Landing stage flight data anomaly detection method based on Gaussian process

Abstract

The invention discloses a method for detecting anomaly of flight data in a landing stage based on a Gaussian process. The method comprises the following steps: step 1, modeling standard flight data in the landing stage by using the Gaussian process; 2, introducing a deviation term for inherent uncertainty and interference factors in the flight process, modeling by using a Gaussian process, and solving posterior distribution of flight data with the deviation term by using a variational inference method; and step 3, performing anomaly detection on the flight data by using the flight data accommodation interval output by the model. Compared with the prior art, the method has the advantages that abnormal data in a training set can be filtered step by step in the model training process, discrimination intervals output by the model are converged step by step, in addition, compared with a model based on the DBSCAN algorithm, the method can give consideration to performance indexes of the false alarm rate and the recall rate at the same time, and the method is suitable for large-scale popularization and application. And the performance problem caused by improper setting of model parameters is avoided.

Description

Technical Field

[0001] The present invention relates to a method for detecting abnormal flight data during the landing phase based on Gaussian process. Background Art

[0002] At present, in the implementation of flight quality monitoring, data analysis is carried out on flight data obtained through a Quick Access Recorder (QAR) or equivalent equipment, mainly to detect abnormal situations related to aviation safety in the flight data, and provide data and information support for improving the operating quality of flight crews and strengthening aviation safety guarantee capabilities. In the advisory circulars on flight quality monitoring issued by the Federal Aviation Administration of the United States and the Civil Aviation Administration of China, the analysis methods of flight data are classified and summarized, mainly including two types: overlimit analysis and statistical analysis. Overlimit analysis refers to the pre-definition of the numerical range under normal circumstances for flight data. If the value of the actually measured flight data exceeds the pre-defined allowable range, it can be determined as an overlimit event. Statistical analysis refers to using the method of numerical statistical analysis to describe the distribution of flight data, quantitatively analyze the deviation and risk degree of each parameter in the flight data, so as to master the abnormal situations and development trends of flight data during the aviation operation process. The biggest difference between the two data analysis methods is that overlimit analysis focuses on individual independent overlimit events, while statistical analysis focuses on the overall situation of the flight data distribution.

[0003] The overlimit analysis method has been put into practical application earlier. In the report submitted by the Flight Safety Foundation (FSF) to the Federal Aviation Administration (FAA) of the United States in 1993, many matters in the specific implementation process of overlimit analysis have been discussed. Since the detection of abnormal flight data by overlimit analysis is mainly through the comparison of the measured value and the pre-defined numerical interval, with a simple principle, easy to implement, fast and efficient, and easy to explain in terms of cause analysis, overlimit analysis is adopted in most theoretical research projects and application software products of flight quality monitoring. For example, NASA has implemented the Aviation Performance Measuring System (APMS) project since 1999, which mainly uses overlimit analysis for aviation safety risk detection. Fala N et al. took the safety event detection in the approach phase as an example to discuss the factors to be considered and the rationality of setting the limit value. In addition, the above-mentioned advisory circulars issued by the Federal Aviation Administration of the United States and the Civil Aviation Administration of China also provide references on common monitoring items, monitoring parameters and reasonable numerical ranges in overlimit analysis in the appendix. However, overlimit analysis requires the pre-definition of the limit value of flight data under normal circumstances, which also leads to the following disadvantages of this method:

[0004] 1) If the defined limit values of certain flight data are not pre - determined, it will lead to the missed detection of some signs closely related to aviation safety or the missed judgment that has already become a fact.

[0005] 2) If the defined limit value range is inappropriate, there will be too high misjudgment rate or missed detection rate of over - limit events, thus seriously affecting the application effect of over - limit analysis.

[0006] 3) The determination of the limit value range is usually based on the existing aviation technology level and the analysis of past aviation safety accidents, and it may be difficult to apply to the changes in technology and equipment in future aviation operations.

[0007] Compared with over - limit analysis, statistical analysis no longer relies on the pre - definition of the limit value range of flight data. Instead, it takes the actually measured flight data as the basis, and uses theoretical knowledge and methods in mathematical statistics and other aspects to explore the potential patterns in flight data and detect data anomalies. Although statistical analysis is not as widely used as over - limit analysis at present and lacks a mature and general guiding implementation plan or standard, the statistical analysis method shows the advantage of being able to directly obtain the actual laws of aviation operations from flight data. Especially when combined with currently advanced and mature machine learning and data mining technologies, it can further improve the effectiveness and accuracy of extracting regular patterns and valuable information from actual flight data.

[0008] Classification of statistical analysis methods: Anomaly detection has always been an important research direction in the fields of machine learning and data mining. Chandola et al. reviewed the theoretical methods and technical solutions for anomaly detection in many fields. Currently, there are mainly two types of methods for using machine learning and data mining technologies to detect anomalies in flight data. One type of method is to use known normal and abnormal flight data for modeling, and compare the data to be detected with the model. If it does not conform to the normal flight mode or is similar to the abnormal flight mode, it is determined as abnormal data. In machine learning theory, this type of method is classified as supervised learning or semi-supervised learning. In the research results related to this type of method, Eric Chu et al. used the historical cruise data of the fleet for model training, mainly using linear and quadratic function models, and also considered external interference factors and model errors to reduce the misjudgment rate. Srivastava et al. used a regression model to estimate fuel consumption data and then compared it with the actual measured values. If there is a large deviation, an anomaly alarm is issued. Melnyk et al. used a vector autoregressive model for flight data modeling. Another type of method is based on unsupervised learning, using specific metrics to measure the differences between data, and determining as abnormal those data that have large differences from most of the data. Since the latter method does not require manual annotation of data, it can effectively reduce labor costs and has more advantages in practical application and promotion. In the related research results, the software Morning report developed by NASA for anomaly detection of flight data mainly uses the k-means clustering algorithm, and the flight data anomaly detection method ClusterAD proposed by LishuaiLi uses the DBSCAN clustering algorithm in principle. Compared with the k-means algorithm, the DBSCAN algorithm does not require pre-determining the number of clustering clusters k, can discover clusters of any shape, and the algorithm itself has a recognition mechanism for noise data and can be used for anomaly detection in flight data. However, its clustering and anomaly detection effects still depend on the setting of two parameters: the domain radius and the minimum number of objects in the domain of the core object. Summary of the Invention

[0009] In order to overcome the above-mentioned shortcomings of the prior art, the present invention proposes a method for anomaly detection of flight data during the landing phase based on Gaussian process. Taking the flight data obtained by QAR or equivalent equipment as the basis, it analyzes the distribution of normal flight data as a whole, and discriminates anomalies through the estimated interval of normal flight data output by the model, belonging to a method of data-driven modeling. Compared with the commonly used over-limit analysis method for flight quality monitoring at present, the method of the present invention eliminates the dependence on professional knowledge and industry experience in the definition of the reasonable limit value range in over-limit analysis, and also avoids the situation of misjudgment or missed judgment of safety incidents caused by the continuous development of aviation technology.

[0010] The technical solution adopted by the present invention to solve its technical problems is: a method for detecting abnormal flight data in the landing phase based on Gaussian process, including the following steps:

[0011] Step 1: Use Gaussian process to model the standard flight data in the landing phase;

[0012] Step 2: After introducing a deviation term for the inherent uncertainties and interference factors during the flight process, use Gaussian process for modeling, and use variational inference method to obtain the posterior distribution of the flight data with the deviation term;

[0013] Step 3: Use the flight data accommodation interval output by the model to detect abnormal flight data.

[0014] Compared with the prior art, the positive effects of the present invention are:

[0015] In view of the deficiencies in the commonly used over-limit analysis for current flight quality monitoring, the present invention proposes a data-driven modeling method based on Gaussian process for detecting abnormal flight data in the landing phase. In addition to modeling the standard values of flight data under normal conditions, the present invention also introduces a deviation term for the inherent uncertainties and interference factors during the flight process, and uses Gaussian process for modeling and solves the problem of the posterior probability of flight data after the introduction of the deviation term through variational inference. Finally, the flight data accommodation interval output by the model is used to determine whether there are abnormalities in the actual flight data. Experimental results show that during the model training process, abnormal data in the training set can be gradually filtered out and the discrimination interval output by the model can gradually converge. In addition, compared with the model based on the DBSCAN algorithm, the method of the present invention can better balance the performance indicators of both the false alarm rate and the recall rate, and avoid performance problems caused by improper setting of model parameters. Description of the Drawings

[0016] The present invention will be described by way of examples with reference to the drawings, where:

[0017] Figure 1 is the result after the first iteration training of the model;

[0018] Figure 2 is the result after the second training of the model;

[0019] Figure 3 is the result after the third training of the model;

[0020] Figure 4 is the result after the fourth training of the model;

[0021] Figure 5 is the result after the fifth training of the model. Detailed Embodiments

[0022] The method of the present invention will be described in detail below in conjunction with the accompanying drawings:

[0023] 1 Flight data anomaly detection model

[0024] 1.1 Overview of Gaussian process

[0025] To avoid the dependence on the rationality of initial parameter setting in the clustering method used in the background art, the present invention selects the Gaussian process as the basis for modeling flight data. Using Bayesian inference theory, the Gaussian process can not only calculate the maximum a posteriori estimate of the predicted value, but also obtain the probability distribution of the predicted value. The present invention utilizes this characteristic of the Gaussian process to calculate the distribution of flight data under normal conditions. When the data to be detected does not conform to the model describing normal flight data, it is determined as abnormal data.

[0026] 1.2 Flight phases and model setting

[0027] Generally, the flight process is divided into multiple phases according to different aircraft operation activities, including engine start, taxiing, takeoff, climb, cruise, descent, approach, landing, and breakaway, etc. Since the probability of abnormal data occurrence in the landing phase is relatively high, for example, situations such as glide path deviation, hard landing, or excessive touchdown distance may occur. Therefore, the present invention selects the detection of flight data anomalies in the landing phase as the research focus. Considering that some specific positions are used as reference points in the flight procedure design of the landing phase, when the present invention uses the Gaussian process to model the flight data in the landing phase, the model also selects the distance from a specific position as the input variable, hereinafter represented by the symbol d, and selects the aerodrome reference point as the reference point. The output variables of the model are the flight data concerned in flight quality monitoring, such as speed, altitude, attitude, etc.

[0028] 1.3 Modeling of standard flight data

[0029] Aircraft usually execute flight missions according to a predetermined flight plan or flight procedure. Therefore, it can be assumed that when the aircraft flies completely accurately in line with the flight plan or flight procedure, the flight data will present standard reference values. Of course, under the influence of factors such as aircraft differences, weather differences, and navigation and surveillance equipment errors, the actually measured flight data will deviate from the standard flight data, which is also the basic idea of over-limit analysis. The setting of the standard flight data in over-limit analysis is based on aviation professional knowledge and actual operation experience, and usually for a limited number of specific monitoring points. To more comprehensively monitor the entire landing phase, the present invention starts from the flight data itself and solves the standard values at various distances within a certain range from the aerodrome reference point through the Gaussian process. The specific idea is as follows:

[0030] The Gaussian process can be regarded as an extension of the Gaussian distribution from describing the distribution of variables to describing the distribution of functions. It is often used to handle complex regression problems such as non-linearity and is usually defined in the following form:

[0031]

[0032] where m(d) and k(d, d') are the mean function and covariance function of the Gaussian process respectively, and the related definitions are as follows:

[0033]

[0034] The mean function m(d) needs to be defined by means of the known distribution of the entire random process variables, while the covariance function k(d, d') is used to describe how f(d) changes with d. Common covariance functions include the squared exponential kernel function and the Matérn function, etc. The flight data concerned in flight quality monitoring mainly refers to various data such as the latitude, longitude, altitude, speed, and attitude of the aircraft. For the sake of generality in description, the symbol g is used to represent the standard value of any type of flight data. It is assumed that the standard values g at each value of the landing phase d studied in the present invention generally follow a Gaussian process distribution. At the same time, since it is difficult to obtain the information of the mean function of the standard value only from the flight data, the constant function 0 is used as the mean function, so that the distribution of the variables in the Gaussian process is more controlled by the covariance function. This is also a common practice in the practical application of the Gaussian process. In this way, when the standard values g = {g i |i = 1, …, N} of the flight data corresponding to a partial distance set d = {d i |i = 1, …, N} are known, the distribution of the data of the other distances d * corresponding to the standard value g * can be calculated by applying the derivation results of the Gaussian process:

[0035]

[0036] where

[0037] k ** = k(d * , d * ) (5)

[0038]

[0039] As mentioned above, due to the inherent uncertainty and interference factors during the flight, there are deviations between the flight data obtained through QAR or equivalent equipment and the flight data standard values. Therefore, the data g in the above model cannot be directly obtained from the flight data used for flight quality monitoring. For this reason, an additional deviation term r is introduced to form the following relationship:

[0040] y i = g i + r i , i = 1, ..., N (8)

[0041] Where y represents the flight data obtained through QAR or equivalent equipment. The deviation term r is similar to the noise term commonly seen in the Gaussian process model. However, in most cases, it is assumed that the noise term satisfies independent and identically distributed, and its probability distribution is a Gaussian distribution with a constant variance. This assumption is mainly for the convenience of subsequent derivations. However, the degrees of influence of uncertain and interference factors at different positions during the landing phase are different. Therefore, in the present invention, it is assumed that the deviation term r satisfies a Gaussian distribution with a mean of 0, and its variance is no longer constant. To ensure the non-negative property of the deviation term variance, the present invention uses another Gaussian process to model the logarithm of the deviation term variance, as follows:

[0042]

[0043] Where k r (d, d') is the covariance function used in the definition of the Gaussian process corresponding to the deviation term variance σ 2r (d), and the constant μ r is used to represent the average level of its deviation term variance.

[0044] It can be seen from equation (8) that the vectors y = (y 1 , y 2 , …, y N ) T and the vectors g = (g 1 , g 2 , …, g N ) T satisfy a linear relationship. Based on the relevant conclusions of the linear Gaussian model, the flight data y 1 , y 2 , …, y N obtained through QAR or equivalent equipment and any other standard value g * corresponding to the distance d * still satisfy a multivariate Gaussian distribution, and its covariance matrix is

[0045]

[0046] Where K D is the diagonal matrix diag(r) of the deviation term on the distances d 1 , d 2 , …, d N , and the diagonal elements r = (r 1 , …, r N ) T. By reusing the derivation conclusion of the Gaussian process, the posterior distribution p(g * |t * ,y,t,r,r * ) of g can be calculated. By adding the deviation term r * , the posterior distribution of the flight data y * used for flight quality monitoring on the distance d * can be obtained: *

[0047]

[0048] where

[0049]

[0050] Since r and r * are unknown, it is necessary to further integrate r and r * to obtain

[0051] p(y * |d * ,y,d) = ∫∫p(y * |d * ,y,d,r,r * )p(r,r * |d * ,y,d)drdr * (15)

[0052] However, p(r,r * |d * ,y,d) cannot be obtained only from the current model assumptions and flight data. Although an approximate solution can be obtained by sampling methods, it has the disadvantages of large computational complexity and long time consumption. The present invention uses the variational inference method to obtain an approximate solution. Based on the mean field method commonly used in variational inference, the logarithm of the marginal probability p(y) can be decomposed as follows:

[0053]

[0054] where KL(·║·) represents the Kullback-Leibler divergence, and L(q(g),q(r)) is the lower bound of log(p(y)). When seeking the distributions q(g) and q(r) to maximize this lower bound, the KL divergence in Equation (16) will be minimized, thereby optimizing the approximate solution of p(g,r|y) in the decomposed form q(g)q(r). By using the derivation conclusion of maximizing the lower bound L(q(g),q(r)) with respect to q(g) and substituting it, an approximate lower bound that only depends on q(r) can be further obtained: ​

[0055]

[0056] where

[0057] Z(q(r)) =

[0058] ∫exp(∫q(r)log p(y|g,r)dr)p(g)dg (18)

[0059] Using the multivariate Gaussian distribution setting commonly used in variational inference for the distribution of q(r), with its mean vector and covariance matrix denoted by μ q and Σ q respectively, according to equations (9) and (10), the lower bound in equation (17) can be further derived as follows:

[0060]

[0061] where tr(·) represents the trace of a matrix, R is a diagonal matrix with its diagonal elements being [R] ii = exp([μ q i -[μ q i ), and K r is the covariance matrix calculated using the covariance function k r (t,t'). According to the relationship between the extreme points and partial derivatives of equation (19), we can obtain:

[0062]

[0063] where Λ represents a positive semi - definite diagonal matrix. So far, the training of the model can be reduced to maximizing the lower bound represented by equation (19), where the parameters to be optimized include the parameters of the covariance functions in the two Gaussian processes corresponding to the standard value g and the deviation term r, the diagonal elements in the matrix Λ, and μ r which controls the average level of the variance of the deviation term. In the model training of the present invention, the common conjugate gradient method is selected for parameter optimization.

[0064] 1.4 Abnormal Flight Data Judgment

[0065] In the case of obtaining an approximate solution using the above - mentioned variational inference, the posterior distribution corresponding to any distance d * to be monitored and the standard value g * can be obtained:

[0066]

[0067] where

[0068] ​​

[0069] In addition, the variance σ of the deviation term 2r is also a Gaussian distribution even when the logarithm of (d) is approximately solved, and the expected value at the distance d* is as follows:

[0070]

[0071] where

[0072]

[0073] When subsequently obtaining the posterior distribution of the flight data y with the deviation term * the present invention selects the maximum probability value of the deviation term to substitute for obtaining an approximate solution, and thus the following result can be obtained:

[0074]

[0075] where the mean of y * is the same as that in Equation (23), and its variance becomes after considering the variances of both the standard value and the deviation term:

[0076]

[0077] The present invention selects the 95% tolerance interval of the posterior distribution of y * in Equation (27) as the discrimination interval for whether the flight data is normal or not. If the flight data actually obtained through QAR or equivalent equipment is not within this interval, then it is determined as abnormal. Thus, the discrimination function for whether the flight data y is abnormal can be described in the following form:

[0078]

[0079] 1.5 Model Training

[0080] When training the above model using the flight data obtained through QAR or equivalent equipment, if the training data contains abnormal flight data, it will affect the discrimination interval output by the model. To avoid manual annotation of the training data, more precisely, to avoid filtering abnormal flight data manually, the model training adopts the method of continuously filtering the training data according to the current model output and then retraining. The specific operation method is as follows: Initially, all the original flight data is used for training. The trained model is used to detect the abnormal data in the training set. After filtering out these abnormal data from the training set, the model is retrained, and then the abnormal data in the training set is filtered again and the model is trained. This process is repeated until the proportion of the abnormal data filtered out from the training set in the current iteration is less than 5%, so that the current training data meets the 95% tolerance interval set by the model. This training method has the effect of gradually converging on the discrimination interval output by the model, which will be verified in the next section.

[0081] 2 Verification Results and Analysis

[0082] 2.1 Training Effect

[0083] For the flight quality monitoring during the landing phase, corresponding flight data items are selected for analysis according to different monitoring items, such as airspeed, roll angle, pitch angle, vertical overload, total weight, etc. Due to limited space, the present invention selects the altitude related to the glide path deviation safety event as an example. More precisely, the flight data item output by the model is the Mean Sea Level in the QAR data, and the input item is the distance from the airport reference point as described above. In addition, the squared exponential kernel function is selected as the covariance function in the Gaussian process for modeling the standard value and the deviation item. The model training uses the QAR data of the same aircraft type at a domestic airport, including a total of 100 flight data during the landing phase. In order to verify the screening and filtering of abnormal data and the model convergence effect of the model training method proposed by the present invention, abnormal data manually selected are specifically selected in the training data. The model is completed after 5 times of training. The abnormal detection, filtering, and modeling effect of the discrimination interval for the training data each time are as Figures 1-5 shown.

[0084] It can be seen from the experimental results that the abnormal data affecting the modeling effect of the discrimination interval are gradually filtered out during the model training process. Most of the data in the original training set are within the finally output discrimination interval, which has better interpretability and intuitiveness for the distribution of flight data under normal conditions compared with the overrun analysis. In addition, the gradual convergence effect of the training process on the discrimination interval output by the model is verified.

[0085] 2.2 Comparative Analysis

[0086] To further verify the detection performance of the model for abnormal flight data, the present invention selects the false alarm rate and recall rate commonly used in abnormal detection as the measurement indicators, and uses the DBSCAN algorithm used in abnormal detection as a comparison. For the sake of easy description, the flight quality monitoring model based on Gaussian process proposed by the present invention is abbreviated as GP - FOQA, and the model for comparison is abbreviated as DBSCAN. The training data of GP - FOQA and the initial data of DBSCAN both use the 100 flight data during the landing phase used in the previous subsection. The test data selects the QAR data for which it has been manually marked as abnormal or not, including 10 abnormal landings and 50 normal landings. The marking work is completed under the guidance of two flight instructors with more than five years of work experience. Since the abnormal detection effect of the DBSCAN algorithm is closely related to two parameters, the domain radius ε and the minimum number of objects MinPts in the domain of the core object, several sets of settings of the two parameters ε and MinPts are selected for comparison. The experimental data are shown in Table 1:

[0087] Experimental Results of False Alarm Rate and Recall Rate in Table 1

[0088]

[0089] As can be seen from Table 1, for the DBSCAN model, when using the two sets of parameter settings (ε: 18, MinPts: 15) and (ε: 15, MinPts: 10), although a relatively high recall rate can be achieved, the false alarm rate is too high. When using the parameter setting (ε: 18, MinPts: 5), the false alarm rate is the highest among several test results, but the relatively low recall rate is not satisfactory. Although the false alarm rates of the other two sets of parameter settings (ε: 20, MinPts: 10) and (ε: 18, MinPts: 10) of this model are lower than those of the GP-FOQA model, there is a large gap in terms of the recall rate. Generally speaking, using the GP-FOQA model can better balance the performance indicators of both the false alarm rate and the recall rate. Moreover, the key point is that there is no need to artificially consider the settings of the two parameters ε and MinPts in the DBSCAN model, avoiding the situation of too high false alarm rate or too low recall rate caused by improper model parameter settings in the actual application process.

Claims

1. A method for detecting anomalies in flight data during landing phase based on Gaussian process, characterized in that: The steps include: Step 1: Use Gaussian process to model the standard flight data of the landing phase; Step 2: After introducing deviation terms to address inherent uncertainties and interference factors in the flight process, Gaussian process modeling is used, and variational inference methods are used to obtain the posterior distribution of flight data with deviation terms; Step 3: Use the flight data accommodation interval output by the model to perform anomaly detection on the flight data.

2. The Gaussian process-based landing phase flight data anomaly detection method according to claim 1, characterized in that: In step 1, when using Gaussian process to model the standard flight data of the landing phase, the distance from the airport reference point is selected as the input variable of the model, and the flight data concerned by flight quality monitoring is selected as the output variable of the model.

3. The method for detecting anomalies in flight data during landing phase based on Gaussian process according to claim 2, characterized in that: The flight data that flight quality monitoring focuses on include: aircraft latitude and longitude, altitude, speed and attitude.

4. The method for detecting anomalies in flight data during landing phase based on Gaussian process according to claim 1, characterized in that: When using Gaussian process modeling, the covariance function used is the squared exponential kernel function.

5. The method for detecting anomalies in flight data during landing phase based on Gaussian process according to claim 1, characterized in that: In step 2, after introducing the deviation term, the Gaussian process model is used and the variational inference method is used to obtain the posterior distribution of the flight data with the deviation term: (1) An additional deviation term r is introduced to establish the following relationship: y i =g i +r i ,i=1,...,N Where y represents the flight data obtained by QAR or equivalent equipment, g is the standard value of the flight data, and the deviation term r is a Gaussian distribution with a mean of 0; (2) Use Gaussian process to model the logarithm of the deviation term variance: where k r (d,d') is the variance of the deviation term σ 2r (d) corresponds to the covariance function used in the Gaussian process definition, μ r is a constant, indicating that it deviates from the average level of the variance of the item; (3) Using flight data y1,y2,…,y N and distance d * The corresponding standard value g * The covariance matrix of the distance d is calculated * Flight data used for flight quality monitoring * The posterior distribution of : Among them: flight data y1,y2,…,y N and distance d * The corresponding standard value g * The covariance matrix of Where K D is about the distances d1,d2,…,d N The diagonal matrix of the upper deviation term is diag(r), and the diagonal elements r=(r1,…,r N ) T ; (4) For r and r * integral: p(y * |d * ,y,d)= ∫∫p(y * |d * ,y,d,r,r * )p(r,r * |d * ,y,d)drdr * (5) Decompose the logarithm of the marginal probability p(y): Where: KL(·║·) represents the KL divergence, L(q(g),q(r)) is the lower bound of log(p(y)); (6) is calculated as follows: in Z(q(r))= ∫exp(∫q(r)log p(y|g,r)dr)p(g)dg (7) Using the mean vector μ of q(r) q and the covariance matrix Σ q Further deduction yields: Where tr(·) represents the trace of the matrix, R is a diagonal matrix whose diagonal elements are [R] ii =exp([μ q ] i -[μ q ] i ), K r is to use the covariance function k r (t,t') calculated covariance matrix; (8) According to the relationship between extreme points and partial derivatives, we can calculate: Where Λ represents a semi-positive definite diagonal matrix; (9) Calculate any distance d that needs to be monitored * Corresponding standard value g * The posterior distribution of : in (10) Calculate the deviation term variance σ 2r The expected value of the logarithm of (d) at distance d*: Where: (11) Obtain the flight data y with deviation terms * The posterior distribution of , we get: in:

6. The Gaussian process-based landing phase flight data anomaly detection method according to claim 5, characterized in that: Flight data y with deviation terms * The 95% tolerance interval of the posterior distribution of is the flight data accommodation interval.

7. The Gaussian process-based landing phase flight data anomaly detection method according to claim 6, characterized in that: The discriminant function of whether the flight data y is abnormal is:

8. The Gaussian process-based landing phase flight data anomaly detection method according to claim 5, characterized in that: The parameters that need to be optimized in model training include the parameters of the covariance function of the two Gaussian processes corresponding to the standard value g and the deviation term r, the diagonal elements in the matrix Λ, and μ for controlling the average level of the deviation term variance r .

9. The Gaussian process-based landing phase flight data anomaly detection method according to claim 8, characterized in that: The conjugate gradient method is used for parameter optimization in model training.

10. The Gaussian process-based landing phase flight data anomaly detection method according to claim 9, characterized in that: The method for training the model using flight data obtained through QAR or equivalent equipment is: initially use all the original flight data to train the model, then use the trained model to detect abnormal data in the training set, then filter out these abnormal data from the training set and train the model again, then filter out the abnormal data in the training set again and continue to train the model, and so on, until the proportion of abnormal data filtered out from the training set this time is less than 5%.

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