Methods for predicting the remaining life of aircraft engines

Abstract

A method for predicting the remaining life of an aero-engine based on symmetric regularized neural ordinary differential equations is proposed. This method utilizes sensors to collect monitoring parameters throughout the aero-engine's entire lifecycle; establishes a first-order neural ordinary differential equation to continuously model the degradation process in the latent variable space, calculating the residual signal as a time-varying signal; establishes a Fourier neural operator to approximate the transfer function of the physical system, mapping operating parameters and latent variables to sensor response parameters, thereby constructing the loss function of the neural network; considers the time scale transformation between different degradation processes, constructs a symmetric regularization term to constrain the invariance of the neural ordinary differential equation to time scale transformations, obtaining latent variable processes with a consistent structure; inputs training and test sample sets into the neural network to obtain the latent variable processes corresponding to the training and test sample sets respectively, and estimates the remaining life of the test sample set based on the nearest neighbor samples on the training sample set.

Description

Technical Field

[0001] This invention relates to the field of aero-engine technology, and in particular to a method for predicting the remaining life of aero-engines based on symmetric canonical ordinary differential equations. Background Technology

[0002] Health monitoring and remaining life prediction of aero-engines are crucial for the operational safety of maintenance equipment. Understanding latent variable modeling is essential for remaining life prediction because it directly reveals how a system degrades over time, functioning similarly to health indicators. Latent variable processes, or health indicators, not only display the current state but also track degradation trajectories, providing predictive information for potential failures. Latent variables are typically represented as vectors, encompassing a wide range of degradation characteristics, while health indicators are usually scalars, providing a global measure of the system as a whole. Both have properties such as trend and monotonicity requirements. However, traditional health indicator methods rely on post-processing techniques to normalize scalars to between 0 and 1, ignoring the differences in degradation processes across a cluster of equipment. In contrast, neural frequent differential equations treat the differences between different degradation processes as equivalent time-scale transformations between degradation trajectories, thus learning a consistent latent variable structure while preserving the differences. Therefore, from the perspective of physical symmetry, neural frequent differential equations are invariant functions of this equivalent time-scale transformation, providing a consistent latent variable process for remaining life prediction without requiring additional normalization post-processing.

[0003] The information disclosed in the background section is only for enhancing the understanding of the background of this invention, and therefore may contain information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0004] This invention provides a method for predicting the remaining life of an aero-engine based on symmetric regularized ordinary differential equations. Based on first-order ordinary differential equations and Fourier neural operators, the degradation process of the system is modeled in the latent variable space. Considering the time scale transformation between different degradation processes, and based on the invariance conditions of the first-order ordinary differential equations, a symmetric regularization term is constructed to constrain the invariance of the ordinary differential equations to time scale transformations, resulting in a latent variable process with a consistent structure. This latent variable process is then used to predict the remaining life, and the remaining life on the test sample set is estimated based on the nearest neighbor samples.

[0005] A method for predicting the remaining life of aero-engines based on symmetric canonical ordinary differential equations includes:

[0006] Step a: Use sensors to collect monitoring parameters throughout the entire life cycle of the aero-engine. The monitoring parameters include the outlet temperature and pressure of the compressor and turbine. The parameters are divided into time sequences according to the number of flight cycles. By downsampling and zero-padding, samples of fixed length are obtained. Training sample sets and test sample sets are constructed respectively and normalized.

[0007] Step b: Establish a first-order neural ordinary differential equation, perform continuous time-series modeling of the degradation process in the latent variable space, calculate the residual signal as a time-varying signal, enhance the representation ability of the neural ordinary differential equation, and make its solution depend on both the initial value and the time-varying residual signal.

[0008] Step c: Establish a Fourier neural operator to approximate the transfer function of the physical system, map the operating parameters and latent variables to the sensor response parameters, and thus construct the loss function of the neural network;

[0009] Step d: Consider the time scale transformation between different degradation processes. Based on the invariance conditions of the first-order ordinary differential equation, construct symmetry regularization terms to constrain the invariance of the god ordinary differential equation to the time scale transformation, and obtain the hidden variable process with a consistent structure.

[0010] Step e involves inputting the training sample set and the test sample set into the neural network to obtain the latent variable processes corresponding to the training sample set and the test sample set, and estimating the remaining lifetime of the test sample set based on the nearest neighbor samples on the training sample set.

[0011] In the aforementioned method for predicting the remaining life of an aero-engine based on symmetric canonical ordinary differential equations, step a involves dividing the monitoring parameters of the entire life cycle according to the number of flight cycles. Each cycle is divided into a sample, and each sample is a multivariate time series. Number of variables To measure the number of variables monitored by the sensor, downsampling and zero-padding are used to ensure that the time length of each sample is accurate. The number of time steps is 1353; the mean and variance are calculated on the training sample set, the samples are normalized to the range [0,1], and the mean and variance are applied to the test sample set for normalization.

[0012] In the aforementioned method for predicting the remaining life of an aero-engine based on symmetric canonical neural ordinary differential equations, in step b, the first-order neural ordinary differential equation is established in the form of:

[0013] ,

[0014] in, These are latent variables used to approximate the real but unknown degradation process. This represents the cycle number of an aircraft engine, that is, the health status of each cycle is determined by a... Represented by vectors It is the dimension of the latent variables; It is the initial value of the ordinary differential equation, set to 0, which represents the initial state of the degradation process; It is an integral variable; It is a neural network that describes the temporal relationships of latent variables; It is a residual signal. Adding a time-varying residual signal makes the solution depend simultaneously on the initial value and the time-varying signal, where the neural network... The specific function form is:

[0015]

[0016] in, The encoder network consists of three residual connection layers and two nonlinear dimensionality reduction layers, which reduce high-dimensional signals to low-dimensional features. The activation function for the final output layer is chosen to be the tanh function. This is a multilayer nonlinear perceptron, consisting of three linear layers and nonlinear activation functions. The ReLU activation function is chosen for the middle layers, and the tanh activation function is chosen for the output layer. The tanh function will... and The range of values ​​is restricted to a bounded interval, satisfying the Lipchitz condition; and These are the parameters of the neural network.

[0017] In the aforementioned method for predicting the remaining life of an aero-engine based on symmetric canonical ordinary differential equations, the residual signal is the residual between the actual signal and the signal under ideal healthy conditions.

[0018] ,

[0019] in, These are the monitoring parameters under ideal health conditions. Subject only to operating parameters To control the system, an independent Fourier neural operator is constructed to approximate the system transfer function under ideal healthy conditions:

[0020] ,

[0021] in, The observation sequence number representing the health status, with a maximum value of . , It is the system transfer function under ideal healthy conditions, and thus... Application to obtain monitoring parameters under ideal health conditions across the entire life cycle:

[0022] .

[0023] In the aforementioned method for predicting the remaining life of aero-engines based on symmetric canonical neural ordinary differential equations, step c involves using Fourier neural operators to construct a mapping between operating parameters and latent variables to sensor monitoring parameters.

[0024] ,

[0025] in, Indicates operating parameters, It is the number of operating parameters. It is a latent variable. These are reconstructed sensor monitoring parameters. It is a Fourier neural operator, based on actual signals. and reconstructed signal The loss function of the neural network is obtained as follows: Fourier neural operators It consists of a lifting layer, an iterative Fourier layer, and a projection layer. The lifting layer transforms low-dimensional latent variables... Mapping to a high-dimensional space; the iterative Fourier layer consists of four forward and inverse Fourier transforms. In each iteration, the input variables first undergo a forward Fourier transform, then a linear transform, and finally an inverse Fourier transform; the projection layer ultimately maps the features to the signal space, i.e., reconstructs the signal. .

[0026] In the aforementioned method for predicting the remaining life of an aero-engine based on symmetric canonical ordinary differential equations, in step d, the time scale transformation between different degradation processes is performed by converting different degradation processes into each other through a scale transformation along the time axis. The invariance condition of the first-order ordinary differential equation is that there exists an equivalent set of solutions to the first-order ordinary differential equation. The elements in this equivalent set are generated by the equivalent transformation, and all elements of this equivalent set are solutions to the ordinary differential equation. The ordinary differential equation is an invariant function of the equivalent transformation. The variables are... Defined as a divine constant differential equation The solution, If these are the parameters of a neural network, then the invariance condition is:

[0027] ,

[0028] in, It is a time scale transformation; It is an invariant function of the final expectation, that is and All Solution exist Generate an equivalent solution set under the transformation.

[0029] Using Taylor transformation, the above invariance condition is derived as follows:

[0030] ,

[0031] in, It is a time scale transformation vector field, These are the parameters for time-scale transformation. It is an infinitesimal generator.

[0032] In the aforementioned method for predicting the remaining life of aero-engines based on symmetric canonical ordinary differential equations, the expression for the infinitesimal generator is as follows: , and They are variables and The vector field, considering its first-order differential term The invariance condition considers the first-order extension of the infinitesimal generator, denoted as... The invariance condition is then derived as follows:

[0033] ,

[0034] in, , Therefore, the invariance condition simplifies to:

[0035] ,

[0036] in, and They are variables and The vector field, by equivalent transformation The form determines it.

[0037] In the aforementioned method for predicting the remaining life of aero-engines based on symmetric canonical ordinary differential equations, latent variables... A power function characterizing the degradation process, and If the coefficients are functions, then the vector field and have to:

[0038] ,

[0039] in, and The equivalent solution after time-scale transformation is the vector field. and Substituting the invariance condition, we obtain the symmetry regularity:

[0040] ,

[0041] or, For an exponential function, the corresponding symmetry regularity is:

[0042]

[0043] Both can be described by the same expression:

[0044]

[0045] in, These are the function coefficients.

[0046] In the aforementioned method for predicting the remaining life of aero-engines based on symmetric canonical neural networks, step e involves inputting a training sample set into a symmetric canonical neural network to obtain the latent variable processes corresponding to the training sample set. Combined with time information, the k-nearest neighbor algorithm is used to estimate the remaining life of the latent variable processes in the test sample set, thus obtaining the remaining life sample pairs. ,in It is the remaining life label.

[0047] In the aforementioned method for predicting the remaining life of aero-engines based on symmetric canonical neural ordinary differential equations, step e involves a neural network comprising two parts: a neural ordinary differential equation and a Fourier neural operator. The neural ordinary differential equation handles the latent variables... To perform modeling, the Fourier neural operator incorporates latent variables. Mapping to the signal space, i.e., reconstructing the signal. Then the final optimization objective for all parameters is determined by the reconstruction loss. and symmetry regularization Since the latent variable process is restricted to a continuous bounded function space, the general approximation theorem of neural networks guarantees convergence.

[0048] Compared with existing technologies, this invention has the following advantages: This invention constructs a neural network ordinary differential equation (NDE) to model the degradation process in the latent variable space; based on the invariance conditions of the first-order NDE, a symmetry regularization is constructed, making the neural network an invariant function of equivalent transformations between different degradation processes, providing a consistent latent variable process for remaining lifetime prediction without requiring additional normalization post-processing. By modeling the degradation process in the latent variable space using the NDE and constructing a symmetry regularization based on the invariance conditions, the solution space of the NDE is constrained, ultimately achieving the remaining lifetime prediction of aero-engines. Attached Figure Description

[0049] Various other advantages and benefits of the present invention will become apparent to those skilled in the art upon reading the detailed description of the preferred embodiments below. The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. It is obvious that the drawings described below are merely some embodiments of the invention, and those skilled in the art can obtain other drawings based on these drawings without any inventive effort. Furthermore, the same reference numerals denote the same parts throughout the drawings.

[0050] In the attached diagram:

[0051] Figure 1 This is a flowchart of a method for predicting the remaining life of an aero-engine based on symmetric canonical ordinary differential equations, provided in one embodiment of this disclosure.

[0052] Figure 2 This is a schematic diagram of the time-scale transformation of the degradation process provided in one embodiment of this disclosure;

[0053] Figure 3 This is a schematic diagram of latent variable process estimation provided in one embodiment of this disclosure;

[0054] Figure 4 This is a schematic diagram illustrating the comparison of hidden variable processes in an aero-engine according to an embodiment of this disclosure;

[0055] Figure 5 This is a schematic diagram illustrating the prediction of the remaining life of an aero-engine according to an embodiment of this disclosure;

[0056] Figure 6 This is a schematic diagram of the neural network training convergence process provided in one embodiment of this disclosure.

[0057] The present invention will be further explained below with reference to the accompanying drawings and embodiments. Detailed Implementation

[0058] The following will refer to the appendix. Figures 1 to 6 Specific embodiments of the invention will be described in more detail below. While specific embodiments of the invention are shown in the accompanying drawings, it should be understood that the invention may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided to enable a more thorough understanding of the invention and to fully convey the scope of the invention to those skilled in the art.

[0059] It should be noted that certain terms are used in the specification and claims to refer to specific components. Those skilled in the art will understand that different terms may be used to refer to the same component. This specification and claims do not distinguish components based on differences in terminology, but rather on differences in function. The terms "comprising" or "including" used throughout the specification and claims are open-ended and should be interpreted as "comprising but not limited to." The following descriptions are preferred embodiments for carrying out the invention; however, these descriptions are for the purpose of understanding the general principles of the specification and are not intended to limit the scope of the invention. The scope of protection of this invention is determined by the appended claims.

[0060] To facilitate understanding of the embodiments of the present invention, further explanations and descriptions will be provided below with reference to the accompanying drawings and specific embodiments. The accompanying drawings do not constitute a limitation on the embodiments of the present invention.

[0061] like Figures 1 to 5 As shown, the method for predicting the remaining life of aero-engines based on symmetric canonical ordinary differential equations includes the following steps:

[0062] Step a: Use sensors to collect monitoring parameters throughout the entire life cycle of the aero-engine. The monitoring parameters include the outlet temperature and pressure of the compressor and turbine. The parameters are divided into time sequences according to the number of flight cycles. By downsampling and zero-padding, samples of fixed length are obtained. Training sample sets and test sample sets are constructed respectively and normalized.

[0063] Step b: Establish a first-order neural ordinary differential equation, perform continuous time-series modeling of the degradation process in the latent variable space, calculate the residual signal as a time-varying signal, enhance the representation ability of the neural ordinary differential equation, and make its solution depend on both the initial value and the time-varying residual signal.

[0064] Step c: Establish a Fourier neural operator to approximate the transfer function of the physical system, map the operating parameters and latent variables to the sensor response parameters, and thus construct the loss function of the neural network;

[0065] Step d: Consider the time scale transformation between different degradation processes. Based on the invariance conditions of the first-order ordinary differential equation, construct symmetry regularization terms to constrain the invariance of the god ordinary differential equation to the time scale transformation, and obtain the hidden variable process with a consistent structure.

[0066] Step e involves inputting the training sample set and the test sample set into the neural network to obtain the latent variable processes corresponding to the training sample set and the test sample set, and estimating the remaining lifetime of the test sample set based on the nearest neighbor samples on the training sample set.

[0067] In a preferred embodiment of the aero-engine remaining life prediction method based on symmetric canonical ordinary differential equations, in step a, the monitoring parameters for the entire life cycle are divided according to the number of flight cycles. Each cycle is divided into a sample, and each sample is a multivariate time series. Number of variables To measure the number of variables monitored by the sensor, downsampling and zero-padding are used to ensure that the time length of each sample is accurate. The number of time steps is 1353; the mean and variance are calculated on the training sample set, the samples are normalized to the range [0,1], and the mean and variance are applied to the test sample set for normalization.

[0068] In a preferred embodiment of the aero-engine remaining life prediction method based on symmetric canonical neural ordinary differential equations, in step b, the first-order neural ordinary differential equation is established in the form of:

[0069] ,

[0070] in, These are latent variables used to approximate the real but unknown degradation process. This represents the cycle number of an aircraft engine, that is, the health status of each cycle is determined by a... Represented by vectors It is the dimension of the latent variables; It is the initial value of the ordinary differential equation, set to 0, which represents the initial state of the degradation process; It is an integral variable; It is a neural network that describes the temporal relationships of latent variables; It is a residual signal. Adding a time-varying residual signal makes the solution depend simultaneously on the initial value and the time-varying signal, where the neural network... The specific function form is:

[0071]

[0072] in, The encoder network consists of three residual connection layers and two nonlinear dimensionality reduction layers, which reduce high-dimensional signals to low-dimensional features. The activation function for the final output layer is chosen to be the tanh function. This is a multilayer nonlinear perceptron, consisting of three linear layers and nonlinear activation functions. The ReLU activation function is chosen for the middle layers, and the tanh activation function is chosen for the output layer. The tanh function will... and The range of values ​​is restricted to a bounded interval, satisfying the Lipchitz condition; and These are the parameters of the neural network.

[0073] In a preferred embodiment of the aero-engine remaining life prediction method based on symmetric canonical neural ordinary differential equations, the residual signal is the residual between the actual signal and the signal under ideal health conditions.

[0074] ,

[0075] in, These are the monitoring parameters under ideal health conditions. Subject only to operating parameters To control the system, an independent Fourier neural operator is constructed to approximate the system transfer function under ideal healthy conditions:

[0076] ,

[0077] in, The observation sequence number representing the health status, with a maximum value of . , It is the system transfer function under ideal healthy conditions, and thus... Application to obtain monitoring parameters under ideal health conditions across the entire life cycle:

[0078] .

[0079] In a preferred embodiment of the aero-engine remaining life prediction method based on symmetric canonical neural ordinary differential equations, in step c, the Fourier neural operator constructs a mapping from operating parameters and latent variables to sensor monitoring parameters:

[0080] ,

[0081] in, Indicates operating parameters, It is the number of operating parameters. It is a latent variable. These are reconstructed sensor monitoring parameters. It is a Fourier neural operator, based on actual signals. and reconstructed signal The loss function of the neural network is obtained as follows: Fourier neural operators It consists of a lifting layer, an iterative Fourier layer, and a projection layer. The lifting layer transforms low-dimensional latent variables... Mapping to a high-dimensional space; the iterative Fourier layer consists of four forward and inverse Fourier transforms. In each iteration, the input variables first undergo a forward Fourier transform, then a linear transform, and finally an inverse Fourier transform; the projection layer ultimately maps the features to the signal space, i.e., reconstructs the signal. .

[0082] In a preferred embodiment of the aero-engine remaining life prediction method based on symmetric canonical ordinary differential equations, in step d, the time scale transformation between different degradation processes is a mutual transformation between different degradation processes through a scale transformation along the time axis. The invariance condition of the first-order ordinary differential equation is that there exists an equivalent set of solutions to the first-order ordinary differential equation. The elements in this equivalent set are generated by the equivalent transformation, and all elements of this equivalent set are solutions to the ordinary differential equation. The ordinary differential equation is an invariant function of the equivalent transformation. The variables... Defined as a divine constant differential equation The solution, If these are the parameters of a neural network, then the invariance condition is:

[0083] ,

[0084] in, It is a time scale transformation; It is an invariant function of the final expectation, that is and All Solution exist Generate an equivalent solution set under the transformation.

[0085] Using Taylor transformation, the above invariance condition is derived as follows:

[0086] ,

[0087] in, It is a time scale transformation vector field, These are the parameters for time-scale transformation. It is an infinitesimal generator.

[0088] In a preferred embodiment of the aero-engine remaining life prediction method based on symmetric canonical ordinary differential equations, the expression of the infinitesimal generator is as follows: , and They are variables and The vector field, considering its first-order differential term The invariance condition considers the first-order extension of the infinitesimal generator, denoted as... The invariance condition is then derived as follows:

[0089] ,

[0090] in, , Therefore, the invariance condition simplifies to:

[0091] ,

[0092] in, and They are variables and The vector field, by equivalent transformation The form determines it.

[0093] In a preferred embodiment of the aero-engine remaining life prediction method based on symmetric canonical neural ordinary differential equations, the latent variables... A power function characterizing the degradation process, and If the coefficients are functions, then the vector field and have to:

[0094] ,

[0095] in, and The equivalent solution after time-scale transformation is the vector field. and Substituting the invariance condition, we obtain the symmetry regularity:

[0096] ,

[0097] or, For an exponential function, the corresponding symmetry regularity is:

[0098]

[0099] Both can be described by the same expression:

[0100]

[0101] in, These are the function coefficients.

[0102] In a preferred embodiment of the aero-engine remaining life prediction method based on symmetric canonical neural network, step e involves inputting the training sample set into the symmetric canonical neural network to obtain the latent variable process corresponding to the training sample set, and combining this with time information to obtain the remaining life sample pairs. ,in It is the remaining life label.

[0103] In a preferred embodiment of the aero-engine remaining life prediction method based on symmetric regularized neural ordinary differential equations, step e involves a neural network comprising two parts: a neural ordinary differential equation and a Fourier neural operator. The neural ordinary differential equation handles the latent variables... To perform modeling, the Fourier neural operator incorporates latent variables. Mapping to the signal space, i.e., reconstructing the signal. Then the final optimization objective for all parameters is determined by the reconstruction loss. and symmetry regularization Since the latent variable process is restricted to a continuous bounded function space, the general approximation theorem of neural networks guarantees convergence.

[0104] In a preferred embodiment of the aero-engine remaining life prediction method based on symmetric regularization neural network, in step e, the test sample set is input into the symmetric regularization neural network to obtain the latent variable process corresponding to the test sample set, and the remaining life of the latent variable process in the test sample set is estimated by using the k-nearest neighbor algorithm.

[0105] Latent variables are features in a neural network; they are variables that are latent. A neural network is a function, and latent variables are the input variables of this function.

[0106] In one embodiment, a flight cycle is a complete operating envelope of an aircraft engine, including takeoff, cruise, and landing phases. The monitoring signal sampling frequency is 1 Hz, and a flight cycle lasts approximately 1 to 5 hours.

[0107] In one embodiment, after time-series segmentation according to flight cycles, the unequal-length samples are downsampled at a ratio of 1:15, and the downsampled samples are padded with zeros to fit the equal-length samples; 9 of the 15 aero engines are selected as the training set, and the remaining 6 are selected as the test sample set.

[0108] In one embodiment, the number of variables monitored by the sensor includes gas path parameters and temperature parameters.

[0109] In one embodiment, such as Figure 1 As shown, a method for predicting the remaining life of an aero-engine based on symmetric canonical ordinary differential equations includes the following steps:

[0110] In the first step, sensors such as those for air pressure and temperature are used to collect monitoring data throughout the entire lifecycle of the aero-engine, with a sampling frequency of 1Hz. The lifecycle data is then segmented into time-series segments according to the flight cycle. Each sample is a multivariate time series. Number of variables The number of sensor-monitored variables includes air path parameters and temperature parameters; unequal-length samples are downsampled at a ratio of 1:15, and the downsampled samples are padded with zeros to fit the equal-length samples; 9 of the 15 aero engines are selected as the training sample set, and the remaining 6 are selected as the test sample set; the mean and variance are calculated on the training sample set, the samples are normalized to the range [0,1], and the mean and variance are applied to the test sample set for normalization.

[0111] In the second step, a first-order neural network ordinary differential equation is established to model the degradation process continuously over time in the latent variable space. This first-order neural network ordinary differential equation consists of an encoder and a multilayer nonlinear perceptron. The encoder is chosen as ResNet to reduce the dimensionality of the high-dimensional residual signal to a low-dimensional space. The multilayer nonlinear perceptron is used to describe the evolution trajectory of the latent variables over time. The functional form of the neural network is:

[0112]

[0113] in, As a latent variable, For residual signals, The encoder network consists of three residual connection layers and two nonlinear dimensionality reduction layers, which reduce high-dimensional signals to low-dimensional features. The activation function for the final output layer is chosen to be the tanh function. This is a multilayer nonlinear perceptron, consisting of three linear layers and nonlinear activation functions. The ReLU function is chosen as the activation function for the middle layers, and the tanh function is chosen as the activation function for the output layer. The tanh function will... and The range of values ​​is restricted to a bounded interval, satisfying the Lipchitz condition; and These are the parameters of the neural network. The residual signal provides time-varying information for the first-order neural network's ordinary differential equations, and is calculated from the difference between the actual signal and the signal under ideal healthy conditions. In order to obtain the signal under ideal health conditions, it is necessary to construct a system transfer function under ideal health conditions. This transfer function is constructed independently of the Fourier neural operator in step three, and its functional form is:

[0114]

[0115] in, and Especially the monitoring parameters and operating parameters under healthy conditions. It is the system transfer function under ideal healthy conditions.

[0116] In the third step, a Fourier neural operator is established to approximate the transfer function of the physical system as it degrades over time. The inputs to this Fourier neural operator are time-varying operating parameters and latent variables, and the output is the system response monitoring parameters. The output of this operator is compared with the actual monitoring parameters to obtain the loss function of the neural network. ,in These are the actual monitoring parameters. This 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... Mapping to a high-dimensional space; the iterative Fourier layer consists of four forward and inverse Fourier transforms. In each iteration, the input variables first undergo a forward Fourier transform, then a linear transform, and finally an inverse Fourier transform; the projection layer ultimately maps the features to the signal space, i.e., reconstructs the signal. .

[0117] In the fourth step, a symmetry regularity is established. This regularity is derived from the invariance conditions of the ordinary differential equation. The invariance conditions of the ordinary differential equation are defined as follows: the new solution obtained by applying a certain equivalent transformation to the solution of the ordinary differential equation also satisfies the equation. The variables are then... Defined as a divine constant differential equation The solution, If these are the parameters of a neural network, then the invariance condition is:

[0118]

[0119] in, It is an equivalent transformation, and defines the time scale transformation between different degradation trajectories; It is an invariant function of the final expectation, that is and All The solution, exist The transformation generates an equivalent solution set. Using the Taylor transformation, the above invariance condition is derived as follows:

[0120]

[0121] in, It is a time scale transformation vector field, These are the parameters for time-scale transformation. 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, denoted as . The invariance condition is then derived as follows:

[0122]

[0123] in, , Therefore, the invariance condition simplifies to:

[0124]

[0125] in, and, Other than variables and The vector field, by equivalent transformation The form determines it. Vector field and Determined by the time scale transformation, without loss of generality, we assume a latent variable process. It is an exponential function. and If the coefficients are functions, then the vector field and We can obtain:

[0126]

[0127] in, and This is the equivalent solution after time-scale transformation. The vector field... and Substituting the invariance condition, we obtain the symmetry regularity:

[0128]

[0129] Similarly, suppose For an exponential function, the corresponding symmetry regularity is:

[0130]

[0131] If both can be described by the same expression, then the symmetry regularization is:

[0132]

[0133] in, These are the function coefficients.

[0134] In the fifth step, the training sample set is input into a symmetrically regularized neural network to obtain the latent variable process corresponding to the training sample set. Combined with time information, the remaining lifespan sample pairs are obtained. ,in This refers to the remaining lifetime label; similarly, the test sample set is input into a symmetrically regularized neural network to obtain the latent variable processes corresponding to the test sample set. Finally, the k-nearest neighbor algorithm is used to estimate the remaining lifetime of the latent variable processes in the test sample set; the training process of the neural network includes two parts: neural ordinary differential equations and Fourier neural operators. Among them, the neural ordinary differential equations are used to evaluate the latent variables. To perform modeling, the Fourier neural operator incorporates latent variables. Mapping to the signal space, i.e., reconstructing the signal. Then the final optimization objective for all parameters is determined by the reconstruction loss. and symmetry regularization Since the latent variable process is restricted to a continuous bounded function space, the general approximation theorem of neural networks guarantees convergence. Optionally, this embodiment was trained iteratively 500 times.

[0135] Figure 2 The diagram illustrates the timescale transformation of the degradation process. The red, blue, and green curves represent three different degradation process trajectories. It can be seen that due to the influence of environmental variables, operating conditions, manufacturing errors, etc., the time to reach the failure threshold will vary for different degradation processes. This difference will lead to the generalization problem in the modeling process. This invention proposes that this difference can be explained by the timescale transformation between different trajectories, thereby introducing the invariance conditions and symmetry regularity of the ordinary differential equation of the nervous system.

[0136] Figure 3 The diagram illustrates the estimation of latent variable processes. First, the latent variables are estimated using a regular differential equation. Perform time series modeling, residual signal The representation of latent variables is enhanced after the encoder is applied; then the operating parameters are... and latent variables The input is fed into the Fourier neural operator to estimate the system monitoring parameters. .

[0137] Figure 4 This is a schematic diagram comparing the hidden variable processes of an aero-engine according to an embodiment of the present invention. It can be seen that the neural ordinary differential equation under symmetry canonicalization can yield a hidden variable process with a consistent structure, thereby avoiding post-processing such as normalization required for health indicators.

[0138] Figure 5This is a schematic diagram of the remaining life prediction of an aero-engine according to an embodiment of the present invention. It can be seen that the evaluation indicators for the prediction results include the root mean square error (RMSE) and the score function. The predictions were tested on two aero-engine fleets, namely N-CMAPSS-DS03 and N-CMAPSS-DS04. The experimental results were compared with three models: deep Gaussian process, Bayesian Transformer, and neural ordinary differential equation. The results are shown in Table 1.

[0139] Figure 6 This diagram illustrates the neural network training convergence process according to an embodiment of the present invention. It shows that during neural network training, both the reconstruction loss and symmetry regularization converge relatively quickly with minimal fluctuations. This rapid convergence is attributed to the rational design of the neural network's ordinary differential equations. Specifically, the tanh function ensures that the neural network's ordinary differential equations satisfy the Lipchitz conditions, thereby constraining the latent variable process to be a continuous bounded variable process. Furthermore, the general approximation theorem for neural networks guarantees the convergence of the neural network.

[0140] In this embodiment, symmetry regularization ensures that the neural network's ordinary differential equation is an invariant function of timescale transformations of different latent variable processes. This results in a consistent structure across different latent variable processes, avoiding post-processing such as normalization required for health indicators, and enhancing the interpretability of latent variables and the performance of remaining lifespan prediction. Figure 4 , Figure 5 As can be seen from the results in Table 1, the proposed symmetric canonical ordinary differential equations achieved good performance in the evaluation index, thus verifying the superiority of the prediction method.

[0141] Limitations. Many forms can be made by those skilled in the art based on the guidance of this specification and without departing from the scope of the claims, and all of these are within the scope of protection of this invention.

Claims

1. A method for predicting the remaining life of an aero-engine based on symmetric canonical ordinary differential equations, characterized in that, Includes the following steps: Step a: Use sensors to collect monitoring parameters throughout the entire life cycle of the aero-engine. The monitoring parameters include the outlet temperature and pressure of the compressor and turbine. The parameters are divided into time sequences according to the number of flight cycles. By downsampling and zero-padding, samples of fixed length are obtained. Training sample sets and test sample sets are constructed respectively and normalized. Step b: Establish a first-order neural ordinary differential equation, perform continuous time-series modeling of the degradation process in the latent variable space, calculate the residual signal as a time-varying signal, enhance the representation ability of the neural ordinary differential equation, and make its solution depend on both the initial value and the time-varying residual signal. Step c: Establish a Fourier neural operator to approximate the transfer function of the physical system, map the operating parameters and latent variables to the sensor response parameters, and thus construct the loss function of the neural network; Step d: Consider the time scale transformation between different degradation processes. Based on the invariance conditions of the first-order ordinary differential equation, construct symmetry regularization terms to constrain the invariance of the god ordinary differential equation to the time scale transformation, and obtain the hidden variable process with a consistent structure. Step e involves inputting the training sample set and the test sample set into the neural network to obtain the latent variable processes corresponding to the training sample set and the test sample set, and estimating the remaining lifetime of the test sample set based on the nearest neighbor samples on the training sample set. in, In step d, the time-scale transformation between different degradation processes is the mutual transformation of different degradation processes through a scale transformation along the time axis. The invariance condition of the first-order ordinary differential equation is that there exists an equivalent set of solutions to the first-order ordinary differential equation. The elements in this equivalent set are generated by the equivalent transformation, and all elements of this equivalent set are solutions to the ordinary differential equation. The ordinary differential equation is an invariant function of the equivalent transformation. The variables... Defined as a divine constant differential equation The solution, If these are the parameters of a neural network, then the invariance condition is: Where g∈G is the time scale transformation; It is an invariant function of the final expectation, that is, z and gz are both The solution z generates an equivalent solution set under the transformation g∈G. Using Taylor transformation, the above invariance condition is derived as follows: in, is the vector field of the time-scale transformation g, and s is the parameter of the time-scale transformation. For infinitesimal generator; The latent variable z is a power function representing the degradation process, or z is an exponential function; The expression for the infinitesimal generator is: ξ and η are vector fields of variables t and z, respectively, considering their first-order differential terms. The invariance condition considers the first-order extension of the infinitesimal generator, denoted as X. (1) The invariance condition is then derived as follows: in, Therefore, the invariance condition simplifies to: Here, ξ and η are the vector fields of variables t and z, respectively, and are determined by the form of the equivalent transformation g.

2. The method for predicting the remaining life of an aero-engine based on symmetric canonical ordinary differential equations according to claim 1, characterized in that, In step a, the monitoring parameters X = [x1, ..., x] for the entire life cycle are divided according to the number of flight cycles. N Each cycle is divided into one sample, and each sample is a multivariate time series. The number of variables p represents the number of variables monitored by the sensor. Through downsampling and zero-padding, the time length T of each sample is made more consistent. i The number of time steps is 1353; the mean and variance are calculated on the training sample set, the samples are normalized to the range [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 aero-engine based on symmetric canonical ordinary differential equations according to claim 2, characterized in that, In step b, the first-order ordinary differential equation is established in the form of: Among them, z i ∈R d These are latent variables used to approximate the real but unknown degradation process. `i` represents the cycle number of the aero-engine, meaning the health status of each cycle is determined by a variable `z`. i The vector representation is used, where d is the dimension of the latent variables; z0 is the initial value of the ordinary differential equation, set to 0, representing the initial state of the degradation process; t is the integration variable; f is the neural network, describing the temporal relationship of the latent variables; Δx i It is a residual signal. A time-varying residual signal is added, making its solution depend simultaneously on the initial value and the time-varying signal. The specific functional form of the neural network f is: Among them, h θ The encoder network consists of three residual connection layers and two nonlinear dimensionality reduction layers, which reduce high-dimensional signals to low-dimensional features. θ The activation function for the final output layer is chosen to be the tanh function. This is a multilayer nonlinear perceptron, consisting of three linear layers and nonlinear activation functions. The activation function for the middle layers is the ReLU function, and the activation function for the output layer is the tanh function. The tanh function will reduce h... θ and The range of θ is restricted to a bounded interval, satisfying the Lipchitz condition; θ and These are the parameters of the neural network.

4. The method for predicting the remaining life of an aero-engine based on symmetric canonical ordinary differential equations according to claim 3, characterized in that, The residual signal is the residual between the actual signal and the signal under ideal healthy conditions: Δx i =x i -x i ′, Where, x i ′ represents the monitoring parameter under ideal health conditions, and x represents the monitoring parameter under ideal health conditions. i Only affected by the operating condition parameter w i To control the system, an independent Fourier neural operator is constructed to approximate the system transfer function under ideal healthy conditions: x j =FNO′(w j ),j=1,2,...,m, Where j represents the observation sequence number of the health state, and its maximum value is m, FNO′ is the system transfer function under ideal health state, and then FNO′ is applied to the whole life cycle sequence to obtain the monitoring parameters under ideal health state: x i ′=FNO′(w i ),i=1,2,...,N。 5. The method for predicting the remaining life of an aero-engine based on symmetric canonical ordinary differential equations 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, This represents the operating condition parameters, where S is the number of operating condition parameters, and T is the number of operating condition parameters. i It is the time length for each sample; z i It is a latent variable. These are the reconstructed sensor monitoring parameters. FNO is a Fourier neural operator, based on the actual signal x. i and reconstructed signals The loss function of the neural network is obtained as follows: The Fourier neural operator FNO consists of a lifting layer, an iterative Fourier layer, and a projection layer. The lifting layer transforms the low-dimensional latent variable z... i Mapping to a high-dimensional space; the iterative Fourier layer consists of four forward and inverse Fourier transforms. In each iteration, the input variables first undergo a forward Fourier transform, then a linear transform, and finally an inverse Fourier transform; the projection layer ultimately maps the features to the signal space, i.e., reconstructs the signal.

6. The method for predicting the remaining life of an aero-engine based on symmetric canonical ordinary differential equations according to claim 1, characterized in that, When the latent variable z is a power function characterizing the degradation process, z(t) = kt α Let k and α be the function coefficients, then the vector fields ξ and η are: in, and As the equivalent solution after time-scale transformation, substituting the vector fields ξ and η into the aforementioned invariance condition yields the symmetry regularity: Alternatively, when z is an exponential function, the corresponding symmetry regularity is: Both can be described by the same expression: Where α is the function coefficient.

7. The method for predicting the remaining life of an aero-engine based on symmetric canonical ordinary differential equations according to claim 3, characterized in that, In step e, the training sample set is input into a symmetrically regularized neural network to obtain the latent variable processes corresponding to the training sample set. Combined with time information, the k-nearest neighbor algorithm is used to estimate the remaining lifetime of the latent variable processes in the test sample set, resulting in the remaining lifetime sample pairs [(z1, y1), ..., (z...]. N y N )], where y i It is the remaining life label.

8. The method for predicting the remaining life of an aero-engine based on symmetric canonical ordinary differential equations according to claim 3, characterized in that, In step e, the neural network consists of two parts: a neural ordinary differential equation and a Fourier neural operator. The neural ordinary differential equation deals with the latent variable z. i To perform modeling, the Fourier neural operator will use the latent variable z i Mapping to the signal space, i.e., reconstructing the signal. The final optimization objective for all parameters is determined by the reconstruction loss. and symmetry regularity J ODE Since the latent variable process is restricted to a continuous bounded function space, the general approximation theorem of neural networks guarantees convergence.

Images