invert the structural state evolution path under multiple time scales, and simultaneously performing forward and reverse operating condition mapping on the evolution path and comparing their equivalence, the method can identify whether the earth-rock dam has undergone irreversible deterioration evolution, significantly improving the reliability and accuracy of earth-rock dam operating state assessment. Attached Figure Description

[0049] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of this application. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0050] Figure 1 A flowchart of an anomaly identification method based on seepage-displacement response is shown in an embodiment of this application;

[0051] Figure 2 A flowchart of an embedding method for a response observation vector field is shown in an embodiment of this application;

[0052] Figure 3 This illustration shows a schematic diagram of the construction of a structural state evolution diagram in an embodiment of this application;

[0053] Figure 4 This illustration shows a schematic diagram of multi-timescale evolution path inversion and graph search in an embodiment of this application;

[0054] Figure 5 A flowchart of an anomaly identification device based on seepage-displacement response is shown in an embodiment of this application;

[0055] Figure 6 A schematic diagram of the hardware structure of an electronic device according to an embodiment of this application is shown. Detailed Implementation

[0056] As described in the background section, traditional methods struggle to distinguish between reversible fluctuations and irreversible degradation under complex operating conditions.

[0057] This application embodiment starts from the coupling relationship between seepage response and displacement response, represents the equivalent structural state inside the dam body in the structural state manifold space, and further constructs a structural state evolution diagram based on the driving relationship of operating conditions. Under the constraints of operating conditions, the evolution path is inverted, and finally irreversible degradation is identified by the equivalence judgment of the sets of forward and reverse paths.

[0058] Specifically, by acquiring seepage response data and displacement response data of earth-rock dams under various operating conditions, a response observation vector field characterizing the coupling relationship between the two is constructed and embedded into the structural state manifold space, thereby depicting the equivalent structural state and its evolution behavior inside the earth-rock dam at the overall structural level. On this basis, by constructing a structural state evolution diagram and combining it with operating condition constraints to invert the structural state evolution path under multiple time scales, and simultaneously mapping the evolution path to forward and reverse operating conditions and comparing their equivalence, the identification of whether the earth-rock dam has undergone irreversible deterioration evolution is realized, which significantly improves the reliability and accuracy of earth-rock dam operating state assessment.

[0059] In other words, compared with traditional safety assessment methods that rely on a single monitoring indicator or static threshold judgment, this invention improves the anomaly identification process from local and instantaneous judgment to dynamic judgment of the overall evolution trend and reversibility of the structure through a closed-loop identification mechanism of response coupling characterization, state manifold modeling, evolutionary relationship constraints and forward and reverse consistency verification. This enables earlier and more accurate identification of potential irreversible deterioration risks inside earth-rock dams.

[0060] To enable those skilled in the art to better understand and implement this solution, the following detailed description of the specific solution, principle, and effect of this disclosure is provided with reference to the accompanying drawings and specific embodiments.

[0061] See Figure 1 The flowchart shown in this application illustrates an anomaly identification method based on seepage-displacement response, as illustrated in the following embodiment. Figure 1 As shown, the following steps can be performed:

[0062] S101, acquire seepage response data and displacement response data of earth-rock dam under various operating conditions, and construct a response observation vector field to characterize the coupled temporal relationship between seepage response and displacement response of the dam body.

[0063] In some embodiments, seepage response data and displacement response data can be derived from various types of monitoring equipment deployed within the dam body and foundation. Seepage response data is used to reflect changes in the hydraulic state inside the dam body, while displacement response data is used to reflect the deformation behavior of the dam structure under external and internal forces.

[0064] By continuously collecting the above data under different operating conditions and performing time synchronization, outlier processing, and scale unification processing, response data from different monitoring sources can be jointly analyzed under the same time reference.

[0065] Furthermore, the seepage response characteristics and displacement response characteristics at the same time point or within the same time window are combined to construct a response observation vector, thereby forming a response observation vector field that evolves with the operating conditions in the time dimension, which is used to comprehensively characterize the coupling time sequence relationship between seepage and displacement.

[0066] S102, the response observation vector field is embedded into the structural state manifold space to obtain the equivalent structural state and its evolution position inside the earth-rock dam.

[0067] In some embodiments, the response observation vector field is typically located in a high-dimensional space, and there are complex nonlinear relationships between the features in each dimension. By embedding this response observation vector field into the structural state manifold space, the high-dimensional response data can be represented in a reduced-dimensional manner while maintaining the original temporal proximity relationships and relative similarities.

[0068] In the embedded low-dimensional space, each time point corresponds to a structural state coordinate. This structural state coordinate is used to characterize the equivalent internal structural state of the dam at that moment and its relative position in the overall state space, thus providing a unified state expression basis for subsequent analysis of the continuous evolution characteristics of the dam's structural state.

[0069] In some embodiments, see Figure 2 The flowchart shown in this application illustrates an embedding method for a response observation vector field, as follows: Figure 2 As shown, the following can be executed:

[0070] S201, Based on the spatiotemporal proximity between data points in the response observation vector field, a weighted adjacency graph is constructed.

[0071] In some embodiments, the data points in the response observation vector field not only have a temporal order relationship, but also exhibit different degrees of similarity in the response feature space. By comprehensively considering the proximity of data points (i.e., the location of the monitoring device) in the temporal dimension and their similarity in the response feature space, a weighted adjacency graph reflecting local structural relationships can be constructed.

[0072] This weighted adjacency graph is used to describe the correlation strength between different observation states, so that data points that are close in time and have similar response characteristics have larger connection weights, while data points with large time intervals or significant response differences have smaller connection weights, thus providing a basis for the subsequent extraction of the intrinsic structure of the observation data.

[0073] S202, determine the symmetric normalized Laplacian matrix corresponding to the weighted adjacency graph, and solve the eigensystem of the Laplacian matrix to obtain the eigenvector sequence arranged in ascending order of eigenvalues.

[0074] In some embodiments, by representing the weighted adjacency graph in a matrix and normalizing it using the corresponding degree matrix, a symmetric normalized Laplace matrix reflecting the graph's structural characteristics can be obtained. This Laplace matrix can characterize the geometric structure of the response observation vector field in its local neighborhood.

[0075] Eigenvalue decomposition of the Laplacian matrix yields a set of eigenvalues ​​and their corresponding eigenvectors. The eigenvectors corresponding to smaller eigenvalues ​​better reflect the overall low-dimensional structure of the data, providing a basic representation for subsequent manifold embedding.

[0076] More specifically, for a given weighted adjacency graph, a symmetric weighted adjacency matrix W is constructed based on the edge weights, and the degree matrix D (whose diagonal elements are the sum of the weights of each vertex) is computed; then... Construct a symmetric normalized Laplace matrix. Wherein, It is an identity matrix.

[0077] When solving for the eigensystem of the Laplacian matrix, numerical methods (such as dense algorithms for small-scale matrices or iterative algorithms for large-scale sparse matrices) are usually used to calculate all eigenvalues ​​and eigenvectors. Finally, all eigenvalues ​​are sorted in ascending order, and the order of the eigenvectors is adjusted accordingly to obtain the desired sequence.

[0078] S203, select the eigenvectors corresponding to the first k smallest non-zero eigenvalues, project the original high-dimensional response observation vector field to the low-dimensional space, and form a coordinate representation in the structure state manifold space.

[0079] In some embodiments, by selecting feature vectors that can reflect the main structural features as low-dimensional representation bases, high-dimensional response observation vectors are mapped to low-dimensional space, so that the originally complex high-dimensional response data can be represented in a continuous and smooth form in low-dimensional space.

[0080] The embedded low-dimensional coordinates not only maintain the relative relationships of the original data in the local neighborhood, but can also be used to intuitively describe the trajectory of the dam structure state during the time evolution process, thus forming a coordinate representation in the structural state manifold space.

[0081] By constructing a weighted adjacency graph based on the spatiotemporal proximity between data points in the response observation vector field, and using the eigenvalue decomposition of the symmetric normalized Laplace matrix to achieve low-dimensional embedding, this invention can map high-dimensional, noisy monitoring data to the structural state manifold space while maintaining the intrinsic geometric relationship between the original seepage response and displacement response, thereby effectively reducing the data dimensionality and weakening the impact of accidental disturbances.

[0082] This embedding method enables the evolution trajectory of the dam structure state to be represented as a continuous and interpretable change path in the manifold space, providing a stable and reliable state representation basis for the subsequent construction of the structural state evolution diagram and the inversion of the evolution path, thereby further supporting and enhancing the ability to accurately identify irreversible deterioration evolution.

[0083] In some embodiments, the anomaly identification method further includes: constructing a multi-layered structural state manifold space.

[0084] Specifically, this includes: dividing the dam body into multiple sub-regions based on the physical structural partitioning of the earth-rock dam; independently embedding the seepage response data and displacement response data of each sub-region into the structural state manifold space to generate corresponding local structural state sub-manifolds; fusing the state coordinates of all local structural state sub-manifolds and performing secondary dimensionality reduction to generate a multi-layer structural state manifold space.

[0085] In some embodiments, considering the complex internal structure of earth-rock dams and the differences in material properties, stress states, and seepage conditions in different parts, the dam body can be divided into zones based on its physical structure or monitoring layout. By dividing the dam body into multiple sub-regions with relatively consistent physical characteristics, the response characteristics of each region can be analyzed separately, thereby improving the ability to perceive changes in local structural states.

[0086] Next, seepage response data and displacement response data are extracted from different sub-regions and processed according to a unified embedding strategy to obtain local structural state submanifolds that reflect the state change characteristics of each sub-region. By independently constructing local submanifolds, the state changes within each sub-region can be characterized in greater detail, which helps to identify potential anomalous evolutionary behaviors within the local region.

[0087] Finally, the local structural state submanifolds corresponding to each sub-region are merged to comprehensively express the state characteristics of different regions of the dam in a unified space. By performing a second-order dimensionality reduction on the merged state coordinates, a multi-layered structural state manifold space is formed. This space can reflect both the local evolution characteristics of each sub-region and the evolution trend of the overall structural state of the dam, thus providing a multi-scale state representation for subsequent overall analysis.

[0088] By dividing the dam body into multiple sub-regions according to the physical structure of the earth-rock dam, constructing local structural state sub-manifolds for each sub-region, and then merging and performing secondary dimensionality reduction on each sub-manifold, this invention achieves hierarchical characterization and collaborative analysis of the structural behavior of different spatial parts of the dam body.

[0089] The construction method of this multi-layered structural state manifold space enables local anomalies to be amplified and made explicit in the corresponding submanifolds, while reflecting their impact on the evolution of the overall dam structure state in the overall manifold. This avoids the problem of local anomalies being masked by average in traditional overall modeling methods, and further improves the sensitivity and reliability of anomaly identification methods under complex dam structure conditions.

[0090] S103, in the structural state manifold space, construct a structural state evolution graph based on the operating condition driving relationship, with equivalent structural states as nodes and the evolution relationship between states as edges.

[0091] In some embodiments, in order to clearly describe the evolution of the dam structure state with time and operating conditions, the structural state coordinates at different times in the structural state manifold space are regarded as nodes in the graph structure.

[0092] Simultaneously, by combining the state changes at adjacent moments or at certain time scales, directed connections between nodes are constructed to represent the possible paths of structural state evolution from one moment to another. Furthermore, when constructing these connections, operational condition changes are introduced, ensuring that the evolutionary relationships between states not only reflect the similarity of the states themselves but also demonstrate the driving effect of operational conditions on structural state evolution, thus forming a structural state evolution diagram and providing a foundation for subsequent path inversion and evolutionary analysis.

[0093] In some embodiments, see Figure 3 The schematic diagram shown in this application embodiment illustrates the construction of a structural state evolution diagram, including:

[0094] S301, define the state coordinates corresponding to each time point in the structural state manifold space as a graph node.

[0095] In some embodiments, the state coordinates arranged over time in the structural state manifold space are discretized into nodes in a graph structure, such that each node corresponds to the equivalent structural state of the dam at a certain moment. Through this node-based representation, the discrete evolution process of the structural state over time can be intuitively expressed in the graph structure.

[0096] S302, calculate the directed transfer intensity from any time node to its successor time node. This intensity is determined by the change in operating conditions within the corresponding time period and the spatial similarity between the two nodes.

[0097] In some embodiments, to quantify the rationality of the structural state evolution from one moment to a subsequent moment, a directed transition intensity is introduced to measure the evolutionary relationship between nodes. This transition intensity comprehensively considers the driving effect of changes in operating conditions on the structural state evolution, as well as the similarity of the structural states in the manifold space, thereby enabling the transition intensity to reflect the physical rationality and continuity of the state evolution. This joint quantification method avoids biases caused by relying solely on state distance or solely on changes in operating conditions.

[0098] In one example, within the structural state manifold space, state nodes corresponding to adjacent time steps are considered as candidate directed transitions, and a transition strength is defined for each candidate transition. This transition strength is jointly determined by the degree of change of the structural state in the manifold space and the corresponding change in operating conditions.

[0099] Specifically, by constructing an objective function, the manifold space state difference term and the operational condition change term are jointly quantified, and time smoothing constraints and penalty terms are introduced to invert and obtain the optimal structural state transition intensity sequence. The greater the transition intensity, the more reasonable the evolution of the dam structure state from the current moment to the subsequent moment under the current operational conditions.

[0100] The objective function is:

[0101]

[0102] .

[0103] in, Indicates the time sequence number; Indicates the total number of time steps; Indicates time The structural state manifold coordinates; Indicates time Operating condition vector; Indicates from arrive The greater the directional transfer intensity, the more reasonable the transfer is under the current operating conditions; This represents the weighting coefficient for the state differences in the manifold space; Indicates the weighting coefficient for changes in operating conditions; This represents the scaling parameter, used for normalization. This represents the robust cost function, used to suppress the effects of noise and outliers; This represents the time smoothing regularization coefficient, used to suppress abrupt changes in intensity.

[0104] S303, based on the preset intensity threshold, select the valid state transition relationship, and construct the structure state evolution diagram with the node as the vertex and the valid directed transition relationship as the edge.

[0105] In some embodiments, the calculated directed transition strength is compared with a preset threshold to select state transition relationships with higher confidence, and these relationships are used as directed edges in the graph structure. By eliminating candidate relationships with low transition strength, the impact of noise or occasional perturbations on the evolution graph structure can be reduced, thereby constructing a more stable and clear structural state evolution graph.

[0106] By defining the state coordinates at different times in the structural state manifold space as graph nodes, and by combining the changes in operating conditions with the similarity of the state space to determine the directed transfer intensity between nodes, this invention can explicitly characterize the evolution relationship of the dam state with time and operating conditions at the structural state level.

[0107] The method of screening effective state evolution relationships based on transfer intensity and constructing structural state evolution diagrams makes the dam structure evolution process no longer dependent on simple time sequence, but subject to the dual constraints of physical condition changes and state similarity, thus providing an evolutionary structural basis that conforms to engineering practice for the inversion of multi-timescale evolution paths.

[0108] S104. Based on the structural state evolution diagram and operating condition constraints, the evolution path of the structural state of the earth-rock dam under multiple time scales is obtained by inversion.

[0109] In some embodiments, the change in operating conditions can be viewed as an external constraint on the evolution of the structural state. By incorporating historical operating condition information into the structural state evolution diagram, possible state transition paths in the diagram can be constrained or filtered to ensure that the selected path aligns with the actual trend of operating condition changes.

[0110] Based on this, by searching for state sequences that satisfy the operating condition constraints and have high overall consistency in the structural state evolution diagram, the evolution path of the dam structure state at different time scales can be obtained by inversion, thereby reflecting the evolution process of the dam structure state from history to the present.

[0111] In some embodiments, Figure 4 The diagram shown in this application illustrates a multi-timescale evolution path inversion and graph search. Figure 4 As shown, it includes:

[0112] S401, the time series of historical operating conditions is transformed into a sequence of conditional constraints for edge selection in the structural state evolution graph.

[0113] In some embodiments, the changes in operating conditions can reflect the external environment and load conditions of the dam. By transforming the historical operating condition time series into a set of conditional constraint information, the selection of state transition relationships can be restricted or guided in subsequent state evolution analysis, so that the state evolution process conforms to the logic of actual operating condition changes.

[0114] S402, under the conditional constraint sequence, a graph search algorithm is used to search for an optimal path from the initial state node to the current state node in the evolution graph. This path must maximize the overall fit between the state sequence corresponding to the path and all observed data. The optimal path obtained by the search is the evolution path of the inverted structural state under multiple time scales.

[0115] In some embodiments, by performing a constrained path search on the structural state evolution diagram, one or more state sequences that can reasonably explain the changes in the observed data can be obtained. These state sequences reflect the evolution of the dam's structural state at different time scales and can be used to analyze long-term trends or stage-specific changes.

[0116] By transforming historical operating condition time series into edge selection conditions in the structural state evolution graph, and using a graph search algorithm to invert the optimal evolution path under these constraints, this invention can ensure that the obtained structural state evolution path maintains the highest consistency with the actual monitoring data globally.

[0117] This approach avoids the problem of traditional point-by-point or local fitting methods being susceptible to noise interference, and makes the evolution path have overall coherence and physical rationality. This provides a reliable evolutionary reference for forward and reverse path mapping and their equivalence discrimination, and further enhances the robustness of the irreversible degradation identification conclusion.

[0118] S105, perform forward and reverse operation condition mapping on the evolution path respectively to generate corresponding forward and reverse structural state path sets.

[0119] In some embodiments, in order to analyze whether the structural state evolution process is reversible, the structural state evolution path is deduced from both forward and reverse perspectives.

[0120] The forward mapping starts from a historical moment and extrapolates the structural state according to the time sequence of the actual operating conditions to form a forward structural state path; the reverse mapping starts from the current or final structural state and extrapolates according to the time sequence opposite to the actual operating conditions to form a reverse structural state path.

[0121] By repeating the above deduction process at different time scales or under different starting conditions, representative sets of forward paths and reverse paths can be formed respectively, thereby improving the stability of subsequent discriminant analysis.

[0122] In some embodiments, step S105 may include:

[0123] S1051, starting from the earliest historical structural state, following the time sequence of actual operating conditions, a step-by-step state transition deduction is performed in the structural state evolution diagram to generate a deduced positive structural state sequence.

[0124] The forward simulation process is used to simulate the evolution path of the dam structure state during actual time, so that the generated state sequence can reflect the state change process of the dam under the actual operating conditions.

[0125] S1052, starting from the current or specific final stage of the structural state, and following the reverse time sequence from the actual operating conditions, perform reverse state transition deduction in the structural state evolution diagram to generate the deduced reverse structural state sequence.

[0126] In other words, backward deduction is used to trace back the possible historical evolution process from the current state. By comparing the results with those of forward deduction, it can be used to analyze whether the structural state evolution process has reversibility characteristics.

[0127] S1053, collect all the state sequences obtained by performing the above deduction at different time scales or different starting points, and respectively constitute the set of forward structure state paths and the set of reverse structure state paths.

[0128] In some embodiments, by performing multiple simulations and forming a set of paths, the risk of a single path being affected by accidental factors can be reduced, making subsequent comparative analyses more stable and representative.

[0129] By taking the historical initial state and the current or final state as starting points respectively, and deducing the structural state evolution diagram according to the actual operating conditions and their reverse order, this invention constructs a set of forward and reverse structural state paths, realizing bidirectional verification of the reversibility of the dam structure evolution.

[0130] This forward and reverse path deduction mechanism makes it possible to quantify and compare whether the structural state can return to its historical state under working condition inversion. It reveals whether the dam body has undergone irreversible deterioration from the perspective of evolution consistency, thus constructing a core criterion that is different from the traditional one-way analysis method.

[0131] S106, in response to the inequivalence of the forward and reverse path sets in the structural state manifold space, determine that the earth-rock dam has undergone irreversible deterioration evolution, and output the identification result.

[0132] In some embodiments, by mapping the forward path set and the reverse path set to the same structural state manifold space for comparative analysis, the consistency of the structural state evolution process under forward and reverse inference conditions can be evaluated.

[0133] When there is a significant difference between the forward path set and the reverse path set, and this difference exceeds the preset equivalence criterion, it indicates that the evolution of the structural state is difficult to reasonably trace back through reverse deduction, thus determining that the dam structure has undergone irreversible deterioration. At this time, the corresponding anomaly identification results are output for subsequent safety assessment, early warning, or response decisions.

[0134] Step S106 may include:

[0135] In the structural state manifold space, the average distance between the paired paths and their corresponding state points at the same time is calculated between the forward path set and the corresponding reverse path set.

[0136] In some embodiments, by aligning the forward and reverse paths in time and calculating the distance between corresponding state points, the degree of deviation between the two types of paths at local time points can be quantified, providing a basic indicator for equivalence determination.

[0137] Calculate the curve similarity distance between the entire set of reverse paths and the set of forward paths.

[0138] In some embodiments, by introducing a curve-level similarity metric, the differences between the two types of paths can be assessed from an overall morphological perspective, thus overcoming the limitations that may arise from relying solely on point-to-point distance.

[0139] If the average distance and the curve similarity distance are both not less than their respective preset equivalence thresholds, then they are determined to be unequal.

[0140] In some embodiments, when both types of distance indicators exceed a preset threshold at the same time, it can be considered that forward deduction and backward backtracking are difficult to form a consistent explanation, thereby determining that the structural state evolution process does not have reversibility characteristics.

[0141] By calculating the distance between state points and the curve similarity distance between the forward path set and the reverse path set in the structural state manifold space, and determining their equivalence based on a preset threshold, this invention transforms the irreversible degradation problem, which originally relied on empirical judgment, into a measurable and reproducible geometric discrimination problem.

[0142] This quantitative discrimination method not only improves the consistency and objectivity of anomaly identification results, but also effectively reduces the influence of human subjective factors, thereby directly supporting and strengthening the reliable identification of irreversible deterioration evolution of earth-rock dams.

[0143] In some optional examples, the anomaly identification method further includes: when irreversible degradation is determined to have occurred, locating key nodes and directed edges in the structural state evolution diagram that cause a significant separation between the forward and reverse paths; based on the coordinates of the key nodes in the manifold space, inverting the response data features that contribute mainly to them and associating them with possible spatial locations within the dam body; and calculating the degree of bifurcation of the forward and reverse paths in the manifold space starting from the key nodes as a quantitative indicator of the degree of irreversible degradation.

[0144] Specifically, by analyzing how path differences change over time, we can identify the moment when the forward and reverse paths begin to deviate continuously and their corresponding nodes, thereby determining the key nodes and directed edges related to irreversible degradation evolution.

[0145] Based on the structural state change characteristics corresponding to key nodes, we analyze their main manifestations in the original response data, and combined with the spatial distribution information of monitoring points, we infer the spatial area of ​​the dam body related to the change, providing a basis for engineering analysis.

[0146] By quantifying the cumulative or changing trends of path deviation after key nodes, an indicator can be formed to characterize the degree of irreversible degradation and evolution, providing a reference for risk classification and decision support.

[0147] By further locating the key nodes and directed edges that cause the separation of the forward and reverse paths after confirming the occurrence of irreversible degradation, and inverting their corresponding response data characteristics and spatial locations, this invention can not only identify whether an anomaly has occurred, but also reveal the potential structural location and degree of evolution of the anomaly.

[0148] This analytical capability, which extends from simply identifying anomalies to understanding their sources and severity, elevates the method from mere anomaly identification to a comprehensive safety assessment approach with diagnostic and decision support capabilities. This significantly enhances its engineering application value in the operation, management, and risk control of earth-rock dams.

[0149] In short, this solution has at least the following advantages:

[0150] This invention integrates seepage response data and displacement response data under multiple operating conditions to construct a response observation vector field reflecting the coupling relationship between the two. This field is then embedded into the structural state manifold space, thereby characterizing the equivalent structural state within the dam body and its evolution over time at the overall structural level. Compared to traditional anomaly detection methods based on single monitoring indicators or static thresholds, this invention can identify potential anomaly trends from a structural evolution perspective, improving the ability to identify early-stage, hidden deterioration.

[0151] This invention constructs a structural state evolution diagram in the structural state manifold space, using equivalent structural states as nodes and evolutionary relationships constrained by both operational condition changes and state similarity as edges. It then inverts the structural state evolution paths across multiple time scales under operational condition constraints. This approach avoids analysis methods that rely solely on time series or local fitting, making the obtained evolution paths more consistent with the actual operating mechanism of the dam and providing a reliable state evolution basis for anomaly identification.

[0152] This invention derives sets of forward and reverse structural state paths in the structural state evolution diagram according to the actual operating condition sequence and its reverse sequence. By comparing the equivalence of these two paths in the structural state manifold space, it determines whether the dam structure evolution is reversible. This method transforms the identification of irreversible degradation from empirical judgment to quantitative discrimination based on the consistency of state evolution, significantly improving the objectivity and stability of anomaly identification results.

[0153] After determining that irreversible degradation has occurred, this invention further locates the key state nodes and evolutionary relationships that lead to the separation of the forward and reverse paths, and inversely reconstructs the response characteristics that mainly contribute to these nodes and the possible corresponding spatial locations of the dam body, while quantifying the degree of bifurcation in the structural state evolution. Therefore, this invention can not only determine whether an anomaly has occurred, but also provide a clear basis for subsequent safety assessments, operation and maintenance decisions, and risk prevention and control.

[0154] The following describes the implementation process of the anomaly identification method based on seepage-displacement response in this application, using a set of exemplary monitoring data. This example is only used to illustrate the technical concept and effects of this disclosure and is not intended to limit the scope of protection of this disclosure.

[0155] In this example, a medium-sized earth-rock dam that is currently in operation is selected as the research object.

[0156] The earth-rock dam is equipped with various monitoring devices during operation to collect long-term seepage response data and displacement response data of the dam body, while simultaneously recording operating condition data.

[0157] During the example time period, the dam body experienced a complete process of reservoir water level rise, stabilization, and fall, which was used to verify the ability of this method to identify the evolution of structural state under typical operating conditions.

[0158] In this example, monitoring data from 180 consecutive days were selected as the analysis sample, with a sampling interval of 1 day.

[0159] The seepage response data includes: seepage pressure values ​​(unit: kPa) at three representative seepage pressure monitoring points and seepage flow (unit: L / s) at a seepage flow monitoring point downstream of the dam.

[0160] The displacement response data includes: the horizontal displacement (unit: mm) of two dam crest measuring points and the vertical displacement (unit: mm) of one dam settlement measuring point.

[0161] During the example time period, the reservoir water level rose from 220m to 235m, and then gradually receded after maintaining a high water level for about 30 days.

[0162] In some embodiments, the seepage response characteristics and displacement response characteristics collected within the same date are combined to form a response observation vector, for example:

[0163]

[0164] in, This represents the seepage pressure value at the i-th seepage pressure measuring point. Indicates seepage flow rate. Indicates horizontal displacement. This indicates vertical settlement.

[0165] By aggregating the response observation vectors at all time points, a response observation vector field is constructed for subsequent analysis of the coupled evolution characteristics of seepage-displacement response.

[0166] In this example, the response observation vector field is embedded into a low-dimensional structured state manifold space.

[0167] In some embodiments, after manifold embedding, the high-dimensional response observation vector at each time step is mapped to a two-dimensional structural state coordinate, for example: .

[0168] Among them, the two-dimensional coordinates are used to characterize the equivalent structural state of the dam body at that moment.

[0169] The example results show that during the rising reservoir water level phase, the structural state coordinates move continuously in a certain direction; during the stable reservoir water level phase, the state points cluster in a relatively concentrated area; and in the early stage of the falling reservoir water level, the state points generally retreat along the original path.

[0170] In this example, the structural state coordinates corresponding to each day in the structural state manifold space are used as graph nodes.

[0171] For adjacent time points and Calculate the changes in operating conditions and the similarity between the states:

[0172] Example values ​​for state space distance:

[0173]

[0174] Example values ​​of changes in operating conditions (reservoir water level changes):

[0175]

[0176] In some embodiments, the directed transition intensity is determined jointly based on the change in operating conditions and the similarity of the state space. Exemplary results show that:

[0177] During the period of stable reservoir water level change, the intensity of relocation Most of them are concentrated in the range of 0.7–0.9; during the stage of rapid changes in reservoir water level or abnormal amplification of response, the intensity of some transfers drops to below 0.4.

[0178] Based on a preset threshold (e.g., 0.5), valid state transition relationships are filtered and retained to construct a structural state evolution diagram.

[0179] In this example, based on the constructed structural state evolution diagram, forward and reverse operation condition mappings are performed respectively. The forward path reflects the structural state evolution of the dam body from low water level to high water level and then back down; the reverse path is used to trace back from the current state to the historical state.

[0180] Example results show that during the rising and stabilizing phases of the reservoir water level, the forward and reverse paths highly overlap in the structural state manifold space; in the later stages of the receding reservoir water level, some reverse paths cannot be traced back to the earlier state region, resulting in an overall path offset.

[0181] In some embodiments, the average distance between the corresponding state points of the forward and reverse paths is calculated to be approximately 0.18; the curve similarity distance is significantly higher than a preset threshold.

[0182] Based on this, it was determined that the evolution of the dam structure during this period had irreversible characteristics, and anomaly identification results were output.

[0183] As can be seen from the above examples, the method disclosed herein can maintain a stable characterization of the structural state evolution during normal operation, and when irreversible deviations occur in the structural state, it can promptly identify abnormal evolution trends by the difference between the sets of forward and reverse paths, thus providing an effective basis for dam safety assessment.

[0184] The above describes in detail the anomaly identification method based on seepage and displacement response through some embodiments. In order to enable those skilled in the art to better understand and implement it, the corresponding device is also described in detail below through some embodiments.

[0185] See Figure 5 The diagram shown is a structural schematic of an anomaly identification device based on seepage and displacement response in an embodiment of this application. Figure 5 As shown, the anomaly identification device 500 based on seepage and displacement response may include:

[0186] The acquisition unit 510 is configured to acquire seepage response data and displacement response data of earth-rock dam under various operating conditions, and construct a response observation vector field to characterize the coupled temporal relationship between the seepage response and displacement response of the dam body.

[0187] Embedding unit 520 is configured to embed the response observation vector field into the structural state manifold space to obtain a characterization of the equivalent structural state inside the earth-rock dam and its evolution position.

[0188] Evolution unit 530 is configured to construct a structural state evolution graph in the structural state manifold space based on the operating condition driving relationship, with equivalent structural states as nodes and inter-state evolution relationships as edges;

[0189] Inversion unit 540 is configured to invert the evolution path of the structural state of the earth-rock dam at multiple time scales based on the structural state evolution diagram and operating condition constraints.

[0190] The identification unit 550 is configured to perform forward and reverse operating condition mapping on the evolution path respectively, generate corresponding forward and reverse structural state path sets, and determine that the earth-rock dam has undergone irreversible deterioration evolution in response to the inequivalence of the forward and reverse path sets in the structural state manifold space, and output the identification result.

[0191] For further details regarding the acquisition unit 510, the embedding unit 520, the evolution unit 530, the inversion unit 540, and the identification unit 550, please refer to the foregoing examples.

[0192] It is understandable that the above division of units is only a logical functional division. In actual implementation, they can be fully or partially integrated into a single physical entity, or they can be physically separated. Furthermore, the above units can be implemented by the processor calling software.

[0193] This application also provides an electronic device for implementing an anomaly identification method based on seepage and displacement response.

[0194] The electronic device includes a memory and a processor, as well as a computer program stored in the memory and executable on the processor. When the processor executes the program, it implements the anomaly identification method based on seepage and displacement response as described in any of the preceding claims.

[0195] It should be noted that the computer system of the electronic device shown below is merely an example and should not impose any limitations on the functionality and scope of use of the embodiments of this application.

[0196] like Figure 6 The diagram shown is a hardware structure schematic of an electronic device according to an embodiment of this application. Figure 6The illustrated electronic device includes a memory 601, a processor 602, and a transceiver 603. The processor 602 is coupled to the memory 601 and the transceiver 603. The memory 601 can be located inside or outside the terminal. The memory 601, processor 602, and transceiver 603 can be connected via a communication bus. The transceiver 603 is used to communicate with other devices or communication networks.

[0197] Optionally, the transceiver 603 can be a transmitter. The memory 601 stores a computer program that can run on the processor 602, and when the processor 602 runs the computer program, the transceiver 603 performs the steps in the communication method provided in the above embodiments.

[0198] It should be understood that in the embodiments of this application, the processor can be a central processing unit (CPU), or it can be other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor can be a microprocessor or any conventional processor.

[0199] It should also be understood that the memory in the embodiments of this application can be volatile memory or non-volatile memory, or may include both volatile and non-volatile memory. Non-volatile memory can be ROM, programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), or flash memory. Volatile memory can be random access memory (RAM), which is used as an external cache. By way of example, but not limitation, many forms of RAM are available, such as static random access memory (SRAM), dynamic random access memory (DRAM), synchronous dynamic random access memory (SDRAM), double data rate synchronous dynamic random access memory (DDR SDRAM), enhanced synchronous dynamic random access memory (ESDRAM), synchronous linked dynamic random access memory (SLDRAM), and direct rambus RAM (DRRAM).

[0200] The above embodiments can be implemented, in whole or in part, by software, hardware, firmware, or any other combination thereof. When implemented using software, the above embodiments can be implemented, in whole or in part, as a computer program product. The computer program product includes one or more computer instructions or computer programs. When the computer instructions or computer program are loaded or executed on a computer, all or part of the processes or functions described in the embodiments of this application are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer program can be stored in a medium or transferred from one medium to another computer-readable storage medium. For example, the computer program can be transferred from one website, computer, server, or data center to another website, computer, server, or data center via wired or wireless means.

[0201] While the embodiments disclosed in this application are as described above, the present invention is not limited thereto. Any person skilled in the art can make various modifications and alterations without departing from the spirit and scope of the invention; therefore, the scope of protection of the present invention should be determined by the scope defined in the claims.

Claims

1. An anomaly identification method based on seepage and displacement response, characterized in that, include: We acquire seepage response data and displacement response data of earth-rock dams under various operating conditions, and construct a response observation vector field to characterize the coupled temporal relationship between the seepage response and displacement response of the dam body. The response observation vector field is embedded into the structural state manifold space to obtain the equivalent structural state and its evolution position inside the earth-rock dam; In the structural state manifold space, a structural state evolution graph is constructed based on the driving relationship of operating conditions, with equivalent structural states as nodes and the evolution relationship between states as edges; Based on the structural state evolution diagram and operating condition constraints, the evolution path of the earth-rock dam's structural state under multiple time scales is obtained by inversion. The evolution path is mapped to forward and reverse operating conditions respectively, generating corresponding sets of forward and reverse structural state paths; In response to the inequivalence of the forward and reverse path sets in the structural state manifold space, the irreversible deterioration evolution of the earth-rock dam is determined, and the identification result is output.

2. The anomaly identification method according to claim 1, characterized in that, Embedding the response observation vector field into the structural state manifold space includes: Based on the spatiotemporal proximity between data points in the response observation vector field, a weighted adjacency graph is constructed. Determine the symmetric normalized Laplacian matrix corresponding to the weighted adjacency graph, and solve the eigensystem of the Laplacian matrix to obtain the sequence of eigenvectors arranged in ascending order of eigenvalues; The eigenvectors corresponding to the first k smallest non-zero eigenvalues ​​are selected, and the original high-dimensional response observation vector field is projected onto the low-dimensional space to form a coordinate representation in the structure state manifold space.

3. The anomaly identification method according to claim 2, characterized in that, Also includes: Construct a multi-layered structural state manifold space, including: Based on the physical structural zoning of the earth-rock dam, the dam body is divided into multiple sub-regions; For each sub-region, the seepage response data and displacement response data are independently embedded into the structural state manifold space to generate the corresponding local structural state submanifold. The state coordinates of all local structural state submanifolds are merged, and a second dimensionality reduction is performed to generate a multi-layer structural state manifold space.

4. The anomaly identification method according to claim 1, characterized in that, The evolution path of the earth-rock dam's structural state across multiple time scales, based on the evolution diagram and operational constraints, is obtained through inversion, including: Define the state coordinates corresponding to each time point in the structural state manifold space as a graph node; Calculate the directed transfer intensity from any time node to its successor time node. This intensity is determined by the change in operating conditions within the corresponding time period and the spatial similarity between the two nodes. Valid state transition relationships are selected based on a preset intensity threshold. The structure state evolution graph is constructed with nodes as vertices and valid directed transition relationships as edges.

5. The anomaly identification method according to claim 1 or 4, characterized in that, The evolution path of the earth-rock dam's structural state across multiple time scales, based on the structural state evolution diagram and operational constraints, is obtained through inversion, including: The time series of historical operating conditions is transformed into a sequence of conditional constraints for edge selection in the structural state evolution graph; Under the given conditional constraints, a graph search algorithm is used to search for an optimal path from the initial state node to the current state node in the evolution graph. This path must maximize the overall fit between the state sequence corresponding to the path and all observed data. The optimal path obtained is the evolution path of the inverted structural state at multiple time scales.

6. The anomaly identification method according to claim 1, characterized in that, The step of mapping the evolution path to forward and reverse operating conditions to generate corresponding sets of forward and reverse structural state paths includes: Starting from the earliest historical structural state, and following the time sequence of actual operating conditions, a step-by-step state transition deduction is performed in the structural state evolution diagram to generate a deduced positive structural state sequence. Starting from the current or specific end-of-term structural state, reverse state transition deduction is performed in the structural state evolution diagram according to the time sequence opposite to the actual operating conditions, generating the deduced reverse structural state sequence. All state sequences obtained by performing the above deduction at different time scales or different starting points are collected to form the set of forward structural state paths and the set of reverse structural state paths, respectively.

7. The anomaly identification method according to claim 1, characterized in that, The inequivalence of the forward and reverse path sets in the structural state manifold space determines that the earth-rock dam has undergone irreversible deterioration evolution, and outputs the identification result, including: In the structural state manifold space, calculate the average distance between the paired paths and the corresponding state points at the same time between the forward path set and the corresponding reverse path set. Calculate the curve similarity distance between the entire set of reverse paths and the set of forward paths; If the average distance and the curve similarity distance are both not less than their respective preset equivalence thresholds, then they are determined to be unequal.

8. The anomaly identification method according to claim 1, characterized in that, Also includes: When irreversible degradation is determined to have occurred, the key nodes and directed edges that cause the forward and reverse paths to begin to separate significantly are located in the structural state evolution diagram. Based on the coordinates of the key nodes in the manifold space, the response data characteristics of their main contributions are inverted and correlated to possible spatial locations within the dam body. The degree of bifurcation of the forward and reverse paths in the manifold space, starting from the key node, is calculated as a quantitative indicator of the degree of irreversible degradation evolution.

9. An anomaly identification device based on seepage and displacement response, characterized in that, include: The acquisition unit is configured to acquire seepage response data and displacement response data of earth-rock dams under various operating conditions, and to construct a response observation vector field to characterize the coupled temporal relationship between the seepage response and displacement response of the dam body. The embedding unit is configured to embed the response observation vector field into the structural state manifold space to obtain a characterization of the equivalent structural state inside the earth-rock dam and its evolution position. An evolution unit is configured to construct a structural state evolution graph in the structural state manifold space based on the driving relationship of the operating conditions, with equivalent structural states as nodes and evolutionary relationships between states as edges; The inversion unit is configured to invert the evolution path of the earth-rock dam's structural state at multiple time scales based on the structural state evolution diagram and operating condition constraints. The identification unit is configured to perform forward and reverse operating condition mapping on the evolution path respectively, generate corresponding forward and reverse structural state path sets, and determine that the earth-rock dam has undergone irreversible deterioration evolution in response to the inequivalence of the forward and reverse path sets in the structural state manifold space, and output the identification result.

10. An electronic device comprising a memory and a processor, wherein the memory stores a computer program executable on the processor, characterized in that, When the processor runs the computer program, it performs the steps of the anomaly identification method based on seepage-displacement response as described in any one of claims 1 to 8.

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