A time series prediction method based on cumulative causality and application

Abstract

The application discloses a kind of based on cumulative causality's time series prediction method and application, belong to time series prediction technical field, for the dynamic system containing observable reason variable, unobservable time-varying reason variable and to be predicted target variable, this method first establishes structural causality model, constructs encoder network representation unobservable reason variable initial value and time-varying value;Again, the cumulative causality of time-varying reason variable and time-varying mechanism is expressed using convolution, and a dynamic convolutional neural network prediction model is established, and the cumulative output result is passed through mask layer.This application provides a kind of based on cumulative causality's prediction method and application suitable for metal component aging deformation prediction and other time series prediction problems, with good potential to strip false association, improve time series prediction accuracy and stability.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of time series prediction, in particular to a time series prediction method based on cumulative causality and application. BACKGROUND

[0002] In the field of time series prediction problems, the prediction target variable is usually caused by multiple cause variables, and the problem of unobservable cause variables is faced. The time series model established only by relying on the statistical correlation between data is easy to learn the false association between variables, which affects the accuracy and stability of the prediction model.

[0003] The causal relationship reflects the essential stable relationship between variables. Introducing a causal method to build a time series prediction model can avoid establishing false associations and ensure the accuracy and stability of the model. Existing causal time series prediction models mainly focus on the influence of cause variables at the current time step, and often assume that the causality mechanism is fixed and unchanged. However, in some problem scenarios, the prediction target is not only affected by the cause variables at the current time step, but also by the cumulative causality of the past time step cause variables, and these cause variables and their causality mechanisms have time-varying characteristics, which belong to the time series prediction problem under the cumulative causality of time-varying cause variables.

[0004] For example, the aging deformation prediction problem of metal components, the final aging deformation of the part is caused by the cumulative effect of residual stress in the aging stage. Under the action of stress relaxation, the residual stress inside the part gradually decreases; at the same time, the material creep rate continuously changes, which reflects the causality mechanism of residual stress. For the above problems, the existing causal time series prediction method cannot accurately model, which restricts the prediction accuracy of the aging deformation.

[0005] The present method breaks through the limitation of the original model that cannot fully model the cumulative causality of time-varying cause variables, and provides a solution to the above key challenges from the method level. SUMMARY

[0006] The purpose of the present application is to provide a time series prediction method based on cumulative causality and application, to solve the problem of low prediction accuracy and poor stability caused by the time series prediction model relying on statistical correlation and failing to fully model cumulative causality and time-varying characteristics in the prior art.

[0007] To achieve the above purpose, the present application provides a time series prediction method based on cumulative causality, which is used for dynamic systems involving cumulative causality, and there are observable cause variables , unobservable time-varying cause variables , and target variables to be predicted , wherein the time-varying cause variable is a variable that changes with time and directly affects the target variable, the cumulative causality is the causality of the cause variable in the time period To the influence of the target variable , the prediction method is as follows:

[0008] S1, establish a structural causal model of the dynamic system:

[0009] (1);

[0010] wherein, is a generating function;

[0011] S2, construct an encoder network model for representing the initial value of the unobservable cause variable , establish a training constraint based on the structural causal model, and input the observable cause variable , the initial value of the target variable , and the initial value of the time step , and output :

[0012] (2);

[0013] S3, construct an encoder network model for representing the time-varying cause variable , input the observable cause variable , the time step , and the representation obtained , and output :

[0014] (3);

[0015] S4, use convolution to express the cumulative causal action of the time-varying cause variable and the time-varying mechanism , establish a dynamic convolutional neural network model, input the observable cause variable , the representation obtained time-varying cause variable and the time step , and output the target variable to be predicted :

[0016] (4);

[0017] wherein, represents convolution operation; represents compression mapping.

[0018] Preferably, the training constraint established based on the structural causal model in step S2 comprises:

[0019] First, for the encoder network model​​ , which are represented by the observed variables at different time steps of the same sample are consistent:

[0020] (5);

[0021] wherein, , represents the i-th component of based on the observed variables at time step , represents a similarity measure operation, N represents the dimension number of the initial value of the unobserved cause variable ;

[0022] Secondly, based on the independent mechanism principle in causal learning, each dimension of is independent:

[0023] (6);

[0024] wherein, represents the i-th component of based on the observed variables at time step ;

[0025] Thirdly, the is independent of , and is achieved by minimizing the mutual information:

[0026] (7);

[0027] wherein, is the mutual information measure of two variables.

[0028] Preferably, in the construction process of the loss function of step S2, formula (5) and formula (6) are combined to represent the target matrix approximates to the unit matrix , and formula (7) is combined to construct the loss function of :

[0029] (8);

[0030] wherein, is an adjustment coefficient.

[0031] Preferably, the cumulative causal effect of the cause variable is defined as the time-varying cause variable and the time-varying mechanism ​​​​convolution, and then the target variable is calculated by discretization :

[0032] (9);

[0033] wherein, is the cumulative causal action duration, denotes the time.

[0034] Preferably, the prediction model established based on the dynamic convolutional neural network comprises a plurality of convolutional layers, and the time-varying mechanism is expressed by a dynamic convolution kernel , based on formula (9), the input observable cause variable , the time-varying cause variable , the output prediction value of each time step , the mask layer is used to filter the prediction value of the specified time step, and then the final prediction value is output by accumulation :

[0035] (10).

[0036] Preferably, the loss function of the prediction model is constructed by using the prediction value and the true value :

[0037] (11).

[0038] The application also proposes an application of the time series prediction method based on cumulative causal action in the problem of aging deformation prediction of metal components, which comprises the following steps: first, learning the unobservable residual stress by causal representation; second, expressing the cumulative causal action of the residual stress, the geometric cause variable and the time-varying creep rate by convolution; and third, establishing a prediction model for time series prediction to obtain the prediction result of the target variable.

[0039] Therefore, the application adopts the above-mentioned time series prediction method based on cumulative causal action, and has the following beneficial effects:

[0040] (1) The application defines the cumulative causal action of the cause variable as the convolution of the time-varying cause variable and the time-varying mechanism in the modeling process of the cumulative causal action of the time-varying cause variable, which breaks through the limitation of the existing model that cannot fully model the cumulative causal action of the time-varying cause variable.

[0041] (2) The application performs causal representation learning on the unobservable time-varying cause variable, obtains the time-varying cause variable through representation learning, and supports time series prediction based on the time-varying cause variable.

[0042] The technical solutions of the application will be further described in detail below with reference to the drawings and embodiments. BRIEF DESCRIPTION OF DRAWINGS

[0043] Figure 1 This is a schematic diagram of a time series prediction method based on cumulative causal effects according to the present invention.

[0044] Figure 2 This is a schematic diagram of the structural causal model for predicting the time-dependent deformation of aircraft structural components according to an embodiment of the present invention. Detailed Implementation

[0045] The present invention will be further described below with reference to the accompanying drawings and examples of deformation over time. However, the present invention is not limited to these embodiments.

[0046] This paper uses the prediction of aging deformation in metal components as an example to illustrate the time-series prediction method based on cumulative causal effects. The aging deformation problem of metal components, represented by aircraft structural parts, is a typical issue in the manufacturing field and has become a key factor affecting dimensional accuracy and stability. Accurate prediction of aging deformation is crucial for precise control. The implementation of this method follows the following... Figure 1 The principle shown is to first represent unobservable residual stress through causal characterization learning, then use convolution to express the cumulative causal effect of residual stress and creep mechanism, and finally establish a prediction model for time series prediction to obtain the target variable.

[0047] The following combination Figure 1 , Figure 2 The technical solution of the present invention will be described in detail in the context of actual scenarios for predicting the aging deformation of metal components. Figure 1 middle , Representing different time steps of the same sample, It refers to the time limit. To adjust the coefficient, It is residual stress. This refers to the residual stress before aging. for Residual stress at time step Indicates based on time step The following characterization , They represent The dimensional components, It is the geometry of the parts. for Time-lapse deformation under time step for Time-step prediction deformation, To predict the time-dependent deformation increment, A matrix for measuring correlation, It is the identity matrix. The loss function for the causal representation module. The loss function of the prediction model, For splicing operations, Represents a structural causal model. For mutual information calculation, For time-varying mechanisms represented by dynamic convolutional kernels, For dot product operation, This represents the convolution operation. For norm, It is a 2-norm. Figure 2 middle This refers to the residual stress before aging. for Residual stress at time step for Time-lapse deformation under time step This refers to the geometry of the component. This embodiment uses the prediction of deformation over time in aircraft structural components 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.

[0048] The specific implementation steps are as follows:

[0049] Step 1: Establish a structural causal model. For example... Figure 2 As shown, based on the mechanism of age-related deformation of metal components, the causal relationship between variables is clarified: age-related deformation Based on part geometry Current residual stress Time of delivery Jointly determined, structural causal model:

[0050] (12);

[0051] in, It is generated function.

[0052] Step 2: Characterize the initial values ​​of the unobservable causal variables;

[0053] S21. Construct the encoder network Training constraints are established based on structural causal models, with observable causal variables. Initial values ​​of the target variable Initial value of time step Input, Output :

[0054] (13);

[0055] S22. Training constraints and loss function, to ensure The rationality of the representation is constrained by three aspects:

[0056] One, the residual stress before aging represented by different time steps should be as consistent as possible, where represents the observed variables based on time step , and is represented by characterized by the first dimensional component of , and

[0057] (14);

[0058] Second, to ensure that the information of the represented variables is sufficient, the initial value of the residual stress represented by different time steps for the same part should be as independent as possible:

[0059] (15);

[0060] Third, to avoid the interference of geometric information with the representation of , the residual stress before aging represented by the representation should be as independent as possible from the geometry of the part, and the model is constrained by minimizing mutual information:

[0061] (16);

[0062] S23, combine formula (14), formula (15), and formula (16) to build a representation model for the residual stress before aging , and the loss function of the representation model is :

[0063] (17);

[0064] and train the model based on this, where is the adjustment coefficient.

[0065] Step 3: Represent the time-varying cause variables. According to the initial residual stress , the geometry of the part , and the time , build a representation model for the time-varying residual stress :

[0066] (18);

[0067] Get the residual stress represented at each time step. ​​​​​

[0068] Step 4: Establishing a dynamic convolutional neural network prediction model, including the following steps:

[0069] S41, cumulative causal effect convolution expression, time-dependent deformation is obtained by discrete calculation , wherein is the cumulative causal effect time length, represents convolution operation:

[0070] (19);

[0071] S42, based on formula (19), a dynamic convolutional neural network is constructed, and the residual stress characterized by learning is taken as input, and time-dependent aging deformation is obtained , through a mask operation, invalid time steps are filtered, and deformations generated in past time steps are accumulated , and finally the predicted aging deformation is obtained:

[0072] (20);

[0073] S43, the predicted value and the true value are used to construct a loss function of the prediction model , and the dynamic convolutional neural network model is trained based on this, and the parameters of the dynamic convolutional neural network and the parameters of the characterization model are optimized:

[0074] (21);

[0075] The trained network model can predict the subsequent time step aging deformation according to the aging deformation initial value , part geometry and aging time .

[0076] Therefore, the above-mentioned time series prediction method and application based on cumulative causal effect break through the limitations of modeling time-varying cause variables cumulative causal effect in the prior art, and innovatively use causal representation learning and dynamic convolutional neural network, which can strip false correlations, improve prediction accuracy and stability in metal component aging deformation prediction and other scenarios, and has wide applicability.

[0077] ​It should be pointed out finally that the above examples are only used to illustrate the technical solutions of the present application but not to limit it, and although the present application has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that the technical solutions of the present application can still be modified or replaced equivalently, and these modifications or equivalent replacements should not make the modified technical solutions deviate from the spirit and scope of the technical solutions of the present application.

Claims

1. A method for time series prediction based on cumulative causality, applied to the prediction of the aging distortion of a metal component, characterized in that, The approach involves first representing unobservable residual stress through causal characterization learning; second, 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 for the target variable. For dynamical systems involving cumulative causal effects, there are observable causal variables. Unobservable time-varying causal variables Target variable to be predicted In this context, the time-varying causal variable is a variable that changes over time and directly affects the target variable, while the cumulative causal effect refers to the effect of the causal variable over a given time period. to Internal relationship with target variable The impact is predicted using the following method: S1, establish a structural causal model of the power system: （1） wherein is a function that generates the function; S2, constructing an encoder network model for characterizing initial values of unobserved cause variables establishing training constraints based on structural causal models to input initial values of observed cause variables , target variables , time steps , output :​ （2） S3, constructing an encoder network model for characterizing time-varying cause variables with observable cause variables , time steps , characterizing resulting as input, output :​ （3） S4, expressing time-varying cause variables using convolution cumulative causal effects of time-varying mechanisms , a dynamic convolutional neural network model is established, inputting observable cause variables , representing the obtained time-varying cause variables and time steps , outputting target variables to be predicted : （4） wherein denotes a convolution operation; denotes a compression mapping.

2. The method of claim 1, wherein the method is based on cumulative causality. The training constraints established in step S2 based on the structural causal model include: First, for the encoder network model the observation variables at different time steps of the same sample consistent: （5） wherein, , denotes the representation of the first dimensional component of based on the observation variable representation at time step , denotes a similarity measure operation, N denotes the dimensionality of the initial values of the unobserved cause variables ; Secondly, based on the principle of independent mechanism in causal learning, the representation of each dimension is independent （6） wherein, represents the i-th component of the state vector at time step based on the observation variable at time step ; Third, the characterization of With Independently of each other, using minimum mutual information implementation: （7） wherein, is a mutual information measure of two variables.

3. The method of claim 2, wherein the method is based on cumulative causality. In the construction process of the loss function of step S2, formula (5) and formula (6) are combined to represent the target matrix approximating a unit matrix , and formula (7) is combined to construct the loss function of :​ ； （8） wherein is an adjustment factor.

4. The method of claim 1, wherein the method is characterized by, The cumulative causal effect of a cause variable is defined as the time-varying cause variable convolution with the time-varying mechanism and further by discretization to obtain the target variable : （9） wherein, is the accumulated causal effect duration, denotes the time instant.

5. The method of claim 1, wherein the method is characterized by, The prediction model established based on the dynamic convolutional neural network comprises a plurality of convolutional layers, and a time-varying mechanism is expressed through a dynamic convolution kernel , based on formula (9), input observable cause variables , time-varying cause variables , output the prediction value of each time step , the mask layer is used to screen the prediction value of the specified time step, and then the final prediction value is output through the accumulation mode : （10）。 6. The method of claim 5, wherein the method is based on cumulative causality. The loss function of the prediction model utilizes the predicted values versus the true values Construction: （11）。

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