A grey model-based equipment system combat effectiveness mutation point discrimination method

Abstract

This invention provides a method for identifying abrupt change points in the combat effectiveness of an equipment system based on a grey model, comprising the following steps: S1, acquiring the combat effectiveness sequence of the equipment system at multiple time points or location points, and the corresponding sequences of multiple influencing factors; S2, setting a sliding window of fixed length, and establishing a grey GM(1,N) model within each window; S3, arranging the driving coefficients calculated by each sliding window in temporal or spatial order to form a driving coefficient matrix; S4, performing small-scale abrupt change point detection and large-scale abrupt change point detection respectively, and obtaining the detection results; the small-scale abrupt change point detection is used to identify sharp statistical anomalies in the driving coefficients at local time points or location points; the large-scale abrupt change point detection is used to identify mean plateau transitions in the driving coefficients over continuous time periods or spatial regions. This invention analyzes abrupt change points in the observation data of the combat effectiveness of an equipment system and its related influencing factors to identify the location or time point of the abrupt change point.

Description

Technical Field

[0001] This invention relates to the field of equipment system testing and application technology, and more particularly to a method for identifying abrupt changes in the combat effectiveness of equipment systems based on a grey model. Background Technology

[0002] An equipment system is a military concept proposed to address the needs of future system-on-system confrontation and joint operations. It refers to an organic whole composed of several interconnected weapons and systems designed to accomplish specific missions. The core of its systematic application lies in the coordinated operation, functional complementarity, and mission support among its components, thereby enabling the overall combat effectiveness to exceed the sum of the effectiveness of its individual subsystems, or to generate new capabilities not possessed by the subsystems. This characteristic is known as the emergent nature of the equipment system. The abrupt change point in the combat effectiveness of an equipment system refers to the moment or location during system operation where combat capabilities appear or disappear, or where the effectiveness trend suddenly changes. It is one of the key manifestations of the dynamic evolution and emergent characteristics of an equipment system.

[0003] Currently, analyses of the combat effectiveness of equipment systems and its influencing factors are mainly divided into two categories: qualitative analysis and quantitative analysis. Qualitative analysis focuses on exploring the mechanisms by which various factors affect system effectiveness; quantitative analysis primarily uses analytical methods, data analysis methods, and simulation methods to evaluate effectiveness. Regarding abrupt change detection, existing technologies are mostly based on statistical methods, such as the least mean square error method, wavelet transform method, Bayesian inference method, Mann-Kendall algorithm, and cumulative sum control chart algorithm. These methods typically rely on large amounts of sample data, identifying inflection points by analyzing the probability distribution or trend changes of time-series data.

[0004] However, in the analysis of abrupt changes in the combat effectiveness of equipment systems, it is often difficult to obtain sufficient statistical observation data, and the data samples are usually characterized by limited data and scarce information. The high data requirements of existing statistical detection methods limit their direct applicability in the analysis of abrupt changes in equipment systems, making effective identification difficult under conditions of limited data. Furthermore, although grey system theory has advantages in handling small samples and uncertainties, and has been applied in areas such as equipment system demonstration and testing, its technical methods for quantitatively identifying abrupt changes in the combat effectiveness of equipment systems still need further development and refinement. Therefore, there is an urgent need to develop an abrupt change identification method suitable for small sample data and capable of incorporating the coupling relationships of multiple factors, in order to improve the analysis and early warning capabilities for the dynamic evolution of the combat effectiveness of equipment systems. Summary of the Invention

[0005] In view of this, the purpose of this invention is to propose a method for identifying abrupt changes in the combat effectiveness of an equipment system based on a grey model, so as to solve the problem that existing technologies are difficult to achieve effective identification under conditions of limited data.

[0006] The technical means employed in this invention are as follows:

[0007] A method for identifying abrupt changes in the combat effectiveness of an equipment system based on a grey model includes the following steps: S1. Obtain the combat effectiveness sequence of the equipment system at multiple time points or locations, as well as the corresponding sequence of multiple influencing factors; S2. Set a fixed-length sliding window and slide it on the time or space sequence with a preset step size; within each window, establish a gray GM(1,N) model based on the combat effectiveness sequence and multiple influencing factor sequences; estimate the development coefficient and driving coefficient of the gray GM(1,N) model within each window; S3. Arrange the driving coefficients calculated by each sliding window in time or space order to form a driving coefficient matrix. The rows of the driving coefficient matrix correspond to the window number, and the columns of the driving coefficient matrix correspond to each influencing factor. S4. Based on the driving coefficient matrix, small-scale mutation point detection and large-scale mutation point detection are performed respectively to obtain the detection results; The small-scale mutation point detection is used to identify sharp statistical anomalies in the driving coefficients at local time points or location points; The large-scale mutation point detection is used to identify mean plateau transitions of driving coefficients over continuous time periods or spatial regions.

[0008] Furthermore, the gray GM(1,N) model is as follows:

[0009] in, The evolution coefficients of the grey GM(1,N) model are given by the parameters. The driving coefficients of the grey GM(1,N) model are denoted as . For parameter columns, The sequence is generated from the nearest neighbor mean of the system's characteristic sequence, where k is the kth time / space point.

[0010] Furthermore, the small-scale mutation point detection employs a hypothesis testing method based on de-statistics for the driving coefficient matrix. B The Middle n The sequence corresponding to each influencing factor Determine the first element in the sequence. k Whether a point is a mutation point requires the following conditions to be met:

[0011] in, Construct a sequence of driving coefficients Candidate extreme points in; This represents the average driving level of influencing factors at other time points or locations after removing extreme points. Given a sample size M and a significance level α The discriminant coefficient below, This is the magnification factor.

[0012] Furthermore, the large-scale mutation point detection employs a bisectioning algorithm based on the sum of squared errors and a penalty term, for the driving coefficient matrix. B The Middle n The sequence corresponding to each influencing factor Find the dividing point within the interval [s, e). This ensures that the reduction in the sum of squared errors after segmentation satisfies: > β in, ; This is the penalty threshold.

[0013] Furthermore, the penalty threshold The formula is as follows:

[0014] in, This is the penalty ratio coefficient.

[0015] Furthermore, in the binary segmentation algorithm, only when the candidate split point... It will only be accepted if the following conditions are met:

[0016] in, For the minimum segment length, Protect bandwidth for global endpoints.

[0017] Furthermore, S4 also includes a direct qualitative analysis step: plotting the driving coefficient matrix. B The curves showing the changes in data in each column over time or spatial location are used to qualitatively predict abrupt change points by observing whether the relative sizes of the driving coefficients of different influencing factors change.

[0018] Furthermore, in S2, the accuracy of the gray GM(1,N) model established within each sliding window is checked, and only the driving coefficients extracted from models with simulation accuracy higher than a preset threshold are retained for constructing matrix B; the formula for calculating the simulation accuracy p is:

[0019] in, This represents the average relative residual.

[0020] The present invention also provides a storage medium comprising a stored program, wherein, when the program is executed, it performs any of the above-mentioned methods for identifying abrupt changes in the combat effectiveness of an equipment system based on a gray model.

[0021] The present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes any of the above-mentioned methods for identifying abrupt changes in the combat effectiveness of an equipment system based on a grey model through the computer program.

[0022] Compared with the prior art, the present invention has the following advantages: This invention, by combining with sliding window modeling technology, achieves effective modeling and dynamic analysis of the combat effectiveness of equipment systems and the coupling relationship of multiple factors under conditions of small sample size and limited information, overcoming the dependence of traditional statistical mutation detection methods on large amounts of data.

[0023] The driving coefficient matrix construction and analysis method provided by this invention, by arranging the estimated driving coefficients of each influencing factor in a sliding window according to time sequence, realizes the visualization and quantitative characterization of the intensity of each influencing factor and its dynamic evolution trajectory, providing a direct basis for interpreting the emergent performance of the system from the data level.

[0024] The collaborative discrimination mechanism for small-scale and large-scale mutation points provided by this invention achieves simultaneous identification and differentiation of two types of spatiotemporal scale mutations: local sharp anomalies and structural state transitions, by adopting hypothesis testing based on de-statistics and mean transition detection based on binary segmentation, respectively. This enables mutation analysis to have both tactical warning and system evaluation value.

[0025] The discrimination path provided by this invention, which combines qualitative analysis and quantitative calculation, first uses the driving coefficient curve to observe the ranking changes for preliminary positioning, and then uses statistical tests and algorithm segmentation for precise verification. This achieves a unified approach of rapid screening and robust confirmation in the mutation point discrimination process, improving the reliability and interpretability of the analysis results.

[0026] The endpoint robustness processing and minimum segment length constraint rules provided by this invention apply stricter thresholds or protection bands to sequence boundary samples in mutation detection and impose minimum persistence requirements on platform transitions, thereby achieving consistency between the identification results and the physical mechanism of equipment system combat evolution and effectively suppressing pseudo-mutations caused by boundary effects and random fluctuations. Attached Figure Description

[0027] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0028] Figure 1 This is a flowchart of the method of the present invention.

[0029] Figure 2 This is a schematic diagram illustrating the changing trend of the driving coefficients of the influencing factors of this invention. Detailed Implementation

[0030] To enable those skilled in the art to better understand the present invention, 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 only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0031] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of the invention described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0032] The evolutionary patterns of equipment system combat effectiveness, especially the timing or location of abrupt change points, are crucial for the operational application of equipment systems and represent a research direction of great interest to equipment system managers. Currently, most literature focuses on qualitative descriptions of the emergent phenomena of equipment system combat effectiveness, rarely addressing quantitative analysis methods. However, for specific issues such as the design of equipment system operational application schemes, qualitative descriptions are insufficient. This invention emphasizes the quantitative analysis of the changing patterns of equipment system combat effectiveness. Given the complex nature of equipment systems—characterized by diversity, dynamism, and uncertainty—quantitative analysis of their combat effectiveness and influencing factors is difficult based on theoretical formulas or large amounts of reliable statistical data; assessments are often limited to small amounts of historical experimental or exercise data. This invention addresses the small-sample data characteristics of equipment system combat effectiveness and its related influencing factors by proposing a gray model-based method for identifying abrupt change points in equipment system combat effectiveness. The principle is first introduced, followed by a calculation example demonstrating the feasibility and effectiveness of the proposed method.

[0033] like Figure 1 As shown, this invention provides a method for identifying abrupt changes in the combat effectiveness of an equipment system based on a grey model, comprising the following steps: S1. Obtain the combat effectiveness sequence of the equipment system at multiple time points or locations, as well as the corresponding sequence of multiple influencing factors; S2. Set a fixed-length sliding window and slide it on the time or space sequence with a preset step size; within each window, establish a gray GM(1,N) model based on the combat effectiveness sequence and multiple influencing factor sequences; estimate the development coefficient and driving coefficient of the gray GM(1,N) model within each window; S3. Arrange the driving coefficients calculated by each sliding window in time or space order to form a driving coefficient matrix. The rows of the driving coefficient matrix correspond to the window number, and the columns of the driving coefficient matrix correspond to each influencing factor. S4. Based on the driving coefficient matrix, small-scale mutation point detection and large-scale mutation point detection are performed respectively to obtain the detection results; The small-scale mutation point detection is used to identify sharp statistical anomalies in the driving coefficients at local time points or location points; The large-scale mutation point detection is used to identify mean plateau transitions of driving coefficients over continuous time periods or spatial regions.

[0034] Grey system theory has significant advantages in dealing with small sample and information-poor time series problems. This invention first introduces the grey GM(1,N) model of equipment system combat effectiveness and its influencing factors.

[0035] Grey GM(1,N) model and parameter estimation; Let the characteristic data modeling sequence of equipment system combat effectiveness be: ; The data sequence of relevant influencing factors on the combat effectiveness of equipment systems is as follows:

[0036]

[0037]

[0038] Where n represents the number of time points or location points experienced by the equipment system during its operation, and N represents the characteristic factors and the number of influencing factors that affect the effectiveness of the equipment system.

[0039] Assumption Original data sequence A sequence of first-order accumulating generation operators (AGO). for The nearest neighbor mean generation sequence (only build) (the sequence generated by the nearest neighbor mean), that is:

[0040] Then it is said:

[0041] For the GM(1,N) model, the parameters are... The evolution coefficients of the GM(1,N) model are called parameters. These are called the driving coefficients of the GM(1,N) model. For parameter columns.

[0042] To establish the aforementioned grey GM(1,N) model of equipment system combat effectiveness and its influencing factors, it is necessary to estimate the model's development and driving coefficients based on the original data sequence. An intermediate data sequence can be constructed from the original data sequence:

[0043] Based on the least squares estimation algorithm, the parameter list of the GM(1,N) model is calculated as follows:

[0044] Therefore, it is called:

[0045] The equations for the GM(1,N) model The whitening equation is also known as the shadow equation.

[0046] The solution to this equation is:

[0047] The approximate time response of the shadow equation is:

[0048] The cumulative reduction and restoration value is:

[0049] As can be seen from the approximate time response formula, the GM(1,N) model is a state model that can estimate and analyze the current state of the system based on the past development trend and influencing factors of the system. The inertia of change in characterizing efficacy itself, i.e. The larger the value, the stronger the dependence of efficiency on historical states. The driving coefficient of GM(1,N) These represent the driving force of each influencing factor on combat effectiveness. This indicates that it promotes effectiveness, and A larger value indicates a stronger influence. Therefore, the relative importance of influencing factors can be analyzed by comparing the magnitudes of the driving coefficients.

[0050] Accuracy of GM(1,N) model; make ( The relative residuals of the system characteristic variables in the GM(1,N) model can be obtained. and average relative residual That is:

[0051] Thus, the simulation accuracy of the GM(1,N) model can be obtained. for:

[0052] Generally speaking, when The calculation result of GM(1,N) is considered valid at this time.

[0053] Theoretical basis for identifying abrupt changes in the effectiveness of system-of-systems warfare; The abrupt changes in system-of-systems combat effectiveness are essentially discontinuous and emergent responses triggered by operational, environmental, and organizational elements at a certain threshold. Because equipment systems are generally deployed in a distributed manner, their internal states are difficult to monitor centrally, exhibiting a gray characteristic of partial knowledge and partial unknowns. Identifying abrupt changes directly from a limited number of noisy observations is particularly challenging. Grey system theory can model and infer trends based on observables under conditions of small samples and incomplete information. Among them, the GM(1,N) model, with its ability to express the coupling relationships of multiple factors, provides an interpretable statistical carrier for abrupt change identification. Simultaneously characterizing the marginal response of system effectiveness to the cumulative situation of various influencing factors within a local window allows mapping unobservable mechanistic changes into traceable coefficient changes.

[0054] Local GM(1,N) models are established for different time periods or spatial segments, and the driving coefficient matrix is ​​obtained by aligning it with the end position of the time or spatial unit at the end of the window. Each column of the matrix represents the coefficient trajectory of a certain influencing factor in adjacent spatiotemporal units, reflecting how its marginal contribution to effectiveness adjusts with the environment, composition, and confrontational situation. Each row of the matrix corresponds to the relative weights and ranking structure of factors within the same spatiotemporal unit. If the system is in a steady state, the trajectories of different factors exhibit only limited fluctuations within continuous units, and the ranking remains basically unchanged. Once the trajectory shows a shape significantly different from the steady state, it can be judged as a potential mutation.

[0055] Sudden changes in the combat effectiveness of equipment systems can be categorized into small-scale and large-scale changes. Small-scale changes emphasize sharp deviations within fine-grained moments or local spatial units, typically such as short-term electronic suppression in a sector, obstruction caused by extreme weather in a narrow area, local sensor saturation, or short-term shocks caused by impromptu maneuvers. Their representation in driving coefficients is usually a significant deviation of the coefficients from the mean within a single window, representing short, rapid, and sharp anomalies. Large-scale changes emphasize leaps in the mean plateau across longer time periods or larger spatial areas, typically such as large-scale changes in visibility and surface conditions due to seasonal transitions, systematic adjustments to formations and tactical rules in multiple regions, or an overall increase in the intensity of confrontation over a period. Their representation in the driving coefficient matrix is ​​usually an overall upward or downward shift of coefficients within several consecutive windows, stabilizing at a new level, accompanied by a persistent change in the relative order of factors, representing a stable, long-lasting, and continuous state shift. These two types are not opposites, but rather two manifestations of the same system at different spatiotemporal scales; the former leans towards tactical-level warnings and localized hardening, while the latter points to operational / system-level weight reallocation, pattern updates, and rhythm reconstruction.

[0056] To ensure consistency between the discrimination based on the driving coefficient matrix and the physical mechanism, robust constraints on boundaries and persistence must be imposed at the theoretical level. When establishing a GM(1,N) model, if the sliding window sequence has weaker information and stronger correlation at the beginning, end, or spatial edges, false positives at isolated points at the ends are easily generated. Therefore, in small-scale discrimination, the significance threshold of boundary samples should be tightened or acceptance should be cautious, while in large-scale discrimination, segmentation near the endpoints should be prohibited and the new platform should meet a minimum persistence length. This means that only when anomalies have sufficient spatiotemporal volume (duration or coverage) are they recognized as state-level changes; only when local deviations exceed the statistical limits of steady-state fluctuations are they recognized as tactical-level shocks. Robust constraints aim to avoid misinterpreting numerical instability or boundary noise as real mutations.

[0057] In summary, GM(1,N) within a sliding frame projects the mechanistic changes of multi-factor coupling into traceable driving coefficient trajectories, enabling small-scale and large-scale abrupt changes to be simultaneously perceived and distinguished within the same data structure. This is achieved using the driving coefficient matrix... The identification approach based on the carrier is thus established: when the trajectory shows an isolated and significant local deviation, a rapid warning is generated for short-term impacts; when the trajectory exhibits a platform-level leap on a continuous unit, statistical confirmation of structural shifts is completed. The two constitute a closed loop of warning-confirmation, enabling potential sudden changes in combat effectiveness to be identified early, explained mechanistically, and responded to with corresponding decision-making at both the tactical and system levels.

[0058] Identification of sudden change points in system combat effectiveness based on driving coefficients; Starting from the first time point or spatial location, select a length of... The first GM(1,N) model is constructed using the original data; subsequently, a sliding window with a step size of 1 is used in time or space, and each time the latest window value is used. Reconstruct the GM(1,N) model from the dataset. Let the total number of samples obtained be... The nth local GM(1,N) model, denoted as the nth model. The linearized equations within each window are:

[0059] superscript Indicates the original sequence, superscript This indicates first-order cumulative generation (AGO). This represents the background value for the system item. The driving coefficient vectors estimated from each window are aligned according to the temporal or spatial end position of the window and stacked to form a driving coefficient matrix of influencing factors. That is:

[0060] Among them, row number Indicate the time or location of the equipment system's operational deployment, listed in sequence. These represent different influencing factors. Based on the theory of identifying abrupt changes in system combat effectiveness, when the ranking structure of driving coefficients changes in a certain spatiotemporal unit, or when the development trend of a certain factor's driving coefficient shows a significant shift, it may trigger abrupt changes in system combat effectiveness. To balance intuitiveness and verifiability, this invention employs two paths: direct qualitative analysis and quantitative calculation. The former quickly locates suspicious abrupt changes through visualization, while the latter uses statistics and cost functions as evidentiary benchmarks and reduces boundary false alarms through endpoint robustness.

[0061] Direct qualitative analysis method; Based on the driving coefficient matrix Plot the time point (or location) on the x-axis and the influencing factor number on the y-axis, and then divide each column... Follow By plotting the changing curves on the same graph, we can obtain... The trend line of the driving coefficient of the influencing factors changes over time. This trend graph can intuitively make qualitative predictions of the sudden change point in the combat effectiveness of the equipment system.

[0062] Generally, the driving coefficients of all influencing factors will fluctuate to a certain extent with time or location. Defined in The influencing factor corresponding to the column with the largest driving coefficient is the primary influencing factor. If its driving coefficient As time decreases, the driving coefficients of one or more other factors increase, especially with a sharp increase over a short period of time, and at a certain point in time... A driving factor exceeding the primary influencing factor exists, i.e.:

[0063] This indicates a significant change in the internal mechanism of the equipment system, which usually foreshadows a potential decrease in combat effectiveness. A sudden change occurs at a certain point. Similarly, if the relative magnitudes of the driving coefficients among other influencing factors are in a certain order... The exchange of values ​​may also trigger structural changes in the system's effectiveness.

[0064] It is important to note that this method can only qualitatively predict the existence of suspected mutations and cannot directly indicate the direction of the mutation. Mutations may lead to a rapid increase in system effectiveness or an accelerated decline; the specific direction requires comprehensive analysis in conjunction with effectiveness output indicators, operational context conditions, and other quantitative data.

[0065] Quantitative calculation discrimination method; The driving coefficient matrix is ​​obtained based on the GM(1,N) sliding model. , No. One influencing factor The driving coefficients at each time point or spatial location constitute a sequence. In the context of equipment system combat effectiveness assessment, this sequence characterizes the spatiotemporal evolution of the marginal contribution intensity of this influencing factor to effectiveness. To align with real-world mechanisms, this invention classifies mutations into small-scale mutations and large-scale mutations. Small-scale mutations correspond to sharp deviations within a fine-grained temporal instant or local spatial unit, while large-scale mutations correspond to state transitions and the formation of new platforms spanning longer time periods or larger spatial regions. These two types of mutations are not mutually exclusive but rather represent two manifestations of the same system at different spatiotemporal scales.

[0066] For the identification of small-scale mutations, this invention employs a hypothesis testing framework based on de-statistics. Let the candidate extreme points be... The mean after removing this point is defined as:

[0067] This represents the average driving level of the influencing factors at other time points or locations after removing extreme points. Next, the deviation of each point relative to this mean is calculated:

[0068] Its fluctuation scale is estimated by removing variance:

[0069] Given. Under the assumption that... Given the following:

[0070] Assuming a finite sample size ( When the variance is relatively small and unknown, the bias statistic follows a sequence with a set of degrees of freedom. of The distribution is because equipment combat effectiveness assessments are often based on finite spatiotemporal samples, and it is difficult to obtain the true variance.

[0071] Table 1 shows the results of different sample sizes M at different significance levels. Below Values.

[0072] Table 1 Numerical table

[0073] Given significance level ,Depend on Discrimination coefficient obtained from distribution Based on this, it is determined that:

[0074] Considering that the variance information of sliding estimation is weaker and more correlated at the beginning and end of time series or spatial boundaries, this invention introduces an endpoint robustness strategy: Let the width of the endpoint protection band be... ,when In this case, either the candidate should be ignored directly, or it should be magnified by a factor of 1. Use stricter thresholds:

[0075] If this inequality holds, it means that at a certain point in time or location... , No. The driving coefficients of each influencing factor deviate significantly from the overall level, and their changes are sufficient to cause small-scale mutations.

[0076] To ensure robustness of the results, it is necessary to start from the sequence. Remove the outlier The above steps are then repeated for the remaining data until the driving coefficient changes of the influencing factor no longer trigger the mutation discrimination condition at all time points or locations. Subsequently, the same analysis process is repeated for other influencing factors, and finally, the key time points or locations that cause small-scale mutations in combat effectiveness and the corresponding influencing factors can be obtained.

[0077] In identifying large-scale abrupt changes, this invention focuses on plateau-like structural switching of driving coefficients over a longer time period or a larger spatial range. For the first... The driving data sequence of each driving factor Use half-open representation for any row interval (length is) The mean of this sequence is:

[0078] Its sum of squared errors (SSE) is:

[0079] At the global level, to suppress excessive segmentation, a total... Criteria for imposing penalties. Let the set of change points be... and order Then the cost function is:

[0080] in Controlling the difficulty of accepting new platforms, i.e., the penalty threshold. The implementation uses a greedy approximation of binary segmentation: within the current interval... Internal enumeration of candidate split points Calculate the decrease:

[0081] when When the penalty threshold is exceeded, in the optimal The process involves segmenting the data and recursively dividing the left and right sub-intervals until no further segmentation is possible. A penalty threshold is also applied. It can be a constant, or it can be determined by a penalty ratio coefficient. Set as the proportion of the series variance To maintain physical interpretability at the boundary, endpoint robustness and minimum segment length constraints are introduced, only when...

[0082] Time can be used as a candidate split point, among which For the minimum segment length, This protects bandwidth for global endpoints. Through the above process, column sequences can be identified over a longer timescale. The turning point into a new stable platform. At the application level, large-scale mutations reflect the overall shift in the contribution intensity of driving factors to a new stable platform when the system undergoes continuous and structural adjustments in tactical operating modes or external environmental conditions. These changes differ from localized small-scale fluctuations, instead manifesting as mean migration over a longer period or over a larger area. By introducing endpoint protection and minimum segment length constraints, it is possible to effectively avoid misjudging sporadic noise or boundary effects as large-scale mutations, thereby ensuring that the identification results are consistent with the macroscopic laws governing the evolution of the system's operational effectiveness.

[0083] The above two categories of judgment are on the same line The trajectories complement each other: small-scale mutations provide rapid warnings of local spatiotemporal units, prompting contingency plans and local hardening; large-scale mutations confirm structural migrations across periods or regions, pointing to weight reconfiguration, pattern updates, and rhythm reconstruction. Through endpoint robustness processing, boundary samples no longer easily trigger alarms or segmentation, and the statistical evidence of mutations remains consistent with the physical mechanisms of the equipment system. The final judgment results can locate instantaneous and local anomalies at a fine-grained level, and also identify continuous and wide-area state transitions at a macro scale, providing a sensitive yet robust quantitative basis for operational planning and resource allocation.

[0084] Example To verify the effectiveness and feasibility of this method, this example selects the combat effectiveness of a certain type of equipment system as the characteristic data sequence, and simultaneously uses the equipment system's interoperability, reconnaissance capabilities, and command and control level as influencing factor data sequences. Based on the driving coefficient matrix of the GM(1,N) model, the abrupt change points of the equipment system's combat effectiveness are identified and analyzed. Relevant data are listed in Table 2.

[0085] Table 2. Example data on combat effectiveness characteristic indicators and influencing factors.

[0086] Grey GM(1,N) modeling and calculation; In this example, when performing GM(1,N) modeling of the combat effectiveness of the equipment system and its influencing factors at different time points or locations, six data points are uniformly selected for calculation to ensure consistency of results and to conform to the metabolic principle of the GM(1,N) model. As the operational application of equipment systems advances, the ability of older data to depict system evolution gradually diminishes. Therefore, continuously introducing the latest data and promptly discarding outdated data during the modeling process can more accurately reflect the current operational characteristics of the equipment system. This is especially true for identifying and analyzing abrupt changes in combat effectiveness. The combat effectiveness of an equipment system may undergo qualitative changes after quantitative accumulation, rendering past data inadequate to represent its current state. Therefore, discarding old data that no longer reflects current characteristics is reasonable and necessary. Since the data includes a total of... If there are 10 time points or 10 location points, then a total of 1000 can be established. A local GM(1,N) model.

[0087] By selecting the relevant data from t=1-6 in Table 2, we can obtain the modeling sequence of characteristic data for the combat effectiveness of the equipment system:

[0088] Meanwhile, the data sequences of the three relevant influencing factors are as follows:

[0089]

[0090]

[0091] The following establishes a GM(1,4) model of the equipment system and its three influencing factors. Subsequent calculations will uniformly retain four significant figures. and , , By performing 1-AGO, we get:

[0092]

[0093]

[0094]

[0095] The nearest neighbor mean generation sequence is:

[0096] Therefore:

[0097]

[0098] so:

[0099] The GM(1,4) fitting model is obtained as follows:

[0100] The model's average relative error Simulation accuracy This indicates that the established local GM(1,N) model is effective and can be used for subsequent analysis.

[0101] By sliding a window with a step size of 1 in time or space, the next local GM(1,N) model is solved. Selecting data from numbers 2 to 7 in Table 2, the modeling sequence of equipment system combat effectiveness characteristics and the data sequences of three related influencing factors are obtained as follows:

[0102]

[0103]

[0104]

[0105] Similar modeling calculations yielded its GM(1,4) fitting model as follows:

[0106] The model's average relative error Simulation accuracy This also demonstrates that the established local GM(1,N) model is effective and can be used for subsequent analysis.

[0107] Similarly, by sliding the window with a step size of 1 in time or space, we continue to select relevant data from numbers 3 to 8, 4 to 9, 5 to 10, 6 to 11, 7 to 12, 8 to 13, and 9 to 14 in Table 2, and calculate their GM(1,4) fitting models as follows: (1)

[0108] (2)

[0109] (3)

[0110] (4)

[0111] (5)

[0112] (6)

[0113] (7)

[0114] The simulation accuracy of the above 7 models All were established.

[0115] Direct qualitative analysis of mutation points based on the driving coefficient matrix Based on the above modeling results, a driving coefficient matrix of three influencing factors on the combat effectiveness of the equipment system in this example is constructed at different time points or locations. , denoted as:

[0116] Based on the transpose matrix above, the changing trends of the driving coefficients of the three influencing factors at different time points or locations were plotted, as follows: Figure 2 As shown in the figure, the thin solid line represents the first influencing factor, interconnection and interoperability. It is clear that in the initial GM(1,N) model, interconnection and interoperability is the main driving factor in this example. However, at time point or location 7, the original main driving factor gradually weakens, while the driving factors of other influencing factors strengthen. The main driving factor changes from influencing factor one to influencing factor two, indicating an adjustment in the effects of internal factors within the equipment system, suggesting a potential sudden change in combat effectiveness. A similar method can qualitatively predict the occurrence of sudden changes in the combat effectiveness of the equipment system at time points or locations 8, 10, 12, and 13.

[0117] By comparing the changing trends of the driving coefficients of all influencing factors, it is possible to predict and identify abrupt changes in the combat effectiveness of an equipment system based on the replacement of the main influencing factors. This only reflects one aspect of the mechanism of abrupt changes in combat effectiveness. If we want to further use the changing trends of the driving coefficients of individual influencing factors for prediction and identification, more in-depth quantitative calculations are required.

[0118] Quantitative discrimination calculation of mutation points based on the driving coefficient matrix; Building upon the qualitative analysis, this invention further utilizes small-scale mutation detection and large-scale mean mutation detection methods to analyze the driving coefficient matrix. Quantitative analysis is conducted to more accurately reveal the abrupt changes in the combat effectiveness of equipment systems.

[0119] Firstly, regarding small-scale mutation detection, this invention uses a significance test method based on subtraction statistics to discriminate the driving coefficient matrix column by column. At the significance level... Below, by referring to the table, we can see that when the sample size is... The critical statistic is Let the width of the end protection strip be... ,when When using magnification factor Use stricter thresholds.

[0120] The driving coefficient sequence corresponding to interconnection and interoperability For example, since small-scale combat effectiveness mutations are caused by sharp deviations within fine-grained time intervals or local spatial units, the time or location of the mutation must correspond to the extreme value of the driving coefficient. This reflects the dominant role of key influencing factors on the overall system performance at a specific moment. Therefore, the maximum value point is used here. ( ) and minimum point ( Let's take an example to illustrate the calculation steps.

[0121] For the maximum point, the mean of the remaining samples Standard deviation Since this point does not fall within the endpoint protection zone, the threshold can be obtained directly. And the deviation at that point

[0122] It significantly exceeds the threshold, therefore it is determined that... The point represents a small-scale mutation point. In contrast, the deviation of the minimum point did not exceed the threshold and was therefore not identified as an anomaly. After removing the maximum point, the above calculation steps were repeated for the remaining samples. Since no points were removed, the process was stopped. This indicates that mutations are mainly concentrated at key extreme value locations, rather than all local peaks causing performance changes.

[0123] The same calculation method was applied to the driving coefficient sequence of reconnaissance capability and command and control level. The results show that the factors influencing command and control level are... Changes in the local area can predict small-scale abrupt changes in the combat effectiveness of the equipment system, while changes in the driving coefficients of factors affecting reconnaissance capabilities do not lead to abrupt changes. This analysis shows that different influencing factors have varying sensitivities to abrupt changes in the effectiveness of the equipment system; some factors play a dominant role at critical points in time, while others have a weaker impact or remain stable. It is emphasized again that such abrupt changes typically manifest as drastic fluctuations in local elements of the system within a short period, often triggered by sudden events or temporary disturbances.

[0124] Secondly, in terms of large-scale mutation detection, this invention employs a mean mutation discrimination method based on binary segmentation to recursively segment each driving coefficient sequence. A penalty threshold is assumed. The penalty proportionality coefficient is determined by the variance of the driving coefficient sequence. Set to 1 to ensure the adaptability of the test; assume minimum segment length. Set to 3 to avoid spurious mutations on excessively short samples; assume a global endpoint protection band. The value is 2, ensuring that the split point does not fall near the beginning or end of the sequence.

[0125] Based on this, taking interconnection and interoperability as an example to illustrate its calculation process, the optimal split point appears at... The mean of the entire interval is first calculated based on the Sum of Squared Errors (SSE) criterion formula:

[0126] Corresponding overall error:

[0127] Let the candidate split point be The entire interval is divided into and Two parts. Left interval Mean:

[0128] right interval Mean:

[0129] The total error after segmentation The decrease was:

[0130] Meanwhile, the penalty term set by the program is the variance of the driving coefficients in that column:

[0131] because

[0132] So in The location (i.e., the original data at the end of the sliding window) This is identified as a large-scale mean abrupt change point. By recursively calculating the newly divided intervals, other large-scale mean abrupt change points can be identified.

[0133] Similarly, for the second column (reconnaissance capability, ) and the third column (command and control level, The calculations were performed, and the optimal splitting points were as follows: and These all constitute large-scale changes in effectiveness, indicating that the equipment system underwent structural adjustments during this stage.

[0134] The above results show that the abrupt changes in the combat effectiveness of equipment systems exhibit multi-scale superposition characteristics: in During this period, the three types of driving factors experienced a shift in their overall mean levels, revealing a structural shift in the system's operational phases; while... At the same time, sharp deviations in interconnectivity, interoperability, and command and control levels also appeared on a small scale, reflecting the cumulative effect of local short-term anomalies. These two factors interacted, jointly constituting a significant point of abrupt change in system effectiveness. This phenomenon indicates that abrupt changes in equipment system effectiveness are driven by both long-term mechanism adjustments and short-term disturbances. Therefore, dynamic monitoring and early warning of system effectiveness require simultaneous attention to both structural changes and local anomalies.

[0135] Figure 2 The fusion detection results of mutation points are presented, with red × marking small-scale mutation points and orange hollow circles marking large-scale mutation points. As can be seen from the figure, small-scale and large-scale mutations partially overlap on the time axis, for example, at... Nearby, short-term spikes and previous mean jumps appeared successively, confirming the above analytical conclusions. This multi-scale mutation detection based on quantitative calculations not only verifies the rationality of the qualitative analysis, but also provides more solid support for revealing the evolution mechanism of the combat effectiveness of equipment systems.

[0136] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for identifying abrupt changes in the combat effectiveness of an equipment system based on a grey model, characterized in that, Includes the following steps: S1. Obtain the combat effectiveness sequence of the equipment system at multiple time points or locations, as well as the corresponding sequence of multiple influencing factors; S2. Set a fixed-length sliding window and slide it on the time or space sequence with a preset step size; within each window, establish a gray GM(1,N) model based on the combat effectiveness sequence and multiple influencing factor sequences; estimate the development coefficient and driving coefficient of the gray GM(1,N) model within each window; S3. Arrange the driving coefficients calculated by each sliding window in time or space order to form a driving coefficient matrix. The rows of the driving coefficient matrix correspond to the window number, and the columns of the driving coefficient matrix correspond to each influencing factor. S4. Based on the driving coefficient matrix, small-scale mutation point detection and large-scale mutation point detection are performed respectively to obtain the detection results; The small-scale mutation point detection is used to identify sharp statistical anomalies in the driving coefficients at local time points or location points; The large-scale mutation point detection is used to identify mean plateau transitions of driving coefficients over continuous time periods or spatial regions.

2. The method for identifying abrupt changes in the combat effectiveness of an equipment system based on a grey model according to claim 1, characterized in that, The gray GM(1,N) model is as follows: in, The evolution coefficients of the grey GM(1,N) model are given by the parameters. The driving coefficients of the grey GM(1,N) model are denoted as . For parameter columns, The sequence is generated from the nearest neighbor mean of the system's characteristic sequence, where k is the kth time / space point.

3. The method for identifying abrupt changes in the combat effectiveness of an equipment system based on a grey model according to claim 1, characterized in that, The small-scale mutation point detection employs a hypothesis testing method based on subtraction statistics for the driving coefficient matrix. B The Middle n The sequence corresponding to each influencing factor Determine the first element in the sequence. k Whether a point is a mutation point requires the following conditions to be met: in, Construct a sequence of driving coefficients Candidate extreme points in; This represents the average driving level of influencing factors at other time points or locations after removing extreme points; Given a sample size M and a significance level α The discriminant coefficient below, This is the magnification factor.

4. The method for identifying abrupt changes in the combat effectiveness of an equipment system based on a grey model according to claim 1, characterized in that, The large-scale mutation point detection employs a bisection algorithm based on the sum of squared errors and a penalty term, for the driving coefficient matrix. B The Middle n The sequence corresponding to each influencing factor Find a dividing point k in the interval [s, e) such that the reduction in the sum of squared errors after dividing satisfies: ＞ β in, ; This is the penalty threshold.

5. The method for identifying abrupt changes in the combat effectiveness of an equipment system based on a grey model according to claim 4, characterized in that, The penalty threshold The formula is as follows: in, This is the penalty ratio coefficient.

6. The method for identifying abrupt changes in the combat effectiveness of an equipment system based on a grey model, as described in claim 5, is characterized in that... In the aforementioned binary segmentation algorithm, only when the candidate split point... k It will only be accepted if the following conditions are met: in, For the minimum segment length, Protect bandwidth for global endpoints.

7. The method for identifying abrupt changes in the combat effectiveness of an equipment system based on a grey model according to claim 1, characterized in that, S4 also includes a direct qualitative analysis step: plotting the driving coefficient matrix. B The curves showing the changes in data in each column over time or spatial location are used to qualitatively predict abrupt change points by observing whether the relative sizes of the driving coefficients of different influencing factors change.

8. The method for identifying abrupt changes in the combat effectiveness of an equipment system based on a grey model according to claim 1, characterized in that, In S2, the accuracy of the gray GM(1,N) model established within each sliding window is checked, and only the driving coefficients extracted from models with simulation accuracy higher than a preset threshold are retained for constructing matrix B; the formula for calculating the simulation accuracy p is: in, This represents the average relative residual.

9. A storage medium, characterized in that, The storage medium includes a stored program, wherein when the program is executed, it performs the method for identifying abrupt changes in the combat effectiveness of an equipment system based on a gray model, as described in any one of claims 1 to 8.

10. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, The processor executes the method for identifying abrupt changes in the combat effectiveness of an equipment system based on a gray model, as described in any one of claims 1 to 8, through the computer program.

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