Time sequence prediction method based on cumulative causal effect and application

Abstract

The invention discloses a time sequence prediction method based on cumulative causality and application, and belongs to the technical field of time sequence prediction.The method comprises the steps that firstly, a structural causality model is established for a power system containing observable reason variables, unobservable time-varying reason variables and to-be-predicted target variables; constructing an initial value and a time variation value of an encoder network characterization unobservable reason variable; and establishing a dynamic convolutional neural network prediction model by using the cumulative causal effect of a time-varying reason variable and a time-varying mechanism of convolutional expression, and outputting a result through a mask layer and accumulation. The prediction method based on the accumulative causal effect and the application are suitable for time sequence prediction problems such as metal component aging deformation prediction and the like, and have good potentials of stripping false correlation and improving time sequence prediction precision and stability.

Description

Technical Field

[0001] The present invention relates to the technical field of time series prediction, and in particular to a time series prediction method and application based on cumulative causal effects. Background Art

[0002] In the field of time series forecasting problems, the predicted target variable is usually caused by multiple causal variables, and some of the causal variables cannot be observed. Time series models that only rely on statistical correlations between data are prone to learning false correlations between variables, affecting the accuracy and stability of the forecasting model.

[0003] Causal relationships reflect the inherently stable relationships between variables. Introducing causal methods into time series forecasting models can avoid creating spurious correlations and ensure model accuracy and stability. Existing causal-based time series forecasting models primarily focus on the impact of the causal variable at the current time step, often assuming that this causal mechanism is fixed and unchanging. However, in some problem scenarios, the forecast target is affected not only by the causal variable at the current time step but also by the cumulative causal effects of causal variables from past time steps. These causal variables and their causal mechanisms are time-varying, resulting in a time series forecasting problem under the cumulative causal effects of time-varying causal variables.

[0004] For example, when predicting the aging deformation of metal components, the final deformation is caused by the accumulation of residual stresses during the aging stage. Under the action of stress relaxation, the residual stress within the component gradually decreases. Simultaneously, the material creep rate, reflecting the causal mechanism of residual stress, continues to change. Existing causal time series prediction methods cannot accurately model these issues, limiting the accuracy of aging deformation prediction.

[0005] This method breaks the limitation of the original model that fails to fully model the cumulative causal effects of time-varying causal variables, and provides a solution to the above key challenges from a methodological level. Summary of the Invention

[0006] The purpose of the present invention is to provide a time series prediction method and application based on cumulative causality, so as to solve the problems of low prediction accuracy and poor stability caused by the time series prediction model in the prior art due to its reliance on statistical correlation, which easily produces false correlations and fails to fully model cumulative causality and time variability.

[0007] To achieve the above objectives, the present invention provides a time series prediction method based on cumulative causal effects. For dynamic systems involving cumulative causal effects, there are observable cause variables. , unobservable time-varying causal variables , target variable to be predicted , where the time-varying cause variable is the variable that changes over time and directly affects the target variable, and the cumulative causal effect is the cause variable in the time period to Internal target variable The prediction method is as follows: S1. Establish a structural causal model of the dynamic system: (1); in, is generated function; S2. Constructing initial values ​​for variables that represent unobservable causes Encoder network model , establish training constraints based on structural causal models, and use observable cause variables , initial value of target variable , initial value of time step For input, output : (2); S3. Construct variables to characterize time-varying causes Encoder network model , with observable causal variables , time step , characterized by For input, output : (3); S4. Using convolution to express time-varying cause variables and time-varying mechanisms The cumulative causal effect of the dynamic convolutional neural network model is established, and the observable cause variables are input. , the time-varying cause variables obtained by characterization With time step , output the target variable to be predicted : (4); in, Represents the convolution operation; Represents a compressed map.

[0008] Preferably, the training constraints established based on the structural causal model in step S2 include: First, for the encoder network model , represented by the observed variables of the same sample at different time steps Consistent: (5); in, 、 Represents time-step-based 、 The observed variables under No. dimensional component, represents the similarity measurement operation, N Represents the initial value of the unobservable causal variable The number of dimensions; Second, based on the principle of independent mechanisms in causal learning, the representation The dimensions of are independent: (6); in, Represents time-step-based The observed variables under No. Dimensional component; Third, representation and Independent of each other, achieved by minimizing mutual information: (7); in, is the mutual information measure of two variables.

[0009] Preferably, in the process of constructing the loss function in step S2, formula (5) and formula (6) are combined to express the target matrix Approximating the identity matrix , and combined with formula (7), construct The loss function :

[0010] (8); in, is the adjustment factor.

[0011] Preferably, the cumulative causal effect of the causal variable is defined as the time-varying causal variable and time-varying mechanisms The convolution of the target variable is obtained by discretization calculation. : (9); in, is the cumulative causal effect duration, Indicates time.

[0012] Preferably, the prediction model based on the dynamic convolutional neural network includes several convolutional layers, which express the time-varying mechanism through the dynamic convolution kernel. , based on formula (9), input observable cause variables , time-varying causal variables , output the predicted value for each time step , use the mask layer to filter the predicted value of the specified time step, and then output the final predicted value by accumulation : (10).

[0013] Preferably, the loss function of the prediction model uses the predicted value and the true value Build: (11).

[0014] The present invention also proposes an application of a time series prediction method based on cumulative causal effects in the problem of predicting the aging deformation of metal components, including first representing unobservable residual stress through causal representation learning, secondly using convolution to express the cumulative causal effects of residual stress, geometric causal variables and time-varying creep rate, and finally establishing a prediction model for time series prediction to obtain the prediction results of the target variable.

[0015] Therefore, the present invention adopts the above-mentioned time series prediction method based on cumulative causality, which has the following beneficial effects: (1) This invention focuses on the modeling process of the cumulative causal effect of time-varying causal variables and defines the cumulative causal effect of causal variables as the convolution of time-varying causal variables and time-varying mechanisms, breaking through the limitation of existing models that fail to fully model the cumulative causal effect of time-varying causal variables; (2) The present invention conducts causal representation learning on unobservable time-varying cause variables, obtains the time-varying cause variables through representation learning, and uses this as a basis to support time series prediction.

[0016] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 This is a schematic diagram of a time series prediction method based on cumulative causal effects according to the present invention; Figure 2 Schematic diagram of a structural causal model for predicting the time-dependent deformation of aircraft structural parts according to an embodiment of the present invention. DETAILED DESCRIPTION

[0018] The present invention will be further described below with reference to the accompanying drawings and examples of aging deformation, but the present invention is not limited to these examples.

[0019] The time-dependent deformation prediction of metal components is used as an example to illustrate the time-dependent prediction method based on cumulative causal effects. The time-dependent deformation problem of metal components represented by aircraft structural parts is a typical problem in the manufacturing field and has become a key factor affecting dimensional accuracy and stability. Accurate prediction of time-dependent deformation is the key to precise control. The implementation of this method follows the following steps: Figure 1 The principle shown is to first represent the unobservable residual stress through causal representation learning, then use convolution to express the cumulative causal effect of residual stress and creep mechanism, and then establish a prediction model for time series prediction to obtain the target variable.

[0020] The following combination Figure 1 、 Figure 2 The technical solution of the present invention is described in detail based on the actual scenario of aging deformation prediction of metal components. Figure 1 middle 、 represents different time steps of the same sample, It is the aging time, is the adjustment coefficient, is the residual stress, is the residual stress before aging, for The residual stress at the time step, Represents time-step-based Lower representation , Respectively No. dimensional component, is the part geometry, for Time-dependent deformation under time steps, for The predicted time-dependent deformation at the time step, is the predicted aging deformation increment, is a matrix to measure the correlation, is the identity matrix, is the loss function of the causal representation module, is the loss function of the prediction model, For splicing operation, represents a structural causal model, is the mutual information calculation, is the time-varying mechanism represented by the dynamic convolution kernel, is the dot product operation, represents the convolution operation, is the norm, is the two-norm. Figure 2 middle is the residual stress before aging, for The residual stress at the time step, for Time-dependent deformation under time steps, This embodiment uses the aging deformation prediction of aircraft structural parts as a specific application. Through causal representation learning and dynamic convolutional neural network modeling, it achieves accurate prediction of the deformation of metal components during the aging process.

[0021] The specific implementation steps are as follows: Step 1: Establish a structural causal model. Figure 2 As shown, based on the mechanism of aging deformation of metal components, the causal relationship between variables is clarified: aging deformation By part geometry , current residual stress and timeliness Co-determination, structural causal model: (12); in, is generated function.

[0022] Step 2: Characterize the initial value of the unobservable causal variable; S21. Build encoder network , establish training constraints based on structural causal models, and use observable cause variables , initial value of target variable , initial value of time step For input, output : (13); S22, training constraints and loss functions, to ensure The rationality of the representation is set by three constraints: First, the residual stress before aging characterized at different time steps Should be as consistent as possible, Represents time-step-based The observed variables under representational No. dimensional component, Represents the similarity measure operation: (14); Second, in order to ensure that the information of the characterization variables is sufficient, the same part is The initial value of residual stress characterized by The dimensional components of Be as independent as possible: (15); Third, to avoid geometric information Interference model Characterization of the residual stress before aging Should be consistent with part geometry As much independence as possible, the model is constrained by minimizing mutual information: (16); S23. Combine formula (14), formula (15), and formula (16) to construct the residual stress before aging Representation model The loss function : (17); And based on this, we train the model. is the adjustment factor.

[0023] Step 3: Characterize the time-varying causal variables. According to the initial residual stress , part geometry and time Establish time-varying residual stress Representation model : (18); The residual stress characterized at each time step is obtained.

[0024] Step 4: Build a dynamic convolutional neural network prediction model, including the following steps: S41. Convolutional expression of cumulative causal effects, and temporal deformation obtained through discretization calculation ,in is the cumulative causal effect duration, Represents the convolution operation: (19); S42. Based on formula (19), a dynamic convolutional neural network is constructed to represent the residual stress and part geometry As input, we get the time-varying deformation , through mask operation, filter out invalid time steps, and accumulate the deformation generated by past time steps , and then get the final predicted time-dependent deformation : (20); S43. Using predicted values and the true value Constructing the loss function of the prediction model , and use it to train the dynamic convolutional neural network model and jointly optimize the dynamic convolutional neural network The parameters and Representation model Parameters: (twenty one); The trained network model can be deformed according to the initial value of time , part geometry , validity period Predicting time-dependent deformations at subsequent time steps .

[0025] Therefore, the present invention adopts the above-mentioned time series prediction method and application based on cumulative causal effects, breaking through the limitations of the existing technology in modeling the cumulative causal effects of time-varying causal variables, and innovatively uses causal representation learning and dynamic convolutional neural networks. It can remove false correlations and improve prediction accuracy and stability in scenarios such as metal component aging deformation prediction, and has wide applicability.

[0026] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit the same. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solutions of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A time series prediction method based on cumulative causality, characterized in that: For dynamical systems involving cumulative causation, there are observable causal variables , unobservable time-varying causal variables , target variable to be predicted , where the time-varying cause variable is the variable that changes over time and directly affects the target variable, and the cumulative causal effect is the cause variable in the time period to Internal target variable The prediction method is as follows: S1. Establish a structural causal model of the dynamic system: （1）； in, is generated function; S2. Constructing initial values ​​for variables that represent unobservable causes Encoder network model , establish training constraints based on structural causal models, and use observable cause variables , initial value of target variable , initial value of time step For input, output : （2）； S3. Construct variables to characterize time-varying causes Encoder network model , with observable causal variables , time step , characterized by For input, output : （3）； S4. Using convolution to express time-varying cause variables and time-varying mechanisms The cumulative causal effect of the dynamic convolutional neural network model is established, and the observable cause variables are input. , the time-varying cause variables obtained by characterization With time step , output the target variable to be predicted : （4）； in, Represents the convolution operation; Represents a compressed map.

2. The time series prediction method based on cumulative causal effects according to claim 1, characterized in that: The training constraints established based on the structural causal model in step S2 include: First, for the encoder network model , represented by the observed variables of the same sample at different time steps Consistent: （5）； in, 、 Represents time-step-based 、 The observed variables under No. dimensional component, represents the similarity measurement operation, N Represents the initial value of the unobservable causal variable The number of dimensions; Second, based on the principle of independent mechanisms in causal learning, the representation The dimensions of are independent: （6）； in, Represents time-step-based The observed variables under No. Dimensional component; Third, representation and Independent of each other, achieved by minimizing mutual information: （7）； in, is the mutual information measure of two variables.

3. The time series prediction method based on cumulative causal effects according to claim 2, characterized in that: In the process of constructing the loss function in step S2, formula (5) and formula (6) are combined to express the target matrix Approximating the identity matrix , and combined with formula (7), construct The loss function : （8）； in, is the adjustment factor.

4. The time series prediction method based on cumulative causal effects according to claim 1, characterized in that: Define the cumulative causal effect of the causal variable as the time-varying causal variable and time-varying mechanisms The convolution of the target variable is obtained by discretization calculation. : （9）； in, is the cumulative causal effect duration, Indicates time.

5. The time series prediction method based on cumulative causal effects according to claim 1, characterized in that: The prediction model based on the dynamic convolutional neural network contains several convolutional layers, which express the time-varying mechanism through dynamic convolution kernels. , based on formula (9), input observable cause variables , time-varying causal variables , output the predicted value for each time step , use the mask layer to filter the predicted value of the specified time step, and then output the final predicted value by accumulation : （10）。 6. The time series prediction method based on cumulative causal effects according to claim 5, characterized in that: The loss function of the prediction model uses the predicted value and the true value Build: （11）。 7. An application of a time series prediction method based on cumulative causality according to any one of claims 1 to 6 to the problem of predicting the aging deformation of metal components, characterized in that: It includes first representing the unobservable residual stress through causal representation learning, secondly using convolution to express the cumulative causal effect of residual stress, geometric cause variables and time-varying creep rate, and finally establishing a prediction model for time series prediction to obtain the prediction results of the target variable.

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