A kpis prediction method based on component decomposition and multiscale slicing

Abstract

This invention discloses a KPIs prediction method based on component decomposition and multi-scale slicing, comprising: acquiring historical time series data of KPIs of the object to be predicted; extracting periodic terms through Fourier transform and Fisher verification, removing periodic terms from the original sequence to obtain a non-periodic mixed sequence, and then separating trend terms and residual terms through smoothing operations; predicting periodic terms using a multi-scale slicing-based FAN module, trend terms using a multilayer perceptron module, and residual terms using a reversible normalization mechanism module; and superimposing and fusing the three prediction results to obtain the final KPIs prediction result. This method, by decomposing the KPIs time series into periodic terms, trend terms, and residual terms and employing targeted prediction modules for each, can fully capture the changing patterns of different components, effectively improving the accuracy and robustness of KPIs prediction.

Description

Technical Field

[0001] This invention relates to the field of intelligent operation and maintenance, and in particular to a KPIs prediction method based on component decomposition and multi-scale slicing. Background Technology

[0002] In fields such as intelligent operations and maintenance (AIOps), industrial internet, and financial risk control, real-time monitoring of key performance indicators (KPIs) such as server CPU utilization and network traffic throughput is crucial for ensuring high system availability. Anomaly detection technology based on time series forecasting, which constructs a normal baseline for KPIs and uses the deviation between real-time observations and predicted values ​​as the basis for anomaly identification, has become a key means of achieving early warning of faults. Widely stationary time series require three conditions to be met: constant mean, finite variance, and variance that does not change over time. If any one of these conditions is not met, it is considered a non-stationary series. KPI data is essentially a typical type of non-stationary time series; it typically consists of a trend term, nested periodic terms, and high-frequency information and noise. The residuals together constitute the KPI series; the existence of a trend causes the series mean to change over time; nested periods cause changes in the amplitude of fluctuations, making the variance no longer constant; after removing the trend and period, the remaining residuals, due to the superposition of high-frequency information and noise, cannot be explained by trends and periodicity, but still exhibit obvious heteroscedasticity, that is, its variance also changes over time; these three parts superimpose each other, making the KPI series exhibit complex dynamic characteristics; existing mainstream methods usually model the trend term that causes the change in mean and the periodic term that causes the change in variance separately, or input them as features into the model for processing.

[0003] Currently, the decomposition and prediction methods for KPIs can be mainly divided into the following three categories: In the traditional statistical methods, Holt-Winters and ETS infer trends by calculating the weighted average and smoothing equation of historical data; ARIMA and its variant SARIMA use difference operations to station the series and fit linear laws; Prophet decomposes trends and cycles based on a generalized additive model.

[0004] Although existing deep learning methods have addressed the non-stationarity of KPI sequences to some extent, they still face two major challenges when dealing with the complex multi-period nesting and high-frequency fluctuations in KPI data: Existing methods confuse the residuals of heteroscedasticity with periodicity during the decomposition process, interfering with the model's learning of the true period. The linear networks used in mainstream prediction models are difficult to effectively handle nested periods and cannot simultaneously take into account both the global large period and the local micro period, thus limiting the prediction accuracy. Summary of the Invention

[0005] This invention provides a KPIs prediction method based on component decomposition and multi-scale slicing to overcome the problems of existing technologies, such as confusing the residuals of heteroscedasticity with periodicity during the decomposition process, interfering with the model's learning of the true period, and the difficulty of effectively handling nested periods using linear networks, which cannot simultaneously take into account both global large periods and local micro periods, thus limiting the prediction accuracy.

[0006] To achieve the above objectives, the technical solution of the present invention is as follows: A KPIs prediction method based on component decomposition and multi-scale slicing includes: S1. Obtain historical time series data of the KPIs of the object to be predicted; S2. Based on the historical time series data of the KPIs of the object to be predicted, the historical KPIs periodic items are obtained by sequentially performing Fourier transform and Fisher verification. S3. Remove the periodic terms of historical KPIs from the historical time series data of the KPIs to be predicted to obtain an aperiodic mixed series; obtain the trend terms of historical KPIs through smoothing based on the aperiodic mixed series; remove the trend terms of historical KPIs from the aperiodic mixed series to obtain the residual terms of historical KPIs. S4. Based on the historical KPIs periodic items, the prediction results of future KPIs periodic items are obtained through the multi-scale slice FAN module. S5. Based on historical KPI trends, obtain future KPI trend prediction results through the multilayer perceptron module; S6. Based on the historical KPI residuals, the prediction results of the future KPI residuals are obtained through the reversible normalization mechanism module. S7. Based on the prediction results of the future KPIs cyclical items, the prediction results of the future KPIs trend items, and the prediction results of the future KPIs residual items, the final prediction results of the future KPIs are obtained through the overlay and fusion operation.

[0007] Furthermore, the specific steps of step S2 are as follows: S21. Based on the historical time series data of the KPIs of the object to be predicted, the amplitude corresponding to the frequency at each historical moment is obtained through Fourier transform. S22. Based on the amplitude corresponding to the frequency at each historical moment, the energy of the frequency is obtained by squaring, and the expression is:

[0008] In the formula, The magnitude of energy at frequency; The amplitude corresponding to the frequency; For frequency; Fourier transform; The KPIs of the object to be predicted are historical time series data; S23. Based on the energy level of the frequency, construct the Fisher check quantity, the expression of which is:

[0009] In the formula, For Fisher's check quantity; Index for frequency; The total number of effective frequency components; Index of the effective frequency components; S24. Construct a critical threshold, and determine the frequency corresponding to the maximum energy of the Fisher check value that is greater than the critical threshold as a significant periodic frequency, add it to the significant frequency set, and set the energy of the frequency to zero. Repeat S23 until there is no more Fisher check value greater than the critical threshold, and finally obtain the selected significant frequency set. S25. Based on the selected set of significant frequencies, the historical KPIs periodic terms are obtained through inverse Fourier transform, and the expression is:

[0010] In the formula, Historical KPIs periodic items; This is the set of significant frequencies selected through screening.

[0011] Furthermore, the specific steps of step S3 are as follows: S31. Remove the periodic items from the historical time series data of the KPIs of the object to be predicted to obtain the aperiodic mixed series, the expression of which is:

[0012] In the formula, It is an aperiodic mixed sequence; S32. Based on the aperiodic mixed sequence, the historical KPI trend term is obtained through smoothing, and the expression is:

[0013] In the formula, Historical KPIs trend items; To adjust the sliding window size; Fill the offset index of the extended segment for the sliding window; This is a blended sequence after edge copying and padding. S33. Remove the historical KPIs trend term from the non-periodic mixed sequence to obtain the historical KPIs residual term, the expression of which is:

[0014] In the formula, This represents the residuals of historical KPIs.

[0015] Furthermore, the specific execution steps of the multi-scale slice-based FAN module are as follows: S41, Settings A collection of patch lengths at different scales; S42. Based on historical KPIs periodic items and A set of patch lengths at different scales is used to obtain sequences after slicing at each scale through a non-overlapping sliding window mechanism; based on the sequences after slicing at each scale, the following steps are performed sequentially: Mapping and flattening operations yield the following results: The periodic characteristics of each KPI are expressed as follows:

[0016] In the formula, For the first The cyclical characteristics of individual KPIs; This refers to the splicing and flattening operation performed along the dimension of the number of patches; for Mapping; Patch partitioning operations; S43, will The periodic features of each KPI are concatenated to obtain a multi-scale global feature, expressed as:

[0017] In the formula, It represents multi-scale global features; For splicing operations; For the first The cyclical characteristics of individual KPIs; S44. Based on the multi-scale global features, the latent variables are obtained through a linear layer, and the expression is:

[0018] In the formula, These are latent variables; This is the weight matrix of the linear layer; For the bias term of the linear layer; S45. Based on the latent variables, after processing them using the sine activation function and the cosine activation function respectively, and concatenating them, the prediction result of the future KPIs periodic items is obtained, and the expression is:

[0019] In the formula, Forecast results of future KPIs periodic items; It is an explicit weight matrix; For explicit bias terms; It is a cosine activation function; It is a sinusoidal activation function.

[0020] Furthermore, the specific execution steps of the multilayer perceptron module are as follows: S51. Based on the historical KPI trend items, the feature representation of the hidden layer is obtained by sequentially applying the weight matrix and activation function. The expression is:

[0021] In the formula, The feature representation of the hidden layer; For activation functions; This is the weight matrix of the hidden layer; For the bias term of the hidden layer; S52. Based on the feature representation of the hidden layer, the prediction results of future KPI trend items are obtained through the output layer. The expression is:

[0022] In the formula, Forecast results of future KPI trend items; This is the weight matrix of the output layer; This is the bias term for the output layer.

[0023] Furthermore, the specific execution steps of the reversible normalization mechanism module are as follows: S61. Divide the historical KPI residuals into multiple patches and calculate the variance within each patch to obtain the variance sequence, expressed as:

[0024] In the formula, For the first The variance of each patch; For variance operators; Patch partitioning operations; To prevent extremely small numbers from being divided by zero; S62. Based on each patch and variance sequence, normalization is performed to obtain the variance-removed residual sequence, expressed as:

[0025] In the formula, The residual sequence after removing variance; S63. Based on the variance sequence, the evolution of the variance for predicting the future is obtained through a multilayer perceptron, expressed as:

[0026] In the formula, To predict future variance evolution; For multilayer perceptrons targeting variance; It is a variance sequence, and ; S64. Based on the variance-removed residual sequence, a normalized residual sequence for predicting the future is obtained through a multilayer perceptron, expressed as:

[0027] In the formula, To predict the normalized residual sequence for the future; For multilayer perceptrons designed for normalized residual sequences; S65. Based on the predicted future variance evolution and the predicted future normalized residual sequence, the predicted future KPI residual terms are obtained through inverse normalization, expressed as:

[0028] In the formula, For the prediction results of the residual terms of future KPIs; This is element-wise multiplication.

[0029] Furthermore, the expression for the final KPI prediction result is as follows:

[0030] In the formula, This is the final KPI forecast result.

[0031] Beneficial effects: This invention performs refined component decomposition on the historical time series of KPIs (separating periodic, trend, and residual terms) and designs differentiated prediction modules for the unique time series characteristics of each component, avoiding the shortcomings of single models in capturing multimodal features when processing complex mixed signals. The periodic, trend, and residual terms are predicted by specially adapted modules, and finally, the results are obtained by superimposing and fusing them, which effectively reduces the superposition effect of prediction errors of each component. The overall prediction accuracy is significantly better than that of traditional single-model methods. By using the multi-scale slice FAN module for prediction, the dependencies and local patterns of periodic signals at different time spans (such as daily, weekly, and monthly cycles) can be captured through slice operations at different scales. This makes the model more adaptable to the dynamic changes of periodic terms and can effectively cope with complex scenarios where the period length is not fixed or the period shape drifts slowly over time, thereby significantly improving the accuracy of periodic term prediction. By smoothing the aperiodic mixed sequence to extract the trend term, the interference caused by short-term random fluctuations is effectively filtered out, so that the extracted trend term can truly reflect the long-term change direction of KPIs. On this basis, a multilayer perceptron module is used to predict the trend term, making full use of the strong fitting ability of the multilayer perceptron (MLP) to nonlinear functions, thus ensuring the stability and reliability of the trend term in long-term prediction. By introducing a reversible normalization mechanism module, the model can predict factors that are difficult to model, such as sudden noise, abnormal fluctuations, and distribution shifts that may be included in the residual term. This mechanism can dynamically normalize the residual term, effectively alleviate the prediction bias caused by the inconsistency between the training data and the test data distribution, enhance the robustness of the model to changes in data distribution, and at the same time retain the ability to capture the local predictable information implicit in the residual term. Attached Figure Description

[0032] 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.

[0033] Figure 1 This is a flowchart illustrating the KPIs prediction method of the present invention; Figure 2 This is a bar chart comparing the average prediction error of KPIs in the PSM dataset in this embodiment of the invention. Figure 3 This is a bar chart comparing the average prediction error of KPIs for the SMD dataset in this embodiment of the invention. Detailed Implementation

[0034] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments 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.

[0035] This embodiment provides a KPIs prediction method based on component decomposition and multi-scale slicing, such as Figure 1 As shown, it includes: S1. Obtain historical time series data of the KPIs of the object to be predicted; In this embodiment, the one having Each time step and The time series representation of KPIs in each dimension is as follows: ; Use an input sequence of length L to predict an output sequence of length H: For ease of explanation, the input and output sequences are defined as follows: and .

[0036] S2. Based on the historical time series data of the KPIs of the object to be predicted, the historical KPIs periodic items are obtained by sequentially performing Fourier transform and Fisher verification. Preferably, the specific steps of step S2 are as follows: S21. Based on the historical time series data of the KPIs of the object to be predicted, the amplitude corresponding to the frequency at each historical moment is obtained through Fourier transform. S22. Based on the amplitude corresponding to the frequency at each historical moment, the energy of the frequency is obtained by squaring, and the expression is:

[0037] In the formula, The magnitude of energy at frequency; The amplitude corresponding to the frequency; For frequency; Fourier transform; The KPIs of the object to be predicted are historical time series data; S23. Due to the sparse concentration of energy in the frequency domain, periodic signals exhibit significant peaks in amplitude; while noise energy is uniformly dispersed in the frequency domain, with amplitudes at individual frequency points significantly lower than those of the periodic term. Based on this, to test the significance of the maximum peak value and extract the periodic term, a Fisher check metric is constructed according to the energy magnitude at each frequency, expressed as:

[0038] In the formula, The Fisher check quantity is defined as the ratio of the maximum energy to the sum of the energies of all frequencies. Index for frequency; The total number of effective frequency components; Index of the effective frequency components; S24. Construct a critical threshold, and determine the frequency corresponding to the maximum energy of the Fisher check value that is greater than the critical threshold as a significant periodic frequency, add it to the significant frequency set, and set the energy of the frequency to zero. Repeat S23 until there is no more Fisher check value greater than the critical threshold, and finally obtain the selected significant frequency set. The expression for the critical threshold is:

[0039] In the formula, This is the critical threshold. The statistical significance level; The total number of frequencies; Specifically, in the m-th iteration, if the currently calculated Fisher check value... Then determine the frequency corresponding to the maximum energy. For significant periodic components, add them to the significant frequency set. and to The spectral energy is reset to zero to eliminate the masking effect of the main period on the detection of subsequent secondary periods; the verification and update process is repeated until the Fisher check is reached. If the iteration stops, the final set of significant frequencies is obtained. ; S25. Based on the selected set of significant frequencies, the historical KPIs periodic terms are obtained through inverse Fourier transform, and the expression is:

[0040] In the formula, Historical KPIs periodic items; This is the set of significant frequencies selected through screening.

[0041] S3. Remove the periodic terms of historical KPIs from the historical time series data of the KPIs to be predicted to obtain an aperiodic mixed series; obtain the trend terms of historical KPIs through smoothing based on the aperiodic mixed series; remove the trend terms of historical KPIs from the aperiodic mixed series to obtain the residual terms of historical KPIs. Preferably, the specific steps of step S3 are as follows: S31. Remove the periodic items from the historical time series data of the KPIs of the object to be predicted to obtain the aperiodic mixed series, the expression of which is:

[0042] In the formula, It is an aperiodic mixed sequence; S32. Based on the aperiodic mixed sequence, the historical KPI trend term is obtained through smoothing, and the expression is:

[0043] In the formula, Historical KPIs trend items; To adjust the sliding window size; Fill the offset index of the extended segment for the sliding window; This is a blended sequence after edge copying and padding. The hybrid sequence after edge replication and padding is obtained through an edge replication strategy; the edge replication strategy is as follows: copying the start end The second first element Copy at the end The last element Construct the filling sequence; S33. Remove the historical KPIs trend term from the non-periodic mixed sequence to obtain the historical KPIs residual term, the expression of which is:

[0044] In the formula, This represents the residuals of historical KPIs.

[0045] S4. Based on the historical KPIs periodic items, the prediction results of future KPIs periodic items are obtained through the multi-scale slice FAN module. Preferably, the specific execution steps of the multi-scale slice-based FAN module are as follows: S41, Settings A collection of patch lengths at different scales; S42. Based on historical KPIs periodic items and A set of patch lengths at different scales is used to obtain sequences after slicing at each scale through a non-overlapping sliding window mechanism; based on the sequences after slicing at each scale, the following steps are performed sequentially: Mapping and flattening operations yield the following results: The periodic characteristics of each KPI are expressed as follows:

[0046] In the formula, For the first The cyclical characteristics of individual KPIs; This refers to the splicing and flattening operation performed along the dimension of the number of patches; for Mapping; Patch partitioning operations; S43, will The periodic features of each KPI are concatenated to obtain a multi-scale global feature, expressed as:

[0047] In the formula, It represents multi-scale global features; For splicing operations; For the first The cyclical characteristics of individual KPIs; S44. In acquiring multi-scale global features Furthermore, traditional linear layers struggle to effectively fit and extrapolate nonlinear periodic terms. This embodiment employs Fourier Analysis Networks (FAN) as the prediction model, introducing a sine and cosine activation mechanism to endow the model with explicit periodic fitting and extrapolation capabilities. Based on the multi-scale global features, latent variables are obtained through a linear layer, and the expression is:

[0048] In the formula, These are latent variables; This is the weight matrix of the linear layer; For the bias term of the linear layer; The Fourier analysis network is existing technology and will not be described in detail here; S45. Based on the latent variables, after processing them using the sine activation function and the cosine activation function respectively, and concatenating them, the prediction result of the future KPIs periodic items is obtained, and the expression is:

[0049] In the formula, Forecast results of future KPIs periodic items; It is an explicit weight matrix; For explicit bias terms; It is a cosine activation function; It is a sinusoidal activation function; Through this design, the multi-scale slice FAN module not only decomposes nested periodic features using multi-scale patches, but also uses trigonometric function basis to ensure that the model can maintain stable periodic extrapolation ability in long sequence prediction, effectively avoiding the periodic decay phenomenon that occurs in traditional models when predicting distant time steps.

[0050] S5. Based on historical KPI trends, obtain future KPI trend prediction results through the multilayer perceptron module; Preferably, the specific execution steps of the multilayer perceptron module are as follows: S51. Based on the historical KPI trend items, the feature representation of the hidden layer is obtained by sequentially applying the weight matrix and activation function. The expression is:

[0051] In the formula, The feature representation of the hidden layer; For activation functions; This is the weight matrix of the hidden layer; For the bias term of the hidden layer; S52. Based on the feature representation of the hidden layer, the prediction results of future KPI trend items are obtained through the output layer. The expression is:

[0052] In the formula, Forecast results of future KPI trend items; This is the weight matrix of the output layer; This is the bias term for the output layer.

[0053] S6. Based on the historical KPI residuals, the prediction results of the future KPI residuals are obtained through the reversible normalization mechanism module. Preferably, the specific execution steps of the reversible normalization mechanism module are as follows: S61. Divide the historical KPI residuals into multiple patches and calculate the variance within each patch to obtain the variance sequence, expressed as:

[0054] In the formula, For the first The variance of each patch; It is a variance operator used to calculate The variance of each patch within the patch, i.e. the local fluctuation intensity of that patch; Patch partitioning operations; To prevent extremely small numbers from being divided by zero; S62. Based on each patch and variance sequence, normalization is performed to obtain the variance-removed residual sequence, expressed as:

[0055] In the formula, The residual sequence after removing variance; S63. Based on the variance sequence, the evolution of the variance for predicting the future is obtained through a multilayer perceptron, expressed as:

[0056] In the formula, To predict future variance evolution; For multilayer perceptrons targeting variance; It is a variance sequence, and ; S64. Based on the variance-removed residual sequence, a normalized residual sequence for predicting the future is obtained through a multilayer perceptron, expressed as:

[0057] In the formula, To predict the normalized residual sequence for the future; For multilayer perceptrons designed for normalized residual sequences; S65. Based on the predicted future variance evolution and the predicted future normalized residual sequence, the predicted future KPI residual terms are obtained through inverse normalization, expressed as:

[0058] In the formula, For the prediction results of the residual terms of future KPIs; This is element-wise multiplication.

[0059] S7. Based on the prediction results of the future KPIs cyclical items, the prediction results of the future KPIs trend items, and the prediction results of the future KPIs residual items, the final prediction results of the future KPIs are obtained through the overlay and fusion operation.

[0060] Preferably, the expression for the final KPIs prediction result is:

[0061] In the formula, This is the final KPI forecast result.

[0062] In this embodiment, decomposition and prediction experiments are conducted using the following KPI dataset: The Server Machine Dataset (SMD) dataset is a collection of KPIs from a large internet company over a period of 5 weeks. The dataset contains data from servers over 5 consecutive weeks, with a 5-minute interval between adjacent data sets. Each machine collects information from 38 dimensions, and the total number of data entries is 1,411,200. The Server Metrics (PSM) dataset is a widely used public benchmark dataset that records 25 key performance metrics, including CPU utilization, memory consumption, and network traffic. This embodiment selects a continuous data segment, which contains 15,499 time steps and a sampling interval of 5 minutes, which can reflect the dynamic changes in the state of the server cluster during operation in a relatively detailed manner. In the experiment, to comprehensively verify the model's predictive performance on numerical target variables and its ability to decompose non-stationary features, the evaluation metrics used included mean absolute error (MAE), mean squared error (MSE), and the augmented Dickey-Fowler test (ADF); detailed descriptions are as follows: 1) The Mean Absolute Error (MAE) measures the average absolute difference between the predicted and actual values. This metric has good interpretability and reflects the degree to which the model deviates from the actual value at each prediction point. 2) The mean squared error of MSE is the average of the squares of the differences between the predicted and the true values; compared to MAE, MSE is more sensitive to outliers and can punish larger errors more severely. 3) ADF augmented Dickey-Fowler test: used to quantify the stationarity of time series; since the core of this embodiment is to deal with the non-stationarity of KPIs, the introduction of ADF test can be used to verify the stationarity of each component after the series is decomposed. The smaller the value, the more thorough the decomposition and the more stable the data after decomposition. In the decomposition experiment, to verify the effectiveness of the decomposition method in this embodiment, the ADF test was used. The smaller the value of the ADF test statistic, the stronger the stationarity of the time series. The experiment calculated the global average ADF value of the original data and the residual series output at different stages of the decomposition model. The specific stages are defined as follows: RAW (Raw Data): Raw time series of KPIs without any processing; S (periods removed only): The first layer of residual sequence after the original sequence has been extracted and periodic terms removed by frequency domain Fisher verification; S+T (Removing Periods and Trends): Based on the S stage, the second layer of residual sequence is further extracted and the long-term trend term is removed using the moving average method. S+T+R (Full Component Decomposition and Normalization): Based on the S+T stage, the final residual sequence is obtained by extracting local variance using multi-scale patch and normalizing it. The experimental results of ADF ablation on the two public datasets, PSM and SMD, are shown in Table 1: Table 1. Results of KPIs Ablation Experiment

[0063] As can be seen from the ablation experiment results in Table 1, the ADF value of the sequence decreases stepwise as the decomposition stage progresses, proving that the decomposition method in this embodiment gradually achieves a deeper level of stationarity. Comparing it with the decomposition strategies of existing mainstream time series prediction models, the following conclusions can be drawn: After removing the periodic term, the sequence nonstationarity shows the most significant decrease. On the PSM dataset, the ADF value drops sharply from the original -3.04 to -5.99, a decrease of 2.95. However, like mainstream long-term time series prediction (Autoformer) and decomposed linear prediction (DLinear) models, their decomposition often stops here, resulting in significant trend and heteroscedastic fluctuations remaining in the sequence. Further removing the trend term on the basis of removing the periodic term leads to a continued decrease in the ADF value. Existing neural network basis expansion analysis (N-BEATS) models employ this "trend + periodic" binary decomposition architecture. Although its stationarity is better than models that only remove the periodic term, the sequence at this stage still contains highly disturbing heteroscedastic nonstationary residuals. After thoroughly decomposing the period and trend, the decomposition method in this embodiment uses a slice normalization mechanism for high-frequency residuals; this step effectively solves the heteroscedasticity fluctuations within the residuals, so that the ADF value of the final input sequence reaches -6.5120 on the PSM dataset and -6.9915 on the SMD dataset, achieving an ideal stationary state. In the prediction experiment, to verify the effectiveness of the proposed prediction method, five representative time series prediction methods were selected for comparative experiments, as follows: Informer: A deep learning model for long time series prediction. It is designed for long time series prediction, adopts a sparse self-attention mechanism to reduce computational complexity, and introduces distillation operation to extract key features to improve the ability to capture long-distance dependencies. The TimeBridge framework for handling nonstationarity in long-term time series forecasting aims to solve the dependency modeling problem in nonstationary time series. It alleviates short-term nonstationarity through internal attention, captures long-term cointegration relationships by utilizing cointegration attention, and restores the data distribution by extracting the variance of the series and restoring it to the output. Long-term forecasting model (Autoformer): Introduces a deep decomposition architecture to decompose the series into trend and seasonal terms, and proposes an autocorrelation mechanism to replace the traditional self-attention to discover periodic dependencies at the subsequence level; PatchTimeSeriesTransformer (PatchTST) model: It adopts a channel-independent strategy and introduces a slicing mechanism to divide the time series into segments as input to the Transformer, which significantly reduces the computational cost while preserving local semantic information. Multi-scale graph network (MSGNet): It uses frequency domain analysis to extract periodic patterns at multiple scales, combines adaptive graph convolutional networks to learn the correlation between sequences at different time scales, and uses attention mechanisms to capture intra-sequence dependencies. To verify the effectiveness of the KPI prediction method in this embodiment, a comparative experiment was conducted with several baseline methods. The experimental results are shown in Table 2, and the comparison results of the average prediction length are as follows: Figure 2 and Figure 3 As shown in Table 2, the prediction results for KPIs data with prediction lengths of 96, 192, 336 and 720 are presented under the condition that the input sequence length is 96. In order to comprehensively evaluate the overall prediction performance of the model under different prediction lengths, the average value of the results corresponding to the above four prediction lengths is calculated and denoted as AVG, which is used to measure the overall prediction ability of the model. The values ​​in bold in Table 2 are the best performance values. Table 2 Comparison of KPI forecasting methods

[0064] The comparison of KPI prediction methods in Table 2 shows that Informer performed the worst on both datasets. Besides information loss due to sparse attention, its fundamental flaw lies in the lack of an explicit time-series decomposition mechanism, forcing it to attempt to learn patterns from raw data mixed with trends, periods, and noise. While Autoformer introduced a decomposition architecture, it used a simple "trend + periodicity" binary decomposition. This approach incorrectly mixed residual terms containing high-frequency information and heteroscedasticity into periodic or trend terms, causing the model to be unable to distinguish between true periodic signals and random noise. PatchTST performed reasonably well on the PSM dataset but failed on SMD. Besides the "channel independence" strategy separating multivariate dependencies, from a decomposition perspective, PatchTST... TST directly patches the original sequence; while this approach preserves local semantics, macroscopic trends and cycles often mask microscopic residual fluctuations. The model overemphasizes smooth features within the patch while ignoring the fine-grained evolution hidden within the patch, dominated by heteroscedastic residuals, leading to a significant drop in accuracy when dealing with highly volatile SMD data. TimeBridge achieved the second-best KPI prediction results on the SMD dataset, demonstrating the importance of handling non-stationarity; however, it only extracts variance from the original data and restores it to the prediction results. This results in two issues: first, object misalignment, i.e., directly extracting statistics from the original sequence, causing microscopic residual fluctuations to be masked by macroscopic trends; and second, it does not perform prediction after variance extraction, failing to consider heteroscedasticity. The KPI prediction method in this embodiment outperforms the best baseline model TimeBridge by 25.6% and 5.2% in MSE and MAE metrics, respectively, on the SMD dataset, and by 2.1% and 1.1% in both metrics on the PSM dataset. This is mainly due to two factors: First, this method performs full component decomposition on the original sequence, enabling the model to accurately learn periodicity and trends without noise interference; second, this method explicitly handles the heteroscedasticity of the residuals, significantly improving the model's prediction accuracy under complex fluctuations by predicting future variance evolution.

[0065] The present invention has the following beneficial effects: This invention performs a refined component decomposition of historical time series KPIs (separating periodic, trend, and residual terms) and designs differentiated prediction modules for the unique temporal characteristics of each component. This avoids the drawback of single models struggling to capture multimodal features when processing complex mixed signals. The periodic, trend, and residual terms are predicted by specially adapted modules, and the results are then fused to obtain a comprehensive result. This effectively reduces the cumulative effect of prediction errors of each component, and the overall prediction accuracy is significantly better than that of traditional single-model methods. By using the multi-scale slice FAN module for prediction, the dependencies and local patterns of periodic signals at different time spans (such as daily, weekly, and monthly cycles) can be captured through slice operations at different scales. This makes the model more adaptable to the dynamic changes of periodic terms and can effectively cope with complex scenarios where the period length is not fixed or the period shape drifts slowly over time, thereby significantly improving the accuracy of periodic term prediction. By smoothing the aperiodic mixed sequence to extract the trend term, the interference caused by short-term random fluctuations is effectively filtered out, so that the extracted trend term can truly reflect the long-term change direction of KPIs. On this basis, a multilayer perceptron module is used to predict the trend term, making full use of the strong fitting ability of the multilayer perceptron (MLP) to nonlinear functions, thus ensuring the stability and reliability of the trend term in long-term prediction. By introducing a reversible normalization mechanism module, the model can predict factors that are difficult to model, such as sudden noise, abnormal fluctuations, and distribution shifts that may be included in the residual term. This mechanism can dynamically normalize the residual term, effectively alleviate the prediction bias caused by the inconsistency between the training data and the test data distribution, enhance the robustness of the model to changes in data distribution, and at the same time retain the ability to capture the local predictable information implicit in the residual term.

[0066] 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 KPIs prediction method based on component decomposition and multi-scale slicing, characterized in that, include: S1. Obtain historical time series data of the KPIs of the object to be predicted; S2. Based on the historical time series data of the KPIs of the object to be predicted, the historical KPIs periodic items are obtained by sequentially performing Fourier transform and Fisher verification. S3. Remove the periodic terms of historical KPIs from the historical time series data of the KPIs to be predicted to obtain an aperiodic mixed series; obtain the trend terms of historical KPIs through smoothing based on the aperiodic mixed series; remove the trend terms of historical KPIs from the aperiodic mixed series to obtain the residual terms of historical KPIs. S4. Based on the historical KPIs periodic items, the prediction results of future KPIs periodic items are obtained through the multi-scale slice FAN module. S5. Based on historical KPI trends, obtain future KPI trend prediction results through the multilayer perceptron module; S6. Based on the historical KPI residuals, the prediction results of the future KPI residuals are obtained through the reversible normalization mechanism module. S7. Based on the prediction results of the future KPIs cyclical items, the prediction results of the future KPIs trend items, and the prediction results of the future KPIs residual items, the final prediction results of the future KPIs are obtained through overlay and fusion operations.

2. The KPIs prediction method based on component decomposition and multi-scale slicing according to claim 1, characterized in that, The specific steps of step S2 are as follows: S21. Based on the historical time series data of the KPIs of the object to be predicted, the amplitude corresponding to the frequency at each historical moment is obtained through Fourier transform. S22. Based on the amplitude corresponding to the frequency at each historical moment, the energy of the frequency is obtained by squaring, and the expression is: In the formula, The magnitude of energy at frequency; The amplitude corresponding to the frequency; For frequency; Fourier transform; The KPIs of the object to be predicted are historical time series data; S23. Based on the energy level of the frequency, construct the Fisher check quantity, the expression of which is: In the formula, For Fisher's check quantity; Index for frequency; The total number of effective frequency components; Index of the effective frequency components; S24. Construct a critical threshold, and determine the frequency corresponding to the maximum energy of the Fisher check value that is greater than the critical threshold as a significant periodic frequency, add it to the significant frequency set, and set the energy of the frequency to zero. Repeat S23 until there is no more Fisher check value greater than the critical threshold, and finally obtain the selected significant frequency set. S25. Based on the selected set of significant frequencies, the historical KPIs periodic terms are obtained through inverse Fourier transform, and the expression is: In the formula, Historical KPIs periodic items; This is the set of significant frequencies selected through screening.

3. The KPIs prediction method based on component decomposition and multi-scale slicing according to claim 2, characterized in that, The specific steps of step S3 are as follows: S31. Remove the periodic items from the historical time series data of the KPIs of the object to be predicted to obtain the aperiodic mixed series, the expression of which is: In the formula, It is an aperiodic mixed sequence; S32. Based on the aperiodic mixed sequence, the historical KPI trend term is obtained through smoothing, and the expression is: In the formula, Historical KPIs trend items; To adjust the sliding window size; Fill the offset index of the extended segment for the sliding window; This is a blended sequence after edge copying and padding. S33. Remove the historical KPIs trend term from the non-periodic mixed sequence to obtain the historical KPIs residual term, the expression of which is: In the formula, This represents the residuals of historical KPIs.

4. The KPIs prediction method based on component decomposition and multi-scale slicing according to claim 3, characterized in that, The specific execution steps of the multi-scale slice-based FAN module are as follows: S41, Settings A collection of patch lengths at different scales; S42. Based on historical KPIs periodic items and A set of patch lengths at different scales is used to obtain sequences after slicing at each scale through a non-overlapping sliding window mechanism; based on the sequences after slicing at each scale, the following steps are performed sequentially: Mapping and flattening operations yield the following results: The periodic characteristics of each KPI are expressed as follows: In the formula, For the first The cyclical characteristics of individual KPIs; This refers to the splicing and flattening operation performed along the dimension of the number of patches; for Mapping; Patch partitioning operations; S43, will The periodic features of each KPI are concatenated to obtain a multi-scale global feature, expressed as: In the formula, It is a multi-scale global feature; For splicing operations; For the first The cyclical characteristics of individual KPIs; S44. Based on the multi-scale global features, the latent variables are obtained through a linear layer, and the expression is: In the formula, These are latent variables; The weight matrix of the linear layer; For the bias term of the linear layer; S45. Based on the latent variables, after processing them using the sine activation function and the cosine activation function respectively, and concatenating them, the prediction result of the future KPIs periodic items is obtained, and the expression is: In the formula, Forecast results of future KPIs periodic items; It is an explicit weight matrix; This is an explicit bias term; It is a cosine activation function; It is a sinusoidal activation function.

5. The KPIs prediction method based on component decomposition and multi-scale slicing according to claim 3, characterized in that, The specific execution steps of the multilayer perceptron module are as follows: S51. Based on the historical KPI trend items, the feature representation of the hidden layer is obtained by sequentially applying the weight matrix and activation function. The expression is: In the formula, The feature representation of the hidden layer; For activation functions; This is the weight matrix of the hidden layer; For the bias term of the hidden layer; S52. Based on the feature representation of the hidden layer, the prediction results of future KPI trend items are obtained through the output layer. The expression is: In the formula, Forecast results of future KPI trend items; This is the weight matrix of the output layer; This is the bias term for the output layer.

6. The KPIs prediction method based on component decomposition and multi-scale slicing according to claim 3, characterized in that, The specific execution steps of the reversible normalization mechanism module are as follows: S61. Divide the historical KPI residuals into multiple patches and calculate the variance within each patch to obtain the variance sequence, expressed as: In the formula, For the first The variance of each patch; For variance operators; Patch partitioning operations; To prevent extremely small numbers from being divided by zero; S62. Based on each patch and variance sequence, normalization is performed to obtain the variance-removed residual sequence, expressed as: In the formula, The residual sequence after removing variance; S63. Based on the variance sequence, the evolution of the variance for predicting the future is obtained through a multilayer perceptron, expressed as: In the formula, To predict future variance evolution; For multilayer perceptrons targeting variance; It is a variance sequence, and ; S64. Based on the variance-removed residual sequence, a normalized residual sequence for predicting the future is obtained through a multilayer perceptron, expressed as: In the formula, To predict the normalized residual sequence for the future; For multilayer perceptrons designed for normalized residual sequences; S65. Based on the predicted future variance evolution and the predicted future normalized residual sequence, the predicted future KPI residual terms are obtained through inverse normalization, expressed as: In the formula, For the prediction results of the residual terms of future KPIs; This is element-wise multiplication.

7. A KPIs prediction method based on component decomposition and multi-scale slicing according to any one of claims 4 to 6, characterized in that, The expression for the final KPI prediction result is as follows: In the formula, This is the final KPI forecast result.

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