Double incremental learning method for non-stationary time series prediction based on adaptive integration
Through the adaptive integration of dual incremental learning method, combined with statistical hypothesis testing and sliding window technology, an online deep representation learning model is constructed, which solves the performance degradation of traditional methods in non-stationary time series prediction, and realizes the vibration state of the electromechanical system Accurate prediction and efficient response.
Patent Information
- Application Number
- CN202411372301.7
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-09-29
- Publication Date
- 2025-01-14
AI Technical Summary
Traditional time series prediction methods have significantly reduced prediction performance when facing non-stationary time series and cannot dynamically adapt to data changes, especially in the prediction of vibration states of electromechanical systems.
Using a dual incremental learning method based on adaptive integration, the changes are detected through statistical hypothesis testing and adaptive sliding window technology, an online deep representation learning model is constructed, and single incremental or double increment updates are performed according to the degree of change to form the final prediction. Model.
It realizes efficient prediction of non-stationary time series, improves prediction accuracy and adaptability, is suitable for various non-stationary time series tasks, and significantly improves prediction performance and response speed.
Smart Images
Figure CN119312161A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of time series prediction, and in particular to a dual-increment learning method for non-stationary time series prediction based on adaptive integration. Background Art
[0002] Many dynamic processes in the real world can be modeled as time series, and time series forecasting is of great significance in social and economic development. Time series forecasting has a wide range of applications, including financial market forecasting, weather forecasting, traffic flow forecasting, medical data analysis, and many other fields. However, the non-stationarity of time series obtained from actual projects may lead to increased difficulty in forecasting. Non-stationary time series usually have significant volatility and trend, which makes traditional forecasting methods ineffective when dealing with these data.
[0003] Traditional time series prediction methods, such as the autoregressive moving average model and the autoregressive integrated moving average model, perform well when dealing with stationary time series, but their prediction performance drops significantly when facing non-stationary time series. This is because these methods rely on the assumption of data stationarity and cannot dynamically adapt to changes in data. To solve this problem, researchers have proposed some improved methods in recent years, such as the weighted moving average method, exponential smoothing method, and prediction models based on machine learning. However, these methods still have limitations when dealing with non-stationary time series and cannot fully cope with dynamic changes in data.
[0004] In the field of electromechanical engineering, the stable operation of mechanical and electrical systems is crucial to ensuring production safety, improving equipment efficiency and extending equipment life. In daily operation, these systems often produce complex vibration phenomena due to various reasons such as material fatigue, environmental factors (such as temperature and humidity changes), load fluctuations and improper operation. These vibration state data constitute a typical non-stationary time series, whose characteristics include but are not limited to sudden changes in amplitude, drift of frequency, and mixed characteristics of periodicity and non-periodicity, which poses great challenges to prediction and diagnosis. Accurately predicting the vibration state of electromechanical systems at future moments can not only provide early warning of potential faults and avoid economic losses caused by unplanned downtime, but also guide the optimization of maintenance strategies and improve the overall reliability and operation efficiency of the system. Therefore, it is particularly important to develop a prediction method that can effectively handle non-stationary vibration time series and has high adaptability and prediction accuracy. Summary of the invention
[0005] To solve the above technical problems, the present invention provides a dual incremental learning method for non-stationary time series prediction based on adaptive integration, which is used for non-stationary time series prediction and provides a general online prediction framework consisting of two modules: the first module detects changes based on statistical hypothesis testing and adaptive sliding window technology, and the second module updates the prediction model based on dual incremental learning and adaptive integrated learning.
[0006] In order to solve the above technical problems, the present invention adopts the following technical solutions:
[0007] A double-incremental learning method for non-stationary time series prediction based on adaptive integration predicts the non-stationary vibration time series composed of vibration state data of an electromechanical system through an updateable prediction model to obtain the vibration state data of the electromechanical system at a future moment; the update process of the prediction model specifically includes the following steps:
[0008] S1. Data preprocessing: acquiring vibration state data of the electromechanical system, composing the vibration state data into a vibration time series, and performing preliminary processing on the vibration time series;
[0009] S2, change detection: using statistical hypothesis testing and adaptive sliding window technology to detect the degree of change in the vibration time series;
[0010] S3, model update: use random vector function links to build an online deep representation learning model as the basic model, and according to the degree of change of the vibration time series, use a single incremental update or double incremental learning mechanism to update the basic model, or create a new basic model and update the weights of the hidden layer of the basic model;
[0011] S4, change detection: The updated basic models are weighted integrated to form the final prediction model.
[0012] Furthermore, step one specifically includes:
[0013] Normalization processing: normalize the acquired vibration time series and scale the vibration time series to a uniform scale;
[0014] Missing value processing: interpolation method is used to fill the missing data in the vibration time series;
[0015] Noise Removal: Use a smoothing filter to remove high-frequency noise from the vibration time series.
[0016] Furthermore, step S2 specifically includes the following steps:
[0017] S21: using a t-test method or a chi-square test method to determine whether the distribution of the vibration time series has changed, if so, triggering a model update according to the degree of change of the vibration time series, and proceeding to step S3;
[0018] The determination of whether the distribution of the vibration time series has changed specifically includes: calculating the mean and variance of the data in each sliding window of the vibration time series, performing hypothesis testing, and calculating the mean μ of the global sliding window. G and the mean μ of the current sliding window C The difference between them is recorded as error distribution, and the threshold of error distribution is calculated by the following formula:
[0019] μ d =μ G -μ C ;
[0020] ∈=t 1-α *σ d ;
[0021] Among them, μ d Represents the mean μ of the global sliding window G and the mean μ of the current sliding window C The difference between them is the error distribution; ∈ represents the degree of change in the data error distribution between the global sliding window and the current sliding window, σ d is the standard deviation of the two error distributions, α is the significance level, and t 1-α represents the t distribution with significance level 1-α;
[0022] When μ d <∈, the variation of the vibration time series reaches a stable level; when μ d >∈, the change degree of the vibration time series reaches the warning level, when μ d >σ d +∈, the degree of change of the vibration time series reaches the change level;
[0023] S22: Dynamically adjust the size of the sliding window according to the real-time error distribution.
[0024] Furthermore, step S22 specifically includes the following steps:
[0025] S221: Setting the size of the initial sliding window;
[0026] S222: Calculate the prediction error in the current sliding window;
[0027] S223: dynamically adjust the size of the sliding window according to the change of the prediction error; when the prediction error increases, increase the size of the sliding window; when the prediction error decreases, reduce the size of the sliding window; the error distribution of the global sliding window and the current sliding window is X G and X C :
[0028]
[0029] Among them, σ G and σ C are the standard deviations of the global sliding window and the current sliding window respectively.
[0030] Furthermore, step S3 specifically includes the following steps:
[0031] S31: Random projection and feature extraction are linked in the deep representation learning model through random vector functions. First, the input vibration time series is mapped to a high dimension through the random projection technology. Specifically, the vibration time series X is projected into a high-dimensional space through the randomly generated weight matrix W1:
[0032] H = W1X + b;
[0033] Among them, W1 is a randomly generated weight matrix, b is a bias term; the projected data H is transformed by a nonlinear activation function to obtain the output of the hidden layer, thereby extracting the high-level features of the input vibration time series;
[0034] S32: The deep representation learning model linked by random vector functions extracts high-level features of the input vibration time series layer by layer by stacking multiple random projection layers. The data H of each layer i It is transformed through a nonlinear activation function and then passed to the next layer for further processing:
[0035] H i+1 =σ(H i *W i+1 +b i+1 );
[0036] Among them, σ represents the nonlinear activation function, W i+1 and b i+1 are the weights and biases of the i+1th layer;
[0037] S33: When the degree of change of the vibration time series is at a stable level, a single incremental update is performed, and only the parameters of the basic model are updated: the parameters of the basic model are incrementally updated according to the new data in the vibration time series;
[0038] S34: when the degree of change of the vibration time series reaches a warning level, performing a double incremental update, increasing the complexity of the basic model, and calculating the weight of the basic model;
[0039] S35: When the degree of change of the vibration time series reaches the change level, discard the data outside the current sliding window in the vibration time series, and use the data in the current sliding window to create a new basic model.
[0040] Further, step S34 specifically includes the following steps:
[0041] S341: Add new hidden layers or nodes to the basic model structure;
[0042] S342: Re-estimate the basic model parameters. During the basic model update process, use the recursive formula to update the weights of the hidden layer of the basic model. The initial weight β of the hidden layer of the basic model (0) for:
[0043]
[0044] As new data blocks arrive, the update formula for the weights of the hidden layer of the basic model is:
[0045]
[0046] Among them, β (k) and Y k is the output weight and target output matrix of the kth data block, K0 is the covariance matrix calculated by the randomly initialized initial hidden layer weight matrix H0 and the target output matrix Y0, which is used to calculate the initial weight, K k is the covariance matrix of the kth data block, P k is the inverse matrix of the covariance matrix of the kth data block, H k is the hidden layer weight matrix of the kth data block.
[0047] Furthermore, step S4 specifically includes the following steps:
[0048] Regularly evaluate the prediction performance of each basic model, and dynamically adjust the weight of each basic model according to the performance evaluation results; each basic model and the corresponding weight constitute the prediction model, and the prediction results of each basic model are combined through weighted average or voting mechanism to obtain the prediction result output by the prediction model.
[0049] Compared with the prior art, the beneficial technical effects of the present invention are:
[0050] Universality: This paper provides a new integrated framework for non-stationary time series prediction, which is applicable to various non-stationary time series prediction tasks. The framework does not depend on specific prediction tasks or influencing factors in the time series, so it has a wide range of application potential.
[0051] Change detection mechanism: This paper proposes a new detection mechanism based on adaptive sliding windows and statistical hypothesis testing, which can more effectively monitor changes in time series. This mechanism overcomes the shortcomings of existing detection methods, especially those designed for classification tasks.
[0052] Basic model design: This paper follows the concept of layer-by-layer generalization and proposes a basic model with deep representation learning capabilities, which is updated according to different detection results. The deep representation learning model linked by random vector functions extracts high-level features from raw data through random projection and kernel methods, enhancing the model's expressiveness and adaptability.
[0053] Dual incremental learning mechanism: This paper proposes a dual incremental learning mechanism to improve the prediction performance and response speed of the model through different update rules. This mechanism triggers different update rules according to the degree of change detected, so that the model can better cope with the changes of non-stationary time series while relatively saving storage space. BRIEF DESCRIPTION OF THE DRAWINGS
[0054] Figure 1 A schematic diagram of a framework of a dual incremental learning method provided according to an embodiment of the present invention;
[0055] Figure 2 A schematic diagram of a deep representation learning model linked by random vector functions provided according to an embodiment of the present invention;
[0056] Figure 3 The prediction results and prediction errors of different algorithms on the DJI dataset. DETAILED DESCRIPTION
[0057] A preferred embodiment of the present invention is described in detail below with reference to the accompanying drawings.
[0058] A dual incremental learning method for non-stationary time series prediction based on adaptive ensemble (AE-DIL) includes the following steps:
[0059] S1. Data preprocessing: Obtain the vibration time series and perform preliminary processing on the vibration time series to eliminate noise and outliers in the data.
[0060] Furthermore, step S1 specifically includes:
[0061] S11: Obtain vibration state data of the electromechanical system from the actual project, and compose the vibration state data into a vibration time series;
[0062] S12: Normalize the vibration time series and scale the vibration time series to a uniform scale to eliminate the impact of dimensional differences on model training; this can be achieved through Min-Max scaling or Z-score normalization methods.
[0063] S13: Missing value processing, using interpolation or other methods to fill in the missing data in the vibration time series to ensure the continuity of the data; for example, linear interpolation, spline interpolation or interpolation methods based on neighboring data points can be used.
[0064] S14: Noise elimination, using smoothing filters or other methods to remove high-frequency noise in the vibration time series. Commonly used methods include moving average filtering, exponential smoothing filtering, and wavelet transform.
[0065] S2. Change detection: Detect the degree of change in the vibration time series using statistical hypothesis testing and adaptive sliding window technology.
[0066] Furthermore, step S2 specifically includes the following steps:
[0067] S21: Determine whether the distribution of the vibration time series has changed significantly by methods such as t-test and chi-square test. If the distribution of the vibration time series changes, the model update mechanism is triggered. For example, a two-sample t-test can be used to compare the mean difference in the new and old data windows. The specific method includes: calculating the mean and variance of the data in each time window, and performing a hypothesis test. In the change detection process, the present invention compares the mean difference in the new and old data windows by the following hypothesis test formula. Calculate the mean μ of the global sliding window G and the mean μ of the current sliding window C The difference between them, where the threshold of the error distribution can be calculated by the following formula:
[0068] μ d =μ G -μ C
[0069] ∈=t 1-α *σ d
[0070] According to the above formula, when μ d >∈ triggers the warning level, when μ d >σ d +∈ triggers a level change.
[0071] Among them, σ dis the standard deviation of the two error distributions, and α is the significance level. Through this statistical test, the present invention can determine whether the change in data reaches the level that requires updating the model.
[0072] S22: Dynamically adjust the size of the sliding window according to the real-time error to flexibly capture the changing trend of the data. When the error rate increases significantly, adjust the size of the sliding window and update the prediction model.
[0073] The size of the sliding window can be adjusted according to the change of the error distribution to ensure that the model can respond to the changes in time. In the process of updating the model, the present invention sets a triple update rule based on the error level:
[0074] Stationary level: When a low error level is detected, the data is considered relatively stable and only regular parameter updates are required.
[0075] Warning level: When the error level exceeds a certain threshold, it is considered that the data has changed to a certain extent, triggering the double incremental learning mechanism and increasing the model complexity.
[0076] Change level: When the error level increases significantly, it is considered that the data has changed significantly, outdated data is discarded, and the basic model is retrained.
[0077] Step S22 specifically includes the following steps:
[0078] S221: Setting the size of the initial sliding window;
[0079] S222: Calculate the prediction error in the current sliding window;
[0080] S223: Dynamically adjust the size of the sliding window according to the error change. For example, when the error increases, increase the window size; when the error decreases, reduce the window size to ensure that the model can respond to data changes in a timely manner. Assuming that the error distributions of the global sliding window and the current window are and respectively, they can be described by the following formula:
[0081]
[0082] Among them, μ G and μ C are the means of the global sliding window and the current sliding window, σ G and σ C are the standard deviations of the global sliding window and the current window, respectively. Based on these distributions, the size of the sliding window is dynamically adjusted to cope with data changes.
[0083] S3. Model update: Use random vector function links to build an online deep representation learning model as the basic model. According to the degree of change of the vibration time series, use a single incremental update or double incremental learning mechanism to update the basic model, or create a new basic model and calculate the weight of the basic model.
[0084] Step S3 specifically includes the following steps:
[0085] S31: Random Projection and Feature Extraction In the deep representation learning model linked by random vector functions, the input vibration time series is first mapped to a high dimension through the random projection technique. Specifically, the input vibration time series X is projected into a high dimensional space through the randomly generated weight matrix W1:
[0086] H = W1X + b;
[0087] Among them, W1 is a randomly generated weight matrix and b is a bias term. The projected data H is transformed by a nonlinear activation function (such as sigmoid or ReLU) to obtain the output of the hidden layer, thereby extracting high-level features of the input vibration time series.
[0088] S32: The deep representation learning model linked by random vector functions extracts high-level features of the input vibration time series layer by layer by stacking multiple random projection layers. The projected data H of each layer i It is transformed through a nonlinear activation function and then passed to the next layer for further processing:
[0089] H i+1 =σ(H i *W i+1 +b i+1 );
[0090] Among them, σ represents the nonlinear activation function, W i+1 and b i+1 are the weights and biases of the i+1th layer.
[0091] S33: Based on the degree of change detected, different update rules are used to incrementally update the model. When the data reaches a stable level, a single incremental update mechanism is used, and the sliding window needs to be updated using the following formula:
[0092] The update formula of the global sliding window size is:
[0093] W G =W G +W C ;
[0094] The update formula for the mean and standard deviation of the error distribution is:
[0095]
[0096] Among them, W G and W C is the global sliding window and the current sliding window, N G and N c They are the number of samples of data in the global sliding window and the number of samples of data in the current sliding window respectively.
[0097] When the data changes to a warning level, a dual incremental learning mechanism is used to increase the complexity of the model, such as increasing the width of the hidden layer; when the data changes significantly, outdated data is discarded and a new basic model is created using the data in the latest window.
[0098] S34: The final output layer linearly combines the data after multiple layers of nonlinear transformation and outputs the predicted value:
[0099]
[0100] Among them, H L is the output of the last layer, X is the input vibration time series, W out is the weight matrix of the output layer, W driect is the weight matrix that connects the input layer directly to the output layer. This combination ensures that the model can simultaneously utilize both linear and nonlinear features of the input vibration time series for prediction.
[0101] S4, change detection: weighted integration of the updated basic models to form the final prediction model. Specifically, it includes the following steps:
[0102] S41: According to the historical performance of the model, different weights are assigned to integrate the prediction results of each basic model. Specific methods include weighted average, voting mechanism, etc.
[0103] The formula for weighted integration is:
[0104]
[0105] in, is the predicted value of the ith base model, w i is the weight of the ith base model, and K is the number of base models.
[0106] S42: Dynamically adjust the model’s weighting strategy based on changes in the vibration time series to improve the overall prediction performance.
[0107] Step S42 specifically includes:
[0108] S421: Regularly evaluate the prediction performance of each base model and record its historical performance. Evaluate the prediction ability of the model by calculating the root mean square error and mean absolute error of the model on the validation set;
[0109] S422: Dynamically adjust the weight of each basic model based on the performance evaluation results. The weight of the basic model with excellent performance is increased, and the weight of the model with poor performance is reduced. The adjustment formula of the weight of the basic model is:
[0110]
[0111] Among them, RMSE i is the root mean square error of the ith base model on the validation set.
[0112] S43: The prediction results of each weighted basic model are integrated to generate a final prediction value. The integrated prediction value can be expressed as:
[0113]
[0114] At the same time, the error between the predicted value and the actual value is monitored, and continuous optimization and adjustment are performed to ensure the prediction accuracy and stability of the model when facing non-stationary time series.
[0115] On the other hand, the present invention further discloses a computer-readable storage medium storing a computer program, wherein when the computer program is executed by a processor, the processor executes the steps of the above method.
[0116] Experimental results:
[0117] The AE-DIL method of the present invention outperforms other baseline models and the current most advanced models on seven benchmark time series datasets. Compared with several baselines and the most advanced models, it shows significant advantages in both prediction accuracy and response speed. The experimental results show that when dealing with non-stationary time series prediction tasks, it can significantly improve the prediction performance and has good generalization ability and adaptability. Specifically, the root mean square error and mean absolute error of the AE-DIL method on each dataset show significant prediction performance improvement. The experimental results show that the RMSE and MAE values of the AE-DIL method are significantly reduced when dealing with non-stationary data, proving its effectiveness. In particular, on the EUR / USD, USD / UKP, DJI and Sunspot datasets, the prediction accuracy of the AE-DIL method is particularly improved, reducing the RMSE values by 41.3%, 66.5%, 62.2% and 69.5%, respectively.
[0118] In addition, the AE-DIL method also performs well in prediction trend and error analysis. Figure 3It shows that when tested with the DJI dataset, the predicted value of the AE-DIL method is almost close to the true value, with the smallest error and the most stable. Compared with other algorithms, the performance of the AE-DIL method in non-stationary time series prediction is significantly better than other models, with good prediction accuracy and stability, and can better cope with dynamic changes in data.
[0119] The method proposed in this paper provides an efficient solution for non-stationary time series prediction by combining the change detection mechanism of adaptive sliding window and statistical hypothesis testing, as well as the model update mechanism of double incremental learning. In practical applications, the AE-DIL method shows good prediction performance and adaptability, and can significantly improve the prediction accuracy of non-stationary time series.
[0120] It is obvious to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the present invention can be implemented in other specific forms without departing from the spirit or essential features of the present invention. Therefore, from any point of view, the embodiments should be regarded as exemplary and non-limiting, and the scope of the present invention is defined by the appended claims rather than the above description, and it is intended that all changes falling within the meaning and scope of the equivalent elements of the claims are included in the present invention, and any reference numerals in the claims should not be regarded as limiting the claims involved.
[0121] In addition, it should be understood that although the present specification is described in terms of implementation modes, not every implementation mode includes only one independent technical solution. This narrative method of the specification is only for the sake of clarity. Those skilled in the art should regard the specification as a whole. The technical solutions in each embodiment may also be appropriately combined to form other implementation modes that can be understood by those skilled in the art.
Claims
1. A dual incremental learning method for non-stationary time series prediction based on adaptive ensemble, characterized in that: The non-stationary vibration time series composed of the vibration state data of the electromechanical system is predicted by an updateable prediction model to obtain the vibration state data of the electromechanical system at a future moment; the updating process of the prediction model specifically includes the following steps: S1. Data preprocessing: acquiring vibration state data of the electromechanical system, composing the vibration state data into a vibration time series, and performing preliminary processing on the vibration time series; S2, change detection: using statistical hypothesis testing and adaptive sliding window technology to detect the degree of change in the vibration time series; S3, model update: Use random vector function links to build an online deep representation learning model as the basic model, and according to the degree of change of the vibration time series, use a single incremental update or double incremental learning mechanism to update the basic model, or create a new basic model and update the weights of the hidden layer of the basic model; S4, change detection: The updated basic models are weighted integrated to form the final prediction model.
2. The dual incremental learning method for non-stationary time series prediction based on adaptive integration according to claim 1 is characterized in that: Step 1 specifically includes: Normalization processing: normalize the acquired vibration time series and scale the vibration time series to a uniform scale; Missing value processing: interpolation method is used to fill the missing data in the vibration time series; Noise Removal: Use a smoothing filter to remove high-frequency noise from the vibration time series.
3. The dual incremental learning method for non-stationary time series prediction based on adaptive integration according to claim 1 is characterized in that: Step S2 specifically includes the following steps: S21: using a t-test method or a chi-square test method to determine whether the distribution of the vibration time series has changed, if so, triggering a model update according to the degree of change of the vibration time series, and proceeding to step S3; The determination of whether the distribution of the vibration time series has changed specifically includes: calculating the mean and variance of the data in each sliding window of the vibration time series, performing hypothesis testing, and calculating the mean μ of the global sliding window. G and the mean μ of the current sliding window C The difference between them is recorded as error distribution, and the threshold of error distribution is calculated by the following formula: m d =μ G -m C ; ∈=t 1-α *s d ; Among them, μ d Represents the mean μ of the global sliding window G and the mean μ of the current sliding window C The difference between them is the error distribution; ∈ represents the degree of change in the data error distribution between the global sliding window and the current sliding window, σ d is the standard deviation of the two error distributions, α is the significance level, and t 1-α represents the t distribution with significance level 1-α; When μ d <∈, the variation of the vibration time series reaches a stable level; when μ d >∈, the change degree of the vibration time series reaches the warning level, when μ d >σ d +∈, the degree of change of the vibration time series reaches the change level; S22: Dynamically adjust the size of the sliding window according to the real-time error distribution.
4. The dual incremental learning method for non-stationary time series prediction based on adaptive integration according to claim 3 is characterized in that: Step S22 specifically includes the following steps: S221: Setting the size of the initial sliding window; S222: Calculate the prediction error in the current sliding window; S223: dynamically adjust the size of the sliding window according to the change of the prediction error; when the prediction error increases, increase the size of the sliding window; when the prediction error decreases, reduce the size of the sliding window; the error distribution of the global sliding window and the current sliding window is X G and X C : Among them, σ G and σ C are the standard deviations of the global sliding window and the current sliding window respectively.
5. The dual incremental learning method for non-stationary time series prediction based on adaptive integration according to claim 3 is characterized in that: Step S3 specifically includes the following steps: S31: Random projection and feature extraction are linked in the deep representation learning model through random vector functions. First, the input vibration time series is mapped to a high dimension through the random projection technology. Specifically, the vibration time series X is projected into a high-dimensional space through the randomly generated weight matrix W1: H = W1X + b; Among them, W1 is a randomly generated weight matrix, b is a bias term; the projected data H is transformed by a nonlinear activation function to obtain the output of the hidden layer, thereby extracting the high-level features of the input vibration time series; S32: The deep representation learning model linked by random vector functions extracts high-level features of the input vibration time series layer by layer by stacking multiple random projection layers. The data H of each layer i It is transformed through a nonlinear activation function and then passed to the next layer for further processing: H i+1 =σ(H i *W i+1 +b i+1 ); Among them, σ represents the nonlinear activation function, W i+1 and b i+1 are the weights and biases of the i+1th layer; S33: When the degree of change of the vibration time series is at a stable level, a single incremental update is performed, and only the parameters of the basic model are updated: the parameters of the basic model are incrementally updated according to the new data in the vibration time series; S34: when the degree of change of the vibration time series reaches a warning level, performing a double incremental update, increasing the complexity of the basic model, and calculating the weight of the basic model; S35: When the degree of change of the vibration time series reaches the change level, discard the data outside the current sliding window in the vibration time series, and use the data in the current sliding window to create a new basic model.
6. The dual incremental learning method for non-stationary time series prediction based on adaptive integration according to claim 5 is characterized in that: Step S34 specifically includes the following steps: S341: Add new hidden layers or nodes to the basic model structure; S342: Re-estimate the basic model parameters. During the basic model update process, use the recursive formula to update the weights of the hidden layer of the basic model. The initial weight β of the hidden layer of the basic model (0) for: As new data blocks arrive, the update formula for the weights of the hidden layer of the basic model is: Among them, β (k) and Y k is the output weight and target output matrix of the kth data block, K k is the covariance matrix calculated from the randomly initialized initial hidden layer weight matrix H0 and the target output matrix Y0, which is used to calculate the initial weights. K k is the covariance matrix of the kth data block, P k is the inverse matrix of the covariance matrix of the kth data block, H k is the hidden layer weight matrix of the kth data block.
7. The dual incremental learning method for non-stationary time series prediction based on adaptive integration according to claim 1 is characterized in that: Step S4 specifically includes the following steps: Regularly evaluate the prediction performance of each basic model, and dynamically adjust the weight of each basic model according to the performance evaluation results; each basic model and the corresponding weight constitute the prediction model, and the prediction results of each basic model are combined through weighted average or voting mechanism to obtain the prediction result output by the prediction model.