An old building curtain wall safety monitoring method and system

Abstract

The application belongs to the technical field of building structure health monitoring, and particularly relates to an old building curtain wall safety monitoring method and system, which comprises the following steps: combining a topological relationship and a reconstruction state to generate a structured measurement operator to compressively observe an original monitoring signal; constructing a hybrid redundant dictionary containing a transformation base and a feature atom set, and updating the feature atom set online by using a reconstruction residual; constructing an atom selection potential field in iterative reconstruction to identify a preferred atom, and determining a candidate atom set according to the contribution degree of the preferred atom; solving a regularization constraint in a candidate subspace to determine an optimal sparse atom subset, updating a support set, and mapping a preliminary reconstruction signal; establishing a constraint projection matrix according to a curtain wall strain coordination relationship to project and adjust strain components, combining the reconstruction signals, and outputting the reconstruction signals. The application reduces the reconstruction calculation complexity, and improves the reconstruction accuracy of sparse monitoring signals in a complex environment.

Description

Technical Field

[0001] This invention relates to the field of building structural health monitoring technology. More specifically, this invention relates to a method and system for safety monitoring of curtain walls in old buildings. Background Technology

[0002] Currently, real-time, 24 / 7 online monitoring of the safety status of curtain walls in old buildings has become an urgent need for urban public safety management. Wireless sensor networks, with their advantages of flexible deployment, low cost, and minimal wiring requirements, are commonly used in building structural health monitoring. However, curtain wall safety monitoring typically requires the dense deployment of numerous sensor nodes to obtain high spatiotemporal resolution parameters such as strain, displacement, and vibration. This puts immense pressure on the entire wireless monitoring network during long-term operation due to the large amount of data transmission, easily leading to bottlenecks such as wireless communication bandwidth congestion and rapid node power depletion. This makes it impossible to meet the practical engineering requirements for long-term, continuous, and stable monitoring of curtain walls in old buildings, especially since battery replacement is often difficult after node deployment.

[0003] Compressed sensing technology allows sensing nodes to acquire data at frequencies far below those required by the Nyquist sampling theorem and transmit a small number of compressed measurements, reducing power consumption for data acquisition and wireless transmission. However, existing compressed sensing and sparse signal reconstruction methods are mostly based on general theoretical models, which have limitations when facing complex safety monitoring scenarios for old building curtain walls. Traditional reconstruction algorithms cannot fully explore and utilize the spatial topology, historical operating states, and inherent strain coordination patterns between panels of the curtain wall structure, leading to distortion of the reconstructed monitoring signals in complex environments, and even the generation of error components that do not conform to objective laws. Conventional sparse reconstruction algorithms often have high computational complexity in processing large amounts of data and cannot identify the evolution process of potential fault characteristics in the curtain wall. Therefore, how to deeply integrate the unique structural patterns and monitoring needs of old building curtain walls, while reducing the computational complexity of reconstruction and improving the accuracy and reliability of sparse signal reconstruction, has become a key problem urgently needing to be solved in the field of wireless safety monitoring of old building curtain walls. Summary of the Invention

[0004] To address the technical problems of existing monitoring methods failing to incorporate objective structural laws in complex environments, resulting in easily distorted reconstructed monitoring signals, high computational complexity, and inability to identify fault evolution processes, this invention provides a safety monitoring method and system for curtain walls of old buildings.

[0005] In a first aspect, the present invention provides a method for safety monitoring of curtain walls in old buildings, comprising: S1: generating a structured measurement operator by combining the topological relationship of the curtain wall and the reconstruction state of the previous cycle; using the structured measurement operator to compress and observe the original monitoring signals of the sensor nodes within the monitoring area of ​​the old building curtain wall to obtain compressed measurement values; constructing a hybrid redundant dictionary including a standard sparse transform basis and a fault feature atom set; and updating the fault feature atom set online using the reconstruction residual of the previous cycle; S2: processing the compressed measurement values ​​using an iterative reconstruction algorithm; and constructing an atomic selection potential that integrates residual correlation, historical activation state, and spatial coupling strength in the atomic selection stage of each iteration. The process involves: 1) Identifying the preferred atom with the highest potential energy through atomic selection potential field; 2) Determining the candidate atom set based on the reconstruction contribution of the preferred atom; 3) Solving a regularization constraint problem within the subspace spanned by the candidate atom set to determine the optimal sparse atom subset; 4) Updating the support set and the signal residual of the current iteration step based on the optimal sparse atom subset, and mapping to generate the initial reconstruction signal; 5) Establishing a constraint projection matrix based on the strain coordination relationship of the curtain wall panel; 6) Extracting the strain components from the initial reconstruction signal and adjusting the projection of the strain components using the constraint projection matrix; 7) Recombining and merging to obtain the updated reconstruction signal; 8) Stopping the iteration when the termination condition is met and outputting the full monitoring signal.

[0006] By adopting the above technical solution, this invention achieves the tracking and observation of new damage characteristics of the curtain wall by combining the curtain wall topology and reconstruction state to generate a structured measurement operator and dynamically updating the hybrid redundancy dictionary. In the iterative reconstruction, an atomic selection potential field is constructed to locate candidate subspaces to solve for the optimal sparse subset, and then constraint projection adjustment is performed based on the strain coordination relationship of the curtain wall panels. This technical solution solves the problems of signal distortion and high computational complexity in existing technologies under complex environments by reducing the search space and introducing physical constraints at the end of the reconstruction, thus improving the reconstruction accuracy and reliability of the full monitoring signal.

[0007] Preferably, the step of generating a structured measurement operator by combining the curtain wall topology and the previous cycle reconstruction state includes: extracting the displacement from the full monitoring signal reconstructed in the previous monitoring cycle to calculate the local reduced strain parameters of each curtain wall unit; inputting an empirical attenuation model with embedded attenuation direction polarity constraints to obtain the stiffness reduction constant of the curtain wall unit that is negatively correlated with the local reduced strain parameters; adjusting the initial healthy state stiffness matrix using the stiffness reduction constant to obtain the online adjusted curtain wall unit stiffness matrix; spatially mapping it to match the spatial dimension of the original monitoring signal to obtain the global stiffness observation mapping matrix; constructing a physical topology connection mask matrix based on the curtain wall topology relationship between sensing nodes to perform sparsification filtering on the preset dimensionality reduction observation matrix; and performing matrix multiplication operations between the filtered dimensionality reduction observation matrix and the global stiffness observation mapping matrix to generate the structured measurement operator.

[0008] By adopting the above technical solution, the present invention directly encodes the physical degradation prior and spatial correlation attributes of old curtain walls into the observation operator, thereby giving the operator the ability to target key damaged areas of the structure during the compressed observation stage and reducing the redundancy of invalid observations.

[0009] Preferably, the online update of the fault feature atom set using the residual reconstruction from the previous cycle includes: extracting the signal residuals generated during the iteration process of the previous monitoring cycle, and constructing a two-dimensional residual data matrix by splicing them in chronological order; performing singular value decomposition on the two-dimensional residual data matrix to extract the left singular vector corresponding to the largest singular value; making the dimension of the left singular vector consistent with the dimension of the atom in the hybrid redundancy dictionary through interpolation or truncation to generate new feature atoms; and adding the new feature atoms to the fault feature atom set to expand the dimension of the hybrid redundancy dictionary, thereby completing the online update of the fault feature atom set.

[0010] By adopting the above technical solution, the present invention enables the dictionary to adaptively extract and characterize newly emerging weak fault modes of the curtain wall that exceed the initial sample library without re-performing full training, effectively avoiding the distortion of the reconstructed signal caused by dictionary mismatch.

[0011] Preferably, the construction of the atom selection potential field integrating residual correlation, historical activation state, and spatial coupling strength includes: calculating the absolute value of the inner product of the signal residual of the current iteration step and each atom in the hybrid redundancy dictionary as a residual correlation index; counting the frequency of each atom being selected into the optimal sparse atom subset within a set number of monitoring periods in the past as a historical activation probability; in the atom correlation network graph of the pre-constructed hybrid redundancy dictionary, counting the total number of connected atoms that satisfy the preset correlation condition and are activated with each atom, multiplying by a set coupling constant to obtain the spatial coupling strength; normalizing the residual correlation index, the historical activation probability, and the spatial coupling strength respectively, and then weighting and summing them using preset weights to obtain the potential energy of each atom, and using the potential energy of each atom to jointly constitute the atom selection potential field.

[0012] By adopting the above technical solution, this invention introduces the temporal persistence and spatial aggregation effect of physical damage to the curtain wall into the search process, guiding the algorithm to prioritize locking the preferred atoms with physical linkage characteristics during iteration, overcoming the blindness of searching with a single residual inner product, and accelerating the reconstruction convergence.

[0013] Preferably, determining the candidate atom set based on the reconstruction contribution of the preferred atom includes: calculating the ratio of the potential energy of the preferred atom to the sum of the potential energies of all current atoms, as the reconstruction contribution of the preferred atom; calculating the difference between 1 and the reconstruction contribution, multiplying the difference by a set network layer constant and rounding down to obtain the target expansion hop count; selecting connected atoms in the topological connectivity path matrix representing the inter-atomic correlation where the shortest path hop count to the preferred atom is not greater than the target expansion hop count; and combining the selected connected atoms with the preferred atom to form the candidate atom set.

[0014] Preferably, the step of solving the regularization constraint problem within the subspace spanned by the candidate atom set to determine the optimal sparse atom subset includes: establishing a regression matrix using the atoms in the candidate atom set as the fitting basis; constructing a local optimization problem with the sum of the signal residual approximation error of the current iteration step and the L1 norm regularization term of the atom weights as the objective function; solving the local optimization problem under the signal residual approximation condition of the current iteration step to obtain the initial weight value of each atom; obtaining the absolute value of the initial weight values ​​of all atoms and sorting them in descending order; selecting atoms whose absolute value is greater than a preset threshold for separation and extraction to form the optimal sparse atom subset.

[0015] Preferably, a constraint projection matrix is ​​established based on the strain compatibility relationship of the curtain wall panel. The strain components in the preliminary reconstructed signal are extracted and projected using the constraint projection matrix. The reconstructed signal is then reassembled and merged to obtain the updated reconstructed signal. This includes: establishing the Saint-Venant strain compatibility equation representing the geometric compatibility of continuous deformation of the curtain wall panel; using a finite difference operator for discretization to generate a second-order discrete coefficient structure matrix; performing singular value decomposition on the second-order discrete coefficient structure matrix to extract the set of all orthogonal vectors spanning the null space of the second-order discrete coefficient structure matrix to construct a projection operator matrix; multiplying the projection operator matrix with the transpose of the projection operator matrix to generate a constraint projection matrix; multiplying the constraint projection matrix with the strain components of the preliminary reconstructed signal to obtain a result vector; and replacing the corresponding strain component content in the preliminary reconstructed signal with the result vector to obtain the updated reconstructed signal.

[0016] By adopting the above technical solution, the present invention filters out pseudo-strain jump points that violate the continuous deformation law of the panel, which are introduced by noise or algorithm fitting errors, ensuring that the reconstructed signal strictly conforms to the objective laws of mechanics and enhancing the reliability of the monitoring data.

[0017] Preferably, the calculation of the local reduced strain parameters of each curtain wall unit includes: obtaining the local node coordinates and geometric dimension parameters of the corresponding curtain wall unit, and constructing a local geometric strain transformation matrix; performing matrix multiplication on the local geometric strain transformation matrix and the column vector of node displacements corresponding to the displacements in the full-volume monitoring signal to obtain a local strain tensor vector containing multiple dimensions; calculating the norm of the local strain tensor vector, and using the norm as the local reduced strain parameter of the corresponding curtain wall unit.

[0018] Preferably, the step of establishing the Saint-Venant strain compatibility equation representing the geometric compatibility of continuous deformation of the curtain wall panel, and using a finite difference operator for discretization to generate a second-order discrete coefficient structure matrix, includes: extracting the strain tensor components of each sensor node in the preliminary reconstructed signal in each dimension of the panel's two-dimensional plane coordinate system; constructing higher-order partial differential equations constraining the strain tensor components in each dimension; setting the grid step size based on the spatial dimensions of the curtain wall panel and the topological distribution of the sensor nodes, and using a second-order central finite difference operator to transform the higher-order partial differential equations into a discrete form containing algebraic difference combinations; and based on preset boundary condition constraints, assembling and filling the coefficients of the algebraic difference combinations corresponding to each sensor node into a global sparse matrix to generate the second-order discrete coefficient structure matrix.

[0019] Secondly, the present invention provides a safety monitoring system for curtain walls of old buildings, including a processor and a memory, wherein the memory stores computer program instructions, and when the computer program instructions are executed by the processor, the above-mentioned method for safety monitoring of curtain walls of old buildings is implemented.

[0020] By adopting the above technical solution, a computer program for the above-mentioned method of safety monitoring of curtain walls of old buildings is generated and stored in a memory so that it can be loaded and executed by a processor. A terminal device can then be made based on the memory and processor for convenient use.

[0021] The technical solution of the present invention has the following beneficial technical effects: This invention combines the topological relationship of the curtain wall with its historical reconstruction state to generate a structured measurement operator. It then fuses a standard sparse transform basis with a fault feature atom set obtained from online updates of the reconstruction residuals to construct a hybrid redundancy dictionary. This enables effective identification of abnormal features in aging curtain walls and improves the directionality of compressed observations. During reconstruction, this invention rapidly identifies preferred atoms by constructing an atom selection potential field that integrates residual correlation, historical activation states, and spatial coupling strength. The candidate atom set is then adaptively determined based on the reconstruction contribution of the preferred atoms. This mechanism reduces the spatial range of the atom search, improving reconstruction efficiency and accuracy while decreasing computational complexity. Furthermore, this invention uses the strain coordination relationship of the curtain wall panels to establish a constraint projection matrix, performing projection adjustments on the initial reconstruction signal. This aims to remove error components that do not conform to physical laws, thereby further enhancing the accuracy and rationality of the full monitoring signal. Attached Figure Description

[0022] Figure 1 This is a flowchart of a safety monitoring method for curtain walls of old buildings according to the present invention; Figure 2 This is a schematic diagram of the statistical distribution of the atomic selection potential field; Figure 3 This is a schematic diagram showing the mapping relationship between the reconstruction contribution coefficient and the target expansion hop count. Detailed Implementation

[0023] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are some embodiments of the present invention, but not all embodiments.

[0024] This invention discloses a method for safety monitoring of curtain walls in old buildings, referring to... Figure 1 This includes steps S1-S3: S1: Measurement operator generation and online update of hybrid redundancy dictionary.

[0025] In an optional embodiment, a structured measurement operator is generated by combining the curtain wall topology and the previous cycle reconstruction state. The structured measurement operator is used to compress the original monitoring signals of the sensor nodes in the monitoring area of ​​the old building curtain wall to obtain compressed measurement values. A hybrid redundancy dictionary is constructed at the data processing terminal. The hybrid redundancy dictionary includes a fixed standard sparse transform basis and a fault feature atom set. The fault feature atom set is updated online using the previous cycle reconstruction residual.

[0026] In the specific execution process, the system first acquires the spatial coordinate data of each sensor node on the curtain wall of the old building. Based on graph theory algorithms, it constructs an adjacency matrix representing the connection relationships between nodes. For example, it uses the NetworkX library to generate a topology graph and extracts the degree and connectivity indices of each node as prior knowledge of the spatial association of the curtain wall structure. At the same time, the system reads the reconstructed state vector output after the previous monitoring cycle's iterative reconstruction and determines the set of sensor nodes in the current cycle that are active based on the positions of the non-zero elements in the state vector. On this basis, the system combines the topology graph information and the distribution of active nodes, for example, using the random Gaussian distribution function of the NumPy library to generate a basic observation matrix. For active nodes and their first-order neighbor nodes, a weighting coefficient greater than 1 is multiplied on the corresponding column vector in the basic observation matrix, thereby enhancing the observation sensitivity of key areas of the curtain wall structure, thus generating a structured measurement operator matrix. Subsequently, the system performs matrix multiplication on the structured measurement operator matrix and the original monitoring signal vector to compress the high-dimensional original signal into a low-dimensional observation space, resulting in a compressed measurement value vector. Preferably, the system first performs normalization preprocessing on the original monitoring signal vector, and then multiplies the structured measurement operator matrix with the normalized signal vector to eliminate the impact of differences in the range of different sensing nodes on the consistency of compressed observations.

[0027] On the data processing terminal side, the system initializes a dictionary matrix, which consists of two parts: a fixed standard sparse transform basis and a dynamically expandable set of fault feature atoms. Specifically, the system calls the Discrete Cosine Transform function to generate the standard sparse transform basis matrix, providing an efficient sparse representation basis for stable monitoring signals under normal curtain wall conditions. Simultaneously, using a historical curtain wall fault signal sample set, the system trains and generates an initial fault feature atom set matrix through K-Singular Value Decomposition (K-SVD) to capture signal features of typical fault modes such as curtain wall panel cracking and keel deformation. The system concatenates the standard sparse transform basis matrix and the fault feature atom set matrix column-wise to construct a hybrid redundant dictionary matrix. After each monitoring cycle, the system extracts the reconstruction residual vector from the previous cycle. For example, it calls the micro-batch dictionary learning algorithm from the Scikit-learn library to iteratively update the element values ​​in the fault feature atom set matrix online, minimizing the residual reconstruction error as the optimization objective. This allows the dictionary to adaptively track emerging weak fault feature patterns during curtain wall structure degradation without re-executing full-sample dictionary training, thus ensuring continuous evolution of dictionary representation capabilities while reducing terminal computational overhead.

[0028] In an optional embodiment, the above-mentioned generation of structured measurement operators by combining the curtain wall topology and the previous cycle reconstruction state includes: extracting the displacement from the full monitoring signal reconstructed in the previous monitoring cycle, and calculating the local reduced strain parameters of each curtain wall unit; inputting the local reduced strain parameters into an empirical attenuation model to calculate the stiffness reduction constant of the curtain wall unit that is negatively correlated with the local reduced strain parameters; adjusting the initial healthy state stiffness matrix using the stiffness reduction constant to obtain the online adjusted curtain wall unit stiffness matrix; spatially mapping the online adjusted curtain wall unit stiffness matrix to match the spatial dimension of the original monitoring signal to obtain the global stiffness observation mapping matrix; constructing a physical topology connection mask matrix based on the curtain wall topology relationship between sensing nodes, and performing sparsification filtering on the preset dimensionality reduction observation matrix; and performing matrix multiplication operation between the filtered dimensionality reduction observation matrix and the global stiffness observation mapping matrix to generate the structured measurement operator.

[0029] More specifically, the system will locally reduce the strain parameters. By inputting an empirical attenuation model with embedded attenuation direction polarity constraints, the stiffness reduction constant of the curtain wall unit is calculated, and the nonlinear mechanical degradation behavior of the old curtain wall under repeated loads is depicted.

[0030] Specifically, the stiffness reduction constant satisfies the following relationship:

[0031] in, This represents the stiffness reduction constant of the i-th curtain wall element, and its value range is... ; Represents an exponential function with the natural constant as its base; This represents the empirical attenuation coefficient, which preferably ranges from 1.5 to 2.5, and is set to 2 in this embodiment; This represents the local equivalent strain parameter of the i-th curtain wall element; Represents a symbolic function; This represents the ultimate strain threshold, which was determined to be 0.005 based on the yield strain characteristics of the curtain wall material through previous experimental testing.

[0032] in, When the strain exceeds the ultimate strain threshold, a positive value is taken to accelerate the reduction of stiffness and reflect the cumulative effect of structural damage; when the strain is below the threshold, a negative value is taken to slow down the reduction and represent the elastic recovery ability of the material.

[0033] The system will determine the stiffness matrix of each curtain wall unit under its initial healthy state. Multiply by the corresponding reduction constant The local stiffness matrix after online adjustment is obtained. All localities are represented by the standard finite element Boolean mapping operator. Assembled into the global coordinate system, a global stiffness observation mapping matrix of size N×N is generated. Select size as The random Gaussian matrix is ​​used as the preset dimension-reduced observation matrix. ,in To reduce the number of observation nodes, for example The reduced-dimensional observation matrix is ​​sparsified and filtered based on the physical topology connection mask matrix between sensor nodes, retaining only the observation channels between adjacent nodes to reduce the amount of data transmitted wirelessly, and is then combined with... Performing matrix multiplication ultimately constructs a matrix of size... Structured measurement operator This enables dynamic tracking of the evolution of damage status in curtain wall structures using an observation matrix.

[0034] In an optional embodiment, the calculation of the local reduced strain parameters of each curtain wall unit includes: obtaining the local node coordinates and geometric dimension parameters of the corresponding curtain wall unit, and constructing a local geometric strain transformation matrix; performing matrix multiplication on the local geometric strain transformation matrix and the column vector of node displacements corresponding to the displacements in the full-scale monitoring signal to obtain a local strain tensor vector containing multiple dimensions; calculating the norm of the local strain tensor vector, and using the norm as the local reduced strain parameter of the corresponding curtain wall unit.

[0035] More specifically, the system extracts the nodal displacement column vector of each curtain wall unit from the N-dimensional full monitoring signal reconstructed in the previous cycle, for example, from the total number of monitoring nodes N=512. ,in M represents the total number of curtain wall units. For the i-th curtain wall unit, the system obtains its local node coordinates and geometric dimensions, and constructs the corresponding local strain-displacement matrix, i.e., the local geometric strain transformation matrix, based on the derivative of the finite element shape function with respect to the node coordinates. This local strain-displacement matrix is ​​then compared with the column vector of node displacements. Matrix multiplication is performed to obtain a local strain tensor vector containing three dimensions: horizontal normal strain, vertical normal strain, and in-plane shear strain. Subsequently, the system calculates the L2 norm of this local strain tensor vector, and through norm operations, maps the multidimensional strain tensor to a single scalar value, which serves as the local reduced strain parameter for the i-th curtain wall element. This parameter comprehensively reflects the overall deformation of the curtain wall unit in three directions: horizontal tension, vertical compression, and in-plane shear, providing a unified quantitative benchmark for the input of the subsequent stiffness reduction model. Preferably, the L2 norm can be replaced by the Frobenius norm to meet the requirements for equivalent characterization of strain energy density of anisotropic materials in curtain wall panels under complex stress states.

[0036] In an optional embodiment, the above-mentioned online update of the fault feature atom set using the residual reconstruction of the previous cycle includes: extracting the signal residual generated during the iteration process of the previous monitoring cycle, and constructing a two-dimensional residual data matrix by splicing them in chronological order; performing singular value decomposition on the two-dimensional residual data matrix to extract the left singular vector corresponding to the largest singular value; making the dimension of the left singular vector consistent with the dimension of the atom in the hybrid redundancy dictionary through interpolation or truncation to generate new feature atoms; and adding the new feature atoms to the fault feature atom set to expand the dimension of the hybrid redundancy dictionary, thereby completing the online update of the fault feature atom set.

[0037] More specifically, after the sparse reconstruction iteration process of the previous monitoring cycle is completed, the system retrieves the signal residual column vectors generated in the first L iteration steps, where the preferred range of L is 10 to 15, and horizontally concatenates the vectors in chronological order to construct a two-dimensional residual data matrix of size N×L, for example, 512×10. The singular value decomposition (SVD) algorithm is used to decompose the two-dimensional residual data matrix, locate the maximum singular value in the residual energy components, and extract the first column vector corresponding to the maximum singular value as the fault trend principal element.

[0038] Specifically, the singular value decomposition of the two-dimensional residual data matrix satisfies the following relation:

[0039] in, This represents a two-dimensional residual data matrix constructed by piecing together data in chronological order. The left singular matrix obtained by decomposition is represented by the column vectors forming an orthonormal basis of the column space. This represents a diagonal matrix, where the elements on the diagonal are the singular values ​​representing the residual energy components. This represents the transpose of the right singular matrix.

[0040] This principal component vector concentrates the variation patterns with the highest energy proportion in the residual data matrix, representing the direction of newly emerging fault features in the curtain wall that the previous dictionary failed to effectively represent. The system determines whether the length of this principal component vector is consistent with the standard length of atoms in the pre-set hybrid redundancy dictionary D. If not, the vector is resampled to the specified dimension of the dictionary using a cubic spline interpolation algorithm, or end truncation and zero-padding are performed, followed by L2 norm normalization. The normalized vector is then transformed into a newly emerging feature atom with unit energy. This newly emerging feature atom is added as a new column vector to the end of the fault feature atom set of the current hybrid redundancy dictionary, dynamically increasing the total number of columns in the dictionary by 1. This online expansion mechanism enables the dictionary to identify newly emerging weak fault features such as curtain wall crack propagation or node loosening that could not be represented in the previous cycle without retraining the full sample dictionary, thus completing the incremental online evolution of the dictionary space. If this online update step is not performed, the dictionary's representation capability will be limited to the fault modes covered by the initial training samples. When the curtain wall structure develops new damage patterns that exceed the initial training range during long-term service, the reconstruction algorithm will produce significant signal distortion due to dictionary mismatch, leading to missed fault detection or false alarms.

[0041] S2: Potential field construction and sparse reconstruction of local subspaces.

[0042] In an optional embodiment, an iterative reconstruction algorithm is used to process the compressed measurement values. In the atomic selection stage of each iteration, an atomic selection potential field is constructed that integrates residual correlation, historical activation state, and spatial coupling strength. The preferred atom with the largest potential energy is identified through the atomic selection potential field. The candidate atom set is determined based on the reconstruction contribution of the preferred atom. The regularization constraint problem is solved in the subspace spanned by the candidate atom set to determine the optimal sparse atom subset. The support set and the signal residual of the current iteration step are updated based on the optimal sparse atom subset, and a preliminary reconstruction signal is generated by mapping.

[0043] In its execution, the system first performs iterative initialization: the residual vector is initialized to be equal to the compressed measurement vector, the support set is initialized to an empty set, and the iteration counter is set to zero. During the atom selection phase of each iteration step, the system calculates the absolute value of the inner product between the current signal residual vector and each column of atoms in the sensor dictionary, serving as a residual correlation index. The sensor dictionary is constructed by multiplying a structured measurement operator matrix with a hybrid redundancy dictionary, with each column corresponding to an atom's observation pattern in the compressed domain. Simultaneously, the system constructs a Markov smoothing filter model based on the support set index of the previous cycle, calculating the activation probability of each atom in the current cycle as a historical activation state index to capture slowly changing, solidified characteristic patterns such as creep or long-term fatigue damage in old building curtain wall materials. Furthermore, the system uses the curtain wall node adjacency matrix to calculate the Pearson correlation coefficient between the activation states of each atom's corresponding node and its spatial neighbors, serving as a spatial coupling strength index to characterize the spread and aggregation effect of physical damage to the curtain wall in local space. Subsequently, the system integrates the residual correlation index, historical activation state index, and spatial coupling strength index using a linear weighted summation algorithm to generate the comprehensive potential energy value of each atom, thereby constructing the atom selection potential field vector.

[0044] In the atom selection potential field vector, the system finds the atom corresponding to the element with the largest potential energy value and identifies it as the preferred atom. The projection length of this preferred atom onto the residual vector is calculated as the reconstruction contribution, and the dynamic target expansion hop count is determined accordingly. In the topological connectivity path matrix representing the inter-atom correlation, the system selects connected atoms whose shortest path hop count to the preferred atom is not greater than the target expansion hop count, for example using Dijkstra's algorithm. These connected atoms are then combined with the preferred atom to form a candidate atom set. Subsequently, the system merges the candidate atom set into the current support set and extracts the column vectors corresponding to the support set indices from the hybrid redundancy dictionary to generate a subspace matrix. The system, for example, calls the Ridge Regression algorithm from the Scikit-learn library, adds an L2 norm regularization term to the subspace matrix, and performs least-squares fitting on the compressed measurement value vector to obtain a temporary reconstruction coefficient vector. The system retains the atoms corresponding to the top K elements with the largest absolute values ​​in the temporary reconstruction coefficient vector as the optimal sparse atom subset, where K is a pre-defined signal sparsity determined through experimental testing based on the frequency distribution characteristics of the curtain wall monitoring signal. The index of the optimal sparse atom subset is updated to the support set for the next iteration step. Subsequently, the system multiplies the structured measurement operator matrix, the subspace matrix corresponding to the optimal sparse atom subset, and the reconstruction coefficients to obtain the compressed domain approximate observation signal. The compressed domain approximate observation signal is subtracted from the compressed measurement value vector to obtain the updated signal residual vector for the current iteration step. The current reconstruction coefficient vector is then mapped back to the original signal space to generate the preliminary reconstruction signal for the current iteration step.

[0045] In an optional embodiment, the above-mentioned construction of an atomic selection potential field integrating residual correlation, historical activation state, and spatial coupling strength includes: calculating the absolute value of the inner product of the signal residual of the current iteration step and each atom in the hybrid redundancy dictionary as a residual correlation index; counting the frequency of each atom being selected into the optimal sparse atom subset within a set number of monitoring periods in the past as a historical activation probability; in the atomic correlation network graph of the pre-constructed hybrid redundancy dictionary, counting the total number of connected atoms that meet the preset correlation conditions and have been activated with each atom, multiplying by a set coupling constant to obtain the spatial coupling strength; after normalizing the residual correlation index, historical activation probability, and spatial coupling strength respectively, performing weighted summation using preset weights to obtain the potential energy of each atom, and using the potential energy of each atom to jointly constitute the atomic selection potential field.

[0046] More specifically, in the atom selection phase of the reconstruction iteration, the system calculates the absolute value of the inner product between the N-dimensional signal residual vector generated in the current step and the atom in the j-th column of the hybrid redundancy dictionary. This absolute value is set as the residual correlation index, which quantitatively represents the ability of the current atom to reduce signal residuals in this iteration. The system retrieves historical data from the database and counts the total number of times the j-th atom was successfully selected into the support set over the past H monitoring periods (preferably H=30 periods). Dividing this by H yields the interval... The historical activation probability within the system reflects the sustained activity of the signal pattern corresponding to the atom in long-term monitoring of the curtain wall, effectively capturing slowly changing solidified structural features such as material creep or fatigue damage. The system imports a dictionary-based atomic correlation network topology pre-established using inter-atomic cosine similarity, with a similarity threshold set to 0.85. Two atoms with a cosine similarity of at least 0.85 are considered highly correlated, and an edge connection is established in the network graph. The system checks the set of atoms successfully activated in the current iteration step, counts the number of connected atoms with edge connections to the target atom j and in an activated state, and multiplies this number by a preset spatial coupling constant. ,For example Spatial coupling strength is calculated, and this index characterizes the effect of the gradual spread and accumulation of physical damage to the curtain wall along the structural connection path in a local space. The system uses a maximum-minimum normalization method to map the index parameters of the above three dimensions to... Within the standard interval, a weighted summation operation is performed using a preset set of weighting coefficients. Preferably, the residual weight is set to 0.6, the historical weight to 0.25, and the coupling weight to 0.15, to obtain the comprehensive potential energy of the j-th atom. After the potential energy values ​​of all dictionary atoms are calculated in parallel, they are assembled together into a one-dimensional atom selection potential field vector to guide the iterative search. (Refer to...) Figure 2The figure shows the normalized potential field values ​​of the residual, historical, and coupling terms corresponding to five representative atoms. Among them, the values ​​of all three components of atom 3 are at a high level, while the values ​​of all components of atom 4 are generally low. By comparing the contribution ratio of the three indicators to the potential energy of different atoms, the rationality and effectiveness of the potential field weighted fusion logic can be intuitively supported.

[0047] In an optional embodiment, determining the candidate atom set based on the reconstruction contribution of the preferred atom includes: calculating the ratio of the potential energy of the preferred atom to the sum of the potential energies of all current atoms, as the reconstruction contribution of the preferred atom; calculating the difference between 1 and the reconstruction contribution, multiplying the difference by a set network layer constant and rounding down to obtain the target expansion hop count; selecting connected atoms in the topological connectivity path matrix representing the inter-atomic correlations whose shortest path hop count to the preferred atom is not greater than the target expansion hop count; and combining the selected connected atoms with the preferred atom to form a candidate atom set.

[0048] More specifically, after locating the preferred atom with the largest absolute potential energy in the potential field, the system divides the atom's potential energy value by the sum of the potential energies of all atoms participating in the calculation in the dictionary, and calculates a value between... Contribution coefficient of interval reconstruction This parameter quantitatively represents the relative contribution of the preferred atom in the current residual reduction process. The system calculates the margin constant for deviations from full contribution. And the margin constant is compared with the pre-calibrated maximum network layer constant. Multiply, where The preferred range is 3 to 5, for example, set to 4, to perform a floor operation on the product result. The output dynamically changes the target expansion hop count. This adaptive mechanism works by: when the preferred atom has a very high fit... When it approaches 1, As the target number approaches zero, the number of hops for expansion decreases accordingly. The system only needs to search a small number of neighboring atoms to complete the current iteration, thus reducing computational overhead. Furthermore, when the single-atom matching degree is low... When smaller, As the target hop count increases, the system expands the search range to acquire more joint feature atoms to jointly fit the residual, avoiding slow convergence due to insufficient representation power of a single atom. The system indexes the dictionary topological connectivity path matrix generated and stored offline. For example, it uses Dijkstra's algorithm to pre-record the shortest paths between each atom node. During iteration, Boolean logic is used to select all surrounding connected atoms whose shortest path hop count to the preferred atom node is no greater than the target hop count. The basis vectors corresponding to all connected atoms in the search are extracted and combined with the preferred atom to perform deduplication and merging, forming a candidate atom set matrix with significantly reduced dimensionality and physical connectivity, thus defining clear data boundaries for subsequent optimization problems in local subspaces. (Refer to...) Figure 3 This figure outlines the relationship between the reconstruction contribution coefficient and the number of hops in the neighborhood search, demonstrating how the coverage of the iterative search automatically adapts and adjusts to fit the spatial correlation characteristics of the curtain wall structure nodes, following the changes in the fitting ability of the preferred atom.

[0049] In an optional embodiment, the above-mentioned solution of the regularization constraint problem within the subspace spanned by the candidate atom set to determine the optimal sparse atom subset includes: establishing a regression matrix using the atoms in the candidate atom set as the fitting basis; constructing a local optimization problem with the sum of the signal residual approximation error of the current iteration step and the L1 norm regularization term of the atom weights as the objective function; solving the local optimization problem under the signal residual approximation condition of the current iteration step to obtain the initial weight value of each atom; obtaining the absolute value of the initial weight values ​​of all atoms and sorting them in descending order; selecting atoms with absolute values ​​greater than a preset threshold for separation and extraction to form the optimal sparse atom subset.

[0050] More specifically, the system uses the candidate atom set matrix obtained after dimensionality reduction screening as the fitting regression basis for the local signal space, constructing a local unconstrained convex optimization problem with the atom weight column vector as the optimization variable. The objective function of this optimization problem consists of two parts: the first part is the least squares mean square approximation error between the signal residual of the current iteration step and the weighted combination of candidate atoms, used to measure the fidelity of the reconstructed signal to the observed data; the second part is the atom weight sparsity regularization penalty term represented by the L1 norm, used to suppress the introduction of redundant atoms, and the regularization adjustment coefficient is used. Balancing the weights between the two, where The preferred parameter range is 0.01 to 0.05, for example, set to 0.02, to achieve an optimal trade-off between reconstruction fidelity and representation sparsity. The system uses, for example, the Alternating Direction Multiplier Method (ADMM) or a fast iterative shrinkage algorithm to iteratively approximate the solution within the local subspace. After a set number of iterations, it outputs the local convergence result, i.e., obtains the initial real weight values ​​of each atom in the candidate atom set. The absolute values ​​of these initial weight values ​​are extracted, arranged in descending order, and a hard truncation preset threshold is generated based on a specific proportion of the current maximum weight absolute value, for example, 10% of the maximum value as the truncation boundary. Atoms in columns with initial weight absolute values ​​greater than this preset threshold are extracted from the candidate basis, while redundant atoms below the threshold are removed. This mechanism, based on dual screening using L1 regularization and hard thresholding, effectively preserves the optimal sparse atomic subset that can identify details of local deformation and high-frequency micro-cracks in old curtain walls. It avoids the defect of traditional greedy algorithms that lose weak fault signal components due to excessive pursuit of sparsity. Then, the optimal sparse atomic subset is updated to the global support set and participates in the signal residual update of the next iteration step.

[0051] S3: Physical constraint projection adjustment and full signal output.

[0052] In an optional embodiment, after each iteration update, a constraint projection matrix is ​​established based on the strain coordination relationship of the curtain wall panel, the strain components in the preliminary reconstructed signal are extracted, and the strain components are projected and adjusted using the constraint projection matrix. The reconstructed signal is then obtained by recombination and merging. The iteration stops when the set termination condition is met, and the full monitoring signal is output.

[0053] In the specific execution process, the system extracts the strain compatibility equation between adjacent sensing nodes as a priori physical constraint based on the elastic mechanics of thin-plate bending theory of the four-point supported glass panel of the curtain wall. Based on the strain compatibility equation, the system constructs a second-order finite-difference Laplace matrix as the constraint matrix, for example, using a sparse matrix generating function. This matrix encodes the spatial continuity condition that must be satisfied between the strain components of each node of the curtain wall panel under elastic deformation conditions. The system calculates the difference between the transpose of the identity matrix and the constraint matrix, and the product of the pseudo-inverse of the constraint matrix. For example, it uses a linear algebraic inverse function to generate the constraint projection matrix. The column space of this projection matrix is ​​the legal strain state subspace that satisfies the physical laws of strain compatibility. After solving for the temporary reconstruction coefficients in each iteration, the system maps the temporary reconstruction coefficient vector back to the full-dimensional original signal space according to the current support set index, generating the current preliminary reconstruction signal vector. The strain tensor components are extracted from the initial reconstructed signal vector to form a strain state subvector. A constraint projection matrix is ​​applied to the current strain state subvector using matrix multiplication, orthogonally projecting the strain components onto the null space that satisfies the physical laws of strain compatibility. This filters out spurious strain components introduced by noise interference or algorithm errors that do not conform to physical laws. The projected strain state subvector is then reassembled with the displacement state subvector unaffected by the constraint to obtain the projected global reconstructed signal vector, effectively reducing error components due to spatial discontinuities in the deformation field. The system calculates the L2 norm energy value of the updated signal residual vector and determines whether this energy value is less than a set tolerance threshold or whether the current iteration count has reached the set maximum iteration count. If neither of these termination conditions is met, the iteration count is incremented, and the system returns to the atom selection stage to continue the next iteration. If the termination condition is met, the iteration stops and the loop exits. For example, the array output function of the NumPy library is called to save the reconstructed signal vector after the last projection adjustment as the full monitoring signal and output it to the terminal interface for visualization, providing high-precision monitoring data support that conforms to physical laws for the assessment and early warning of the safety status of the curtain wall.

[0054] In an optional embodiment, the above-mentioned process of establishing a constraint projection matrix based on the strain compatibility relationship of the curtain wall panel, extracting strain components from the preliminary reconstructed signal, and projecting and adjusting the strain components using the constraint projection matrix to obtain an updated reconstructed signal includes: establishing the Saint-Venant strain compatibility equation representing the geometric compatibility of continuous deformation of the curtain wall panel; using a finite difference operator for discretization to generate a second-order discrete coefficient structure matrix; performing singular value decomposition on the second-order discrete coefficient structure matrix to extract the set of all orthogonal vectors spanning the null space of the second-order discrete coefficient structure matrix to construct a projection operator matrix; multiplying the projection operator matrix with the transpose of the projection operator matrix to generate a constraint projection matrix; multiplying the constraint projection matrix with the strain components of the preliminary reconstructed signal to obtain a result vector; and using the result vector to replace the corresponding strain component content in the preliminary reconstructed signal to obtain the updated reconstructed signal.

[0055] More specifically, after outputting the preliminary reconstruction results at the end of a single iteration, the system, based on the theory of elastic thin plates, constructs a high-order Saint-Venant strain compatibility equation set to ensure the continuity of panel deformation, taking into account the geometric dimensions and stress boundary conditions of the tested old curtain wall panel with four-point or multi-point support. Singular value decomposition is performed on the second-order discrete coefficient structure matrix to extract all orthonormal basis vectors spanning the null space of the matrix. These are then concatenated column-wise to form the projection operator matrix Q, whose dimension is determined by the dimension of the null space. Let the rank of the matrix be k, then the dimension of Q is 3N×(3N-k). The system calculates the dot product of this projection operator matrix and its transpose. Generate a symmetric idempotent constraint projection matrix with a fixed size of 3N×3N and eigenvalues ​​that are either 0 or 1. This matrix satisfies the mathematical properties of the projection operator. and To ensure consistency in the results of multiple projection operations, the constraint projection matrix is ​​left-multiplied by the strain state sub-vector in the noisy preliminary reconstructed signal estimated by the least squares method. This projection adjustment process filters out high-frequency spurious fluctuation components and pseudo-strain points that violate geometric compatibility criteria, ensuring that the projected strain field automatically meets the physical continuity requirements of panel deformation. The system uses the filtered and corrected result vector to replace the corresponding strain component content in the original signal, completing the projection adjustment of the signal constraint reconstruction. This effectively improves the physical interpretability and numerical computational stability of subsequent monitoring reconstruction under noisy interference environments. Without this projection adjustment step, the strain components in the reconstructed signal may contain unreasonable jumps that violate the conditions for continuous panel deformation. These jumps will be misjudged as structural anomalies in subsequent damage identification and safety assessment, thus triggering false alarms and reducing the reliability of the monitoring system.

[0056] In an optional embodiment, the aforementioned establishment of the Saint-Venant strain compatibility equation representing the geometric compatibility of continuous deformation of the curtain wall panel, and the discretization processing using a finite difference operator to generate a second-order discrete coefficient structure matrix, includes: extracting the strain tensor components of each sensor node in each dimension of the panel's two-dimensional plane coordinate system from the preliminary reconstructed signal; constructing higher-order partial differential equations constraining the strain tensor components of each dimension; setting the grid step size based on the spatial dimensions of the curtain wall panel and the topological distribution of the sensor nodes, and using a second-order central finite difference operator to transform the higher-order partial differential equations into a discrete form containing algebraic difference combinations; and based on preset boundary condition constraints, assembling and filling the coefficients of the algebraic difference combinations corresponding to each sensor node into a global sparse matrix to generate a second-order discrete coefficient structure matrix.

[0057] More specifically, the system extracts the strain tensor components of each sensing node in the preliminary reconstructed signal in the two-dimensional plane coordinate system of the panel, including the horizontal normal strain. Vertical normal strain and in-plane shear strain Based on the geometric compatibility principle in continuum mechanics that prevents tearing and overlapping after deformation, a higher-order partial differential equation constrains the three strain tensor components. This equation expresses the physical constraint that the sum of the second-order rate of change of the horizontal normal strain in the vertical direction and the second-order rate of change of the vertical normal strain in the horizontal direction at any point within the panel must be equal to the mixed second-order partial derivative of the in-plane shear strain.

[0058] Specifically, higher-order partial differential equations satisfy the following relation:

[0059] in, This represents the horizontal normal strain at any point within the panel. This represents the vertical normal strain at any point within the panel. This represents the in-plane shear strain at any point within the panel. and These represent the horizontal and vertical coordinates in the two-dimensional plane coordinate system of the panel, respectively.

[0060] The system combines the physical dimensions of the curtain wall panels and the topology distribution of the sensor nodes to set the horizontal grid step size. Grid step size in the vertical direction ,For example , The higher-order partial differential equations are discretized and expanded using a second-order central finite difference operator, transforming each second-order spatial partial derivative into a linear algebraic difference combination involving the strain values ​​of the four adjacent nodes (upper, lower, left, and right) centered on the local central node. For each non-boundary node within the panel, a discrete compatibility equation can be formulated as follows.

[0061] Specifically, the discrete coordination equations satisfy the following relation:

[0062] in, and These represent the horizontal row and column indices and the vertical row and column indices of the sensor node in the two-dimensional grid of the panel, respectively. Indicates coordinate index as The horizontal normal strain at the node; Indicates coordinate index as Vertical normal strain at the node; Indicates coordinate index as The in-plane shear strain at the node, the relationship involved in the formula is as follows , Both are row and column index offsets of the corresponding adjacent nodes; This indicates the horizontal grid step size set during grid discretization. This indicates the vertical grid step size set during grid discretization.

[0063] The system traverses all non-boundary internal nodes within the curtain wall monitoring area, combining boundary condition constraints with four-point or multi-point supports to eliminate the degrees of freedom of the boundary nodes. The coefficients of the algebraic difference combination corresponding to each node are assembled and filled into the corresponding rows and columns of the global sparse matrix, generating a second-order discrete coefficient structure matrix characterizing the global spatial geometric continuity criterion. For example, a standard five-point finite difference template is used to perform second-order difference discretization on this partial differential equation, corresponding to the horizontal normal strain. Vertical normal strain and in-plane shear strain Three strain components are used to calculate and generate a sparse and banded symmetric second-order discrete coefficient structure matrix of size 3N×3N. This matrix constructs the continuous strain coordination criterion of each monitoring point of the curtain wall panel in space in the compact form of a system of algebraic equations, providing a rigorous mathematical basis for subsequent zero-space projection and physical constraint filtering.

[0064] The experimental conditions were set on an old curtain wall experimental platform with 512 monitoring nodes. The number of compressed observation nodes was set to 128. The experiment was conducted for 30 consecutive monitoring cycles under strong wind vibration and temperature noise interference with a signal-to-noise ratio of 20 dB, collecting 5000 sets of curtain wall panel node displacement and strain data. The control group used a basic reconstruction model based on the traditional orthogonal matching pursuit algorithm combined with a Gaussian random measurement matrix. Ablation group one added only a structured measurement operator and an online dictionary expansion module to the control group. Ablation group two added only a multidimensional potential field atom selection and constraint projection module to the control group. The experimental group was a complete optimized model containing all the proposed modules of this invention. Under continuous monitoring, the average reconstruction error of the control group was 14.5%, the peak signal-to-noise ratio was 23.2 dB, and the weak fault identification rate was 72%. The average reconstruction error of ablation group one decreased to 9.6%, the peak signal-to-noise ratio increased to 27.8 dB, and the weak fault identification rate reached 83%. In ablation group 2, the average reconstruction error decreased to 8.4%, the peak signal-to-noise ratio was 29.5 dB, and the weak fault identification rate was 86%. In the experimental group, the average reconstruction error of the complete scheme decreased to 3.2%, the peak signal-to-noise ratio jumped to 34.6 dB, and the weak fault identification rate reached a maximum of 97.5%.

[0065] Figure 2 The diagram illustrates the statistical distribution of the potential field for atom selection. Each group of four parallel bars represents the residual correlation index, historical activation probability, spatial coupling strength, and weighted comprehensive potential energy, respectively. The height of the bar represents the magnitude of the corresponding index value. The image shows that the component values ​​of atom 3 are all high, and its comprehensive potential energy is significantly higher than that of other atoms. This proves that the potential field weighted fusion logic successfully identified key feature atoms with physical connectivity, guiding the algorithm to accurately lock onto the preferred atom during iterative search. Observing the component distribution of atoms with different indices, it can be found that the indicators for atom 4 are all low, and its comprehensive potential energy is also weakened. This corresponds to the algorithm feature described in the specific implementation that uses multi-dimensional indicators to comprehensively evaluate the contribution of atom reconstruction.

[0066] Figure 3 This diagram illustrates the mapping relationship between the reconstruction contribution coefficient and the target expansion hop count. The stepped solid lines represent the hop count values ​​corresponding to different contribution intervals. The vertical position of the line segments represents the size of the expanded search range. The image shows that the target expansion hop count is not fixed but decreases in a stepped manner as the reconstruction contribution coefficient increases. This proves that the algorithm successfully achieves adaptive dynamic adjustment of the atomic neighborhood search range without performing unnecessary global searches when the first-choice atom has extremely strong fitting ability. Observing the drop points of the curve, it can be found that the target expansion hop count decreases accordingly each time the contribution coefficient crosses a specific threshold interval. This corresponds to the mathematical feature described in the specific implementation method of using a floor function to automatically reduce the search neighborhood.

[0067] This invention also discloses a safety monitoring system for curtain walls of old buildings, including a processor and a memory. The memory stores computer program instructions, and when the computer program instructions are executed by the processor, a safety monitoring method for curtain walls of old buildings according to this invention is implemented.

[0068] The system also includes other components well known to those skilled in the art, such as communication buses and communication interfaces, the settings and functions of which are known in the art and will not be described in detail here.

[0069] It should be noted that those skilled in the art can make various modifications and improvements without departing from the inventive concept, and these all fall within the scope of protection of this invention. Therefore, the scope of protection of this patent should be determined by the appended claims.

Claims

1. A method for safety monitoring of curtain walls in old buildings, characterized in that, include: S1: Combine the topological relationship of the curtain wall and the reconstruction state of the previous cycle to generate a structured measurement operator. Use the structured measurement operator to compress the original monitoring signals of the sensor nodes in the monitoring area of ​​the old building curtain wall to obtain compressed measurement values. A hybrid redundant dictionary consisting of a standard sparse transform basis and a fault feature atom set is constructed, and the fault feature atom set is updated online using the reconstruction residual from the previous cycle. S2: An iterative reconstruction algorithm is used to process compressed measurements. In the atomic selection stage of each iteration, an atomic selection potential field is constructed that integrates residual correlation, historical activation state and spatial coupling strength. The preferred atom with the largest potential energy is identified by the atomic selection potential field, and the candidate atom set is determined based on the reconstruction contribution of the preferred atom. Solve the regularization constraint problem in the subspace spanned by the candidate atom set to determine the optimal sparse atom subset, update the support set and the signal residual of the current iteration step based on the optimal sparse atom subset, and map to generate the preliminary reconstructed signal; S3: Establish a constraint projection matrix based on the strain coordination relationship of the curtain wall panel, extract the strain components in the preliminary reconstruction signal, and use the constraint projection matrix to project and adjust the strain components. Reassemble and merge to obtain the updated reconstruction signal. Stop the iteration when the iteration process meets the termination condition and output the full monitoring signal.

2. The method for safety monitoring of curtain walls in old buildings according to claim 1, characterized in that, The process of generating a structured measurement operator by combining the curtain wall topology and the previous cycle reconstruction state includes: extracting the displacement from the full monitoring signal reconstructed in the previous monitoring cycle to calculate the local reduced strain parameters of each curtain wall unit; inputting an empirical attenuation model with embedded attenuation direction polarity constraints to obtain the stiffness reduction constant of the curtain wall unit that is negatively correlated with the local reduced strain parameters; adjusting the initial healthy state stiffness matrix using the stiffness reduction constant to obtain the online adjusted curtain wall unit stiffness matrix; spatially mapping it to match the spatial dimension of the original monitoring signal to obtain the global stiffness observation mapping matrix; constructing a physical topology connection mask matrix based on the curtain wall topology relationship between sensing nodes to perform sparsification filtering on the preset dimensionality reduction observation matrix; and performing matrix multiplication between the filtered dimensionality reduction observation matrix and the global stiffness observation mapping matrix to generate the structured measurement operator.

3. The method for safety monitoring of curtain walls in old buildings according to claim 1, characterized in that, The method of using the residual reconstruction from the previous cycle to update the fault feature atom set online includes: extracting the signal residual generated during the iteration process of the previous monitoring cycle, and constructing a two-dimensional residual data matrix by splicing them in chronological order; performing singular value decomposition on the two-dimensional residual data matrix to extract the left singular vector corresponding to the largest singular value; making the dimension of the left singular vector consistent with the dimension of the atom in the hybrid redundancy dictionary through interpolation or truncation to generate a new feature atom; and adding the new feature atom to the fault feature atom set to expand the dimension of the hybrid redundancy dictionary, thereby completing the online update of the fault feature atom set.

4. The method for safety monitoring of curtain walls in old buildings according to claim 1, characterized in that, The construction of the atom selection potential field integrating residual correlation, historical activation state, and spatial coupling strength includes: calculating the absolute value of the inner product of the signal residual of the current iteration step and each atom in the hybrid redundancy dictionary as a residual correlation index; counting the frequency of each atom being selected into the optimal sparse atom subset within a set number of monitoring periods in the past as a historical activation probability; in the atom correlation network graph of the pre-constructed hybrid redundancy dictionary, counting the total number of connected atoms that meet the preset correlation conditions and are activated with each atom, multiplying by a set coupling constant to obtain the spatial coupling strength; normalizing the residual correlation index, the historical activation probability, and the spatial coupling strength respectively, and then weighting and summing them using preset weights to obtain the potential energy of each atom, and using the potential energy of each atom to jointly constitute the atom selection potential field.

5. The method for safety monitoring of curtain walls in old buildings according to claim 1, characterized in that, The step of determining the candidate atom set based on the reconstruction contribution of the preferred atom includes: calculating the ratio of the potential energy of the preferred atom to the sum of the potential energies of all current atoms, as the reconstruction contribution of the preferred atom; calculating the difference between 1 and the reconstruction contribution, multiplying the difference by a set network layer constant and rounding down to obtain the target expansion hop count; selecting connected atoms in the topological connectivity path matrix representing the inter-atomic correlation where the shortest path hop count to the preferred atom is not greater than the target expansion hop count; and combining the selected connected atoms with the preferred atom to form the candidate atom set.

6. The method for safety monitoring of curtain walls in old buildings according to claim 1, characterized in that, The step of solving a regularization constraint problem within the subspace spanned by the candidate atom set to determine the optimal sparse atom subset includes: establishing a regression matrix using the atoms in the candidate atom set as the fitting basis; constructing a local optimization problem with the sum of the signal residual approximation error of the current iteration step and the L1 norm regularization term of the atom weights as the objective function; solving the local optimization problem under the signal residual approximation condition of the current iteration step to obtain the initial weight value of each atom; obtaining the absolute value of the initial weight values ​​of all atoms and sorting them in descending order; selecting atoms whose absolute value is greater than a preset threshold for separation and extraction to form the optimal sparse atom subset.

7. The method for safety monitoring of curtain walls in old buildings according to claim 1, characterized in that, Based on the strain compatibility relationship of the curtain wall panel, a constraint projection matrix is ​​established. The strain components in the preliminary reconstructed signal are extracted and projected using the constraint projection matrix. The reconstructed signals are then combined to obtain the updated reconstructed signals. This process includes: establishing the Saint-Venant strain compatibility equation representing the geometric compatibility of continuous deformation of the curtain wall panel; using a finite difference operator for discretization to generate a second-order discrete coefficient structure matrix; performing singular value decomposition on the second-order discrete coefficient structure matrix to extract the set of all orthogonal vectors spanning the null space of the second-order discrete coefficient structure matrix to construct a projection operator matrix; multiplying the projection operator matrix with the transpose of the projection operator matrix to generate the constraint projection matrix; multiplying the constraint projection matrix with the strain components of the preliminary reconstructed signal to obtain a result vector; and replacing the corresponding strain component content in the preliminary reconstructed signal with the result vector to obtain the updated reconstructed signal.

8. The method for safety monitoring of curtain walls in old buildings according to claim 2, characterized in that, The calculation of the local reduced strain parameters of each curtain wall unit includes: obtaining the local node coordinates and geometric dimension parameters of the corresponding curtain wall unit, and constructing a local geometric strain transformation matrix; performing matrix multiplication on the local geometric strain transformation matrix and the column vector of node displacements corresponding to the displacements in the full-scale monitoring signal to obtain a local strain tensor vector containing multiple dimensions; calculating the norm of the local strain tensor vector, and using the norm as the local reduced strain parameter of the corresponding curtain wall unit.

9. A method for safety monitoring of curtain walls in old buildings according to claim 7, characterized in that, The process of establishing the Saint-Venant strain compatibility equation representing the geometric compatibility of continuous deformation of the curtain wall panel, and discretizing it using a finite difference operator to generate a second-order discrete coefficient structure matrix, includes: extracting the strain tensor components of each sensor node in the two-dimensional plane coordinate system of the panel in the preliminary reconstructed signal; constructing higher-order partial differential equations constraining the strain tensor components in each dimension; setting the grid step size based on the spatial dimensions of the curtain wall panel and the topological distribution of the sensor nodes, and using a second-order central finite difference operator to transform the higher-order partial differential equations into a discrete form containing algebraic difference combinations; and based on preset boundary condition constraints, assembling and filling the coefficients of the algebraic difference combinations corresponding to each sensor node into a global sparse matrix to generate the second-order discrete coefficient structure matrix.

10. A safety monitoring system for curtain walls of old buildings, characterized in that, include: A processor and a memory, wherein the memory stores computer program instructions that, when executed by the processor, implement a method for safety monitoring of curtain walls of old buildings according to any one of claims 1-9.

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