Single-axis rotation inertial navigation indexing mechanism few-sample fault diagnosis method

Abstract

The invention discloses a few-sample fault diagnosis method for a single-axis rotary inertial navigation indexing mechanism. The method comprises the following steps: S1, constructing a rotary inertial navigation twin model and four types of common fault models; s2, constructing a simulation fault database; s3, constructing a single-axis rotation inertial navigation indexing mechanism fault diagnosis model; s4, performing zero-sample pre-training on the model by adopting a simulation fault database, and performing transfer learning-based small-sample training on the model by combining a small number of real samples; s5, inputting IMU assembly signals output by single-axis rotation inertial navigation in real time into the trained fault diagnosis model, and completing fault diagnosis of the indexing mechanism; according to the method, the limitation of data scarcity on model training is effectively relieved, the adaptability and accuracy of fault diagnosis in an actual system are improved, the problems of existing rotary inertial navigation in a fault diagnosis technology with few samples are solved, the fault judgment accuracy rate reaches 99.28%, the error amount of the accuracy rate 1 sigma is less than 0.01%, the precision is high, and the practicability is good.

Description

Technical Field

[0001] This invention relates to the field of rotary inertial navigation fault diagnosis technology, and in particular to a method for diagnosing faults in a single-axis rotary inertial navigation indexing mechanism with a small number of samples. Background Technology

[0002] With the continuous advancement of inertial navigation technology, rotating inertial navigation systems (INS) are increasingly becoming a key area of ​​research in high-precision, long-duration navigation due to their ability to effectively suppress the accumulation and divergence of INS errors through rotation modulation technology. However, while the introduction of indexing mechanisms improves system performance, it also makes critical components (such as motors, bearings, and encoders) more susceptible to failure due to wear, aging, or overload, thus threatening the reliability and safety of the system. Therefore, efficient fault diagnosis and condition monitoring for rotating INS, especially accurate identification in the early stages of fault occurrence, has significant engineering application value and practical significance.

[0003] Existing fault diagnosis methods typically rely on the monitoring and signal analysis of multi-sensor data (such as acceleration, acoustic signals, and temperature) and combine them with machine learning techniques to build diagnostic models. However, these methods have high requirements for the quantity and quality of fault samples. In practical applications, the scarcity of fault data is common, especially for early fault samples, which are often difficult to obtain or incomplete. Furthermore, fault injection experiments or data annotation processes for rotating machinery are not only costly but also pose significant risks, potentially endangering personnel and property safety.

[0004] Digital twin technology, as an emerging technology integrating virtual modeling and real-time data interaction, offers an innovative solution to this problem. Through high-fidelity simulation modeling, digital twins can generate diverse fault samples, providing rich data support for fault diagnosis research under complex operating conditions. However, digital twins have high requirements for the fault modes, device system output characteristics, and fault mechanisms of rotating inertial navigation systems, thus posing a challenge to achieving high-precision fault diagnosis based on a limited number of samples. Summary of the Invention

[0005] The purpose of this invention is to provide a method for diagnosing faults in single-axis rotary inertial navigation indexing mechanisms with a limited number of samples, thereby solving the aforementioned technical problems.

[0006] Therefore, the technical solution of the present invention is as follows:

[0007] A method for diagnosing faults in a single-axis rotating inertial navigation system with a limited number of samples, comprising the following steps:

[0008] S1. Construct a rotating inertial navigation twin model based on a single-axis rotating inertial navigation system, and four fault models based on control jitter fault, control overspeed fault, control stop jitter fault and bearing fault respectively.

[0009] S2. Based on the rotating inertial navigation twin model, normal sample data is obtained through simulation. Then, based on the normal sample data, different fault models are superimposed to obtain different fault sample data through simulation. A simulation fault database is constructed, which includes normal sample data and different fault sample data obtained through simulation.

[0010] S3. Construct a fault diagnosis model for a single-axis rotating inertial navigation indexing mechanism. It uses two convolutional neural networks to perform time-frequency analysis on gyroscope information and accelerometer information respectively, and then fuses the processed information to output the diagnosis results.

[0011] S4. First, a zero-sample pre-training of the fault diagnosis model of the single-axis rotating inertial navigation indexing mechanism is performed using a simulated fault database. Then, a small number of real samples are combined to perform a few-sample training of the fault diagnosis model of the single-axis rotating inertial navigation indexing mechanism based on transfer learning.

[0012] S5. Input the IMU component signal output in real time from the single-axis rotating inertial navigation system into the trained fault diagnosis model to diagnose the fault of the indexing mechanism.

[0013] Further, in step S1, the rotating inertial navigation twin model based on the single-axis rotating inertial navigation system is as follows:

[0014]

[0015] In the formula, ω ox ω oy and ω oz These are the gyroscope outputs on the X, Y, and Z axes of a rotating inertial navigation system, respectively; K gx K gy and K gz These are the gyroscope scaling factors on the X, Y, and Z axes, respectively; γ xy γ is the gyroscope mounting error angle between the X and Y axes. xz γ is the gyroscope mounting error angle between the X and Z axes. yx γ is the gyroscope mounting error angle between the Y and X axes. yz γ is the gyroscope mounting error angle between the Y and Z axes. zx γ is the gyroscope mounting error angle between the Z-axis and X-axis. zy The gyroscope mounting error angle between the Z and Y axes; ω ix ω iy and ω iz These are the gyroscope inputs on the X, Y, and Z axes of a rotating inertial navigation system, respectively; ε x ε y and ε z These represent the gyroscope zero-bias errors on the X, Y, and Z axes of a rotating inertial navigation system, respectively; n gx n gy and ngz These represent the random noise errors of the gyroscope along the X, Y, and Z axes of a rotating inertial navigation system, respectively.

[0016]

[0017] In the formula, f ox f oy and f oz These are the accelerometer outputs on the X, Y, and Z axes of the rotating inertial navigation system, respectively; K ax K ay and K az These are the accelerometer scale factors on the X, Y, and Z axes, respectively; δ xy The accelerometer installation error angle between the X and Y axes, δ xz The accelerometer installation error angle between the X and Z axes, δ yx The accelerometer installation error angle between the Y-axis and X-axis, δ yz The accelerometer installation error angle between the Y and Z axes, δ zx The accelerometer installation error angle between the Z-axis and X-axis, δ zy The accelerometer installation error angle between the Z and Y axes; f ix f iy and f iz These are the accelerometer inputs on the X, Y, and Z axes of the rotating inertial navigation system, respectively. and These represent the accelerometer zero-bias errors on the X, Y, and Z axes of a rotating inertial navigation system, respectively; n ax n ay and n az These represent the random noise errors of the accelerometers on the X, Y, and Z axes of the rotating inertial navigation system, respectively.

[0018] The gyroscope input expressions for the X, Y, and Z axes in a rotating inertial navigation system are as follows:

[0019]

[0020] The accelerometer input expressions for the X, Y, and Z axes in a rotating inertial navigation system are:

[0021]

[0022] In the above two equations, Δγ is the roll installation error angle between the rotating frame of the rotating inertial navigation system and the inertial measurement unit, and Δθ is the pitch installation error angle between the rotating frame of the rotating inertial navigation system and the inertial measurement unit. ω is the reading of the encoder disk of the rotating frame of the rotating inertial navigation system. mo (t) represents the actual rotational modulation angular velocity. Let ω be the initial attitude angle of the rotating frame of the rotating inertial navigation system.bx ω by and ω bz These represent the angular velocities of the load system in the rotating inertial navigation system along the X, Y, and Z axes, respectively. bx f by and f bz These represent the accelerations of the load system in the rotating inertial navigation system along the X, Y, and Z axes, respectively.

[0023] Furthermore, in step S1, the four fault models are:

[0024] (1) Construct a control jitter fault model, the expression of which is:

[0025]

[0026] In the formula, ω mo (t) represents the actual rotational modulation angular velocity, ω mc (t) represents the theoretical rotational modulation angular velocity, A c f is the amplitude of angular velocity jitter. c The frequency of the jitter. Let n(t) be the jitter phase, n(t) be the control angular velocity noise signal, and f be the phase jitter. bx (t) represents the acceleration of the fault signal equivalent to the X-axis of the load system, f by (t) represents the acceleration of the fault signal equivalent to the Y-axis of the load system, A cj To control the slight acceleration on the horizontal axis caused by vibration, c represents the damping coefficient. To interfere with random phase, To control the angle between the jitter point and the horizontal accelerometer;

[0027] 2) Construct a control overrun fault model, the expression of which is:

[0028]

[0029] In the formula, ω mo (t) represents the actual rotational modulation angular velocity, ω now ω is the modulation angular velocity before the rotation, k is the angular acceleration before the rotation, and ω is the angular acceleration before the rotation. max Let n(t) be the theoretically stable angular velocity with full control, and f be the control angular velocity noise signal. bx (t) represents the acceleration of the fault signal equivalent to the X-axis of the load system, f by (t) represents the acceleration of the fault signal equivalent to the Y-axis of the load system, A ra The horizontal axis acceleration caused by the rapid rotation, To interfere with random phase, f ra The characteristic frequency of the fault signal;

[0030] 3) Construct a control start-stop jitter fault model, the expression of which is:

[0031]

[0032] In the formula, ω mo (t) represents the actual rotational modulation angular velocity, ω m The theoretical control rotational angular velocity, h(t) is the decaying jitter signal, n(t) is the control angular velocity noise signal, and t forwawd For the forward rotation time period, t reverse For the reverse rotation time period, c represents the attenuation coefficient, and f j This indicates the characteristic frequency of the jitter fault, and A0 represents the initial amplitude of the impact signal controlling the jitter angular velocity. For the initial phase of the interference, f bx (t) represents the acceleration of the fault signal equivalent to the X-axis of the load system, f by (t) represents the acceleration of the fault signal equivalent to the Y-axis of the load system, A sj To control the small acceleration of the horizontal axis caused by vibration, To interfere with random phase, The angle between the point of rotation stop and the horizontal accelerometer;

[0033] 4) Construct a bearing fault model, the expression of which is:

[0034]

[0035] In the formula, ω o (t) represents the signal generated by the bearing failure on the gyroscope, A0 is the initial amplitude of the angular velocity impact signal generated by the bearing failure, and f b Indicates the characteristic frequency of bearing failure. Let c represent the initial phase of the disturbance, c represent the attenuation coefficient, n(t) represent the control angular velocity noise signal, and f represent the initial phase of the disturbance. bx (t) represents the acceleration of the fault signal equivalent to the X-axis of the load system, f by (t) represents the acceleration of the fault signal equivalent to the Y-axis of the load system, A fb This refers to the small acceleration of the equivalent horizontal axis of the carrier caused by bearing failure. To interfere with random phase, This is the equivalent angle between the bearing failure point and the horizontal accelerometer.

[0036] Furthermore, the specific implementation steps of step S2 are as follows:

[0037] 201. Set the base of the rotating inertial navigation system to a stationary state, and set the trajectory of the indexing mechanism according to the actual rotation modulation path of the rotating inertial navigation system; substitute the motion information of the single-axis rotating inertial navigation system base into the rotating inertial navigation twin model, and obtain normal sample data through simulation.

[0038] 202. The fuzzy frequency fault simulation method is used to obtain different fault sample data. The steps are as follows: 1) Determine the sampling frequency of the rotating inertial navigation system and obtain the frequency band that can be covered in the frequency domain analysis according to the Nyquist sampling theorem; 2) Divide the frequency band into multiple frequency domain bands and take the median of each frequency domain band as the characteristic frequency domain; 3) Substitute the characteristic frequency domain of each frequency domain band into each fault model in turn to obtain the fault angular velocity data and fault acceleration data in each characteristic frequency domain.

[0039] S203. The three-axis signals from the gyroscope and accelerometer in the normal sample data and fault sample data are summed and simplified. The expression is as follows:

[0040]

[0041] In the formula, ω(t) is the output angular velocity of the three-axis gyroscope, ω(t)=[ω ox ω oy ω oz f(t) is the output acceleration of the triaxial accelerometer, f(t) = [f ox f oy f oz ].

[0042] Furthermore, in step S3, the fault diagnosis model of the single-axis rotary inertial navigation indexing mechanism includes a first preprocessing module, a second preprocessing module, a first convolutional neural network, a second convolutional neural network, a fully connected layer, and an output module;

[0043] The first and second preprocessing modules have the same structure, and are respectively connected to the gyroscope information output terminal and the accelerometer information output terminal; each preprocessing module converts the original time-domain signal into a two-dimensional color time-frequency diagram through continuous wavelet transform;

[0044] The inputs of the first and second convolutional neural networks are connected to the outputs of the first and second preprocessing modules, respectively. Each convolutional neural network consists of a first convolutional module, a first batch normalization module, a first activation module, a first pooling module, a second convolutional module, a second batch normalization module, a second activation module, a second pooling module, a third convolutional module, a third batch normalization module, a third activation module, and a third pooling module connected in sequence. The first convolutional module consists of eight filters connected in sequence, the second convolutional module consists of sixteen filters connected in sequence, and the third convolutional module consists of thirty-two filters connected in sequence. In each convolutional module, the filters use a convolutional layer with a 3×3 kernel and a stride of 1. Each activation module uses the ReLU activation function. Each pooling module uses a max-pooling layer with a pooling size of 2×2 and a stride of 2.

[0045] The fully connected layer is connected to the third pooling module of each of the two convolutional neural networks. It has five neurons to correspond to the output control jitter fault, control overrun fault, control stop jitter fault, bearing fault or normal; the output module consists of a softmax function layer and a classification output layer connected in sequence.

[0046] Furthermore, in the zero-shot pre-training and transfer learning-based few-shot training in step S4, the SGD optimizer is used, with a batch size of 128, a learning rate of 0.01, and the learning rate decreasing every 5 epochs at a rate of 0.9. The cross-entropy loss function is used.

[0047] Furthermore, in step S4, the amount of real samples used is 1% to 10% of the amount of sample data used in the zero-sample pre-training.

[0048] Compared with existing technologies, this method for fault diagnosis of single-axis rotating inertial navigation systems using a limited number of samples is designed based on digital twin technology and transfer learning technology. It utilizes digital twins to generate simulated fault samples and combines them with a small amount of actually collected fault data to complete the construction and training of the fault diagnosis model. This effectively alleviates the limitation of data scarcity on model training and improves the adaptability and accuracy of fault diagnosis in actual systems. Experimental verification shows that the fault discrimination accuracy of this method reaches 99.28%, and the accuracy 1σ error is less than 0.01%, confirming that the method has high precision and good practicality. Attached Figure Description

[0049] Figure 1 This is a flowchart of the method for diagnosing few-sample faults in a single-axis rotary inertial navigation indexing mechanism according to the present invention;

[0050] Figure 2(a) is a schematic diagram of the accelerometer signal of the normal sample obtained after step S1 in the embodiment of the present invention under different characteristic frequencies.

[0051] Figure 2(b) is a schematic diagram of the accelerometer signal under different characteristic frequencies of the control stop jitter fault obtained after step S1 in the embodiment of the present invention.

[0052] Figure 2(c) is a schematic diagram of the accelerometer signal obtained by step S1 of the present invention under different characteristic frequencies for bearing fault simulation.

[0053] Figure 2(d) is a schematic diagram of the accelerometer signal obtained by step S1 in the embodiment of the present invention under different characteristic frequencies.

[0054] Figure 2(e) is a schematic diagram of the accelerometer signal under different characteristic frequencies obtained by step S1 in the embodiment of the present invention;

[0055] Figure 3(a) is a schematic diagram of the gyroscope signal of the normal sample obtained after step S1 in the embodiment of the present invention under different characteristic frequencies.

[0056] Figure 3(b) is a schematic diagram of the gyroscope signal under different characteristic frequencies under the control stop jitter fault obtained after step S1 in the embodiment of the present invention.

[0057] Figure 3(c) is a schematic diagram of the gyroscope signal under different characteristic frequencies of the bearing fault obtained after step S1 in the embodiment of the present invention.

[0058] Figure 3(d) is a schematic diagram of the gyroscope signal under different characteristic frequencies obtained by step S1 in the embodiment of the present invention to illustrate the control jitter fault.

[0059] Figure 3(e) is a schematic diagram of the gyroscope signal under different characteristic frequencies under the control fly-through fault obtained after step S1 in the embodiment of the present invention.

[0060] Figure 4 In an embodiment of the present invention, continuous wavelet transform is used to... Figures 2(a) to 2(b) The diagram shown is a time-frequency graph obtained by converting the simulated bearing fault diagram.

[0061] Figure 5 This is a schematic diagram of the fault diagnosis model of a single-axis rotating inertial navigation indexing mechanism in an embodiment of the present invention;

[0062] Figure 6 This is a schematic diagram illustrating the principle of transfer learning in an embodiment of the present invention;

[0063] Figure 7 This is a schematic diagram illustrating fault classification and binary classification confusion based solely on the results of a zero-sample fault diagnosis task using gyroscope signals in an embodiment of the present invention.

[0064] Figure 8 This is a schematic diagram illustrating fault classification and binary classification confusion based solely on the results of a zero-sample fault diagnosis task using accelerometer signals in an embodiment of the present invention.

[0065] Figure 9 This is a schematic diagram illustrating fault classification and binary classification confusion based on the results of a zero-sample fault diagnosis task based on the fusion of gyroscope and accelerometer signals in an embodiment of the present invention.

[0066] Figure 10 This is a schematic diagram illustrating fault classification and binary classification confusion based solely on the results of a fault diagnosis task using only a few samples of accelerometer signals in an embodiment of the present invention.

[0067] Figure 11 This is a schematic diagram illustrating fault classification and binary classification confusion based on the results of a few-sample fault diagnosis task based on the fusion of gyroscope and accelerometer signals in an embodiment of the present invention;

[0068] Figure 12 This is a comparison chart showing the impact of transfer learning on the diagnostic performance of the model using different proportions of real samples in embodiments of the present invention.

[0069] Figure 13 This is a comparison chart showing the impact of the zero-sample training and transfer learning training methods of the present invention on the diagnostic performance of the model after training it with only a small number of real samples, as described in the embodiments of the present invention. Detailed Implementation

[0070] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, but the following embodiments are by no means intended to limit the present invention.

[0071] See Figure 1 The specific implementation steps of the method for diagnosing faults in a single-axis rotating inertial navigation system with few samples are described below.

[0072] S1. Construct a rotating inertial navigation twin model based on a single-axis rotating inertial navigation system, and four fault models based on control jitter fault, control overspeed fault, control stop jitter fault, and bearing fault, respectively.

[0073] Specifically, the implementation steps of step S1 are described as follows.

[0074] S101. Construct a rotating inertial navigation twin model based on a single-axis rotating inertial navigation system, including:

[0075]

[0076] In the formula, ω ox ω oy and ω oz These are the gyroscope outputs on the X, Y, and Z axes of a rotating inertial navigation system, respectively; K gx K gy and K gz These are the gyroscope scaling factors on the X, Y, and Z axes, respectively; γ xy γ is the gyroscope mounting error angle between the X and Y axes. xz γ is the gyroscope mounting error angle between the X and Z axes. yx γ is the gyroscope mounting error angle between the Y and X axes. yz γ is the gyroscope mounting error angle between the Y and Z axes. zx γ is the gyroscope mounting error angle between the Z-axis and X-axis. zy The gyroscope mounting error angle between the Z and Y axes; ω ix ω iy and ω iz These are the gyroscope inputs on the X, Y, and Z axes of a rotating inertial navigation system, respectively; ε x ε yand ε z These represent the gyroscope zero-bias errors on the X, Y, and Z axes of a rotating inertial navigation system, respectively; n gx n gy and n gz These represent the random noise errors of the gyroscope along the X, Y, and Z axes of a rotating inertial navigation system.

[0077]

[0078] In the formula, f ox f oy and f oz These are the accelerometer outputs on the X, Y, and Z axes of the rotating inertial navigation system, respectively; K ax K ay and K az These are the accelerometer scale factors on the X, Y, and Z axes, respectively; δ xy The accelerometer installation error angle between the X and Y axes, δ xz The accelerometer installation error angle between the X and Z axes, δ yx The accelerometer installation error angle between the Y-axis and X-axis, δ yz The accelerometer installation error angle between the Y and Z axes, δ zx The accelerometer installation error angle between the Z-axis and X-axis, δ zy The accelerometer installation error angle between the Z and Y axes; f ix f iy and f iz These are the accelerometer inputs on the X, Y, and Z axes of the rotating inertial navigation system, respectively. and These represent the accelerometer zero-bias errors on the X, Y, and Z axes of a rotating inertial navigation system, respectively; n ax n ay and n az These represent the random noise errors of the accelerometers on the X, Y, and Z axes of the rotating inertial navigation system, respectively.

[0079] In the input model of the rotating inertial navigation twin, the gyroscope inputs on the X, Y, and Z axes of the rotating inertial navigation system, i.e., ω ix ω iy and ω iz The expression is:

[0080]

[0081] In the output model of a rotating inertial navigation twin, the accelerometer inputs on the X, Y, and Z axes of the rotating inertial navigation system, i.e., f ix f iy and f iz The expression is:

[0082]

[0083] In the above two equations, Δγ is the roll installation error angle between the rotating frame of the rotating inertial navigation system and the inertial measurement unit, and Δθ is the pitch installation error angle between the rotating frame of the rotating inertial navigation system and the inertial measurement unit. ω is the reading of the encoder disk of the rotating frame of the rotating inertial navigation system. mo (t) represents the actual rotational modulation angular velocity. Let ω be the initial attitude angle of the rotating frame of the rotating inertial navigation system. bx ω by and ω bz These represent the angular velocities of the load system in the rotating inertial navigation system along the X, Y, and Z axes, respectively. bx f by and f bz These represent the accelerations along the X, Y, and Z axes of the rotating inertial navigation system, respectively.

[0084] S102. Construct a fault model.

[0085] There are four main types of fault states that may occur in rotating inertial navigation systems: control jitter fault, control overspeed fault, control stop jitter fault, and bearing fault. Therefore, a corresponding fault model is first constructed for each type of fault state.

[0086] (1) Construct a control jitter fault model.

[0087] The rotating inertial navigation system is driven by a motor and undergoes regular forward and reverse rotation modulation. The ideal rotational angular velocity is ω. mc When the control system is unstable, due to the integral action of the controller, the mean value of the control angular velocity and the control angle will fluctuate around the true value. Due to control jitter and mechanical error, a small acceleration excitation will be generated on the horizontal axis, which can be equivalent to a rapidly decaying disturbance acceleration on the horizontal axis of the carrier.

[0088] Based on this, a control jitter fault model is constructed, the expression of which is:

[0089]

[0090] In the formula, ω mo (t) represents the actual rotational modulation angular velocity, ω mc (t) represents the theoretical rotational modulation angular velocity, A c f is the amplitude of angular velocity jitter. c The frequency of the jitter. Let n(t) be the jitter phase, n(t) be the control angular velocity noise signal, and f be the phase jitter. bx (t) represents the fault signal equivalent to the X-axis acceleration of the load system, f by (t) represents the equivalent Y-axis acceleration of the load system due to the fault signal, A cjTo control the slight acceleration on the horizontal axis caused by vibration, c represents the damping coefficient. To interfere with random phase, To control the angle between the jitter point and the horizontal accelerometer.

[0091] (2) Construct a control flyaway fault model.

[0092] When the control system eventually becomes unstable, the rotational angular velocity of the rotating inertial navigation system will gradually increase from the initial indexing velocity to the maximum indexing velocity, possibly accompanied by control jitter; the maximum indexing velocity is approximately equal to the full control velocity. Similarly, due to mechanical errors, a control overrun fault can be equivalent to a small acceleration excitation on the horizontal axis outside the carrier, with the disturbance frequency depending on the rotational speed.

[0093] Based on this, a control overrun fault model is constructed, the expression of which is:

[0094]

[0095] In the formula, ω mo (t) represents the actual rotational modulation angular velocity, ω now ω is the modulation angular velocity before the rotation, k is the angular acceleration before the rotation, and ω is the angular acceleration before the rotation. max Let n(t) be the theoretically stable angular velocity with full control, and f be the control angular velocity noise signal. bx (t) represents the fault signal equivalent to the X-axis acceleration of the load system, f by (t) represents the equivalent Y-axis acceleration of the load system due to the fault signal, A ra The horizontal axis acceleration caused by the rapid rotation, To interfere with random phase, f ra The fault signal characteristic frequency is related to the rotational angular velocity.

[0096] (3) Construct a control start-stop jitter fault model.

[0097] During the forward and reverse switching process of rotation modulation in a rotating inertial navigation system, improper adjustment of control parameters or significant external interference may lead to jitter during angular velocity switching. Similarly, control jitter during rotation and stop can be equivalent to an external acceleration excitation on the horizontal axis of the carrier, but due to the slower signal attenuation, this signal lasts longer than jitter or bearing failure.

[0098] Based on this, a control stop jitter fault model is constructed, the expression of which is:

[0099]

[0100] In the formula, ω mo (t) represents the actual rotational modulation angular velocity, ω mThe theoretical control rotational angular velocity, h(t) is the decaying jitter signal, n(t) is the control angular velocity noise signal, and t forwawd For the forward rotation time period, t reverse For the reverse rotation time period, c represents the attenuation coefficient, and f j This indicates the characteristic frequency of the jitter fault, and A0 represents the initial amplitude of the impact signal controlling the jitter angular velocity. For the initial phase of the interference, f bx (t) represents the fault signal equivalent to the X-axis acceleration of the load system, f by (t) represents the equivalent Y-axis acceleration of the load system due to the fault signal, A sj To control the small acceleration of the horizontal axis caused by vibration, To interfere with random phase, The angle between the point of rotation stop and the horizontal accelerometer.

[0101] (4) Constructing a bearing fault model:

[0102] When a bearing fails, the faulty part will generate an impact signal with exponential decay characteristics. The rotating inertial navigation system will generate an exponentially decaying impulse signal of angular velocity and acceleration at the fault point.

[0103] Based on this, a bearing fault model is constructed, the expression of which is:

[0104]

[0105] In the formula, ω o (t) represents the signal generated by the bearing failure on the gyroscope, A0 is the initial amplitude of the angular velocity impact signal generated by the bearing failure, and f b Indicates the characteristic frequency of bearing failure. Let c represent the initial phase of the disturbance, c represent the attenuation coefficient, n(t) represent the control angular velocity noise signal, and f represent the initial phase of the disturbance. bx (t) represents the fault signal equivalent to the X-axis acceleration of the load system, f by (t) represents the equivalent Y-axis acceleration of the load system due to the fault signal, A fb This refers to the small acceleration of the equivalent horizontal axis of the carrier caused by bearing failure. To interfere with random phase, This is the equivalent angle between the bearing failure point and the horizontal accelerometer.

[0106] S2. Based on the rotating inertial navigation twin model constructed in step S101, normal sample data is obtained through simulation. Then, based on the normal sample data, different fault sample data are obtained by superimposing different fault models constructed in step S102 to construct a simulation fault database.

[0107] The specific implementation steps of step S2 are described below.

[0108] S201. Based on the rotational inertial navigation modulation strategy, set the rotational speed of the single-axis rotational inertial navigation around the celestial axis, as well as the periodic rotation angles of forward and reverse rotation, to simulate and obtain normal sample data.

[0109] Specifically, in this embodiment, the simulation steps for normal sample data are as follows:

[0110] (1) Set the base of the rotating inertial navigation system to a stationary state, and set the trajectory of the indexing mechanism according to the actual rotation modulation path of the rotating inertial navigation: the single-axis rotating inertial navigation rotates 360° around the celestial axis at a forward rotation speed of 12° / s, and then rotates in the reverse direction, repeating the cycle.

[0111] (2) Due to factors such as the rotation mechanism, gravity field and Earth's rotation angular velocity, different rotations of the rotation mechanism will lead to different IMU outputs. Therefore, the IMU output obtained through the above steps (1) is substituted into the rotating inertial navigation twin model to obtain the normal IMU output under different rotation conditions, that is, the simulation obtains normal sample data.

[0112] S202. Based on the normal sample data obtained from the simulation in step S201, different fault sample data are obtained by sequentially superimposing different fault models.

[0113] Since fault characteristic frequencies are difficult to calculate and estimate at the system level, a fuzzy frequency simulation method is used to cover normal sample data as much as possible, thereby simulating fault sample data corresponding to different fault types. Specifically, the noise characteristics of the simulated gyroscope and accelerometer are generated from actual data to obtain relevant noise parameters.

[0114] In this step, different fault sample data are obtained using the fuzzy frequency fault simulation method. Specifically, the operation steps of the fuzzy frequency fault simulation method are as follows: 1) Determine the sampling frequency of the rotating inertial navigation system so as to obtain the frequency band that can be covered in the frequency domain analysis according to the Nyquist sampling theorem; 2) Divide the frequency band into multiple frequency domain bands and take the median of each frequency domain band as the characteristic frequency domain; 3) Substitute the characteristic frequency domain of each frequency domain band into each fault model in turn to obtain the fault angular velocity data and fault acceleration data in each characteristic frequency domain.

[0115] This embodiment uses the simulation process of bearing fault data as an example for detailed explanation. The sampling frequency of the rotating inertial navigation system is 50Hz. According to the Nyquist sampling theorem, wavelet transform is performed on the time-frequency domain to obtain a time-frequency diagram covering the frequency band [0,25]Hz in the frequency domain. This frequency band is divided into five frequency bands, each with a bandwidth of 5Hz, and the median value of each frequency band is taken for characteristic frequency domain simulation. Furthermore, by setting the characteristic frequencies of bearing faults to 2.5Hz, 7.5Hz, 12.5Hz, 17.5Hz, and 22.5Hz, fuzzy simulation of bearing faults at multiple frequencies is achieved.

[0116] In this invention, the fuzzy frequency simulation method solves the current problems of difficulty in obtaining and updating detailed dynamic parameters of the indexing mechanism at the system level, difficulty in calculating and estimating typical fault characteristic frequencies, and the problem that objectively existing control error uncertainties can also lead to fault characteristic frequencies of different control systems, thus realizing the acquisition of effective data.

[0117] S203. Considering the form of the three-axis gyroscope and accelerometer information output synchronously by the rotating inertial navigation system, directly using it for feature processing may lead to an overly complex subsequent fault or state discrimination network structure. Therefore, the three-axis signals of the gyroscope and accelerometer in the normal sample data and fault sample data are summed respectively, so that the simplified data can be used for feature processing, thereby better mining the three-axis information features of the gyroscope and accelerometer.

[0118] Specifically, the expression for step S203 is:

[0119]

[0120] In the formula, ω(t) is the output angular velocity of the three-axis gyroscope, ω(t)=[ω ox ω oy ω oz f(t) is the output acceleration of the triaxial accelerometer, f(t) = [f ox f oy f oz ].

[0121] like Figures 2(a) to 2(e) The figures show accelerometer signal diagrams obtained through the above steps under different characteristic frequencies for normal samples, control stop jitter faults, bearing faults, control jitter faults, and control overspeed faults. In each accelerometer signal diagram, the top and bottom images show the signal diagrams of normal or fault samples at five frequencies: 2.5Hz, 7.5Hz, 12.5Hz, 17.5Hz, and 22.5Hz. As can be seen from the figures, in addition to the normal samples, the above simulation method can also generate and cover the accelerometer characteristic signals caused by typical faults in a single-axis rotating inertial navigation system.

[0122] like Figures 3(a) to 3(e) The figures show schematic diagrams of gyroscope signals obtained through the above steps under different characteristic frequencies for normal samples, control stop jitter faults, bearing faults, control jitter faults, and control overspeed faults. In each gyroscope signal diagram, the signals from top to bottom are those of normal or fault samples at five frequencies: 2.5Hz, 7.5Hz, 12.5Hz, 17.5Hz, and 22.5Hz. As can be seen from the figures, in addition to the normal samples, the above simulation method can also generate and cover the gyroscope characteristic signals caused by typical faults in a single-axis rotating inertial navigation system.

[0123] S3. Construct a fault diagnosis model for a single-axis rotating inertial navigation indexing mechanism. It uses two convolutional neural networks to perform time-frequency analysis on gyroscope and accelerometer information respectively, and then fuses the processed information to output the diagnosis results.

[0124] Specifically, see Figure 5 The fault diagnosis model for a single-axis rotating inertial navigation system includes a first preprocessing module, a second preprocessing module, a first convolutional neural network, a second convolutional neural network, a fully connected layer, and an output module; among which,

[0125] The first and second preprocessing modules have the same structure, with the gyroscope information output terminal and the accelerometer information output terminal connected respectively. Each preprocessing module performs time-frequency analysis on the input raw time-domain signal through continuous wavelet transform (CWT) to convert the one-dimensional vibration signal into a two-dimensional color time-frequency image, which is then used as input information for a convolutional neural network to extract more effective fault features and achieve a good balance between time-domain and frequency-domain resolution. In this embodiment, the preprocessing module is configured to convert the raw time-domain signal into a 156×190×3 color image.

[0126] like Figure 4 The image shows the application of continuous wavelet transform to... Figures 2(a) to 2(e) The diagram shown is a time-frequency plot obtained by converting the simulated bearing fault diagram. (See also...) Figure 4 The five images in the figure, from left to right, are time-frequency images with characteristic frequencies of 2.5Hz, 7.5Hz, 12.5Hz, 17.5Hz and 22.5Hz, respectively. The figure shows that the fuzzy simulation method can cover the characteristic frequency band (vertical axis) of the fault time-frequency map of the rotating inertial navigation system's indexing mechanism under the condition of unknown fault characteristic frequencies. The fault time-domain feature points can be expanded and covered by signal sliding windows.

[0127] The input terminals of the first convolutional neural network and the second convolutional neural network are respectively connected to the output terminals of the first preprocessing module and the second preprocessing module to process the time-frequency image obtained based on gyroscope information conversion and the time-frequency image obtained based on accelerometer information conversion, respectively. Each convolutional neural network consists of a first convolutional module, a first batch normalization module, a first activation module, a first pooling module, a second convolutional module, a second batch normalization module, a second activation module, a second pooling module, a third convolutional module, a third batch normalization module, a third activation module, and a third pooling module connected in sequence. The first convolutional module consists of eight filters connected in sequence, the second convolutional module consists of sixteen filters connected in sequence, and the third convolutional module consists of thirty-two filters connected in sequence. In each convolutional module, the filters use a 3×3 convolutional layer with a stride of 1. The batch normalization module, also known as the BN module, is used in the convolutional neural network to improve training efficiency and stability. The first, second, and third activation modules all use the ReLU activation function. The first, second, and third pooling modules all use a 2×2 max-pooling layer with a stride of 2.

[0128] The fully connected layer is connected to the output of the third pooling module of the first convolutional neural network and the output of the third pooling module of the second convolutional neural network, respectively. The fully connected layer has five neurons to output the results of the fault diagnosis model of the single-axis rotating inertial navigation system. Specifically, the five neurons correspond to five fault diagnosis categories, namely, control jitter fault, control overspeed fault, control stop jitter fault, bearing fault, and normal.

[0129] The output module consists of a softmax function layer and a classification output layer connected in sequence. The softmax function layer is used to output probabilities, and the classification output layer is used to find the class with the highest probability among the output probabilities and output it.

[0130] The fault diagnosis model for this single-axis rotating inertial navigation system employs two convolutional neural networks. By processing the output information from the gyroscope and the accelerometer separately and then fusing them for judgment, the model helps to improve the accuracy and robustness of fault diagnosis, thus achieving more effective fault diagnosis.

[0131] S4. First, the fault diagnosis model of the single-axis rotating inertial navigation system constructed in step S3 is pre-trained with zero samples using the simulation fault database constructed in step S2. Then, the fault diagnosis model of the single-axis rotating inertial navigation system constructed in step S3 is trained with a small number of samples based on transfer learning using a small number of real samples.

[0132] This invention addresses the problem that fault data for rotating inertial navigation (INS) indexing mechanisms is often scarce or difficult to collect, resulting in a limited training set for fault diagnosis. To reduce reliance on real fault samples, this invention designs a pre-training method. After constructing a fault diagnosis model for a single-axis rotating INS indexing mechanism, fault mode simulation is first performed based on a digital twin model. This simulated fault data allows fault knowledge to be transferred to the rotating INS output under various fault modes, enabling the model to pre-train and essentially distinguish time-frequency map samples of different rotating INS system faults. Then, transfer learning is used to further train the model with a small number of real samples, ensuring accurate fault diagnosis capabilities.

[0133] The specific implementation steps of step S4 are as follows:

[0134] S401. Using the simulation fault database constructed in step S2, perform zero-sample fault diagnosis pre-training on the fault diagnosis model of the single-axis rotating inertial navigation indexing mechanism.

[0135] In step S401, pre-training is performed using an NVIDIA GeForce RTX 4070Ti Super platform with the SGD optimizer set to a batch size of 128 and a learning rate of 0.01. The learning rate decreases every 5 epochs at a rate of 0.9, and the loss function is the cross-entropy loss function.

[0136] S402. Based on the zero-sample fault diagnosis pre-training, further combine a small number of real samples to carry out few-sample fault diagnosis training based on transfer learning.

[0137] Transfer learning is a method that improves performance by transferring known knowledge or experience from a source domain to a target domain, using the rich data and pre-trained models in the source domain to compensate for the lack of data in the target domain.

[0138] See Figure 6 In this step, the specific method of transfer learning is as follows: the current parameters of the first and second convolutional neural networks after pre-training are frozen, and the fully connected layer of the fault diagnosis model of the single-axis rotating inertial navigation system is trained using a small amount of real fault data to realize transfer learning from the digital twin source domain to the physical entity fault target domain, thereby further improving the accuracy of the single-axis rotating inertial navigation system fault diagnosis model in outputting fault diagnosis results.

[0139] Specifically, the training method for this few-sample fault diagnosis is the same as step S401, and during the training process, the amount of real samples used is 1% to 10% of the amount of simulated samples used in the pre-training.

[0140] After the above steps S1 to S4, the fault diagnosis model can be put into actual fault diagnosis of the indexing mechanism. Specifically, the IMU component signal output in real time by the single-axis rotary inertial navigation system is input into the trained fault diagnosis model according to the set method, so as to realize continuous fault diagnosis of the indexing mechanism during operation.

[0141] The method of the present invention was further applied to a real single-axis rotating inertial navigation system to verify the effectiveness of the method and the accuracy of fault diagnosis through experiments.

[0142] In this experimental verification, the experimental platform adopts a single-axis rotating inertial navigation system, which includes a three-axis quartz flexible accelerometer, a three-axis fiber optic gyroscope, a rotation mechanism assembly (including a motor, angle encoder disk, and bearings), and corresponding mechanical structures. The zero-bias stability of the gyroscope and accelerometer is 0.005° / h and 20μg, respectively. The inertial measurement unit is driven by the rotation mechanism to perform regular rotation modulation, rotating forward and backward at a speed of 12° / s without interval, rotating 360° (30s) forward and 360° (30s) backward, and acquiring system data at a sampling rate of 50Hz.

[0143] This experiment uses 2s of time-domain data (a total of 100 sampling points) for wavelet transform to generate a time-frequency graph. At the same time, during the experiment, the pre-training dataset generated by the simulation and the dataset collected by the actual system are classified and coded, as shown in Table 1 below.

[0144] Table 1:

[0145] Data categories normal Control and stop bearing failure Controlling jitter spinning Label 0 1 2 3 4 Simulation pre-training sample number 1000 1000 1000 1000 1000 Actual number of samples collected 1500 1500 1500 1500 831

[0146] It should be noted that, regarding the simulation pre-training samples and actual collected samples shown in Table 1, in the actual pre-training process of the fault diagnosis model of the single-axis rotating inertial navigation system, 80% of the simulation pre-training samples were used as the training set and 20% as the test set; while in the sample transfer learning training process of the fault diagnosis model of the single-axis rotating inertial navigation system, only 1% to 10% of the actual collected samples in the pre-training were used to complete the transfer learning training, and the remaining actual collected samples were used to test the effect.

[0147] First, zero-shot fault diagnosis pre-training was performed on the fault diagnosis model of the single-axis rotating inertial navigation system. Specifically, the zero-shot fault diagnosis experiment used a digital twin model of the single-axis rotating inertial navigation system to generate fault samples. The signals from the gyroscope and accelerometer were obtained through simulation, and the fault discrimination network of the fault diagnosis model of the single-axis rotating inertial navigation system was trained.

[0148] like Figure 7The diagram shows the fault classification and binary classification confusion based solely on the results of a fault diagnosis task using zero samples of gyroscope signals. Figure 7 The four parts from left to right are: a percentage diagram of the confusion matrix of all categories of gyroscope signal samples, a diagram of the number of samples in the confusion matrix of all categories of gyroscope signal samples, a diagram of the percentage of the confusion matrix of normal / faulty gyroscope signal samples, and a diagram of the number of samples in the confusion matrix of normal / faulty gyroscope signal samples.

[0149] like Figure 8 The diagram shows the fault classification and binary classification confusion based solely on the results of a fault diagnosis task using zero-sample accelerometer signals. Figure 8 The four parts from left to right are: a percentage diagram of the full-class confusion matrix of accelerometer signal samples, a diagram of the number of samples in the full-class confusion matrix of accelerometer signal samples, a diagram of the percentage of the binary confusion matrix of normal / faulty accelerometer signal samples, and a diagram of the number of samples in the binary confusion matrix of normal / faulty accelerometer signal samples.

[0150] like Figure 9 The diagram shows the fault classification and binary classification confusion of the zero-sample fault diagnosis task results based on the fusion signals of gyroscope and accelerometer. Figure 9 The four parts from left to right are: a percentage diagram of the full-class confusion matrix of the fused signal samples, a diagram of the number of samples in the full-class confusion matrix of the fused signal samples, a diagram of the percentage of the binary confusion matrix of normal / faulty samples of the fused signal, and a diagram of the number of samples in the binary confusion matrix of normal / faulty samples of the fused signal.

[0151] from Figures 7-9 The three cases shown are the results obtained based on gyroscope signals only (without accelerometer signal input), accelerometer signals only (without gyroscope signal input), and gyroscope-accelerometer signal fusion. It can be seen that in the model training results based on zero samples, typical faults exhibit unclear class boundaries in both the accelerometer signal only and fused signal cases, while the recognition effect of typical faults is better in the case of gyroscope signals only.

[0152] Next, based on the pre-training, a small-sample transfer learning training was performed on the fault diagnosis model of the single-axis rotating inertial navigation system using real samples. The amount of real samples used in the transfer learning training was 10% of the simulation samples. After training, the fault classification and binary classification confusion map results are as follows. Figures 10-11 As shown.

[0153] like Figure 10 The diagram shows the fault classification and binary classification confusion in a fault diagnosis task based solely on a few samples of accelerometer signals. Figure 10 The four parts from left to right are: a percentage diagram of the full-class confusion matrix of accelerometer signal samples, a diagram of the number of samples in the full-class confusion matrix of accelerometer signal samples, a diagram of the percentage of the binary confusion matrix of normal / faulty accelerometer signal samples, and a diagram of the number of samples in the binary confusion matrix of normal / faulty accelerometer signal samples.

[0154] like Figure 11 The diagram shows the fault classification and binary classification confusion of the few-sample fault diagnosis task based on the fusion signals of gyroscope and accelerometer. Figure 11 The four parts from left to right are: a percentage diagram of the full-class confusion matrix of the fused signal samples, a diagram of the number of samples in the full-class confusion matrix of the fused signal samples, a diagram of the percentage of the binary confusion matrix of normal / faulty samples of the fused signal, and a diagram of the number of samples in the binary confusion matrix of normal / faulty samples of the fused signal.

[0155] from Figures 10-11 The diagram shows the results obtained using only accelerometer signals (without gyroscope signal input) and the fusion method based on gyroscope and accelerometer signals. It can be seen that after further training with fewer samples, typical faults exhibit clearer category boundaries when using fused signals, which is significantly better than typical faults using only accelerometer signals. This demonstrates that when a certain number of real samples are available for transfer learning, fused signals can significantly improve the accuracy and robustness of the model's diagnostic results.

[0156] As above Figures 7-11 The single test results shown represent the accuracy error distribution of the sample tests under different conditions. To verify the stability of this fault diagnosis method, Table 2 below shows the results of seven repeated tests for each method.

[0157] Table 2:

[0158]

[0159] In Table 2, under the test conditions, "gyroscope signal" refers to a method that uses only gyroscope signals for fault identification; "accelerometer signal" refers to a method that uses only accelerometer signals for fault identification; "accelerometer and gyroscope signal fusion" refers to a method that uses both gyroscope and accelerometer signals for fault identification; "zero samples" means that the model is pre-trained only, and during the pre-training process, 80% of the simulation samples shown in Table 1 are used as the training set and 20% as the test set, and after training, the model is directly tested using real samples; "few samples" means that, based on the above pre-training, the model is further trained using 10% of the real samples shown in Table 1, and the model is tested using the remaining real samples; "class accuracy" refers to the accuracy of the trained model in correctly identifying whether a signal is normal or faulty and the fault type under different test conditions; "health fault classification accuracy" refers to the accuracy of the trained model in identifying whether a signal is normal or faulty under different test conditions.

[0160] As shown in Table 2, under zero-sample conditions, the fault diagnosis accuracy based on gyroscope signals reaches 83.92%, and the fault binary classification accuracy reaches 96.86%, demonstrating the usability of zero-sample fault diagnosis based on the twin model and fuzzy frequency fault simulation method. Furthermore, based on 10% of the samples, transfer learning based on signal fusion achieves a fault discrimination accuracy of 99.28%, with an accuracy 1σ error of less than 0.01%, proving that the fault diagnosis method based on signal fusion and transfer learning effectively improves robustness.

[0161] To further verify the impact of the amount of real samples used in the method of this invention on the training results of transfer learning, while keeping the zero-sample training conditions the same, real samples of 1%, 2%, 3%, 4%, 5%, 6%, 7%, 8%, 9%, and 10% of the amount of simulated data samples were randomly extracted in sequence, and transfer learning training was performed on each sample. The accuracy and effectiveness of the model in fault identification after completing the transfer learning training were verified under different proportions of real samples.

[0162] like Figure 12 The figure shows a comparison of the impact of different proportions of real samples on the model's diagnostic performance during transfer learning. In the figure, the red line represents the accuracy curve of the model's judgment of normal and fault outcomes, while the blue line represents the accuracy curve of the model's judgment of normal and five specific fault types. The results show that using 1% real samples for transfer learning achieves a 95% accuracy rate in identifying specific fault types, effectively verifying the accuracy and effectiveness of the zero-sample training and few-sample training method of this invention for fault diagnosis. When the amount of real samples is increased to 10%, the accuracy rate of specific fault type identification approaches 100%.

[0163] like Figure 13 The figure shows a comparison of the diagnostic performance of the zero-shot training and transfer learning training methods of this invention versus training the model using only a small number of real samples. In the figure, the red line represents the accuracy curve of the five possible outcomes (normal and specific fault types) using the method of this invention, while the blue line represents the accuracy curve of the five possible outcomes (normal and specific fault types) after training the model constructed in step S3 directly using only a small number of real samples. The results show that the two methods are compared using the mean ± standard deviation of accuracy. The midpoint of the error bar represents the mean accuracy, and the error bar represents the standard deviation of accuracy. Under different proportions of real samples, the diagnostic accuracy of the method of this invention is significantly better than that of the data-driven method, further validating the effectiveness of the proposed method.

[0164] The parts of this invention not disclosed in detail are well-known in the art. Although illustrative specific embodiments of the invention have been described above to help those skilled in the art understand the invention, it should be understood that the invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the invention as defined and determined by the appended claims, and all inventions utilizing the concept of this invention are protected.

Claims

1. A method for diagnosing faults in a single-axis rotary inertial navigation system with a limited number of samples, characterized in that, The steps are as follows: S1. Construct a rotating inertial navigation twin model based on a single-axis rotating inertial navigation system, and four fault models based on control jitter fault, control overspeed fault, control stop jitter fault and bearing fault respectively. S2. Based on the rotating inertial navigation twin model, normal sample data is obtained through simulation. Then, based on the normal sample data, different fault models are superimposed to obtain different fault sample data through simulation. A simulation fault database is constructed, which includes normal sample data and different fault sample data obtained from simulation. S3. Construct a fault diagnosis model for a single-axis rotating inertial navigation indexing mechanism. It uses two convolutional neural networks to perform time-frequency analysis on gyroscope information and accelerometer information respectively, and then fuses the processed information to output the diagnosis results. S4. First, a zero-sample pre-training of the fault diagnosis model of the single-axis rotating inertial navigation indexing mechanism is performed using a simulated fault database. Then, a small number of real samples are combined to perform a few-sample training of the fault diagnosis model of the single-axis rotating inertial navigation indexing mechanism based on transfer learning. S5. Input the IMU component signal output in real time from the single-axis rotating inertial navigation system into the trained fault diagnosis model to diagnose the fault of the indexing mechanism.

2. The method for diagnosing faults in a single-axis rotating inertial navigation system with few samples according to claim 1, characterized in that, In step S1, the rotating inertial navigation twin model based on the single-axis rotating inertial navigation system is as follows: In the formula, ω ox ω oy and ω oz These are the gyroscope outputs on the X, Y, and Z axes of a rotating inertial navigation system, respectively; K gx K gy and K gz These are the gyroscope scaling factors on the X, Y, and Z axes, respectively; γ xy γ is the gyroscope mounting error angle between the X and Y axes. xz γ is the gyroscope mounting error angle between the X and Z axes. yx γ is the gyroscope mounting error angle between the Y and X axes. yz γ is the gyroscope mounting error angle between the Y and Z axes. zx γ is the gyroscope mounting error angle between the Z-axis and X-axis. zy The gyroscope mounting error angle between the Z and Y axes; ω ix ω iy and ω iz These are the gyroscope inputs on the X, Y, and Z axes of a rotating inertial navigation system, respectively; ε x ε y and ε z These represent the gyroscope zero-bias errors on the X, Y, and Z axes of a rotating inertial navigation system, respectively; n gx n gy and n gz These represent the random noise errors of the gyroscope along the X, Y, and Z axes of a rotating inertial navigation system, respectively. In the formula, f ox f oy and f oz These are the accelerometer outputs on the X, Y, and Z axes of the rotating inertial navigation system, respectively; K ax K ay and K az These are the accelerometer scale factors on the X, Y, and Z axes, respectively; δ xy The accelerometer installation error angle between the X and Y axes, δ xz The accelerometer installation error angle between the X and Z axes, δ yx The accelerometer installation error angle between the Y-axis and X-axis, δ yz The accelerometer installation error angle between the Y and Z axes, δ zx The accelerometer installation error angle between the Z-axis and X-axis, δ zy The accelerometer installation error angle between the Z and Y axes; f ix f iy and f iz These are the accelerometer inputs on the X, Y, and Z axes of the rotating inertial navigation system, respectively. and These represent the accelerometer zero-bias errors on the X, Y, and Z axes of a rotating inertial navigation system, respectively; n ax n ay and n az These represent the random noise errors of the accelerometers on the X, Y, and Z axes of the rotating inertial navigation system, respectively. The gyroscope input expressions for the X, Y, and Z axes in the rotating inertial navigation system are as follows: The accelerometer input expressions for the X, Y, and Z axes in a rotating inertial navigation system are: In the above two equations, Δγ is the roll installation error angle between the rotating frame of the rotating inertial navigation system and the inertial measurement unit, and Δθ is the pitch installation error angle between the rotating frame of the rotating inertial navigation system and the inertial measurement unit. ω is the reading of the encoder disk of the rotating frame of the rotating inertial navigation system. mo (t) represents the actual rotational modulation angular velocity. Let ω be the initial attitude angle of the rotating frame of the rotating inertial navigation system. bx ω by and ω bz These represent the angular velocities of the load system in the rotating inertial navigation system along the X, Y, and Z axes, respectively. bx f by and f bz These represent the accelerations of the load system in the rotating inertial navigation system along the X, Y, and Z axes, respectively.

3. The method for diagnosing faults in a single-axis rotating inertial navigation system with few samples according to claim 1, characterized in that, In step S1, the four fault models are: (1) Construct a control jitter fault model, the expression of which is: In the formula, ω mo (t) represents the actual rotational modulation angular velocity, ω mc (t) represents the theoretical rotational modulation angular velocity, A c f is the amplitude of angular velocity jitter. c The frequency of the jitter. Let n(t) be the jitter phase, n(t) be the control angular velocity noise signal, and f be the phase jitter. bx (t) represents the acceleration of the fault signal equivalent to the X-axis of the load system, f by (t) represents the acceleration of the fault signal equivalent to the Y-axis of the load system, A cj To control the slight acceleration on the horizontal axis caused by vibration, c represents the damping coefficient. To interfere with random phase, To control the angle between the jitter point and the horizontal accelerometer; 2) Construct a control overrun fault model, the expression of which is: In the formula, ω mo (t) represents the actual rotational modulation angular velocity, ω now ω is the modulation angular velocity before the rotation, k is the angular acceleration before the rotation, and ω is the angular acceleration before the rotation. max Let n(t) be the theoretically stable angular velocity with full control, and f be the control angular velocity noise signal. bx (t) represents the acceleration of the fault signal equivalent to the X-axis of the load system, f by (t) represents the acceleration of the fault signal equivalent to the Y-axis of the load system, A ra The horizontal axis acceleration caused by the rapid rotation, To interfere with random phase, f ra The characteristic frequency of the fault signal; 3) Construct a control start-stop jitter fault model, the expression of which is: In the formula, ω mo (t) represents the actual rotational modulation angular velocity, ω m The theoretical control rotational angular velocity, h(t) is the decaying jitter signal, n(t) is the control angular velocity noise signal, and t forwawd For the forward rotation time period, t reverse For the reverse rotation time period, c represents the attenuation coefficient, and f j This indicates the characteristic frequency of the jitter fault, and A0 represents the initial amplitude of the impact signal controlling the jitter angular velocity. For the initial phase of the interference, f bx (t) represents the acceleration of the fault signal equivalent to the X-axis of the load system, f by (t) represents the acceleration of the fault signal equivalent to the Y-axis of the load system, A sj To control the small acceleration of the horizontal axis caused by vibration, To interfere with random phase, The angle between the point of rotation stop and the horizontal accelerometer; 4) Construct a bearing fault model, the expression of which is: In the formula, ω o (t) represents the signal generated by the bearing failure on the gyroscope, A0 is the initial amplitude of the angular velocity impact signal generated by the bearing failure, and f b Indicates the characteristic frequency of bearing failure. Let c represent the initial phase of the disturbance, c represent the attenuation coefficient, n(t) represent the control angular velocity noise signal, and f represent the initial phase of the disturbance. bx (t) represents the acceleration of the fault signal equivalent to the X-axis of the load system, f by (t) represents the acceleration of the fault signal equivalent to the Y-axis of the load system, A fb This refers to the small acceleration of the equivalent horizontal axis of the carrier caused by bearing failure. To interfere with random phase, This is the equivalent angle between the bearing failure point and the horizontal accelerometer.

4. The method for diagnosing faults in a single-axis rotary inertial navigation system according to claim 1, characterized in that, The specific implementation steps of step S2 are as follows:

201. Set the base of the rotating inertial navigation system to a stationary state, and set the trajectory of the indexing mechanism according to the actual rotation modulation path of the rotating inertial navigation system; substitute the motion information of the single-axis rotating inertial navigation system base into the rotating inertial navigation twin model, and obtain normal sample data through simulation.

202. The fuzzy frequency fault simulation method is used to obtain different fault sample data. The steps are as follows: 1) Determine the sampling frequency of the rotating inertial navigation system and obtain the frequency band that can be covered in the frequency domain analysis according to the Nyquist sampling theorem; 2) Divide the frequency band into multiple frequency domain bands and take the median of each frequency domain band as the characteristic frequency domain; 3) Substitute the characteristic frequency domain of each frequency domain band into each fault model in turn to obtain the fault angular velocity data and fault acceleration data in each characteristic frequency domain. S203. The three-axis signals from the gyroscope and accelerometer in the normal sample data and fault sample data are summed and simplified. The expression is as follows: ω(t)=ω ox (t)+ω oy (t)+ω oz (t) f(t)=f ox (t)+f oy (t)+f oz (t), In the formula, ω(t) is the output angular velocity of the three-axis gyroscope, ω(t)=[ω ox ω oy ω oz f(t) is the output acceleration of the triaxial accelerometer, f(t) = [f ox f oy f oz ].

5. The method for diagnosing faults in a single-axis rotating inertial navigation system with few samples according to claim 1, characterized in that, In step S3, the fault diagnosis model of the single-axis rotary inertial navigation indexing mechanism includes a first preprocessing module, a second preprocessing module, a first convolutional neural network, a second convolutional neural network, a fully connected layer, and an output module; The first and second preprocessing modules have the same structure, and are respectively connected to the gyroscope information output terminal and the accelerometer information output terminal; each preprocessing module converts the original time-domain signal into a two-dimensional color time-frequency diagram through continuous wavelet transform; The inputs of the first and second convolutional neural networks are connected to the outputs of the first and second preprocessing modules, respectively. Each convolutional neural network consists of a first convolutional module, a first batch normalization module, a first activation module, a first pooling module, a second convolutional module, a second batch normalization module, a second activation module, a second pooling module, a third convolutional module, a third batch normalization module, a third activation module, and a third pooling module connected in sequence. The first convolutional module consists of eight filters connected in sequence, the second convolutional module consists of sixteen filters connected in sequence, and the third convolutional module consists of thirty-two filters connected in sequence. In each convolutional module, the filters use a convolutional layer with a 3×3 kernel and a stride of 1. Each activation module uses the ReLU activation function. Each pooling module uses a max-pooling layer with a pooling size of 2×2 and a stride of 2. The fully connected layer is connected to the third pooling module of each of the two convolutional neural networks. It has five neurons to output jitter fault, overspeed fault, stop jitter fault, bearing fault or normal. The output module consists of a softmax function layer and a classification output layer connected in sequence.

6. The method for diagnosing faults in a single-axis rotating inertial navigation system with few samples according to claim 1, characterized in that, In step S4, the zero-shot pre-training and transfer learning-based few-shot training use the SGD optimizer with a batch size of 128, a learning rate of 0.01, and a decrease in the learning rate of 0.9 every 5 epochs. The cross-entropy loss function is used.

7. The method for diagnosing faults in a single-axis rotary inertial navigation system according to claim 1, characterized in that, In step S4, the amount of real samples used is 1% to 10% of the amount of sample data used in the zero-sample pre-training.

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