Adaptive simulation step size control method and system based on multi-resolution extrapolation

Abstract

The application provides an adaptive simulation step length control method and system based on multi-resolution deduction, relates to the technical field of adaptive control, and acquires traffic characteristic data of each node in a simulation network and resource load data of a corresponding virtual host; after the traffic characteristic data and the resource load data are aligned through resampling, splicing and fusion are performed to generate an associated state vector; a trajectory matrix is constructed based on the associated state vector, a plurality of evolution matrices are obtained; a state transition operator is constructed based on the evolution matrices, a main eigenvalue modulus value and a distribution offset of an eigenvalue set in a complex plane are determined; by comparing the main eigenvalue modulus value with a preset threshold value and comparing a difference between the distribution offset and a preset reference offset with a preset difference value, the simulation step length in a high-resolution simulation mode is reduced and controlled. The simulation computing power is distributed on demand, and the capture accuracy and adaptive response capability of a local abnormal state of a network are improved.

Description

Technical Field

[0001] This application relates to the field of adaptive control technology, and in particular to an adaptive simulation step size control method and system based on multi-resolution derivation. Background Technology

[0002] With the continuous development of simulation and evolutionary modeling technologies for large and complex systems, higher requirements are being placed on the computational efficiency and simulation accuracy of simulation systems in fields such as aerospace and industrial digital twins.

[0003] Existing simulation step size control techniques mostly employ adjustment mechanisms based on single-state threshold triggering, or rely on preset mapping rules to switch between models of different resolutions. These methods typically passively scale the time step to adapt to the current system dynamics during simulation by monitoring specific state change rates or local error indices.

[0004] However, when dealing with complex tasks characterized by high nonlinearity and cross-scale coupling, existing technologies struggle to achieve optimal matching of computational resources in the time and spatial domains. Because the adjustment process lacks foresight regarding system evolution trends, it easily leads to lag in response during periods of drastic state fluctuations or frequent step size oscillations during system stability, thus affecting the overall stability and convergence speed of the simulation. Therefore, existing technologies suffer from the technical challenge of achieving an optimal balance between computational efficiency and simulation accuracy in complex dynamic environments. Summary of the Invention

[0005] The purpose of this application is to provide an adaptive simulation step size control method and system based on multi-resolution extrapolation, so as to solve the technical problem in the prior art that it is difficult to achieve the optimal balance between computational efficiency and extrapolation accuracy in complex dynamic environments.

[0006] Firstly, this application provides an adaptive simulation step size control method based on multi-resolution derivation, including: Obtain traffic characteristic data of each node in the simulated network and resource load data of the corresponding virtual host. The traffic characteristic data includes traffic characteristic entropy, IP address distribution breadth sequence and protocol anomaly deviation sequence. The resource load data includes utilization fluctuation sequence, memory page swapping frequency sequence and driver call frequency sequence. After resampling, the traffic feature data and resource load data are aligned and then spliced ​​together to generate an associated state vector. A trajectory matrix is ​​constructed based on the associated state vector. The trajectory matrix is ​​decomposed and reconstructed through singular spectrum analysis to obtain a non-stationary trend signal. Multiple evolution matrices are obtained by calculating the temporal evolution gradient of the non-stationary trend signal and performing feature space projection mapping. A state transition operator is constructed based on the evolution matrix. By performing eigenvalue decomposition on the state transition operator, the magnitude of the principal eigenvalue and the distribution offset of the eigenvalue set in the complex plane are determined. By comparing the principal eigenvalue magnitude with a preset threshold and the difference between the distribution offset and the preset baseline deviation with a preset difference, abnormal state nodes are identified. The simulation process of the abnormal state nodes is switched to high-resolution simulation mode, and the step size adjustment coefficient is determined using the principal eigenvalue magnitude to reduce the simulation step size in high-resolution simulation mode.

[0007] Optionally, the traffic feature data and resource load data are aligned and then concatenated after resampling to generate an associated state vector, including: The reference sampling frequency is obtained by calculating the least common multiple of the first sampling frequency of traffic characteristic data and the second sampling frequency of resource load data. Using the reference sampling frequency as the target sampling rate, linear interpolation is used to resample the traffic characteristic data and resource load data to obtain the first sampled data set corresponding to the traffic characteristic data and the second sampled data set corresponding to the resource load data. Based on the node identifier of each node, the feature vectors of the sampled data belonging to the same node and the same time in the first sampled data set and the second sampled data set are concatenated to obtain the composite feature vector of each node at different times. All composite feature vectors are combined to obtain a composite feature group. Based on the preset feature projection matrix, the composite feature group is projected into the feature space to obtain the associated state vector.

[0008] Optionally, a trajectory matrix is ​​constructed based on the associated state vector, including: Using a preset window length and sliding step size, the associated state vector is cyclically slid sampled to obtain multiple sub-sequence segments; Following the chronological order, all subsequence segments are vertically concatenated into matrix blocks to obtain the trajectory matrix.

[0009] Optionally, the trajectory matrix is ​​decomposed and reconstructed through singular spectral analysis to obtain a non-stationary trend signal. Then, by calculating the temporal evolution gradient of the non-stationary trend signal and performing feature space projection mapping, multiple evolution matrices are obtained, including: Singular value decomposition is performed on the trajectory matrix to obtain an initial mode set, which includes multiple singular values ​​and the eigenvector corresponding to each singular value; The proportion of each singular value in the sum of all singular values ​​in the initial mode set is calculated to obtain the energy contribution rate of each singular value. The eigenvectors corresponding to the singular values ​​whose energy contribution rates meet the preset ratio requirements are then reconstructed to obtain the non-stationary trend signal. Calculate the rate of change of the non-stationary trend signal at any adjacent simulation time in the global simulation process to obtain the time-series evolution gradient; Based on the physical connection topology between nodes in the simulated network, a topology mapping matrix is ​​constructed, and the temporal evolution gradient is reconstructed and spatially expanded using the topology mapping matrix to obtain the evolution matrix of each node at different simulation times.

[0010] Optionally, a state transition operator is constructed based on the evolution matrix. By performing eigenvalue decomposition on the state transition operator, the magnitude of the principal eigenvalues ​​and the distribution offset of the eigenvalue set in the complex plane are determined, including: The two evolution matrices of each node at any adjacent simulation time are solved by operator mapping to obtain multiple state transition operators corresponding to each node; For each state transition operator, eigenvalue decomposition is performed to obtain multiple eigenvalue sets. The modulus of the eigenvalue with the largest absolute value in each eigenvalue set is taken as the modulus of the principal eigenvalue of the corresponding state transition operator. Using the geometric origin of the complex plane as the reference point, and the displacement distance of the mean center point of different eigenvalues ​​in each eigenvalue set relative to the reference point, we take the distribution offset of each eigenvalue set as the distribution offset.

[0011] Optionally, abnormal state nodes are determined by comparing the magnitude of the principal feature value with a preset threshold and the difference between the distribution offset and the preset benchmark deviation with a preset difference, including: Calculate the absolute difference between each distribution offset and the preset benchmark offset to obtain multiple offset difference values; If, at any simulation moment, the magnitude of the principal eigenvalue of the same node is greater than a preset threshold, or the offset difference of the same node is greater than a preset difference, then the corresponding node is determined to be an abnormal state node.

[0012] Optionally, the simulation process of the abnormal state node is switched to a high-resolution simulation mode, and the step size adjustment coefficient is determined using the principal eigenvalue magnitude to control the reduction of the simulation step size in the high-resolution simulation mode, including: Switch the simulation process of each abnormal state node from low-resolution simulation mode to high-resolution simulation mode; Based on the modulus of the main feature value of each abnormal state node at the trigger determination time, the preset step size mapping relationship table is queried to obtain the step size adjustment coefficient corresponding to each abnormal state node. When multiple abnormal state nodes are identified, the minimum value among all step size adjustment coefficients is selected as the target step size adjustment coefficient, and the target step size adjustment coefficient is used to synchronously reduce the global simulation step size in the high-resolution simulation mode.

[0013] Secondly, this application provides an adaptive simulation step-size control system based on multi-resolution derivation, including: The acquisition module is used to acquire traffic characteristic data of each node in the simulation network and resource load data of the corresponding virtual host. The traffic characteristic data includes traffic characteristic entropy, IP address distribution breadth sequence and protocol anomaly deviation sequence. The resource load data includes utilization fluctuation sequence, memory page swapping frequency sequence and driver call frequency sequence. The fusion module is used to align traffic feature data and resource load data through resampling and then splice and fuse them to generate an associated state vector; The reconstruction module is used to construct a trajectory matrix based on the associated state vector. After decomposing the trajectory matrix through singular spectrum analysis, it reconstructs the non-stationary trend signal and obtains multiple evolution matrices by calculating the temporal evolution gradient of the non-stationary trend signal and performing feature space projection mapping. The decomposition module is used to construct state transition operators based on the evolution matrix. By performing eigenvalue decomposition on the state transition operators, the modulus of the principal eigenvalues ​​and the distribution offset of the eigenvalue set in the complex plane are determined. The comparison module is used to identify abnormal state nodes by comparing the principal eigenvalue magnitude with a preset threshold and the difference between the distribution offset and the preset baseline deviation with a preset difference. It then switches the simulation process of the abnormal state nodes to the high-resolution simulation mode and uses the principal eigenvalue magnitude to determine the step size adjustment coefficient to reduce the simulation step size in the high-resolution simulation mode.

[0014] Thirdly, this application provides an electronic device, comprising: Memory, used to store computer programs; A processor is used to implement the steps of the adaptive simulation step size control method based on multi-resolution deduction as described in the first aspect above when performing computer programs.

[0015] Fourthly, this application provides a computer-readable storage medium storing a computer program that, when executed by a processor, can implement the steps of the adaptive simulation step size control method based on multi-resolution deduction as described in the first aspect above.

[0016] The adaptive simulation step size control method based on multi-resolution inference provided in this application achieves multi-dimensional deep perception of the internal operating state and external interaction behavior of simulation nodes by synchronously collecting network-level traffic characteristic data and host-level resource load data. It solves the problem of distortion in correlation analysis caused by inconsistent data timing. It enables explicit expression of system evolution trends, enhancing the predictive ability to capture the dynamic evolution laws of complex tasks. It achieves rapid response during drastic state fluctuations, avoiding the response lag or step size oscillations common in existing technologies, and achieving an optimal balance between computational efficiency and inference accuracy.

[0017] Furthermore, this application constructs a state transition operator describing the evolution law of a node's state by solving the operator mapping problem for two evolution matrices of a node at any adjacent simulation time. Subsequently, eigenvalue decomposition is performed on the operator, extracting the eigenvalue with the largest absolute value as the principal eigenvalue modulus. Using the origin of the complex plane geometry as a reference, the displacement distance of the mean center point of the entire eigenvalue set is calculated, thus obtaining the distribution offset reflecting the degree of deviation of the evolution trajectory in the complex plane. This overcomes the technical barrier of finding optimal spatiotemporal matching of computational resources in cross-scale coupled scenarios, improving the convergence stability of the simulation system. Attached Figure Description

[0018] 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 some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0019] Figure 1 A flowchart illustrating the adaptive simulation step size control method based on multi-resolution deduction provided in this application embodiment; Figure 2 This is a schematic diagram illustrating the distribution shift of eigenvalues ​​of the state transition operator in the complex plane and the change in geometric center. Figure 3 A flowchart illustrating a method for synchronously reducing the global simulation step size, provided in an embodiment of this application; Figure 4 A schematic diagram of the structure of an adaptive simulation step size control system based on multi-resolution deduction provided in an embodiment of this application; Figure 5 This is a schematic diagram of the hardware structure of the electronic device provided in the embodiments of this application. Detailed Implementation

[0020] This application addresses the bottlenecks in complex tasks such as aerospace and industrial digital twins, where existing technologies based on passive adjustment mechanisms using single state thresholds or preset rules struggle to cope with the highly nonlinear and cross-scale coupling characteristics of systems, leading to bottlenecks such as response lag, frequent step size oscillations, and resource mismatch.

[0021] This application constructs a correlation state vector that can characterize multidimensional complex relationships by synchronously fusing network layer traffic characteristic data and host layer resource load data. It then uses singular spectrum analysis to extract non-stationary trend signals and maps them into an evolution matrix that can quantify the dynamic laws of the system. Subsequently, it abandons the traditional scalar error discrimination and innovatively constructs a state transition operator and performs eigenvalue decomposition. By using the principal eigenvalue magnitude and complex plane distribution offset, it captures the subtle instability signs of the system evolving from a stationary state to a transient state from an algebraic perspective. This establishes a predictive judgment mechanism that ensures accurate identification of abnormal state nodes before drastic state fluctuations and real-time reduction of the simulation step size in high-resolution mode. This fundamentally solves the technical problem of balancing computational efficiency and inference accuracy in simulation systems under complex dynamic environments.

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

[0023] The core of this application is to provide an adaptive simulation step size control method based on multi-resolution derivation, and a flowchart of one specific implementation is shown below. Figure 1 As shown, the method includes: Step 101: Obtain the traffic characteristic data of each node in the simulation network and the resource load data of the corresponding virtual host. The traffic characteristic data includes traffic characteristic entropy, IP address distribution breadth sequence and protocol anomaly deviation sequence. The resource load data includes utilization fluctuation sequence, memory page swapping frequency sequence and driver call frequency sequence.

[0024] In this step, acquisition probes need to be deployed synchronously at the network layer and host layer to obtain raw data. To ensure the accuracy and reproducibility of data extraction, all the above feature data are rigorously mathematically quantified based on a preset sampling time window. Specifically, the traffic feature entropy is calculated using the Shannon information entropy formula, taking the probability of each network protocol type within the time window, such as TCP, UDP, ICMP, etc., as the basic random variable. The calculation formula is as follows: ,in For the first The probability of occurrence of a certain protocol type of data packet is quantified by the entropy value, which reflects the degree of disorder in network traffic distribution. The distribution breadth sequence of IP addresses refers to a one-dimensional numerical sequence formed by counting and recording the total number of deduplicated destination IP addresses interacted with by a node within a single time window, reflecting the discrete scale of the objects interacting with the node. The protocol anomaly deviation sequence is constructed by pre-extracting standard field features of the TCP / IP protocol header under normal network communication, such as fixed header length and valid combinations of flag bits, to build a baseline. Based on this, the ratio of the number of abnormal data packets that do not conform to the baseline rules to the total number of data packets in each time window is calculated, thereby quantifying the degree to which data packets deviate from the standard specifications.

[0025] On the host side, utilization fluctuation sequences reflect the instantaneous computational pressure on the processor. Memory page swapping frequency sequences reveal the strain on system memory resources. Driver call frequency sequences reflect the underlying hardware interaction frequency. Simultaneous collection of these two types of data provides a complete, multi-dimensional assessment basis for capturing abnormal node states.

[0026] Step 102: Align the traffic feature data and resource load data through resampling and then splice and fuse them to generate an associated state vector.

[0027] Step 201: Obtain the reference sampling frequency by calculating the least common multiple of the first sampling frequency of traffic characteristic data and the second sampling frequency of resource load data.

[0028] Because the two types of data have different physical hardware timers, resulting in inconsistent sampling frequencies, it is necessary to calculate their least common multiple. For example, if the first sampling frequency is 10 Hz and the second sampling frequency is 15 Hz, then the least common multiple of the two, 30 Hz, is used as the reference sampling frequency to unify the time measurement standard.

[0029] Step 202: Using the reference sampling frequency as the target sampling rate, resample the traffic characteristic data and resource load data using linear interpolation to obtain the first sampled data set corresponding to the traffic characteristic data and the second sampled data set corresponding to the resource load data.

[0030] The resampling process is implemented by finding the nearest known timestamps to the left and right sides of each target timestamp in the original sequence. The resampled value corresponding to the target timestamp is equal to the original sampled value of the nearest left timestamp, plus the time difference between the target timestamp and the nearest left timestamp, and then multiplied by the rate of change of the data between the two nearest timestamps. This operation is performed on the sequence in all dimensions to generate a first sampled data set and a second sampled data set that are perfectly aligned on the time axis.

[0031] Step 203: Based on the node identifier of each node, the feature vectors of the sampled data belonging to the same node and the same time in the first sampled data set and the second sampled data set are concatenated to obtain the composite feature vector of each node at different times. All composite feature vectors are combined to obtain a composite feature group.

[0032] Virtual network protocol addresses or media access control addresses are used as unique node identifiers. At each baseline sampling time point, aligned traffic characteristics and resource load data are concatenated end-to-end based on the node identifier to form a composite feature vector. This composite feature vector fully characterizes the node's external communication performance and internal computational load at a specific instant. The composite feature vectors from all time points are arranged vertically in chronological order to form a composite feature group.

[0033] Step 204: Based on the preset feature projection matrix, project the composite feature group into the feature space to obtain the associated state vector.

[0034] Because directly concatenated composite feature sets suffer from redundancy and multicollinearity (where high correlation exists between different feature dimensions, such as increased CPU load often accompanying network traffic surges), unprocessed multicollinearity can lead to distorted subsequent model calculations. Therefore, principal component analysis (PCA) is needed to extract core features. The specific implementation process is as follows: First, the composite feature set is mean-reduced to zero for each dimension. Then, its covariance matrix is ​​calculated, and eigenvalue decomposition is performed to obtain all orthogonal eigenvectors. The eigenvectors are then sorted in descending order of eigenvalues, and the top few eigenvectors whose cumulative variance contribution rate reaches a specific standard are assembled into a preset feature projection matrix. This specific standard is denoted as _____. , The value ranges from 0.90 to 0.99. Based on normal operating samples, since... Starting from this point, the adjustment increments are gradually increased by 0.01. The associated state vector is reconstructed by inverse projection using the corresponding feature projection matrix; the first state vector is defined when the relative error between the reconstructed data and the unreconstructed data is no greater than 0.05. As a specific scale standard for the current simulation task. When If increasing the relative error to 0.99 still does not meet the requirement, then take... .

[0035] Finally, the composite feature set is multiplied by the feature projection matrix and projected onto a low-dimensional orthogonal subspace to obtain the associated state vector after removing redundant environmental noise.

[0036] Step 103: Construct a trajectory matrix based on the associated state vector, decompose and reconstruct the trajectory matrix through singular spectrum analysis to obtain a non-stationary trend signal, and obtain multiple evolution matrices by calculating the temporal evolution gradient of the non-stationary trend signal and performing feature space projection mapping.

[0037] In this embodiment, each preset parameter is determined according to the normal operating sample corresponding to the simulation task to be executed. The normal operating sample refers to the continuous state data obtained when the simulation model is running in low-resolution mode without injected faults, without state exceeding limits, and without faults. Each simulation task selects no fewer than 200 consecutive sampling time points of normal operating samples. When the same simulation model only changes its initial state without changing the model parameters, node connections, low-resolution time step, or low-resolution spatial grid scale, the already determined preset parameters are used. When the simulation model parameters, node connections, low-resolution time step, or low-resolution spatial grid scale changes, each preset parameter is re-determined based on the changed normal operating sample. Once each preset parameter is determined, it remains unchanged during the execution of the simulation task, and parameter updates and resolution switching are only performed after a global simulation time step ends.

[0038] Step 301: Using a preset window length and sliding step size, perform cyclic sliding sampling on the associated state vector to obtain multiple sub-sequence segments.

[0039] Preset window length Represented by the number of consecutive sampling points contained in the associated state vector. The value range is 5 to 50. Based on normal operation samples, the autocorrelation coefficients of each feature dimension of the associated state vector are calculated within 1 to 25 sampling intervals, ensuring that the absolute value of the autocorrelation coefficient of each feature dimension is not greater than 50 for the first time. The number of sampling intervals corresponding to the time interval is used as the correlation length of that feature dimension; when the absolute value of the autocorrelation coefficient of a feature dimension is greater than 25 within 25 sampling intervals... At that time, the correlation length of this feature dimension is determined to be 25. The maximum value among the correlation lengths of all feature dimensions is denoted as... Preset window length Pick ;when hour, Take 5, when hour, Set the value to 50. Sliding step size. according to Determined, therefore The value range is from 1 to 12 sampling points. (Determine) and Then, the window is moved forward from left to right along the timeline, capturing each segment sequentially. 3 consecutive sampling points, and the starting positions of two adjacent intercepts are spaced apart. Multiple sampling points yield multiple sub-sequence segments.

[0040] Step 302: According to the time sequence, vertically concatenate all subsequence segments into matrix blocks to obtain the trajectory matrix.

[0041] By stacking and assembling all the horizontal row vector subsequences in chronological order of their generation, row by row, vertically from top to bottom, a trajectory matrix is ​​constructed, thus extending the one-dimensional temporal state topology to a multi-dimensional dynamic phase space. A multi-dimensional dynamic phase space is a mathematical abstract space reconstructed in system dynamics using coordinate axes with different time delays; it can fully represent the evolutionary topology of the system in all possible states.

[0042] Step 311: Perform singular value decomposition on the trajectory matrix to obtain an initial mode set, which includes multiple singular values ​​and the eigenvector corresponding to each singular value.

[0043] The specific decomposition process is as follows: The product of the transpose of the trajectory matrix and the trajectory matrix itself is calculated to construct the system's autocorrelation matrix. The autocorrelation matrix is ​​a mathematical tool used to measure the self-similarity and evolutionary inertia of a sequence at different times. Eigenvalue decomposition is then performed on this autocorrelation matrix to obtain all positive eigenvalues. The arithmetic square roots of the positive eigenvalues ​​are taken as singular values, and the corresponding mutually orthogonal eigenvectors are also calculated. These eigenvalues ​​and eigenvectors, arranged in descending order of energy, together constitute the initial mode set.

[0044] Step 312: Calculate the proportion of each singular value in the sum of all singular values ​​in the initial mode set, obtain the energy contribution rate of each singular value, and reconstruct the signal of the eigenvector corresponding to the singular value whose energy contribution rate meets the preset ratio requirement to obtain the non-stationary trend signal.

[0045] The first one, arranged in descending order of value. The singular values ​​are denoted as The total number of singular values ​​is denoted as , No. The energy contribution rate of each singular value is based on Calculation. The preset ratio requirement is based on the cumulative energy contribution rate threshold. express, The value ranges from 0.85 to 0.95. Following the order of the singular values, the energy contribution rate is accumulated sequentially starting from the first singular value, and this will make... The smallest positive integer that is true Corresponding front Each singular value was determined to be a singular value that met the preset ratio requirements. Based on normal operation samples, from... The adjustment increments are gradually increased in increments of 0.01. And calculate the relative reconstruction error between the corresponding reconstructed signal and the associated state vector; set the value at which the relative reconstruction error is first no greater than 0.10. This serves as the threshold for the cumulative energy contribution rate of the current simulation task. When If increasing the value to 0.95 still does not meet the relative reconstruction error requirement, then take... Before Tensor products are calculated on the eigenvectors corresponding to the singular values ​​to generate corresponding first-order submatrices; the anti-diagonal elements of each first-order submatrix are arithmetically averaged, and the resulting one-dimensional sequences are superimposed to obtain a non-stationary trend signal.

[0046] Step 313: Calculate the rate of change of the non-stationary trend signal at any adjacent simulation time in the global simulation process to obtain the time-series evolution gradient.

[0047] The time-series evolution gradient is obtained by calculating the difference between the signal value at the current simulation moment and the signal value at the previous simulation moment, and then dividing by the physical simulation time step of the two.

[0048] Step 314: Construct a topology mapping matrix based on the physical connection topology between nodes in the simulation network, and use the topology mapping matrix to reconstruct the dimensions and expand the space of the temporal evolution gradient to obtain the evolution matrix of each node at different simulation times.

[0049] The process of constructing the topology mapping matrix is ​​as follows: obtain the network connectivity matrix, using the number 1 to indicate the existence of a direct physical communication link between nodes and the number 0 to indicate no connection, and establish the adjacency matrix. Count the total number of connections for each node to construct a diagonal degree matrix. Then the graph Laplacian matrix is ​​calculated. Its formula is shown in formula (1): (1) In the formula, Represents the graph Laplace matrix. Degree matrix, The adjacency matrix is ​​represented by the graph Laplacian matrix. The calculated graph Laplacian matrix is ​​used as the topological mapping matrix. The temporal evolution gradient vector is multiplied by the topological mapping matrix to obtain the global spatial gradient vector that includes the global topological diffusion effect.

[0050] To reconstruct the dimension of this one-dimensional global spatial gradient vector so that it can independently represent the local micro-evolutionary state of each node, this embodiment employs a matrix dimension-up reconstruction method combining a sliding time window and spatial neighborhood truncation. The specific implementation process is as follows: for any node in the network... According to the adjacency matrix Extract all its directly connected elements. One-hop neighbor node; then, extract the current simulation time and its immediate neighbors on the timeline. Each historical simulation moment, i.e., the length is Time window; will node and The neighboring nodes are here The spatial gradient values ​​at consecutive time points are extracted and concatenated row by row to form the value for that node. Construct a size of A two-dimensional matrix.

[0051] By extracting and layering local spatiotemporal information, local gradient perturbations are linearly combined along the network topology, ultimately expanding in the spatial domain to generate an evolutionary matrix specific to each node. This evolutionary matrix not only contains the node's own historical evolutionary trend but also integrates the coupled perturbation information of its physical neighborhood, solving the technical challenge that simple scalars or vectors cannot characterize the local dynamic evolution process of complex systems.

[0052] Step 104: Construct a state transition operator based on the evolution matrix. By performing eigenvalue decomposition on the state transition operator, determine the principal eigenvalue magnitude and the distribution offset of the eigenvalue set in the complex plane.

[0053] Step 401: Solve the operator mapping problem for the two evolution matrices of each node at any adjacent simulation time to obtain multiple state transition operators corresponding to each node.

[0054] Assume that the evolution of the system state in small discrete time intervals follows a linear mapping rule. To solve for the state transition operator that represents the evolution law, the following minimization objective function based on the Frobenius norm is constructed: It should be noted that this expression is not an equation, but rather an objective function used to find the optimal solution. Specifically, it aims to find an optimal state transition operator. This makes the actual evolution matrix at the next moment... The error between the theoretical prediction matrix and the actual prediction matrix is ​​minimized. The theoretical prediction matrix is ​​the state transition operator. Evolution matrix at the current time The product of. In the formula, This represents the state transition operator matrix to be optimized. This represents the evolution matrix at the current moment. This represents the evolution matrix at the next time step. This represents finding the Frobenius norm of a matrix, which is the arithmetic square root of the sum of the squares of the absolute values ​​of all elements in the matrix.

[0055] The specific solution process for the above objective function is as follows: Based on the least squares optimization theory in matrix algebra, to obtain the matrix equation... optimal approximation solution It is necessary to perform an evolution matrix at the current moment. Find the right pseudo-inverse matrix. First, calculate the pseudo-inverse matrix of the evolution matrix at the current time step. The correct way to find this pseudo-inverse matrix is: calculate the evolution matrix... With its own transpose matrix The product of Find the inverse matrix of the product result, and finally use the transpose of the evolution matrix. Multiplying by the inverse matrix on the right, the formula is expressed as follows: After accurately obtaining the right pseudo-inverse matrix, the evolution matrix at the next time step is then multiplied by the obtained pseudo-inverse matrix, i.e. This allows us to find the state transition operator that minimizes the error. This solution method, which strictly follows the algebraic projection theorem, ensures the mathematical completeness and accuracy of the state transition operator in multidimensional space mapping.

[0056] Step 402: Perform eigenvalue decomposition on each state transition operator to obtain multiple eigenvalue sets, and take the modulus of the eigenvalue with the largest absolute value in each eigenvalue set as the modulus of the principal eigenvalue of the corresponding state transition operator.

[0057] The solved state transition operator matrix is ​​subjected to eigenvalue decomposition to obtain all its complex eigenvalues, forming an eigenvalue set. For each complex eigenvalue in the set, its corresponding modulus is calculated. The modulus is calculated by taking the square root of the sum of the squares of the real and imaginary parts. The result with the largest modulus in the set is selected as the principal eigenvalue modulus of the corresponding state transition operator. The closer the principal eigenvalue modulus is to 1, the closer the dynamic evolution of the system is to an unstable divergent state.

[0058] Step 403: Using the geometric origin of the complex plane as the reference point, and taking the displacement distance of the mean center point of different eigenvalues ​​in each eigenvalue set relative to the reference point as the distribution offset of each eigenvalue set.

[0059] The specific calculation process is as follows: Calculate the arithmetic mean of the real parts and the arithmetic mean of the imaginary parts of all eigenvalues ​​in the set. Using these two arithmetic means as the x and y coordinates, the mean center point can be accurately located in the complex plane. Using the origin of the complex plane as the standard reference point, and utilizing the Euclidean distance between the two points, the arithmetic square root of the sum of the squares of the real and imaginary part mean values ​​is obtained. This final arithmetic square root is the distribution offset, used to reflect the drift and degradation trend of the overall space of all characteristic modes of the system.

[0060] like Figure 2 As shown, Figure 2 This is a schematic diagram illustrating the distribution shift of eigenvalues ​​of the state transition operator in the complex plane and the change in geometric center.

[0061] Figure 2 A cross coordinate system is shown to mark complex positions. The intersection of the horizontal and vertical axes is the geometric origin of the complex plane, which serves as the absolute reference point for evaluating the degree of deviation. During network operation, multiple mathematical solutions representing the evolutionary state of nodes are generated. Each discrete point in the complex plane represents an eigenvalue calculated through eigenvalue decomposition. All points converge to form an eigenvalue set. In this eigenvalue set, the point farthest from the geometric origin (i.e., with the largest absolute value) is extracted as the principal eigenvalue. Its magnitude is generally the most dangerous signal, determining whether the evolutionary process will collapse. The center position of all discrete points in the figure can be regarded as the physical centroid of this group of eigenvalues, representing the average bias of the overall state, that is, the mean center point of different eigenvalues ​​in each eigenvalue set. The distance of this mean center point from the geometric origin reflects the severity of the node's deviation from the normal state. The displacement distance of this mean center point relative to the reference point is used as the distribution offset of the eigenvalue set.

[0062] Furthermore, the large circle formed by dashed lines in the diagram serves as a mathematical safety warning line, representing the critical boundary surface of the stability unit circle. Essentially, it is the boundary of a preset threshold used for comparing the principal eigenvalue's magnitude. Once the principal eigenvalue crosses this boundary, it signifies that the network will experience severe oscillations. In short, this diagram transforms the purely textual mathematical process of solving for the eigenvalue set, finding the principal eigenvalue with the largest absolute value, and calculating the degree of deviation from the physical center of gravity into a visually perceptible geometric image.

[0063] Step 105: By comparing the principal eigenvalue magnitude with a preset threshold and the difference between the distribution offset and the preset baseline deviation with a preset difference, abnormal state nodes are identified. The simulation process of the abnormal state nodes is switched to high-resolution simulation mode, and the step size adjustment coefficient is determined using the principal eigenvalue magnitude to reduce the simulation step size in high-resolution simulation mode.

[0064] Step 501: Calculate the absolute difference between each distribution offset and the preset benchmark offset to obtain multiple offset difference values.

[0065] For each node in the simulation network Calculate the distribution offset of the node at each sampling time within the normal operating sample, and determine the arithmetic mean of all distribution offsets as the preset baseline offset for the node. Preset baseline deviation The value of is between 0 and 1; when the calculated arithmetic mean is greater than 1, Set to 1. Set the node at the current simulation time... The distribution offset is denoted as The offset difference value of this node is according to Calculation. The preset benchmark deviation mentioned below refers to the deviation from the currently determined node. .

[0066] Step 502: If at any simulation time, the magnitude of the principal feature value of the same node is greater than the preset threshold, or the offset difference of the same node is greater than the preset difference, then the corresponding node is determined to be an abnormal state node.

[0067] The preset threshold used for comparison with the magnitude of the principal eigenvalue is denoted as . , The value range is from 0.90 to 1.00. Based on normal operation samples, the modulus of the principal eigenvalues ​​of all nodes at each sampling time is calculated, and the 99th percentile of the modulus of all principal eigenvalues ​​is taken as... The candidate value; when the candidate value is less than 0.90, When the value is 0.90, and the candidate value is greater than 1.00, Set the value to 1.00. For each node. Calculate the standard deviation of the distribution offset of this node in the normally operating samples. and in accordance with Determine the preset difference value corresponding to this node. Preset difference value The value range is from 0.02 to 0.30; when hour, Take 0.02, when hour, Take 0.30. For node When its principal eigenvalue modulus is greater than or its offset difference value Greater than At that time, the node The node is determined to be in an abnormal state. The preset difference mentioned below refers to the difference between the current node being determined and the node in question. .

[0068] For example, in an industrial digital twin network simulation task with 500 normal operation sampling times, the 99th percentile of the modulus of the principal eigenvalues ​​of all nodes is 0.97. Then, the preset threshold... Take 0.97. Node If the arithmetic mean of the distribution offset in the normal operating samples is 0.22 and the standard deviation is 0.05, then the preset baseline deviation of this node is... Set the value to 0.22, the preset difference. Pick When node At the current simulation moment, when the principal eigenvalue magnitude is 0.98 and the distribution offset is 0.40, the offset difference value is: ,node The principal eigenvalue modulus is greater than And the offset difference value is greater than , will node The node was determined to be in an abnormal state.

[0069] like Figure 3 As shown, Figure 3 This is a flowchart illustrating a method for synchronously reducing the global simulation step size, as provided in an embodiment of this application.

[0070] Step 511: Switch the simulation process of each abnormal state node from low-resolution simulation mode to high-resolution simulation mode.

[0071] Among them, the low-resolution simulation mode uses a low-resolution time step. and low-resolution spatial grid scale The high-resolution simulation mode employs a high-resolution time step. and high-resolution spatial grid scale The target step size adjustment coefficient determined in steps 512 and 513 below is denoted as... When there is only one abnormal state node, This is the step size adjustment coefficient for that node. When multiple abnormal state nodes exist, This is the minimum step size adjustment factor among all abnormal state nodes. The high-resolution time step is based on... Confirmed. Due to Pick , or The high-resolution time step is correspondingly one-half, one-quarter, or one-eighth of the low-resolution time step. When At that time, spatial refinement factor Take 2; when or At that time, spatial refinement factor Take 4. The high-resolution spatial grid scale is based on... Therefore, the high-resolution spatial grid scale is either half or a quarter of the low-resolution spatial grid scale. Low-resolution time step and low-resolution spatial grid scale It is determined by the initial configuration of the simulation model and remains unchanged during the execution of the same simulation task.

[0072] In order to accurately allocate computing power, the precision of the computational solution for the abnormal state nodes is improved by forcibly switching their background simulation process to a high-resolution simulation mode that requires more computing resources.

[0073] To ensure that the physical coupling continuity of the global simulation network is not disrupted when local nodes switch resolution abruptly, this application introduces a sub-loop spatiotemporal boundary interpolation engine into the underlying system architecture. Specifically, when switching to high-resolution mode, abnormal state nodes will automatically split and execute multiple micro-time step sub-loop calculations within a macroscopic time step of the global low-resolution resolution. In each high-frequency sub-loop iteration, the external neighbor node data required by the abnormal state node is generated by extracting state snapshots of neighbor nodes at the previous and current macroscopic time steps and using Lagrange polynomials for smooth interpolation in the time dimension. Simultaneously, the high-frequency response data output by the abnormal state node is downsampled and aggregated using an integral averaging device before being broadcast to the global network at the next macroscopic synchronization time. Through the above-mentioned isolated sub-loop and boundary interpolation mechanism, seamless and smooth switching between high and low resolutions for local nodes in complex networks is achieved, avoiding simulation data exceeding limits or system crashes.

[0074] In each low-resolution global simulation time interval First, calculate the non-abnormal state nodes and boundary nodes according to the low-resolution time step. The temporary state at any given time, and saves the abnormal state nodes. The state at that moment. Then, the abnormal state node is restored to... The state at any given time, and execution on nodes in abnormal states. Secondary isolation sub-loop, in which .when Take respectively , and hour, We take values ​​of 2, 4, and 8 respectively. The time step for each isolation sub-loop is... , No. The end time of the second isolation sub-loop is ,in Take 1 to 1 in sequence .

[0075] The external neighbor node data required for isolating the sub-loop is determined through Lagrange interpolation. During the first global simulation time interval, or when the boundary state of the previous global synchronization time cannot be obtained, the boundary node is used... and First-order Lagrange time interpolation is performed on the states at two time points; starting from the second global simulation time interval, when the boundary nodes can be obtained... , and When considering the states at three time points, second-order Lagrange time interpolation is performed using these three states. For spatial boundary interpolation, first-order Lagrange interpolation is used when two adjacent low-resolution grid nodes are available, and second-order Lagrange interpolation is used when three adjacent low-resolution grid nodes are available. When located at the edge of a spatial boundary, the two or three closest single-sided low-resolution grid nodes to that edge are used. The order of both time and spatial interpolation is no higher than second-order.

[0076] The statistical window of the integrator averager coincides with a low-resolution global simulation time interval, with the window starting at... The window endpoint is The window contains The second isolation sub-loop. For traffic, throughput, or state increment data output by abnormal state nodes to low-resolution nodes, the second... The output of the second isolation sub-loop is denoted as The integral average result is based on Calculation. For the state data representing the abnormal state node at the synchronization time, the first method is used. The state at the end of the next isolation sub-loop is used as the node's state. The state at any given time is not integrated and averaged.

[0077] Finish After the second isolation sub-loop, the abnormal state node is in The state at time step replaces the temporary state corresponding to that node during the low-resolution computation, and in... The integral average result is submitted to the global simulation process at any given time. Other intermediate time-point states generated by the isolated sub-loop are only used for local calculations of the current abnormal state node and are not used as synchronization states for the global simulation process. Because... For integers, the first The end time of the second isolation sub-loop and Overlap; after completing the data exchange at this moment, the global simulation process enters the next low-resolution global simulation time interval. When the target step size adjustment coefficient or spatial refinement factor changes, the new value is applied after the current low-resolution global simulation time interval ends and the data exchange is completed.

[0078] Step 512: Based on the modulus of the main feature value of each abnormal state node at the trigger determination time, query the preset step size mapping relationship table to obtain the step size adjustment coefficient corresponding to each abnormal state node.

[0079] abnormal state nodes The modulus of the principal eigenvalue at the trigger determination time is denoted as . The step size adjustment coefficient corresponding to this node is denoted as For nodes that have already been determined to be in an abnormal state according to step 502, when hour, Pick ;when hour, Pick ;when hour, Pick A node is identified as an abnormal node because its offset difference exceeds a preset difference, and the magnitude of its principal feature value is not greater than a certain threshold. At that time, according to The corresponding relationship will Determined as The preset step size mapping relationship has a step size adjustment coefficient range of [value range missing]. to Preset threshold When redetermining according to the aforementioned rules, the boundary values ​​of the mapping interval and The update is synchronized, and the value of the step size adjustment coefficient remains unchanged.

[0080] For example, a simulation task has 500 normal operation sampling times. The maximum correlation length of each feature dimension of the associated state vector. If the value is 6, then the preset window length is... Take 12, sliding step size If the value is 3, and the cumulative energy contribution rate threshold corresponding to the first occurrence of a relative reconstruction error not exceeding 0.10 is 0.90, then the preset ratio requirement is... If the value is set to 0.90, and the 99th percentile of the modulus of all node principal eigenvalues ​​is 0.97, then the preset threshold is set. Take 0.97. Node Preset reference deviation The value is 0.22, and the standard deviation of the distribution offset is 0.05, then the preset difference value is... Take 0.15. When node The modulus of the principal eigenvalue at the trigger determination time When the value is 1.04 and the distribution offset is 0.40, the offset difference is 0.18, and the node... The node was determined to be in an abnormal state. Because... , ,and ,node Step size adjustment coefficient Pick When the low-resolution time step is 20 milliseconds, the high-resolution time step is 5 milliseconds.

[0081] Step 513: When multiple abnormal state nodes are identified, select the minimum value among all step size adjustment coefficients as the target step size adjustment coefficient, and use the target step size adjustment coefficient to synchronously reduce the global simulation step size in the high-resolution simulation mode.

[0082] When multiple abnormal state nodes emerge simultaneously in the network and generate multiple step size adjustment coefficients, a minimum value operation is performed to filter out the smallest value, which is then established as the global target step size adjustment coefficient. By directly multiplying the current global simulation physics deduction step size by this target step size adjustment coefficient, the entire system is forced to advance at the highest finest time span, thus achieving synchronous reduction control of the step size.

[0083] Figure 4 This is a schematic diagram of a specific implementation of the adaptive simulation step size control system based on multi-resolution derivation provided in this application embodiment, with reference to... Figure 4 The system may include: The acquisition module 21 is used to acquire traffic characteristic data of each node in the simulation network and resource load data of the corresponding virtual host. The traffic characteristic data includes traffic characteristic entropy, IP address distribution breadth sequence and protocol anomaly deviation sequence. The resource load data includes utilization fluctuation sequence, memory page swapping frequency sequence and driver call frequency sequence. The fusion module 22 is used to align traffic feature data and resource load data through resampling and then splice and fuse them to generate an associated state vector; The reconstruction module 23 is used to construct a trajectory matrix based on the associated state vector, decompose and reconstruct the trajectory matrix through singular spectrum analysis to obtain a non-stationary trend signal, and obtain multiple evolution matrices by calculating the temporal evolution gradient of the non-stationary trend signal and performing feature space projection mapping. The decomposition module 24 is used to construct a state transition operator based on the evolution matrix. By performing eigenvalue decomposition on the state transition operator, the modulus of the principal eigenvalue and the distribution offset of the eigenvalue set in the complex plane are determined. The comparison module 25 is used to identify abnormal state nodes by comparing the principal feature value magnitude with a preset threshold and the difference between the distribution offset and the preset benchmark deviation with a preset difference value, switch the simulation process of the abnormal state nodes to the high-resolution simulation mode, and use the principal feature value magnitude to determine the step size adjustment coefficient to reduce the simulation step size in the high-resolution simulation mode.

[0084] The adaptive simulation step size control system based on multi-resolution deduction in this application is used to implement the aforementioned adaptive simulation step size control method based on multi-resolution deduction. Therefore, the specific implementation of the adaptive simulation step size control system based on multi-resolution deduction can be found in the embodiment section of the adaptive simulation step size control method based on multi-resolution deduction above. The specific implementation can be referred to the description of the corresponding embodiments, which will not be repeated here.

[0085] Figure 5 A schematic diagram of the hardware structure of the electronic device provided in an embodiment of this application is shown.

[0086] This application also provides an electronic device, including: a memory for storing a computer program; and a processor for implementing the steps of the adaptive simulation step size control method based on multi-resolution deduction as described above when executing the computer program.

[0087] The electronic device may include a processor 510 and a memory 520 storing computer program instructions.

[0088] Specifically, the processor 510 may include a central processing unit (CPU), an application-specific integrated circuit (ASIC), or one or more integrated circuits that can be configured to implement the embodiments of this application.

[0089] Memory 520 may include mass storage for data or instructions. For example, and not limitingly, memory 520 may include a hard disk drive (HDD), floppy disk drive, flash memory, optical disk, magneto-optical disk, magnetic tape, or Universal Serial Bus (USB) drive, or a combination of two or more of these. Where appropriate, memory 520 may include removable or non-removable (or fixed) media. Where appropriate, memory 520 may be internal or external to the integrated gateway disaster recovery device. In a particular embodiment, memory 520 is non-volatile solid-state memory.

[0090] Memory may include read-only memory (ROM), random access memory (RAM), disk storage media devices, optical storage media devices, flash memory devices, and electrical, optical, or other physical / tangible memory storage devices. Therefore, typically, memory includes one or more tangible (non-transitory) computer-readable storage media (e.g., memory devices) encoded with software including computer-executable instructions, and is operable to perform operations described with reference to the method according to the first aspect of this disclosure when the software is executed (e.g., by one or more processors).

[0091] The processor 510 reads and executes computer program instructions stored in the memory 520 to implement any of the adaptive simulation step size control methods based on multi-resolution deduction in the above embodiments.

[0092] In one example, the electronic device may also include a communication interface 530 and a bus 540. Wherein, such as Figure 5 As shown, the processor 510, memory 520, and communication interface 530 are connected through bus 540 and complete communication with each other.

[0093] The communication interface 530 is mainly used to realize communication between various modules, devices, units and / or equipment in the embodiments of this application.

[0094] Bus 540 includes hardware, software, or both, that couples components of an online data traffic metering device together. For example, and not limitingly, the bus may include an Accelerated Graphics Port (AGP) or other graphics bus, an Enhanced Industry Standard Architecture (EISA) bus, a Front Side Bus (FSB), HyperTransport (HT) interconnect, an Industry Standard Architecture (ISA) bus, an Infinite Bandwidth Interconnect, a Low Pin Count (LPC) bus, a memory bus, a Microchannel Architecture (MCA) bus, a Peripheral Component Interconnect (PCI) bus, a PCI-Express (PCI-X) bus, a Serial Advanced Technology Attachment (SATA) bus, a Video Electronics Standards Association Local (VLB) bus, or other suitable buses, or combinations of two or more of these. Where appropriate, bus 540 may include one or more buses. Although specific buses are described and illustrated in embodiments of this application, any suitable bus or interconnect is contemplated herein.

[0095] This application also provides a computer-readable storage medium storing a computer program, which, when executed by a processor, can implement the steps of any of the above-described adaptive simulation step size control methods based on multi-resolution deduction.

[0096] In one exemplary embodiment, the aforementioned computer-readable storage medium may include, but is not limited to, various media capable of storing computer programs, such as USB flash drives, read-only memory, random access memory, portable hard drives, magnetic disks, or optical disks.

[0097] Embodiments of the present invention also provide a computer program product, which includes a computer program that, when executed by a processor, implements the steps in any of the embodiments of the adaptive simulation step size control method based on multi-resolution deduction.

[0098] Those skilled in the art will further recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, computer software, or a combination of both. To clearly illustrate the interchangeability of hardware and software, the components and steps of the various examples have been generally described in terms of functionality in the foregoing description. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementations should not be considered beyond the scope of this invention.

[0099] The above provides a detailed description of the adaptive simulation step size control method and system based on multi-resolution deduction provided in this application. Specific examples have been used to illustrate the principles and implementation methods of this application. The descriptions of the embodiments above are merely for the purpose of helping to understand the method and its core ideas. It should be noted that those skilled in the art can make various improvements and modifications to this application without departing from its principles, and these improvements and modifications also fall within the protection scope of this application.

Claims

1. An adaptive simulation step size control method based on multi-resolution derivation, characterized in that, include: The traffic characteristic data of each node in the simulated network and the resource load data of the corresponding virtual host are obtained. The traffic characteristic data includes traffic characteristic entropy, IP address distribution breadth sequence and protocol anomaly deviation sequence. The resource load data includes utilization fluctuation sequence, memory page swapping frequency sequence and driver call frequency sequence. The traffic feature data and the resource load data are aligned by resampling and then spliced ​​together to generate an associated state vector. A trajectory matrix is ​​constructed based on the associated state vector. The trajectory matrix is ​​decomposed and reconstructed through singular spectrum analysis to obtain a non-stationary trend signal. Multiple evolution matrices are obtained by calculating the temporal evolution gradient of the non-stationary trend signal and performing feature space projection mapping. A state transition operator is constructed based on the evolution matrix. By performing eigenvalue decomposition on the state transition operator, the magnitude of the principal eigenvalue and the distribution offset of the eigenvalue set in the complex plane are determined. By comparing the principal eigenvalue magnitude with a preset threshold and the difference between the distribution offset and the preset baseline deviation with a preset difference, abnormal state nodes are identified. The simulation process of the abnormal state nodes is switched to high-resolution simulation mode, and the step size adjustment coefficient is determined using the principal eigenvalue magnitude to reduce the simulation step size in the high-resolution simulation mode.

2. The method according to claim 1, characterized in that, After resampling and aligning the traffic feature data and the resource load data, they are concatenated and fused to generate an associated state vector, including: The reference sampling frequency is obtained by calculating the least common multiple of the first sampling frequency of the traffic characteristic data and the second sampling frequency of the resource load data; Using the reference sampling frequency as the target sampling rate, linear interpolation is used to resample the traffic feature data and the resource load data to obtain a first sampled data set corresponding to the traffic feature data and a second sampled data set corresponding to the resource load data. Based on the node identifier of each node, the feature vectors of the sampled data belonging to the same node and the same time in the first sampled data set and the second sampled data set are concatenated to obtain the composite feature vector of each node at different times. All composite feature vectors are combined to obtain a composite feature group. Based on a preset feature projection matrix, the composite feature group is projected into the feature space to obtain the associated state vector.

3. The method according to claim 1, characterized in that, Constructing a trajectory matrix based on the associated state vector includes: Using a preset window length and sliding step size, the associated state vector is cyclically slid sampled to obtain multiple sub-sequence segments; Following the chronological order, all subsequence segments are vertically concatenated into matrix blocks to obtain the trajectory matrix.

4. The method according to claim 1, characterized in that, The trajectory matrix is ​​decomposed and reconstructed using singular spectral analysis to obtain a non-stationary trend signal. Multiple evolution matrices are obtained by calculating the temporal evolution gradient of the non-stationary trend signal and performing feature space projection mapping, including: The trajectory matrix is ​​subjected to singular value decomposition to obtain an initial mode set, which includes multiple singular values ​​and an eigenvector corresponding to each singular value; The proportion of each singular value in the sum of all singular values ​​in the initial mode set is calculated to obtain the energy contribution rate of each singular value. The feature vectors corresponding to the singular values ​​whose energy contribution rates meet the preset ratio requirements are reconstructed to obtain the non-stationary trend signal. The rate of change of the non-stationary trend signal at any adjacent simulation time in the global simulation process is calculated to obtain the time-series evolution gradient. Based on the physical connection topology between nodes in the simulation network, a topology mapping matrix is ​​constructed, and the temporal evolution gradient is reconstructed and spatially expanded using the topology mapping matrix to obtain the evolution matrix of each node at different simulation times.

5. The method according to claim 1, characterized in that, A state transition operator is constructed based on the evolution matrix. By performing eigenvalue decomposition on the state transition operator, the magnitude of the principal eigenvalues ​​and the distribution offset of the eigenvalue set in the complex plane are determined, including: The two evolution matrices of each node at any adjacent simulation time are solved by operator mapping to obtain multiple state transition operators corresponding to each node; For each state transition operator, eigenvalue decomposition is performed to obtain multiple eigenvalue sets. The modulus of the eigenvalue with the largest absolute value in each eigenvalue set is taken as the modulus of the principal eigenvalue of the corresponding state transition operator. Using the geometric origin of the complex plane as a reference point, the displacement distance of the mean center point of different eigenvalues ​​in each eigenvalue set relative to the reference point is used as the distribution offset of each eigenvalue set.

6. The method according to claim 1, characterized in that, Abnormal state nodes are determined by comparing the magnitude of the principal feature value with a preset threshold and the difference between the distribution offset and the preset benchmark deviation with a preset difference, including: Calculate the absolute difference between each distribution offset and the preset benchmark offset to obtain multiple offset difference values; If, at any simulation moment, the magnitude of the principal feature value belonging to the same node is greater than a preset threshold, or the value of the offset difference belonging to the same node is greater than a preset difference, then the corresponding node is determined to be an abnormal state node.

7. The method according to claim 1, characterized in that, Switching the simulation process of the abnormal state node to high-resolution simulation mode, and using the principal eigenvalue modulus to determine the step size adjustment coefficient, in order to reduce the simulation step size in the high-resolution simulation mode, includes: Switch the simulation process of each abnormal state node from low-resolution simulation mode to high-resolution simulation mode; Based on the modulus of the main feature value of each abnormal state node at the trigger determination time, the preset step size mapping relationship table is queried to obtain the step size adjustment coefficient corresponding to each abnormal state node. When multiple abnormal state nodes are identified, the minimum value among all step size adjustment coefficients is selected as the target step size adjustment coefficient, and the target step size adjustment coefficient is used to synchronously reduce the global simulation step size in the high-resolution simulation mode.

8. An adaptive simulation step-size control system based on multi-resolution derivation, characterized in that, include: The acquisition module is used to acquire traffic characteristic data of each node in the simulation network and resource load data of the corresponding virtual host. The traffic characteristic data includes traffic characteristic entropy, IP address distribution breadth sequence and protocol anomaly deviation sequence. The resource load data includes utilization fluctuation sequence, memory page swapping frequency sequence and driver call frequency sequence. The fusion module is used to align the traffic feature data and the resource load data through resampling and then splice and fuse them to generate an associated state vector; The reconstruction module is used to construct a trajectory matrix based on the associated state vector, decompose and reconstruct the trajectory matrix through singular spectrum analysis to obtain a non-stationary trend signal, and obtain multiple evolution matrices by calculating the temporal evolution gradient of the non-stationary trend signal and performing feature space projection mapping. The decomposition module is used to construct a state transition operator based on the evolution matrix, and to determine the principal eigenvalue magnitude and the distribution offset of the eigenvalue set in the complex plane by performing eigenvalue decomposition on the state transition operator. The comparison module is used to identify abnormal state nodes by comparing the magnitude of the principal feature value with a preset threshold and the difference between the distribution offset and the preset benchmark deviation with a preset difference value, switch the simulation process of the abnormal state node to a high-resolution simulation mode, and use the magnitude of the principal feature value to determine the step size adjustment coefficient to reduce the simulation step size in the high-resolution simulation mode.

9. An electronic device, characterized in that, include: Memory, used to store computer programs; A processor, configured to implement the steps of the adaptive simulation step size control method based on multi-resolution derivation as described in any one of claims 1 to 7 when executing the computer program.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, enables the implementation of the adaptive simulation step size control method based on multi-resolution deduction as described in any one of claims 1 to 7.

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