Method for predicting residual life of aero-engine

Abstract

The invention discloses an aero-engine residual life prediction method based on a symmetric regular inferior differential equation, and the method comprises the steps: collecting monitoring parameters of a full life cycle of an aero-engine through a sensor; establishing a first-order Shentu differential equation, carrying out continuous time sequence modeling on the degradation process in a hidden variable space, and calculating a residual signal as a time-varying signal; establishing a Fourier neural operator to approximate a transfer function of a physical system, and mapping the working condition parameters and the hidden variables to sensor response parameters so as to construct a loss function of a neural network; time scale transformation between different degradation processes is considered, a symmetric regular term is constructed, the invariance of the Sheng differential equation on the time scale transformation is restrained, and a hidden variable process with a consistent structure is obtained; and inputting the training sample set and the test sample set into the neural network to obtain hidden variable processes corresponding to the training sample set and the test sample set, and estimating the residual life of the test sample set according to nearest neighbor samples on the training sample set.

Description

Technical Field

[0001] The invention relates to the technical field of aeroengines, and in particular to a method for predicting the remaining life of an aeroengine based on a symmetric regularized Neural Ordinary Differential Equation. Background Art

[0002] Health status monitoring and remaining life prediction of aircraft engines are crucial to maintaining the operational safety of equipment. Understanding latent variable modeling is very important for remaining life prediction because it directly shows how a system degrades over time, and its function is similar to that of health indicators. The latent variable process or health indicator not only shows the current state, but also tracks the degradation trajectory and provides predictive information for potential failures. Hidden variables are usually represented as vectors and contain a wide range of degradation characteristics, while health indicators are usually scalars that provide a global measure for the system as a whole. Both have property requirements such as trend and monotonicity. However, traditional health indicator methods rely on post-processing techniques to normalize scalars to between 0 and 1, ignoring the differences between different degradation processes in the equipment cluster. In contrast, the neural ordinary differential equation regards the differences between different degradation processes as equivalent time scale transformations between degradation trajectories, thereby learning a consistent latent variable structure while retaining the differences. Therefore, from the concept of symmetry in physics, it can be seen that the neural ordinary differential equation is an invariant function of this equivalent time scale transformation, providing a consistent latent variable process for remaining life prediction without the need for additional normalization post-processing.

[0003] The above information disclosed in this Background section is only for enhancement of understanding of the background of the invention and therefore it may contain information that does not form the prior art that is already known to a person of ordinary skill in the art. Summary of the invention

[0004] The present invention provides a method for predicting the remaining life of an aircraft engine based on a neural ordinary differential equation under symmetric regularization. Based on a first-order neural ordinary differential equation and a Fourier neural operator, the degradation process of the system is modeled in a latent variable space, and the time scale transformation between different degradation processes is considered. Based on the invariance condition of the first-order ordinary differential equation, a symmetry regularization term is constructed to constrain the invariance of the neural ordinary differential equation to the time scale transformation, and a latent variable process with a consistent structure is obtained. The latent variable process is then used to predict the remaining life, and the remaining life on a test sample set is estimated according to the nearest neighbor sample.

[0005] A method for predicting the remaining life of an aircraft engine based on a symmetric regularized Neural Ordinary Differential Equation includes: Step a, using sensors to collect monitoring parameters of the entire life cycle of the aircraft engine, the monitoring parameters include the outlet temperature and air pressure of the compressor and turbine, and performing time series segmentation according to the number of flight cycles. By downsampling and zero padding, fixed-length samples are obtained, and training sample sets and test sample sets are constructed respectively, and normalization is performed; Step b, establishing a first-order neural ordinary differential equation, performing continuous time series modeling on the degradation process in the latent variable space, calculating the residual signal as a time-varying signal, and enhancing the representation capability of the neural ordinary differential equation so that its solution depends on both the initial value and the time-varying residual signal; Step c, establishing a Fourier neural operator to approximate the transfer function of the physical system, mapping the operating parameters and latent variables to the sensor response parameters, thereby constructing the loss function of the neural network; Step d, considering the time scale transformation between different degradation processes, based on the invariance conditions of the first-order ordinary differential equation, construct the symmetry regularization term, constrain the invariance of the neural ordinary differential equation to the time scale transformation, and obtain the hidden variable process with consistent structure; In step e, the training sample set and the test sample set are input into the neural network to obtain the latent variable processes corresponding to the training sample set and the test sample set respectively, and the remaining life of the test sample set is estimated according to the nearest neighbor samples on the training sample set.

[0006] In the method for predicting the remaining life of an aircraft engine based on a symmetric regularized ordinary differential equation, in step a, the monitoring parameters of the entire life cycle are divided according to the number of flight cycles. , each cycle is divided into a sample, each sample is a multivariate time series , number of variables The number of variables monitored by the sensor is reduced by downsampling and zero padding to make the time length of each sample The number of time steps is 1353. The mean and variance are calculated on the training sample set, the samples are normalized to [0, 1], and the mean and variance are applied to the test sample set for normalization.

[0007] In the method for predicting the remaining life of an aircraft engine based on a symmetric regularized neural ordinary differential equation, in step b, the first-order neural ordinary differential equation established is in the form of: , in, is a hidden variable used to approximate the true but unknown degradation process, Indicates the number of cycles of the aircraft engine, that is, the health status of each cycle is represented by a Vector representation, is the dimension of the latent variable; is the initial value of the ordinary differential equation, which is set to 0, indicating the initial value state of the degradation process; is the integration variable; It is a neural network that describes the temporal relationship of latent variables; is the residual signal, adding a time-varying residual signal so that its solution depends on both the initial value and the time-varying signal, where the neural network The specific function form is:

[0008] in, It is an encoder network, which consists of three layers of residual connection networks and two layers of nonlinear dimensionality reduction layers, which reduces the high-dimensional signal to low-dimensional features. Finally, the activation function of the output layer is selected as the tanh function; It is a multi-layer nonlinear perceptron, which consists of three linear layers and a nonlinear activation function. The activation function of the middle layer is the ReLU function, and the activation function of the output layer is the tanh function. The tanh function converts and The range of is limited to a bounded interval so that it satisfies the Lipchitz condition; and are the parameters of the neural network.

[0009] In the method for predicting the remaining life of an aircraft engine based on a symmetric regularized neural ordinary differential equation, the residual signal is the residual between the actual signal and the signal under an ideal healthy state: , in, Monitoring parameters under ideal health conditions Monitoring parameters under ideal health conditions Only affected by the operating parameters , an independent Fourier neural operator is constructed to approximate the system transfer function in the ideal healthy state: , in, Indicates the observation sequence number of the health state, and the maximum value is , is the system transfer function in an ideal healthy state, and then Applied to the whole life cycle sequence to obtain monitoring parameters under ideal health status: .

[0010] In the method for predicting the remaining life of an aircraft engine based on a symmetric regularized neural ordinary differential equation, in step c, a Fourier neural operator constructs a mapping of operating condition parameters and latent variables to sensor monitoring parameters: , in, Indicates the working condition parameters, is the number of operating parameters, is a hidden variable, is the reconstructed sensor monitoring parameter, It is a Fourier neural operator based on the actual signal and reconstruct the signal , the loss function of the neural network is , Fourier neural operator It consists of a lifting layer, an iterative Fourier layer, and a projection layer. The lifting layer converts low-dimensional latent variables Mapped to high-dimensional space; the iterative Fourier layer consists of four Fourier forward transforms and inverse transforms. In each iteration, the input variable is first Fourier transformed, then linearly transformed, and finally inverse Fourier transformed; the projection layer finally maps the features to the signal space, that is, reconstructs the signal .

[0011] In the method for predicting the remaining life of an aircraft engine based on a symmetric regularized neural ordinary differential equation, in step d, the time scale transformation between different degradation processes is that different degradation processes are transformed into each other through scale transformation along the time axis, and the invariance condition of the first-order ordinary differential equation is that there is an equivalent set of solutions to the first-order ordinary differential equation, the elements in the equivalent set are generated by the equivalent transformation, all elements of the equivalent set are solutions to the ordinary differential equation, the ordinary differential equation is an invariant function of the equivalent transformation, and the variable Defined as the Neural Ordinary Differential Equation The solution, is the parameter of the neural network, then the invariance condition is: , in, is the time scale transformation; is the invariant function of the final expectation, that is and Both Solution exist Generate equivalent solution sets under transformation, Using Taylor transform, the above invariance condition is derived as: , in, is the time scale transformation The vector field of is the parameter of the time scale transformation, is an infinitesimal generator.

[0012] In the method for predicting the remaining life of an aircraft engine based on a symmetric regularized neural ordinary differential equation, the expression of the infinitesimal generator is: , and The variables are and The vector field, considering its first-order differential term , the invariance condition considers the first-order extension of the infinitesimal generator, denoted as , then the invariance condition is derived as: , in, , , so the invariance condition simplifies to: , in, and The variables are and The vector field of The form is determined.

[0013] In the method for predicting the remaining life of an aircraft engine based on a symmetric regularized neural ordinary differential equation, the hidden variable is the power function that characterizes the degradation process, and is the function coefficient, then the vector field and have to: , in, and is the equivalent solution after time scale transformation, and the vector field and Substituting the invariance conditions, we get the symmetry regularization: , or, is an exponential function, and the corresponding symmetry regularization is:

[0014] It turns out that both can be described by the same expression:

[0015] in, are the function coefficients.

[0016] In the method for predicting the remaining life of an aircraft engine based on a neural network under symmetry regularization, in step e, the training sample set is input into the neural network under symmetry regularization to obtain the hidden variable process corresponding to the training sample set, and the remaining life of the hidden variable process in the test sample set is estimated by using the k-nearest neighbor algorithm in combination with time information to obtain the remaining life sample pair ,in Is the remaining life label.

[0017] In the method for predicting the remaining life of an aircraft engine based on a symmetric regularized neural ordinary differential equation, in step e, the neural network includes two parts: a neural ordinary differential equation and a Fourier neural operator, wherein the neural ordinary differential equation has a hidden variable To model, the Fourier neural operator transforms the latent variables Mapping to signal space, that is, reconstructing the signal ; Then the final optimization target of all parameters is the reconstruction loss and symmetry regularization Since the latent variable process is confined to a continuous bounded function space, the universal approximation theorem of neural networks guarantees convergence.

[0018] Compared with the prior art, the present invention has the following advantages: the present invention constructs a neural ordinary differential equation to model the degradation process in the hidden variable space; based on the invariance condition of the first-order ordinary differential equation, a symmetry regularization is constructed to make the neural network an invariant function of equivalent transformations between different degradation processes, providing a consistent hidden variable process for the remaining life prediction without the need for additional normalization post-processing. The degradation process is modeled in the hidden variable space through the neural ordinary differential equation, and the symmetry regularization is constructed according to the invariance condition to constrain the solution space of the neural ordinary differential equation, and finally the remaining life prediction of the aircraft engine is realized. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] By reading the detailed description of the preferred specific embodiments below, various other advantages and benefits of the present invention will become clear to those of ordinary skill in the art. The drawings in the specification are only for the purpose of illustrating the preferred embodiments and are not considered to be limitations of the present invention. Obviously, the drawings described below are only some embodiments of the present invention. For those of ordinary skill in the art, other drawings can also be obtained based on these drawings without creative work. Moreover, the same reference numerals are used to represent the same components throughout the drawings.

[0020] In the attached picture: Figure 1 It is a flowchart of a method for predicting the remaining life of an aircraft engine based on a symmetric regularized Neural Ordinary Differential Equation provided by an embodiment of the present disclosure; Figure 2 is a schematic diagram of time scale transformation of a degradation process provided by an embodiment of the present disclosure; Figure 3 is a schematic diagram of latent variable process estimation provided by an embodiment of the present disclosure; Figure 4 is a schematic diagram of a comparison of aircraft engine hidden variable processes provided by an embodiment of the present disclosure; Figure 5 is a schematic diagram of the remaining life prediction of an aircraft engine provided by an embodiment of the present disclosure; Figure 6 It is a schematic diagram of a neural network training convergence process provided by an embodiment of the present disclosure.

[0021] The present invention is further explained below in conjunction with the accompanying drawings and embodiments. DETAILED DESCRIPTION

[0022] The following will refer to the attached Figures 1 to 6 Specific embodiments of the present invention are described in more detail. Although specific embodiments of the present invention are shown in the accompanying drawings, it should be understood that the present invention can be implemented in various forms and should not be limited by the embodiments set forth herein. On the contrary, these embodiments are provided to enable a more thorough understanding of the present invention and to fully convey the scope of the present invention to those skilled in the art.

[0023] It should be noted that certain words are used in the specification and claims to refer to specific components. Those skilled in the art should understand that technicians may use different nouns to refer to the same component. This specification and claims do not use the difference in nouns as a way to distinguish components, but use the difference in the functions of the components as the criterion for distinction. As mentioned throughout the specification and claims, "including" or "comprising" is an open term, so it should be interpreted as "including but not limited to". The subsequent description of the specification is a preferred embodiment of the present invention, but the description is based on the general principles of the specification and is not intended to limit the scope of the present invention. The scope of protection of the present invention shall be determined by the attached claims.

[0024] To facilitate understanding of the embodiments of the present invention, further explanation will be given below by taking specific embodiments as examples in conjunction with the accompanying drawings, and each of the accompanying drawings does not constitute a limitation on the embodiments of the present invention.

[0025] like Figures 1 to 5 As shown in FIG. 1 , the remaining life prediction method of an aircraft engine based on a symmetric regularized Neural Ordinary Differential Equation includes the following steps: Step a, using sensors to collect monitoring parameters of the entire life cycle of the aircraft engine, the monitoring parameters include the outlet temperature and air pressure of the compressor and turbine, and performing time series segmentation according to the number of flight cycles. By downsampling and zero padding, fixed-length samples are obtained, and training sample sets and test sample sets are constructed respectively, and normalization is performed; Step b, establishing a first-order neural ordinary differential equation, performing continuous time series modeling on the degradation process in the latent variable space, calculating the residual signal as a time-varying signal, and enhancing the representation capability of the neural ordinary differential equation so that its solution depends on both the initial value and the time-varying residual signal; Step c, establishing a Fourier neural operator to approximate the transfer function of the physical system, mapping the operating parameters and latent variables to the sensor response parameters, thereby constructing the loss function of the neural network; Step d, considering the time scale transformation between different degradation processes, based on the invariance conditions of the first-order ordinary differential equation, construct the symmetry regularization term, constrain the invariance of the neural ordinary differential equation to the time scale transformation, and obtain the hidden variable process with consistent structure; In step e, the training sample set and the test sample set are input into the neural network to obtain the latent variable processes corresponding to the training sample set and the test sample set respectively, and the remaining life of the test sample set is estimated according to the nearest neighbor samples on the training sample set.

[0026] In a preferred embodiment of the method for predicting the remaining life of an aircraft engine based on a symmetric regularized neural ordinary differential equation, in step a, the monitoring parameters of the entire life cycle are divided according to the number of flight cycles. , each cycle is divided into a sample, each sample is a multivariate time series , number of variables The number of variables monitored by the sensor is reduced by downsampling and zero padding to make the time length of each sample The number of time steps is 1353. The mean and variance are calculated on the training sample set, the samples are normalized to [0, 1], and the mean and variance are applied to the test sample set for normalization.

[0027] In a preferred implementation of the method for predicting the remaining life of an aircraft engine based on a symmetric regularized neural ordinary differential equation, in step b, the first-order neural ordinary differential equation established is in the form of: , in, is a hidden variable used to approximate the true but unknown degradation process, Indicates the number of cycles of the aircraft engine, that is, the health status of each cycle is represented by a Vector representation, is the dimension of the latent variable; is the initial value of the ordinary differential equation, which is set to 0, indicating the initial value state of the degradation process; is the integration variable; It is a neural network that describes the temporal relationship of latent variables; is the residual signal, adding a time-varying residual signal so that its solution depends on both the initial value and the time-varying signal, where the neural network The specific function form is:

[0028] in, It is an encoder network, which consists of three layers of residual connection networks and two layers of nonlinear dimensionality reduction layers, which reduces the high-dimensional signal to low-dimensional features. Finally, the activation function of the output layer is selected as the tanh function; It is a multi-layer nonlinear perceptron, which consists of three linear layers and a nonlinear activation function. The activation function of the middle layer is the ReLU function, and the activation function of the output layer is the tanh function. The tanh function converts and The range of is limited to a bounded interval so that it satisfies the Lipchitz condition; and are the parameters of the neural network.

[0029] In a preferred implementation of the method for predicting the remaining life of an aircraft engine based on a symmetric regularized neural ordinary differential equation, the residual signal is the residual between the actual signal and the signal under an ideal healthy state: , in, Monitoring parameters under ideal health conditions Monitoring parameters under ideal health conditions Only affected by the operating parameters , an independent Fourier neural operator is constructed to approximate the system transfer function in the ideal healthy state: , in, Indicates the observation sequence number of the health state, and the maximum value is , is the system transfer function in an ideal healthy state, and then Applied to the whole life cycle sequence to obtain monitoring parameters under ideal health status: .

[0030] In a preferred implementation of the method for predicting the remaining life of an aircraft engine based on a symmetric regularized neural ordinary differential equation, in step c, a Fourier neural operator constructs a mapping of operating condition parameters and latent variables to sensor monitoring parameters: , in, Indicates the working condition parameters, is the number of operating parameters, is a hidden variable, is the reconstructed sensor monitoring parameter, It is a Fourier neural operator based on the actual signal and reconstruct the signal , the loss function of the neural network is , Fourier neural operator It consists of a lifting layer, an iterative Fourier layer, and a projection layer. The lifting layer converts low-dimensional latent variables Mapped to high-dimensional space; the iterative Fourier layer consists of four Fourier forward transforms and inverse transforms. In each iteration, the input variable is first Fourier transformed, then linearly transformed, and finally inverse Fourier transformed; the projection layer finally maps the features to the signal space, that is, reconstructs the signal .

[0031] In a preferred implementation of the method for predicting the remaining life of an aircraft engine based on a symmetric regularized neural ordinary differential equation, in step d, the time scale transformation between different degradation processes is that different degradation processes are transformed into each other through scale transformation along the time axis, and the invariance condition of the first-order ordinary differential equation is that there is an equivalent set of solutions to the first-order ordinary differential equation, the elements in the equivalent set are generated by the equivalent transformation, all elements of the equivalent set are solutions to the ordinary differential equation, the ordinary differential equation is an invariant function of the equivalent transformation, and the variable Defined as the Neural Ordinary Differential Equation The solution, is the parameter of the neural network, then the invariance condition is: , in, is the time scale transformation; is the invariant function of the final expectation, that is and Both Solution exist Generate equivalent solution sets under transformation, Using Taylor transform, the above invariance condition is derived as: , in, is the time scale transformation The vector field of is the parameter of the time scale transformation, is an infinitesimal generator.

[0032] In a preferred embodiment of the method for predicting the remaining life of an aircraft engine based on a symmetric regularized neural ordinary differential equation, the expression of the infinitesimal generator is: , and The variables are and The vector field, considering its first-order differential term , the invariance condition considers the first-order extension of the infinitesimal generator, denoted as , then the invariance condition is derived as: , in, , , so the invariance condition simplifies to: , in, and The variables are and The vector field of The form is determined.

[0033] In the preferred embodiment of the method for predicting the remaining life of an aircraft engine based on a symmetric regularized neural ordinary differential equation, the hidden variable is the power function that characterizes the degradation process, and is the function coefficient, then the vector field and have to: , in, and is the equivalent solution after time scale transformation, and the vector field and Substituting the invariance conditions, we get the symmetry regularization: , or, is an exponential function, and the corresponding symmetry regularization is:

[0034] It turns out that both can be described by the same expression:

[0035] in, are the function coefficients.

[0036] In a preferred embodiment of the method for predicting the remaining life of an aircraft engine based on a neural network under symmetry regularization, in step e, the training sample set is input into the neural network under symmetry regularization to obtain the hidden variable process corresponding to the training sample set, and the remaining life sample pair is obtained by combining the time information. ,in Is the remaining life label.

[0037] In a preferred embodiment of the method for predicting the remaining life of an aircraft engine based on a symmetric regularized neural ordinary differential equation, in step e, the neural network includes two parts: a neural ordinary differential equation and a Fourier neural operator, wherein the neural ordinary differential equation has a hidden variable To model, the Fourier neural operator transforms the latent variables Mapping to signal space, that is, reconstructing the signal ; Then the final optimization target of all parameters is the reconstruction loss and symmetry regularization Since the latent variable process is confined to a continuous bounded function space, the universal approximation theorem of neural networks guarantees convergence.

[0038] In a preferred implementation of the method for predicting the remaining life of an aircraft engine based on a neural network under symmetry regularization, in step e, the test sample set is input into a neural network under symmetry regularization to obtain a hidden variable process corresponding to the test sample set, and the k-nearest neighbor algorithm is used to estimate the remaining life of the hidden variable process in the test sample set.

[0039] Hidden variables are features in a neural network, and are variables called latents. A neural network is a function, and latent variables are the input variables of this function.

[0040] In one embodiment, a flight cycle is a complete operating envelope of an aircraft engine, including take-off, cruise, and landing phases. The monitoring signal sampling frequency is 1 Hz, and a flight cycle lasts approximately 1 hour to 5 hours.

[0041] In one embodiment, after time segmentation according to the flight cycle, the unequal length samples are downsampled at a ratio of 1:15, and the downsampled samples are padded with zeros to equal length samples; 9 are selected from 15 aircraft engines as training sets, and the remaining 6 are selected as test sample sets.

[0042] In one embodiment, the number of variables monitored by the sensor includes gas path parameters and temperature parameters.

[0043] In one embodiment, Figure 1 As shown, a method for predicting the remaining life of an aircraft engine based on a symmetric regularized Neural Ordinary Differential Equation comprises the following steps: In the first step, air pressure, temperature and other sensors are used to collect monitoring data of the aircraft engine's entire life cycle, with a sampling frequency of 1 Hz. The entire life cycle data is time-series segmented according to the flight cycle , each sample is a multivariate time series , number of variables The number of variables monitored by the sensor includes gas path parameters and temperature parameters; the unequal length samples are downsampled at a ratio of 1:15, and the downsampled samples are padded with zeros to equal length samples; 9 out of 15 aircraft engines are selected as training sample sets, and the remaining 6 are used as test sample sets; the mean and variance are calculated on the training sample set, the samples are normalized to [0,1], and the mean and variance are applied to the test sample set for normalization.

[0044] In the second step, a first-order neural ordinary differential equation is established to model the degradation process in a continuous time series in the latent variable space. The first-order neural ordinary differential equation consists of an encoder and a multi-layer nonlinear perceptron. The encoder is ResNet, which reduces the high-dimensional residual signal to a low-dimensional space; the multi-layer nonlinear perceptron is used to describe the evolution trajectory of the latent variable over time. The functional form of the neural network is:

[0045] in, is a hidden variable, is the residual signal, It is an encoder network, which consists of three layers of residual connection networks and two layers of nonlinear dimensionality reduction layers, which reduces the high-dimensional signal to low-dimensional features. Finally, the activation function of the output layer is selected as the tanh function; It is a multi-layer nonlinear perceptron, which consists of three linear layers and a nonlinear activation function. The activation function of the middle layer is the ReLU function, and the activation function of the output layer is the tanh function. and The range of is limited to a bounded interval so that it satisfies the Lipchitz condition; and is the parameter of the neural network. The residual signal provides time-varying information for the first-order neural ordinary differential equation, which is calculated by the difference between the actual signal and the signal under the ideal healthy state. , where; In order to obtain the signal under the ideal healthy state, it is necessary to construct a system transfer function under the ideal healthy state. The transfer function is constructed by the Fourier neural operator independent of step three, and the function form is:

[0046] in, and Especially the monitoring parameters and operating parameters under healthy state, is the system transfer function under ideal health conditions.

[0047] In the third step, a Fourier neural operator is established to approximate the transfer function of the physical system degraded over time. The input of the Fourier neural operator is the time-varying operating parameters and hidden variables, and the output is the system response monitoring parameters. The output of the operator is compared with the actual monitoring parameters, and the loss function of the neural network is obtained as follows: ,in is the actual monitoring parameter, is the output of the neural operator. The Fourier neural operator consists of a lifting layer, an iterative Fourier layer, and a projection layer. The lifting layer converts the low-dimensional latent variables Mapped to high-dimensional space; the iterative Fourier layer consists of four Fourier forward transforms and inverse transforms. In each iteration, the input variable is first Fourier transformed, then linearly transformed, and finally inverse Fourier transformed; the projection layer finally maps the features to the signal space, that is, reconstructs the signal .

[0048] In the fourth step, a symmetry regularization is established, which is derived from the invariance condition of the ordinary differential equation. The invariance condition of the ordinary differential equation is defined as the new solution of the ordinary differential equation obtained under the action of a certain equivalent transformation also satisfies the equation; the variable Defined as the Neural Ordinary Differential Equation The solution, is the parameter of the neural network, then the invariance condition is:

[0049] in, is an equivalent transformation and defines the time scale transformation between different degradation trajectories; is the invariant function of the final expectation, that is and Both The solution, exist Using Taylor transformation, the above invariance condition is derived as follows:

[0050] in, is the time scale transformation The vector field of is the parameter of the time scale transformation, is defined as an infinitesimal generator. Considering its first-order differential term , the invariance condition needs to consider the first-order extension of the infinitesimal generator, which is denoted as , then the invariance condition is derived as:

[0051] in, , . Therefore, the invariance condition simplifies to:

[0052] in, and, Not a variable and The vector field of The form of the vector field is determined by and Determined by the time scale transformation, without loss of generality, assuming that the hidden variable process is a power function, and is the function coefficient, then the vector field and We can get:

[0053] in, and is the equivalent solution after time scale transformation. and Substituting the invariance condition, we get the symmetry regularization:

[0054] Similarly, assuming is an exponential function, and the corresponding symmetry regularization is:

[0055] It is found that both can be described by the same expression, so the symmetry rule is:

[0056] in, are the function coefficients.

[0057] In the fifth step, the training sample set is input into the neural network under symmetry regularization to obtain the hidden variable process corresponding to the training sample set, and the remaining life sample pair is obtained by combining the time information. ,in is the remaining life label; similarly, the test sample set is input into the neural network under symmetry regularization to obtain the hidden variable process corresponding to the test sample set, and finally the k-nearest neighbor algorithm is used to estimate the remaining life of the hidden variable process in the test sample set; the training process of the neural network includes two parts: the neural ordinary differential equation and the Fourier neural operator. Among them, the neural ordinary differential equation is used for the hidden variable To model, the Fourier neural operator transforms the latent variables Mapping to signal space, that is, reconstructing the signal ; Then the final optimization target of all parameters is the reconstruction loss and symmetry regularization Composition, since the latent variable process is restricted to a continuous bounded function space, the universal approximation theorem of the neural network guarantees the convergence. Optionally, this embodiment is iteratively trained for 500 times.

[0058] Figure 2 A schematic diagram of the time scale transformation of the degradation process is shown. The red, blue and green curves in the figure represent three different degradation process trajectories respectively. It can be seen that due to the influence of environmental variables, operating conditions, manufacturing errors, etc., the time for different degradation processes to reach the failure threshold will be different. This difference will lead to generalization problems in the modeling process. The present invention believes that this difference can be explained by the time scale transformation between different trajectories, thereby deriving the invariance conditions and symmetry regularization of the Neural Ordinary Differential Equation.

[0059] Figure 3 The schematic diagram of latent variable process estimation is shown. First, the latent variable is estimated using the Neural Ordinary Differential Equation. Perform time series modeling, residual signal After the encoder, the representation of latent variables is enhanced; then the working condition parameters and hidden variables Input into the Fourier neural operator to estimate the system monitoring parameters .

[0060] Figure 4 3 is a schematic diagram of the comparison of hidden variable processes of aircraft engines according to an embodiment of the present invention. It can be seen that the neural ordinary differential equations under symmetry regularization can obtain hidden variable processes with consistent structures, thereby avoiding post-processing such as normalization required by similar health indicators.

[0061] Figure 5 It is a schematic diagram of the remaining life prediction of an aircraft engine according to an embodiment of the present invention. It can be seen that the evaluation indicators of the prediction results include the root mean square error (RMSE) and the score function, and the test was carried out on two aircraft engine fleets, namely N-CMAPSS-DS03 and N-CMAPSS-DS04. The experimental results were compared with three models, namely deep Gaussian process, Bayesian Transformer and Neural Ordinary Differential Equation, and the results are shown in Table 1.

[0062] Figure 6This is a schematic diagram of the convergence process of neural network training in an embodiment of the present invention. It can be seen that during the training process of the neural network, both the reconstruction loss and the symmetry regularization can converge quickly and with small fluctuations. This fast convergence process benefits from the reasonable design of the neural network ordinary differential equation, that is, the tanh function makes the neural network ordinary differential equation satisfy the Lipchitz condition, thereby constraining the hidden variable process to be a continuous bounded variable process, and then the universal approximation theorem of the neural network guarantees the convergence of the neural network.

[0063] In this embodiment, the symmetry regularization makes the neural ordinary differential equation an invariant function of the time scale transformation of different latent variable processes, so that different latent variable processes have a consistent structure, avoiding post-processing such as normalization required for similar health indicators, and enhancing the interpretability of latent variables and the performance of remaining life prediction. Figure 4 , Figure 5 As can be seen from the results in Table 1, the proposed symmetric regularized neural ordinary differential equation achieves good performance in the evaluation indicators, thus verifying the superiority of the prediction method.

[0064] Restrictive. Under the guidance of this specification and without departing from the scope of protection of the claims of the present invention, a person skilled in the art can make many forms, all of which are protected by the present invention.

Claims

1. A method for predicting the remaining life of an aircraft engine based on a symmetric regularized Neural Ordinary Differential Equation, characterized in that: The steps include: Step a, using sensors to collect monitoring parameters of the entire life cycle of the aircraft engine, the monitoring parameters include the outlet temperature and air pressure of the compressor and turbine, and performing time series segmentation according to the number of flight cycles. By downsampling and zero padding, fixed-length samples are obtained, and training sample sets and test sample sets are constructed respectively, and normalization is performed; Step b, establishing a first-order neural ordinary differential equation, performing continuous time series modeling on the degradation process in the latent variable space, calculating the residual signal as a time-varying signal, and enhancing the representation capability of the neural ordinary differential equation so that its solution depends on both the initial value and the time-varying residual signal; Step c, establishing a Fourier neural operator to approximate the transfer function of the physical system, mapping the operating parameters and latent variables to the sensor response parameters, thereby constructing the loss function of the neural network; Step d, considering the time scale transformation between different degradation processes, based on the invariance conditions of the first-order ordinary differential equation, construct the symmetry regularization term, constrain the invariance of the neural ordinary differential equation to the time scale transformation, and obtain the hidden variable process with consistent structure; In step e, the training sample set and the test sample set are input into the neural network to obtain the latent variable processes corresponding to the training sample set and the test sample set respectively, and the remaining life of the test sample set is estimated according to the nearest neighbor samples on the training sample set.

2. The method for predicting the remaining life of an aircraft engine based on a symmetric regularized Neural Ordinary Differential Equation according to claim 1, characterized in that: Preferably, in step a, the monitoring parameters of the entire life cycle are divided according to the number of flight cycles. , each cycle is divided into a sample, each sample is a multivariate time series , number of variables The number of variables monitored by the sensor is reduced by downsampling and zero padding to make the time length of each sample The number of time steps is 1353. The mean and variance are calculated on the training sample set, the samples are normalized to [0, 1], and the mean and variance are applied to the test sample set for normalization.

3. The method for predicting the remaining life of an aircraft engine based on a symmetric regularized Neural Ordinary Differential Equation according to claim 1, characterized in that: In step b, the first-order neural ordinary differential equation is established in the form of: ， in, is a hidden variable used to approximate the true but unknown degradation process, Indicates the number of cycles of the aircraft engine, that is, the health status of each cycle is represented by a Vector representation, is the dimension of the latent variable; is the initial value of the ordinary differential equation, which is set to 0, indicating the initial value state of the degradation process; is the integration variable; It is a neural network that describes the temporal relationship of latent variables; is the residual signal, adding a time-varying residual signal so that its solution depends on both the initial value and the time-varying signal, where the neural network The specific function form is: ； in, It is an encoder network, which consists of three layers of residual connection networks and two layers of nonlinear dimensionality reduction layers, which reduces the high-dimensional signal to low-dimensional features. Finally, the activation function of the output layer is selected as the tanh function; It is a multi-layer nonlinear perceptron, which consists of three linear layers and a nonlinear activation function. The activation function of the middle layer is the ReLU function, and the activation function of the output layer is the tanh function. The tanh function converts and The range of is limited to a bounded interval so that it satisfies the Lipchitz condition; and are the parameters of the neural network.

4. The method for predicting the remaining life of an aircraft engine based on a symmetric regularized Neural Ordinary Differential Equation according to claim 3 is characterized in that: The residual signal is the residual difference between the actual signal and the signal in the ideal healthy state: ， in, Monitoring parameters under ideal health conditions Monitoring parameters under ideal health conditions Only affected by the operating parameters , an independent Fourier neural operator is constructed to approximate the system transfer function in the ideal healthy state: ， in, Indicates the observation sequence number of the health state, and the maximum value is , is the system transfer function in an ideal healthy state, and then Applied to the whole life cycle sequence to obtain monitoring parameters under ideal health status: 。 5. The method for predicting the remaining life of an aircraft engine based on a symmetric regularized Neural Ordinary Differential Equation according to claim 1, characterized in that: In step c, the Fourier neural operator constructs a mapping from operating condition parameters and latent variables to sensor monitoring parameters: ， in, Indicates the working condition parameters, is the number of operating parameters, is a hidden variable, is the reconstructed sensor monitoring parameter, It is a Fourier neural operator based on the actual signal and reconstruct the signal , the loss function of the neural network is , Fourier neural operator It consists of a lifting layer, an iterative Fourier layer, and a projection layer. The lifting layer converts low-dimensional latent variables Mapped to high-dimensional space; the iterative Fourier layer consists of four Fourier forward transforms and inverse transforms. In each iteration, the input variable is first Fourier transformed, then linearly transformed, and finally inverse Fourier transformed; the projection layer finally maps the features to the signal space, that is, reconstructs the signal .

6. The method for predicting the remaining life of an aircraft engine based on a symmetric regularized Neural Ordinary Differential Equation according to claim 1, characterized in that: In step d, the time scale transformation between different degradation processes is that different degradation processes are transformed into each other through scale transformation along the time axis. The invariance condition of the first-order ordinary differential equation is that the solution of the first-order ordinary differential equation exists an equivalent set, the elements in the equivalent set are generated by the equivalent transformation, all elements of the equivalent set are solutions of the ordinary differential equation, and the ordinary differential equation is an invariant function of the equivalent transformation. Defined as the Neural Ordinary Differential Equation The solution, is the parameter of the neural network, then the invariance condition is: , in, is the time scale transformation; is the invariant function of the final expectation, that is and Both Solution exist Generate equivalent solution sets under transformation, Using Taylor transform, the above invariance condition is derived as: ， in, is the time scale transformation The vector field of is the parameter of the time scale transformation, is an infinitesimal generator.

7. The method for predicting the remaining life of an aircraft engine based on a symmetric regularized Neural Ordinary Differential Equation according to claim 6, characterized in that: The expression of the infinitesimal generator is , and The variables are and The vector field, considering its first-order differential term , the invariance condition considers the first-order extension of the infinitesimal generator, denoted as , then the invariance condition is derived as: ， in, , , so the invariance condition simplifies to: ， in, and The variables are and The vector field of The form is determined.

8. The method for predicting the remaining life of an aircraft engine based on a symmetric regularized Neural Ordinary Differential Equation according to claim 7, characterized in that: Hidden variables is the power function that characterizes the degradation process, and is the function coefficient, then the vector field and have to: ， in, and is the equivalent solution after time scale transformation, and the vector field and Substituting the invariance conditions, we get the symmetry regularization: ， or, is an exponential function, and the corresponding symmetry regularization is: ， It turns out that both can be described by the same expression: ， in, are the function coefficients.

9. The method for predicting the remaining life of an aircraft engine based on a symmetric regularized Neural Ordinary Differential Equation according to claim 1, characterized in that: In step e, the training sample set is input into the neural network under symmetry regularization to obtain the hidden variable process corresponding to the training sample set, and the k-nearest neighbor algorithm is used to estimate the remaining life of the hidden variable process in the test sample set in combination with time information to obtain the remaining life sample pair ,in Is the remaining life label.

10. The method for predicting the remaining life of an aircraft engine based on a symmetric regularized Neural Ordinary Differential Equation according to claim 1, characterized in that: In step e, the neural network includes two parts: the neural ordinary differential equation and the Fourier neural operator. The neural ordinary differential equation is used to calculate the hidden variable To model, the Fourier neural operator transforms the latent variables Mapping to signal space, that is, reconstructing the signal ; Then the final optimization target of all parameters is the reconstruction loss and symmetry regularization Since the latent variable process is confined to a continuous bounded function space, the universal approximation theorem of neural networks guarantees convergence.

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