An inertial measurement unit slow drift fault detection method and system in a dynamic environment and a storage medium

Abstract

This application discloses a method, system, and storage medium for detecting slowly varying faults in inertial measurement units (IMUs) under dynamic environments. Addressing the technical challenges of difficult identification, high false alarm rates, and missed alarm rates in IMUs, this application introduces a Gaussian process regression model and a particle swarm optimization (PSO) algorithm for multidimensional feature estimation of the IMU. A dynamic envelope model of the normal signal is constructed using the Gaussian process regression model, and the PSO algorithm is used to optimize the multidimensional statistical feature thresholds within the envelope. This achieves high-precision detection of slowly varying faults without the need for fault data, making it suitable for scenarios with small data volumes and high noise levels. Experiments demonstrate that this method can meet the diagnostic needs of various IMU faults, can be applied to different types of IMUs, exhibits better generalization ability, and has higher fault diagnosis accuracy.

Description

Technical Field

[0001] This application relates to an inertial system fault detection system and method, belonging to the field of inertial navigation, and particularly to a method, system and storage medium for detecting slowly changing faults in an inertial measurement unit under dynamic environments. Background Technology

[0002] The electrical system is responsible for the rocket's flight control, navigation, and communication. It acquires flight data in real time using high-precision sensors to adjust its flight attitude and trajectory, preventing deviations from the predetermined path. The electrical systems of large launch vehicles are modular, integrated, and modular; their stability and reliability determine the success of the launch mission. Therefore, the electrical system must possess high fault tolerance and fault detection capabilities.

[0003] An inertial navigation system (INS) is a crucial component of an electrical system. It utilizes inertial measurement units (IMUs) to measure the angular velocity, acceleration, and other information of the carrier, and can calculate the current velocity, position, and attitude based on initial conditions. INS does not rely on external signals and is an autonomous navigation system, widely used in rockets, satellites, and unmanned aerial vehicles (UAVs). The most commonly used INS on rockets is the strapdown inertial navigation system (SINS), which directly mounts gyroscopes and accelerometers to the carrier, offering advantages such as small size, low cost, and high performance. Current launch vehicles often employ redundant strapdown inertial navigation systems, installing multiple IMUs in an orthogonal or oblique configuration. Common configurations include three sets of six-meter redundancy, a single unit with ten-meter redundancy, and dodecahedral redundancy. As rocket flight time increases, IMUs experience functional degradation and parameter drift due to component aging. In the initial stages of slowly varying faults such as sensor drift, the signal changes are weak, and traditional fixed threshold methods (such as the 3σ criterion) are easily affected by noise, resulting in a high false alarm rate. Therefore, commonly used threshold-based fault diagnosis methods are difficult to identify such slowly varying faults. The gradual accumulation of slowly varying faults will affect the measurement accuracy of the IMU, thereby contaminating navigation information and causing rocket flight instability. Therefore, IMU fault diagnosis is of great significance for ensuring the safety and stability of the rocket's electrical system.

[0004] In recent years, scholars both domestically and internationally have conducted extensive research on IMU fault diagnosis, mainly categorized into expert system-based methods, model-based methods, and data-driven methods. However, each of these methods has the following limitations:

[0005] 1) Expert system-based methods are less effective at identifying unknown faults, and traditional methods have relatively large thresholds, which can easily lead to false alarms.

[0006] 2) While model-based methods offer good interpretability, they are heavily reliant on mathematical models. Nonlinear factors such as sensor drift and temperature errors can lead to a mismatch between the model and actual signals, causing the false alarm rate to increase exponentially with operating time. Those skilled in the art have attempted to address this by increasing model complexity (e.g., by introducing a temperature compensation term), but this has limited effectiveness in engineering applications due to limitations in real-time computing capabilities. Therefore, mathematical modeling of inertial navigation systems is challenging and yields low accuracy, impacting the efficiency of fault diagnosis.

[0007] 3) Data-driven methods often employ deep learning or machine learning. While these algorithms are not limited by mathematical models or expert knowledge, they require a large amount of data, including both normal and fault samples, to train the model. In practical applications, historical data from rockets or satellites mostly consists of normal samples, while fault samples are scarce, which can affect the accuracy of the algorithm. Therefore, reducing reliance on fault samples and increasing the utilization rate of normal samples is crucial.

[0008] In addition, some data-driven methods have poor interpretability, making it difficult to intuitively explain the decision-making process of the model and the physical meaning of the diagnostic results. Summary of the Invention

[0009] According to one aspect of this application, a method for detecting gradually changing faults in inertial measurement units (IMUs) under dynamic environments is provided. This method does not rely on fault data and can achieve high-precision detection of gradually changing faults. Experimental results of this application show that this method can detect various faults in IMUs, with an average fault detection rate of 97.80%, demonstrating high engineering practical value.

[0010] The method for detecting slowly changing faults in an inertial measurement unit under dynamic conditions includes:

[0011] (1) Use normal data from the inertial measurement unit to train a Gaussian process regression model to predict the dynamic output envelope of the normal signal;

[0012] (2) Calculate the multidimensional statistical characteristics of normal signals;

[0013] (3) The extreme values ​​of each statistical feature within the dynamic output envelope are obtained by using the particle swarm optimization algorithm and used as the fault detection threshold.

[0014] (4) Acquire signals from the inertial measurement unit in real time, compare the calculated multidimensional statistical features with the fault detection threshold, and determine whether the sample is faulty.

[0015] In dynamic environments, existing technologies often rely on analytical models such as linear estimation and Kalman filtering to process inertial navigation data. This application introduces Gaussian Process Regression (GPR), a non-parametric model. Traditional GPR techniques only address static electrical signals and rely on single features, while the IMU output is a multi-dimensional dynamic signal containing three-axis angular velocity and acceleration, whose noise model and feature coupling differ significantly from circuit signals. Therefore, this application combines GPR with Particle Swarm Optimization (PSO) to collaboratively estimate multi-dimensional features. First, the application uses the GPR model to predict the dynamic output envelope of the normal signal, defining a "normal fluctuation range" to provide signal model support for the PSO algorithm and prevent it from getting trapped in local optima. Then, the PSO algorithm searches for the optimal threshold combination in multi-dimensional space, using multi-feature logic to solve the technical problem of identifying weak features of slowly changing faults. This application essentially establishes a three-layer architecture of "signal modeling - feature space transformation - intelligent decision-making", which can effectively solve the problem of "small sample, multi-dimensional, slowly changing fault" IMU detection that cannot be handled by existing technologies.

[0016] Optionally, step (1) specifically includes:

[0017] (11) Select a certain type of rocket in the flight simulation computer, determine the launch window and target trajectory; drive the turntable to move, and record the three-axis angular velocity of the rocket inertial navigation system in real time according to the given sampling frequency and sampling time; select the research object of fault detection and collect its normal data; and then perform fault injection.

[0018] (12) Use the sliding window method to preprocess the normal dataset collected in step (11), determine the size and span of the window, realize the dynamic update of the dataset, and cyclically construct new datasets.

[0019] (13) Divide the newly constructed dataset into a training set and a test set, and perform normalization preprocessing on the data;

[0020] (14) Determine the kernel function based on the waveform trend of the normal signal;

[0021] (15) Initialize the Gaussian process regression model, including: setting the initial hyperparameters of the kernel function, determining the number of iterations, and establishing the prior model;

[0022] (16) Use the training set data to train the Gaussian process regression model, optimize the hyperparameters using the conjugate gradient method, and obtain the optimal solution;

[0023] (17) Input the test set into the posterior model of the Gaussian process regression model, output the mean and variance of the predicted values, and obtain the uncertainty estimate of the prediction, which is the dynamic output envelope of the normal signal.

[0024] (18) Use predictive performance evaluation metrics to evaluate the model.

[0025] Optionally, in step (11), the fault injection is performed using mathematical modeling, and the types of faults include, but are not limited to, the following:

[0026] ① Bias fault: After the fault occurs, the output value y f There is a constant deviation c between y(t) and the actual value y(t). f The time of fault occurrence is defined as follows: A deviation *c* is added to the normal sample to simulate the fault sample. A uniform distribution U(a,b) is used to characterize the deviations of different amplitudes. This fault can be considered a hard fault, and its mathematical expression is as follows:

[0027]

[0028] ② Gradual drift fault: After the fault occurs, the output value y f (t) varies slowly at an offset rate k; here, a linear distribution L(0,d) is used to generate a set of linearly increasing numbers to characterize the drift fault that varies with time at a rate k. This fault can be considered a soft fault, and its mathematical expression is as follows:

[0029]

[0030] ③ Accuracy Degradation Fault: After the fault occurs, the measurement accuracy of the inertial device deteriorates, and the output value y... f Multiplying (t) by the scaling factor s results in a scaling error, expressed mathematically as follows:

[0031]

[0032] Alternatively, based on the principle of Gaussian process regression, the normal output envelope modeling of the inertial measurement unit can be described as follows:

[0033] y = f(x) + ε

[0034] Where y is the observed value, i.e., the signal output of a certain inertial device, and ε is the residual that follows a Gaussian distribution, i.e. Let f(x) be the variance of the residuals, x be the input vector, and f(x) follow a Gaussian prior distribution:

[0035] f(x)~GP(m(x),k(x,x'))

[0036] Where m(x)i ) is the mean function, usually set to 0, k(x) i ,x i The covariance function is: k(x,x')=E[(f(x)-m(x))(f(x')-m(x'))];

[0037] To facilitate the establishment of a normal output envelope model, the output signal of the inertial measurement unit is divided into a training set and a test set. A prior distribution is established using the training set, and then transformed into a posterior distribution using samples from the test set. The observed values ​​y in the training set and the predicted values ​​f* in the test set then satisfy a joint prior distribution:

[0038]

[0039] Where X and X * The input matrices for the training and test sets are respectively, K(X,X) * K(X,X), K(X) * ,X * ) and K(X,X * All are covariance functions, and I is the identity matrix;

[0040] Calculate the posterior distribution of the predicted value f*:

[0041]

[0042] The mean of the predicted values ​​on the test set The variance of the predicted values ​​is

[0043] Given the mean and variance, the probability distribution of the predicted value can be obtained, i.e., the envelope prediction within a certain confidence interval. Assuming a confidence level of 1-α, the confidence interval satisfied by the GPR predicted value, i.e., the normal signal of the inertial measurement unit, is:

[0044]

[0045] Among them, l b and u b These are the upper and lower bounds of the confidence interval, z α / 2 These are the two-sided α quantiles of a standard normal distribution.

[0046] The confidence level can be selected as 30%, 70%, 90%, etc.

[0047] Preferably, a confidence interval of 95% is set here to provide a relatively wide range, which helps to capture the true predicted value under conditions of high uncertainty. This allows the normal envelope to encompass a more comprehensive range of normal situations, which is beneficial for reducing the false alarm rate. Therefore, the dynamic output envelope of the normal signal is:

[0048] As can be seen from the above equation, the core of normal output envelope modeling based on GPR lies in the mean function m(x) i ) and covariance function k(x i ,x i The choice of covariance function is crucial. When the mean function is preset to 0, the prediction result of GPR is related to the chosen covariance function. The covariance function describes the correlation between samples, transforming nonlinear relationships into linear ones; its practical meaning is the same as that of the kernel function. Different covariance functions affect the smoothness of the prediction, model complexity, and confidence level.

[0049] Therefore, preferably, the kernel function of the Gaussian process regression model is selected from one or more of the following combinations: quadratic exponential kernel function, rational quadratic kernel function, Matern32 kernel function, and periodic kernel function PER.

[0050] ① The quadratic exponential kernel function SE is shown in the following formula:

[0051]

[0052] Where r=|x i -x j |,σ 2 The signal variance of the SE kernel function determines the average distance of the function values ​​relative to the mean; l is the scaling parameter, affecting the smoothness of the model. The SE kernel function is a local kernel function, with hyperparameters θ1 = {σ...} 2 ,l}.

[0053] ② The rational quadratic kernel function RQ is shown in the following formula:

[0054]

[0055] Here, α is the scaling mixing parameter, which affects the shape of the kernel function and is related to the model's fitting ability. The RQ kernel function can be viewed as the sum of multiple different SE kernel functions, and it better reflects the tortuous and fluctuating data trends than SE. Hyperparameter θ2={σ 2 ,l,α}.

[0056] ③ The Matern32 kernel function is shown in the following formula:

[0057]

[0058] The Matern32 kernel function is suitable for non-stationary data, is quite flexible, and has strong interpretability. Its hyperparameter θ3={σ 2 ,l}.

[0059] ④ The periodic kernel function PER is shown in the following formula:

[0060]

[0061] Where p is the period, the PER kernel function is suitable for periodic data, and its hyperparameter θ4 = {σ 2 ,l,p}.

[0062] Each of the above kernel functions has different characteristics. When the data is complex, a single kernel function may not provide a good fit. Combining multiple kernel functions in different ways, giving them the modeling capabilities of multiple kernel functions, can effectively improve the flexibility and scalability of Gaussian process regression modeling and enhance the model's expressive power. Therefore, a kernel function composed of two or more kernel functions can be called a combined kernel function. Common combination methods include addition and multiplication.

[0063] k(x,x')=k1(x,x')+k2(x,x'),

[0064] k(x,x')=k1(x,x')×k2(x,x').

[0065] Optionally, the method further includes performance evaluation of the Gaussian process regression model, including:

[0066] Mean absolute error (MAE) and root mean square error (RMSE) are selected as evaluation indicators for prediction performance to measure the difference between predicted and actual values, as shown in the following formula:

[0067]

[0068] Among them, y i and These are the actual value output by the inertial measurement unit and the predicted value by the Gaussian process regression model, respectively, where N is the number of sampling points for the signal;

[0069] The smaller the MAE and RMS values, the closer the actual and predicted values ​​are, and the higher the prediction accuracy of the Gaussian process regression model.

[0070] Optionally, the performance evaluation also includes:

[0071] Predicted Interval Coverage Rate (PICP) and Predicted Interval Regularized Average Width (PINAW) are selected as evaluation metrics for interval prediction, used to measure the width and reliability of the confidence interval, as shown in the following formulas:

[0072]

[0073] Where R is the average width of the confidence interval predicted by the Gaussian process regression model, and U i and L i These are the upper and lower bounds of the confidence interval, respectively; if c i =1, the prediction interval includes the true value; otherwise, c i=0;

[0074] The larger the PICP value, the more true values ​​the confidence interval contains;

[0075] For a given PICP value, the smaller the PINAW value, the higher the prediction accuracy of GPR.

[0076] Optionally, step (2) includes: calculating the time-domain and frequency-domain characteristics of the normal signal;

[0077] The time-domain features include root mean square, centroid, mean, median, kurtosis, and standard deviation, which can reflect the frequency composition of the signal and are used to identify signals whose frequency components change.

[0078] The frequency domain features include the centroid frequency, which reflects the frequency composition of the signal and is used to identify signals whose frequency components change.

[0079] Furthermore, the normal output envelope obtained based on GPR modeling contains a large number of curves. Calculating the multidimensional statistical features of all curves within the envelope would be computationally intensive and time-consuming, failing to quickly and effectively filter out key information. Calculating only the statistical features of the upper and lower bounds of the envelope, while computationally less, has limitations and cannot reflect the overall characteristics of the normal output. This application uses statistical features as fault detection thresholds, and their extreme values ​​are crucial for fault identification, affecting the quality of the fault detection method. Therefore, this application introduces the Particle Swarm Optimization (PSO) algorithm to calculate the maximum and minimum values ​​of the aforementioned statistical features. The PSO algorithm has strong global search capabilities, finding the optimal solution globally within the normal envelope and avoiding local extrema. In addition, the PSO algorithm converges quickly, finding the optimal solution in a short time, reducing computational complexity and time consumption.

[0080] Therefore, the basic principle of the Particle Swarm Optimization (PSO) algorithm in this application is as follows:

[0081] The output of the particle swarm algorithm is satisfied. The normal distribution curve; if the number of sampling points for the normal output curve is N, then the range of values ​​for each sampling point is... The binary encoded particle swarm optimization algorithm (BPSO) is used to find the optimal position within the maximum number of iterations and output the global optimal position and the corresponding fitness function value, which are the maximum and minimum values ​​of the statistical features, and are used as the fault detection threshold.

[0082] Optionally, step (4) includes:

[0083] Calculate the multidimensional statistical features of different fault types and compare them with the fault detection threshold in step (3). When at least three feature values ​​exceed the fault detection threshold, it is determined to be a fault.

[0084] Optionally, the method further includes evaluating the fault detection method using at least one of the following evaluation metrics:

[0085] FPR, or False Alarm Rate, represents the probability of misreporting a normal sample as a fault. The calculation formula is as follows:

[0086] FPR = FP / (FP+TN);

[0087] FNR is the false alarm rate, which represents the probability of misclassifying a faulty sample as normal. The calculation formula is as follows:

[0088] FNR = FN / (FN+TP);

[0089] FDR stands for Fault Detection Rate, which represents the ability to correctly detect faulty samples. The calculation formula is as follows:

[0090] FDR = TP / (TP+FN);

[0091] Where TP represents the number of normal samples that were correctly detected, FN represents the number of normal samples that were falsely reported as faults, FP represents the number of faults that were not detected, and TN represents the number of abnormal samples that were correctly identified.

[0092] According to another aspect of this application, an inertial measurement unit slowly changing fault detection system in a dynamic environment is provided, comprising: a processor;

[0093] and a computer program stored in a memory and executable on a processor, wherein the processor executes the computer program to implement all or part of the steps in the above-described method for detecting slowly changing faults in an inertial measurement unit under dynamic conditions.

[0094] According to another aspect of this application, a computer-readable storage medium is provided, on which a computer program is stored, which, when executed by a processor, implements all or part of the steps in the above-described method for detecting slowly changing faults in an inertial measurement unit under dynamic conditions.

[0095] The beneficial effects that this application can produce include:

[0096] 1) This application uses only normal data to train the model, and effectively utilizes prior knowledge and limited data through the Bayesian framework, making it more suitable for practical application scenarios where fault samples are sparse.

[0097] 2) The Gaussian process regression (GPR) model in this application provides the confidence interval for prediction based on the complete posterior distribution, exhibiting good model interpretability. The normal output envelope can be dynamically adjusted according to signal fluctuations and noise, fully considering the distribution of normal signals. Furthermore, the dynamic features based on GPR can overcome the limitations of single-dimensional signal modeling, characterizing the complex distribution of IMU signals through multi-dimensional feature extraction (e.g., 6-dimensional time domain + 1-dimensional frequency domain).

[0098] 3) This application optimizes multidimensional features using the Particle Swarm Optimization (PSO) algorithm to reasonably determine the fault threshold, reduce the false alarm rate, and realize the slow-changing fault detection of the IMU in dynamic environments. Specifically, based on the PSO algorithm, the extreme values ​​of multidimensional features can be searched within the normal envelope defined by the GPR as the detection threshold, realizing the transformation from "probability interval to engineering threshold".

[0099] 4) This application combines the cross-domain GPR model and PSO algorithm to target the characteristics of IMU signals, and realizes the dynamic determination of multi-dimensional feature thresholds under small data volume. The synergistic effect significantly reduces the false alarm rate and missed alarm rate. Attached Figure Description

[0100] Figure 1 This is an overall flowchart of an inertial measurement unit slowly changing fault detection method in a dynamic environment according to one embodiment of this application; Figure 2 The X-axis angular rate after fault injection in one embodiment of this application is denoted as U(15,20), L(0,25), and 1.4, respectively, for bias fault, drift fault, and accuracy degradation fault. Figure 3 This is a schematic diagram of the sliding window data construction in one embodiment of this application; Figure 4 This is a predicted envelope diagram of the dynamic output of a normal signal based on a Gaussian process regression model in one embodiment of this application. Figure 5 The multidimensional statistical characteristics of the inertial measurement unit test set in Embodiment 1 of this application; Figure 6 This is the normalized statistical feature map in Embodiment 1 of this application; Figure 7 The relative positions of the statistical characteristic values ​​of the nine faults in Embodiment 1 of this application with respect to the normal extreme value range; Figure 8 This is the predicted envelope diagram of the dynamic output of the normal signal based on the Gaussian process regression model in Embodiment 2 of this application; Figure 9The X-axis angular rate after fault injection in Embodiment 2 of this application; where, respectively, are the bias fault U(4,6), the drift fault L(0,15), and the accuracy degradation fault 1.4; Figure 10 These are the extreme values ​​of statistical features of the UAV test set based on PSO in Embodiment 2 of this application; Figure 11 This refers to the relative positions of the statistical characteristic values ​​of the nine faults in Embodiment 2 of this application with respect to the normal extreme value range. Detailed Implementation

[0101] The present application is described in detail below with reference to the embodiments, but the present application is not limited to these embodiments.

[0102] During pre-launch testing of a launch vehicle's electrical system, a threshold-based fault detection method is typically used. When test data exceeds a set threshold, a fault is identified, and further investigation is initiated. This method is relatively simple but relies heavily on human experience, making it prone to missed detections. As a crucial component of the launch vehicle's electrical system, the strapdown inertial navigation system (INS) is vulnerable. A fault in one of its inertial components can contaminate navigation data, affecting the INS's functionality and, in severe cases, interfering with the rocket's normal flight. INS faults are categorized as soft faults and hard faults. Soft faults change slowly and are difficult to detect; traditional threshold methods struggle to identify them quickly and accurately and cannot adapt to changes in the system's external environment.

[0103] Therefore, this application proposes a method for detecting slowly varying faults in inertial measurement units (INS) under dynamic environments. This method incorporates Gaussian process regression and particle swarm optimization (PSO) algorithms, particularly effective for detecting soft faults. Due to the scarcity of rocket fault samples, this application can train a Gaussian process regression model using only normal data to reasonably predict the dynamic output envelope of normal signals. Then, the PSO algorithm is used to determine a reasonable fault detection threshold, improving the accuracy of INS soft fault detection and reducing the impact of local interference on diagnostic results.

[0104] The method for detecting slowly changing faults in an inertial measurement unit under dynamic conditions includes the following steps:

[0105] (1) Use normal data from the inertial measurement unit to train a Gaussian process regression model to predict the dynamic output envelope of the normal signal;

[0106] (2) Calculate the multidimensional statistical characteristics of normal signals;

[0107] (3) The extreme values ​​of each statistical feature within the dynamic output envelope are obtained by using the particle swarm optimization algorithm and used as the fault detection threshold.

[0108] (4) Acquire signals from the inertial measurement unit in real time, compare the calculated multidimensional statistical features with the fault detection threshold, and determine whether the sample is faulty.

[0109] The Gaussian Process Regression (GPR) model is a nonparametric model based on Gaussian processes, capable of reasonably modeling nonlinear relationships. Compared to other prediction models, GPR not only provides accurate predictions but also expresses the probability distribution of the prediction problem in the form of confidence intervals. Because GPR utilizes prior information and Bayesian inference, it exhibits better predictive performance than traditional machine learning methods when the amount of data for the prediction problem is small.

[0110] From the perspective of statistics and machine learning, the modeling problem of the normal output envelope of the inertial measurement unit belongs to the probabilistic regression problem. Therefore, Gaussian process regression is chosen to calculate the confidence interval of the signal and complete the interval prediction of the normal signal.

[0111] Based on the principle of Gaussian process regression, the normal output envelope modeling of the inertial measurement unit can be described as follows:

[0112] y = f(x) + ε

[0113] Where y is the observed value, i.e., the signal output of a certain inertial device, and ε is the residual that follows a Gaussian distribution, i.e. Let f(x) be the variance of the residuals, x be the input vector, and f(x) follow a Gaussian prior distribution:

[0114] f(x)~GP(m(x),k(x,x'))

[0115] Where m(x) i ) is the mean function, usually set to 0, k(x) i ,x i The covariance function is: k(x,x')=E[(f(x)-m(x))(f(x')-m(x'))];

[0116] To facilitate the establishment of a normal output envelope model, the output signal of the inertial measurement unit is divided into a training set and a test set. A prior distribution is established using the training set, and then transformed into a posterior distribution using samples from the test set. The observed values ​​y in the training set and the predicted values ​​f in the test set are then... * Satisfies joint prior distribution:

[0117]

[0118] Where X and X * The input matrices for the training and test sets are respectively, K(X,X) *K(X,X), K(X) * ,X * ) and K(X,X * All are covariance functions, and I is the identity matrix;

[0119] Calculate the posterior distribution of the predicted value f*:

[0120]

[0121] The mean of the predicted values ​​on the test set The variance of the predicted values ​​is

[0122] Given the mean and variance, the probability distribution of the predicted value can be obtained, i.e., the envelope prediction within a certain confidence interval. Assuming a confidence level of 1-α, the confidence interval satisfied by the GPR predicted value, i.e., the normal signal of the inertial measurement unit, is:

[0123]

[0124] Among them, l b and u b These are the upper and lower bounds of the confidence interval, z α / 2 These are the two-sided α quantiles of a standard normal distribution.

[0125] In a preferred embodiment, where the confidence interval is set to 95%, the dynamic output envelope of the normal signal is:

[0126] As can be seen from the above equation, the core of normal output envelope modeling based on GPR lies in the mean function m(x) i ) and covariance function k(x i ,x i The choice of covariance function is crucial. When the mean function is preset to 0, the prediction result of GPR is related to the chosen covariance function. The covariance function describes the correlation between samples, transforming nonlinear relationships into linear ones; its practical meaning is the same as that of the kernel function. Different covariance functions affect the smoothness of the prediction, model complexity, and confidence level.

[0127] In one implementation, commonly used kernel functions for Gaussian process regression include, but are not limited to:

[0128] ① The quadratic exponential kernel function SE is shown in the following formula:

[0129]

[0130] Where r=|x i -x j |,σ 2The signal variance of the SE kernel function determines the average distance of the function values ​​relative to the mean; l is the scaling parameter, affecting the smoothness of the model. The SE kernel function is a local kernel function, with hyperparameters θ1 = {σ...} 2 ,l}.

[0131] ② The rational quadratic kernel function RQ is shown in the following formula:

[0132]

[0133] Here, α is the scaling mixing parameter, which affects the shape of the kernel function and is related to the model's fitting ability. The RQ kernel function can be viewed as the sum of multiple different SE kernel functions, and it better reflects the tortuous and fluctuating data trends than SE. Hyperparameter θ2={σ 2 ,l,α}.

[0134] ③ The Matern32 kernel function is shown in the following formula:

[0135]

[0136] The Matern32 kernel function is suitable for non-stationary data, is quite flexible, and has strong interpretability. Its hyperparameter θ3={σ 2 ,l}.

[0137] ④ The periodic kernel function PER is shown in the following formula:

[0138]

[0139] Where p is the period, the PER kernel function is suitable for periodic data, and its hyperparameter θ4 = {σ 2 ,l,p}.

[0140] Furthermore, as can be seen from the above kernel functions, different kernel functions have different characteristics. When the data is complex, the fitting effect of a single kernel function is not good. Combining multiple kernel functions in different ways, giving them the modeling capabilities of multiple kernel functions, can effectively improve the flexibility and scalability of Gaussian process regression modeling and enhance the expressive power of the model. We define a kernel function composed of two or more kernel functions as a combined kernel function. Common combination methods include addition and multiplication.

[0141] k(x,x')=k1(x,x')+k2(x,x'),

[0142] k(x,x')=k1(x,x')×k2(x,x').

[0143] In one implementation, based on the basic principles of Gaussian process regression and the kernel function selection method, a process for modeling the normal output envelope band is given for fault detection of strapdown inertial navigation systems. Specifically, step (1) includes:

[0144] (11) Collect the normal output signal of the inertial measurement unit, process the data using the sliding window method, determine the size and span of the window, and realize the dynamic update of the dataset.

[0145] (12) Divide the normal signal dataset into training set and test set, and perform normalization preprocessing on the data.

[0146] (13) Determine a suitable kernel function. Based on the waveform trend of the normal signal, compare the prediction effects of various kernel functions and select the kernel function with the best effect.

[0147] (14) Initialize the GPR model. Set the initial hyperparameters of the kernel function, determine the number of iterations, and establish the prior model.

[0148] (15) Use the training set data to train the GPR model, and use the conjugate gradient method to optimize the hyperparameters to obtain the optimal solution.

[0149] (16) Input the test set into the posterior model of GPR, output the mean and variance of the predicted values, and obtain the uncertainty estimate of the prediction, i.e. the output envelope of the normal signal.

[0150] (17) Use predictive performance evaluation metrics to evaluate the model.

[0151] The GPR model can be used to obtain the envelope of normal data from an inertial measurement unit (IMU). This estimated envelope can be considered as a confidence interval for the possible existence of normal signals. If a point-by-point analysis method is used to interpret the data—that is, data exceeding the estimated envelope is considered faulty, and data within the envelope is considered normal—this visual comparison increases the complexity of fault identification and is prone to errors, increasing false alarm and missed alarm rates. Therefore, to improve the efficiency of fault detection, it is necessary to determine an appropriate fault detection threshold. This application selects multidimensional statistical features to characterize the signal's changing trend. Statistical features can change with the signal and still characterize the signal's basic properties even when noise and external interference occur. Therefore, we use statistical features as the interpretation standard to improve the robustness and accuracy of fault detection.

[0152] In one implementation, step (2) includes selecting seven statistical features to characterize the changing trend of the inertial measurement unit signal: root mean square, centroid, mean, median, kurtosis, standard deviation, and centroid frequency. The first six are time-domain statistical features, which can reflect the changing characteristics of the signal over time and are suitable for detecting abrupt changes and gradual trends in the signal. Centroid frequency is a frequency-domain feature, which can reflect the frequency composition of the signal and is used to identify signals whose frequency components change.

[0153] ① Root mean square (r), used to describe the energy level of the signal:

[0154]

[0155] Where N is the number of sampling points of the signal, x i (i = 1, 2, ..., N) represents the input signal to be measured.

[0156] ② Centroid c, used to characterize the geometric center position of the signal:

[0157]

[0158] For the output signal of the inertial measurement unit, c represents the center of the region enclosed by the signal curve and the horizontal axis. N is the number of signal sampling points, x i (i = 1, 2, ..., N) represents the input signal to be measured.

[0159] ③The mean m is the average value of all sampled data points of the output signal:

[0160]

[0161] It can reflect the offset trend of the inertial measurement unit signal and belongs to global statistics.

[0162] ④ The median (mid) is used to describe the center point within the dynamic range of a signal:

[0163]

[0164] This value helps identify abnormal states.

[0165] ⑤ Kurtosis k reflects the steepness of the signal waveform and can capture subtle changes in fault signals:

[0166]

[0167] A higher kurtosis indicates a greater difference between faulty samples and normal samples.

[0168] ⑥ Standard deviation s, used to describe the degree of deviation of the signal:

[0169]

[0170] The larger the standard deviation, the more drastic the signal change.

[0171] ⑦ The centroid frequency f is used to reflect the concentrated distribution of signal energy. The differences between different fault types are quite obvious, and it can effectively distinguish normal samples from faulty samples:

[0172]

[0173] Where f(n) is the frequency component of the signal, and u(n) is the amplitude component of the signal.

[0174] Furthermore, the dynamic output envelope of the normal signal contains a large number of curves. Calculating the multidimensional statistical features of all curves within the envelope would be computationally intensive and time-consuming, making it impossible to quickly and effectively filter out key information. Calculating only the statistical features of the upper and lower bounds of the envelope, while computationally less, has limitations and cannot reflect the overall characteristics of the normal output. This paper uses statistical features as fault detection thresholds, and their extreme values ​​are important criteria for fault identification, affecting the quality of the fault detection method. Therefore, this application introduces the Particle Swarm Optimization (PSO) algorithm to calculate the maximum and minimum values ​​of the aforementioned statistical features. The PSO algorithm has strong global search capabilities, enabling it to find the optimal solution within the global scope of the normal envelope, avoiding the acquisition of local extrema. In addition, the PSO algorithm has a fast convergence speed, finding the optimal solution in a short time, reducing computational complexity and time consumption.

[0175] The output of the Gaussian process regression model satisfies The normal distribution curve. If the number of sampling points for the normal output curve is N, then the range of values ​​for each sampling point is... The range of values ​​is large, making it difficult to calculate.

[0176] Therefore, in one implementation, the Binary Encoded Particle Swarm Optimization (BPSO) algorithm can effectively handle discrete decision variables. P points are selected at equal intervals at each sampling point, resulting in a coding bit length p = [log₂P]. Next, algorithm parameters are set, and the particle positions and velocities are initialized, with particle positions randomly distributed between [0,1]. Then, statistical features are selected as the fitness function, and the particle positions are decoded from binary to actual feature values. Then, according to the following formula, the velocity and position of each particle are updated based on the fitness value combined with the individual optimum and the global optimum. Finally, optimization is performed within the maximum number of iterations, outputting the global optimum position and the corresponding fitness function value, i.e., the maximum and minimum values ​​of the statistical features:

[0177] vij ( t +1) = wvij (t )+ c 1× rand ×( pbestij - xij ( t ))+ c 2× rand ×( gbestj - xij ( t ))

[0178] x ij (t+1)=x ij (t)+v ij (t+1)

[0179] w = w s -(w s -w e )×(t / T max )

[0180] Among them, v ij and x ij Let i = 1, 2, ..., M be the particle's velocity and position, respectively. M is the population size, j = 1, 2, ..., D, where D = N × p is the particle dimension. c1 and c2 are the individual learning factor and the social learning factor, respectively, controlling the particle's acceleration. ij For the optimal position of an individual, gbest j To achieve global optimality, a linearly decreasing method is chosen to calculate the inertia weight w. s and w e These are the maximum and minimum inertia weight coefficients, respectively, where t is the iteration number and T is the minimum inertia weight coefficient. max This represents the maximum number of iterations.

[0181] In a preferred embodiment, step (3) includes:

[0182] (31) The normal output envelope is binary encoded to represent the position and velocity of the particles in binary.

[0183] (32) Parameter initialization: Randomly initialize each particle.

[0184] (33) Use statistical features as fitness functions.

[0185] (34) Update the position and velocity of the particles and perform iterative optimization.

[0186] (35) When the number of iterations is at its maximum, the fitness function value is decoded into a real number, and the global optimum is output as the maximum or minimum value of the feature, which is the threshold for fault detection.

[0187] In one implementation, step (4) includes:

[0188] (41) Collect the output signal of the inertial measurement unit under normal conditions, divide it into training set and test set, and input the normalized data into the GPR model for training.

[0189] (42) Compare the prediction performance of the GPR model under different kernel functions and select the kernel function with the best results. Use the test set to output the prediction mean and variance of the GPR model to obtain the envelope of the normal output signal, which serves as the basis for fault detection.

[0190] (43) Calculate the multidimensional statistical characteristics of the normal output signal.

[0191] (44) Using multidimensional statistical features as fitness functions, the PSO algorithm is used to find the maximum and minimum values ​​of each feature, which are then used as fault detection thresholds.

[0192] (45) Using a fault simulation method, faults are injected into the normal signals collected in the experiment. The multidimensional statistical features of different fault types are calculated and compared with the fault thresholds in step (44). If at least three feature values ​​exceed the threshold, it is determined to be a fault.

[0193] In one embodiment, the method for detecting slowly changing faults in an inertial measurement unit under dynamic conditions further includes: using the model's predictive performance and interval prediction capability as evaluation indicators in order to more comprehensively evaluate the model performance of Gaussian process regression.

[0194] In one specific implementation, the mean absolute error (MAE) and root mean square error (RMSE) are selected as prediction performance evaluation indicators to measure the difference between the predicted value and the true value.

[0195]

[0196]

[0197] Among them, y i and These are the actual value output by the inertial measurement unit and the predicted value by the Gaussian process regression model, respectively, where N is the number of sampling points for the signal;

[0198] The smaller the MAE and RMS values, the closer the actual and predicted values ​​are, and the higher the prediction accuracy of the Gaussian process regression model.

[0199] In one specific implementation, the performance evaluation further includes:

[0200] Predicted Interval Coverage Rate (PICP) and Predicted Interval Regularized Average Width (PINAW) are selected as evaluation metrics for interval prediction, used to measure the width and reliability of the confidence interval, as shown in the following formulas:

[0201]

[0202] Where R is the average width of the confidence interval predicted by the Gaussian process regression model, and U i and L i These are the upper and lower bounds of the confidence interval, respectively; if c i =1, the prediction interval includes the true value; otherwise, c i =0;

[0203] The larger the PICP value, the more true values ​​the confidence interval contains;

[0204] For a given PICP value, the smaller the PINAW value, the higher the prediction accuracy of GPR.

[0205] Strapdown inertial navigation system (INS) is a crucial component of rocket electrical systems. Due to the harsh flight environment and the effects of external interference and component aging, internal inertial devices are prone to failure, increasing INS errors and causing deviations from the intended trajectory, thus reducing the reliability and stability of the electrical system. Common failure types of inertial devices include bias faults, gradual drift faults, and accuracy degradation faults.

[0206] Therefore, in one specific implementation, in step (11), the fault injection is performed using mathematical modeling, and the type of fault includes, but is not limited to, one of the following:

[0207] ① Bias fault: After the fault occurs, the output value y f There is a constant deviation c between y(t) and the actual value y(t). f The time of fault occurrence is defined as follows: A deviation *c* is added to the normal sample to simulate the fault sample. A uniform distribution U(a,b) is used to characterize the deviations of different amplitudes. This fault can be considered a hard fault, and its mathematical expression is as follows:

[0208]

[0209] ② Gradual drift fault: After the fault occurs, the output value y f (t) varies slowly at an offset rate k; here, a linear distribution L(0,d) is used to generate a set of linearly increasing numbers to characterize the drift fault that varies with time at a rate k. This fault can be considered a soft fault, and its mathematical expression is as follows:

[0210]

[0211] ③ Accuracy Degradation Fault: After the fault occurs, the measurement accuracy of the inertial device deteriorates, and the output value y... f Multiplying (t) by the scaling factor s results in a scaling error, expressed mathematically as follows:

[0212]

[0213] To verify the effectiveness of the proposed IMU fault detection method in practical engineering, this application conducted experimental analyses of two embodiments: IMU data from a laboratory semi-physical simulation system and a publicly available IMU dataset from Northwestern Polytechnical University. As inertial devices are high-reliability products, fault samples are scarce in practical applications. Therefore, fault samples were generated using the aforementioned fault model based on normal data. The fault settings for the two cases are shown in Table 1 below. X and Y represent the fault types in Embodiment 1 and Embodiment 2, respectively.

[0214] Table 1 Fault settings for Examples 1 and 2

[0215]

[0216] Example 1

[0217] (1) Data description and preprocessing

[0218] First, a fault detection experiment was conducted using a laboratory-based semi-physical simulation system for rocket flight. This system consists of an onboard computer, a three-axis turntable, a fiber optic inertial measurement unit (IMU), and a real-time flight simulation computer. The three-axis turntable generates the three-axis simulated attitude of the rocket during flight, with a velocity range of 0–60° / s and an angular position resolution of 0.1°. The 8K20-M fiber optic inertial measurement unit, containing three gyroscopes and three accelerometers, provides the three-axis angular velocity and acceleration signals of the rocket. As the three-axis turntable operates, the onboard computer receives the gyroscope and accelerometer data generated by the fiber optic IMU and feeds back timing commands to the real-time flight simulation computer. The computer runs a dynamic model to obtain the changes in various parameters during rocket flight.

[0219] like Figure 1 As shown, the data preprocessing steps are as follows:

[0220] Step 1: In the flight simulation computer, select a specific rocket model and determine the launch window and target trajectory. Drive the turntable to move and record the three-axis angular velocities of the rocket's inertial navigation system in real time, with a sampling frequency of 20Hz and a sampling time of 150s. Select the X-axis angular velocity as the research object for fault detection and collect normal data. The fault injection time is uniformly set to 90s to 150s, for a total of 60s. Refer to the above for the settings of the three types of faults; the fault samples are as follows. Figure 2 As shown.

[0221] Step 2: Preprocess the collected normal dataset using the sliding window method. This method can transform historical information in a one-dimensional time series into features, effectively capturing its time dependence, enabling the GPR model to dynamically and continuously learn data features and improve prediction accuracy. Set the sliding window size kim = 10 and the prediction span zim = 1. Construct a new dataset iteratively, with each row containing kim historical data points as input features and zim data points after each time point as output target values. Since the number of sampling points for the normal samples in Step 1 is N, the new dataset has (N - kim - zim + 1) rows and (kim + 1) columns, as shown below. Figure 3 As shown.

[0222] Step 3: Divide the newly constructed dataset into training and test sets in a 6:4 ratio. Normalize each column of data to the range [0,1] using the following formula to ensure data scale consistency and thus improve the convergence speed of the GPR model.

[0223]

[0224] Where, x norm The normalized value is x. max and x min These are the maximum and minimum values, respectively.

[0225] (2) Results Analysis

[0226] First, following the GPR modeling process in section A, GPR model prediction was performed on the normal dataset. The training set was input into the GPR model, different kernel functions were selected for modeling, and confidence intervals were estimated on the test set. Here, single kernel functions, combined kernel functions (additional or multiplicative), and four evaluation metrics were used to quantitatively analyze the prediction performance of different kernel functions. The results are shown in Table 2 below.

[0227] Table 2 Evaluation metrics for different kernel functions in Example 1 (Note: PICP values ​​greater than 95% are marked in bold)

[0228]

[0229] Analyzing the results in Table 2: Based on the properties of the interval prediction index, PICP must be greater than the 95% confidence level, and a larger PICP includes more true values. When MAE and RMSE are not significantly different, SE has the largest PICP and PINAW. Although a smaller PINAW indicates a narrower prediction interval, for predicting normal output intervals, an excessively narrow output interval can easily lead to false alarms. Therefore, this embodiment selects the SE kernel function, using the normal output envelope of the test set obtained from the GPR model as shown below. Figure 4As shown, the SE kernel function is robust, has strong anti-interference ability, and has a length scale parameter, which better matches the changing trend of IMU time series.

[0230] The multidimensional statistical features were set as fitness functions, and the maximum and minimum values ​​of the features were calculated using the PSO algorithm within the normal output envelope interval. The calculation results are shown in Table 3 below.

[0231] Table 3. Statistical eigenvalues ​​based on PSO

[0232]

[0233] The extreme values ​​of the statistical features are used as the fault detection threshold. The multidimensional statistical features of the nine fault test sets in B are calculated and compared with the threshold, such as... Figure 5 As shown in the figure. The gray shading indicates that the feature value exceeds the range of extreme values. To reduce the false alarm rate and improve reliability, a fault is determined when at least three features exceed the threshold.

[0234] To more intuitively represent the relationship between statistical features and thresholds, each statistical feature value is normalized relative to the threshold. The normalized feature map is shown below. Figure 6 As shown in the figure, the seven selected statistical features can effectively distinguish between normal samples and faulty samples, thus improving the accuracy of fault detection.

[0235] In addition, the relative positions of statistical eigenvalues ​​with respect to the normal envelope are as follows: Figure 7 As shown. The gray area represents the range formed by the normal output threshold, and the different colored markers correspond to the seven statistical characteristics of the nine faults. Combined with... Figure 5 and Figure 6 The experimental results show that at least three statistical features corresponding to each fault output exceed the estimated normal threshold range, indicating that the method proposed in this paper accurately detects the drift fault, bias fault, and accuracy reduction fault of the rocket inertial navigation system.

[0236] (3) Comparison method

[0237] To further verify the superiority of the proposed method, it is compared with other fault detection methods. Method 1 is a fault detection method based on GPR-GA, which uses the genetic algorithm GA to optimize the extreme values ​​of statistical features. Method 2 is a fault diagnosis method for IMU based on the STFT-ResNet method. It first uses short-time Fourier transform to convert the one-dimensional time series into a two-dimensional time-frequency graph, and then inputs it into a residual neural network model to achieve fault classification. To maintain consistency, Monte Carlo analysis is used to obtain 500 normal samples and 500 fault samples of various fault states of the inertial navigation system as model inputs. Due to the large sample size, false alarms and missed alarms may occur in the experiment. The evaluation index is shown below.

[0238] FPR, or False Alarm Rate, represents the probability of misreporting a normal sample as a fault. The calculation formula is as follows:

[0239] FPR = FP / (FP+TN);

[0240] FNR is the false alarm rate, which represents the probability of misclassifying a faulty sample as normal. The calculation formula is as follows:

[0241] FNR = FN / (FN+TP);

[0242] FDR stands for Fault Detection Rate, which represents the ability to correctly detect faulty samples. The calculation formula is as follows:

[0243] FDR = TP / (TP+FN);

[0244] Where TP represents the number of normal samples that were correctly detected, FN represents the number of normal samples that were falsely reported as faults, FP represents the number of faults that were not detected, and TN represents the number of abnormal samples that were correctly identified.

[0245] Table 4 Comparison of detection results from different methods

[0246]

[0247] As shown in Table 4 above, the false alarm rate of the method in this application is only 3.80%, and the average fault detection rate is as high as 97.80%. Therefore, compared with the other two methods, the fault detection effect of this application is better, and it can effectively distinguish between faulty samples and normal samples of the IMU. In fact, the GPR-GA method is not good at identifying weak early faults. This is because the parameter adjustment of the GA algorithm is complex, its local search ability is poor, and the fault threshold range obtained is wide, which easily includes weak fault samples. The PSO algorithm, through maintaining the diversity of the population and dynamic parameter adjustment, can effectively deal with the noise and uncertainty of the data, and has higher robustness than the GA algorithm. In addition, the STFT-ResNet method is not good at identifying bias faults, which may be because the STFT time-frequency diagram of this type of fault is similar to that of normal samples, and the ResNet model cannot accurately distinguish them. In summary, this application has outstanding fault identification capabilities for bias faults, gradual drift faults, and accuracy degradation faults of IMUs.

[0248] Example 2

[0249] (1) Data Description

[0250] To further verify the adaptability of this method, Case Study 2 uses a publicly available dataset from Yan Gongmin's team at Northwestern Polytechnical University as the research object for fault detection. A set of UAV inertial navigation flight data was selected, with a flight speed of 100 m / s, a flight distance of 100 km, a total acquisition time of 4000 s, and a frequency of 200 Hz. IMU data from a stable 20-segment flight phase was used, with the sliding window size kim = 20 and the prediction span zim = 5 to construct the dataset. The dataset was randomly divided into training and test sets in a 6:4 ratio, and then normalized.

[0251] (2) Results Analysis

[0252] Following the modeling process in section A, GPR prediction was performed on the normal dataset of the UAV inertial navigation system. Single kernel functions, combined kernel functions (additional or multiplicative), and other methods were used. The prediction results are shown in Table 5 below.

[0253] Table 5 Evaluation metrics for different kernel functions in Case Study 2 (Note: PICP values ​​greater than 95% are displayed in bold)

[0254]

[0255] First, kernel functions with a PICP confidence level below 95% are excluded due to their poor reliability. Since this data lacks periodicity, the PER periodic kernel function is unsuitable. Second, because the SE kernel function has the lowest MAE and RMSE, and the GPR kernel function offers the highest prediction accuracy, we choose the SE kernel function among SE, RQ, and Matern kernel functions. The normal output envelope predicted based on the GPR model is shown below. Figure 8 As shown in the figure, the SE kernel function is suitable for smooth and continuous data, and is more consistent with the changing trends of non-periodic IMU sequences.

[0256] Faults were injected into the normal dataset of the drone, with fault durations ranging from 12 to 20 seconds, totaling 8 seconds. Three types of fault samples were provided. Figure 9 As shown in Table 6 below. Then, the PSO algorithm is used to calculate the maximum and minimum values ​​of the seven statistical features within the normal output envelope interval.

[0257] Table 6. Statistical characteristics and extreme values ​​of the PSO-based UAV test set

[0258]

[0259] Calculate the multidimensional statistical features of the nine fault test sets in the table and compare them with the extreme values ​​of PSO. A fault is identified when the number of features exceeding the threshold is ≥3. Fault detection results are as follows: Figure 10 As shown in the figure. The gray shading indicates that the eigenvalue exceeds the range of extreme values.

[0260] The relative positions of the statistical characteristic values ​​of the UAV with respect to the normal envelope are as follows: Figure 11 As shown. Combined with Figure 10 and Figure 11 It can be seen that each type of fault has at least three characteristic values ​​exceeding the target threshold, and this method can effectively detect inertial group faults in UAV flight data.

[0261] Using the Monta Carlo analysis method, 500 normal state data and 500 fault samples of various fault labels were obtained from the UAV dataset. The fault detection results are shown in Table 7 below.

[0262] Table 7. Multidimensional statistical characteristics of the UAV test set

[0263]

[0264] The false alarm rate was 3.00%, and the average fault detection rate was 98.22%. Therefore, this application can reduce the false alarm rate of inertial navigation system (INS) fault diagnosis, improve the accuracy of fault diagnosis, and achieve effective identification of multiple types of faults.

[0265] In summary, to address the difficulty in identifying slowly varying faults in redundant inertial navigation systems and to improve the reliability of rocket electrical systems, this application proposes a fault detection method based on GPR and PSO for multidimensional feature estimation, which can be used to identify IMU bias faults, drift faults, and accuracy degradation faults.

[0266] This application utilizes IMU data from a rocket semi-physical simulation system and publicly available IMU datasets from Northwestern Polytechnical University for experimental verification, as detailed in Examples 1 and 2 above. The fault detection rates reach 97.80% and 98.22%, respectively, demonstrating that this application can meet the diagnostic needs of various IMU faults and can be applied to different types of IMUs, showcasing its wide applicability. Furthermore, comparing the method of this application with existing fault diagnosis methods shows that the average fault detection rate of this application is improved by 19.18% and 11.52% compared to GPR-GA and STFT-ResNet methods, respectively. Therefore, compared to other data-driven models, this application has better generalization ability and higher fault diagnosis accuracy. Future research should consider the real-time nature of fault detection, extending this method to fault diagnosis of different rocket models and its application in the construction of digital launch sites, thereby improving the intelligence level of rocket testing.

[0267] This application also provides an inertial measurement unit slowly changing fault detection system in a dynamic environment, including: a processor;

[0268] and a computer program stored in a memory and executable on a processor, wherein the processor executes the computer program to implement all or part of the steps in the above-described method for detecting slowly changing faults in an inertial measurement unit under dynamic conditions.

[0269] This application also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements all or part of the steps in the above-described method for detecting slowly changing faults in an inertial measurement unit under dynamic conditions.

[0270] The above description is merely a few embodiments of this application and is not intended to limit this application in any way. Although this application discloses preferred embodiments as described above, it is not intended to limit this application. Any changes or modifications made by those skilled in the art without departing from the scope of the technical solution of this application using the disclosed technical content are equivalent to equivalent implementation cases and fall within the scope of the technical solution.

Claims

1. A method for detecting slowly changing faults in an inertial measurement unit under dynamic conditions, characterized in that, The method includes: (1) Use normal data from the inertial measurement unit to train a Gaussian process regression model to predict the dynamic output envelope of the normal signal; (2) Calculate the multidimensional statistical characteristics of normal signals; (3) The extreme values ​​of each statistical feature within the dynamic output envelope are obtained by using the particle swarm optimization algorithm and used as the fault detection threshold. (4) Acquire signals from the inertial measurement unit in real time, compare the calculated multidimensional statistical features with the fault detection threshold, and determine whether the sample is faulty.

2. The method for detecting slowly changing faults in an inertial measurement unit under dynamic conditions according to claim 1, characterized in that, Step (1) specifically includes: (11) Select a certain type of rocket in the flight simulation computer, determine the launch window and target trajectory; drive the turntable to move, and record the three-axis angular velocity of the rocket inertial navigation system in real time according to the given sampling frequency and sampling time; select the research object of fault detection and collect its normal data; and then perform fault injection. (12) Use the sliding window method to preprocess the normal dataset collected in step (11), determine the size and span of the window, realize the dynamic update of the dataset, and cyclically construct new datasets. (13) Divide the newly constructed dataset into a training set and a test set, and perform normalization preprocessing on the data; (14) Determine the kernel function based on the waveform trend of the normal signal; (15) Initialize the Gaussian process regression model, including: setting the initial hyperparameters of the kernel function, determining the number of iterations, and establishing the prior model; (16) Use the training set data to train the Gaussian process regression model, optimize the hyperparameters using the conjugate gradient method, and obtain the optimal solution; (17) Input the test set into the posterior model of the Gaussian process regression model, output the mean and variance of the predicted values, and obtain the uncertainty estimate of the prediction, which is the dynamic output envelope of the normal signal. (18) Use predictive performance evaluation metrics to evaluate the model.

3. The method for detecting slowly changing faults in an inertial measurement unit under dynamic conditions according to claim 2, characterized in that, The fault injection is performed using mathematical modeling, and the fault types include at least one of the following: ① Bias fault: after the fault occurs, the output value y f (t) has a constant deviation c from the actual value y(t), t f is the time when the fault occurs; That is, a deviation c is added to the normal sample to simulate the fault sample, and the deviation of different amplitudes is represented by a uniform distribution U(a,b). This fault can be regarded as a hard fault, and the mathematical expression is as follows: (ii) Gradual drift fault: after the fault occurs, the output value y f (t) slowly changes at a drift rate k; in this case, a linear profile L(0, d) is used to generate a set of linearly increasing numbers to represent the drift fault that changes over time at a rate k, which can be considered as a soft fault, and the mathematical expression is as follows: ③ Accuracy Degradation Fault: After the fault occurs, the measurement accuracy of the inertial device deteriorates, and the output value y... f Multiplying (t) by the scaling factor s results in a scaling error, expressed mathematically as follows:

4. The method for detecting slowly changing faults in an inertial measurement unit under dynamic conditions according to claim 2, characterized in that, The dynamic output envelope of the normal signal is described as follows: y = f(x) + ε Where y is the observed value, i.e., the signal output of a certain inertial device, and ε is the residual that follows a Gaussian distribution, i.e. Let f(x) be the variance of the residuals, x be the input vector, and f(x) follow a Gaussian prior distribution: f(x)~GP(m(x),k(x,x')) Where m(x) i ) is the mean function, usually set to 0, k(x) i ,x i The covariance function is: k(x,x')=E[(f(x)m(x))(f(x')-m(x'))]; The training set is used to establish a prior distribution, which is then transformed into a posterior distribution in the test set samples. The observed values ​​y in the training set and the predicted values ​​f* in the test set then satisfy a joint prior distribution: Where X and X * The input matrices for the training and test sets are respectively, K(X,X) * K(X,X), K(X) * ,X * ) and K(X,X * All are covariance functions, and I is the identity matrix; Calculate the posterior distribution of the predicted value f*: The mean of the predicted values ​​on the test set The variance of the predicted values ​​is The probability distribution of the predicted values ​​is obtained based on the mean and variance of the predicted values, i.e., the envelope prediction within a certain confidence interval. Assuming a confidence level of 1-α, the confidence interval satisfied by the GPR prediction, i.e., the normal signal of the inertial measurement unit, is: Among them, l b and u b These are the upper and lower bounds of the confidence interval, z α / 2 These are the two-sided α quantiles of a standard normal distribution; Preferably, the kernel function of the Gaussian process regression model is selected from one or more combinations of the following: quadratic exponential kernel function, rational quadratic kernel function, Matern32 kernel function, and periodic kernel function PER; Preferably, the method further includes performance evaluation of the Gaussian process regression model, including: Mean absolute error (MAE) and root mean square error (RMSE) are selected as evaluation indicators for prediction performance to measure the difference between predicted and actual values, as shown in the following formula: Among them, y i and These are the actual value output by the inertial measurement unit and the predicted value by the Gaussian process regression model, respectively, where N is the number of sampling points for the signal; The smaller the MAE and RMS values, the closer the actual value and the predicted value are, and the higher the prediction accuracy of the Gaussian process regression model. Preferably, the performance evaluation further includes: Predicted Interval Coverage Rate (PICP) and Predicted Interval Regularized Average Width (PINAW) are selected as evaluation metrics for interval prediction, used to measure the width and reliability of the confidence interval, as shown in the following formulas: Where R is the average width of the confidence interval predicted by the Gaussian process regression model, and U i and L i These are the upper and lower bounds of the confidence interval, respectively; if c i =1, the prediction interval includes the true value; otherwise, c i =0; The larger the PICP value, the more true values ​​the confidence interval contains; With a fixed PICP, the smaller the PINAW, the higher the prediction accuracy of GPR.

5. The method for detecting slowly changing faults in an inertial measurement unit under dynamic conditions according to claim 4, characterized in that, The output of the particle swarm algorithm is satisfied. The normal distribution curve; if the number of sampling points for the normal output curve is N, then the range of values ​​for each sampling point is... The binary encoded particle swarm optimization algorithm (BPSO) is used to find the optimal position within the maximum number of iterations and output the global optimal position and the corresponding fitness function value, which are the maximum and minimum values ​​of the statistical features, and are used as the fault detection threshold.

6. The method for detecting slowly changing faults in an inertial measurement unit under dynamic conditions according to claim 1, characterized in that, Step (2) includes: calculating the time-domain and frequency-domain features of a normal signal. The time-domain features include root mean square, centroid, mean, median, kurtosis, and standard deviation. The frequency-domain features include the centroid frequency.

7. The method for detecting slowly changing faults in an inertial measurement unit under dynamic conditions according to claim 1, characterized in that, Step (4) includes: Calculate the multidimensional statistical features of different fault types and compare them with the fault detection threshold in step (3). When at least three feature values ​​exceed the fault detection threshold, it is determined to be a fault.

8. The method for detecting slowly changing faults in an inertial measurement unit under dynamic conditions according to claim 1, characterized in that, The method also includes evaluating the fault detection method using at least one of the following evaluation metrics: FPR, or False Alarm Rate, represents the probability of misreporting a normal sample as a fault. The calculation formula is as follows: FPR = FP / (FP+TN); FNR is the false alarm rate, which represents the probability of misclassifying a faulty sample as normal. The calculation formula is as follows: FNR = FN / (FN+TP); FDR stands for Fault Detection Rate, which represents the ability to correctly detect faulty samples. The calculation formula is as follows: FDR = TP / (TP+FN); Where TP represents the number of normal samples that were correctly detected, FN represents the number of normal samples that were falsely reported as faults, FP represents the number of faults that were not detected, and TN represents the number of abnormal samples that were correctly identified.

9. A slowly varying fault detection system for an inertial measurement unit under dynamic conditions, characterized in that, The system includes: a processor; and a computer program stored in a memory and executable on a processor, wherein the processor executes the computer program to implement the method for detecting slowly changing faults of an inertial measurement unit in a dynamic environment as described in any one of claims 1 to 8.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by the processor, the program implements the method for detecting slowly changing faults in an inertial measurement unit under dynamic conditions as described in any one of claims 1 to 8.

Images