A method for predicting inertial faults based on confidence rule base

Abstract

A method for predicting inertial navigation system faults based on a confidence rule base belongs to the field of fault prediction of inertial navigation devices, and is characterized in that: by static testing of a laser inertial navigation system, a confidence rule base model is established with the accumulated pulse quantity per unit time as input and the navigation error as output; the navigation error per unit time is then used to reflect the fault state of the laser inertial navigation system, and a fault threshold of navigation accuracy is set to reflect the fault state of the laser inertial navigation system, thereby realizing fault prediction of the laser inertial navigation system. The method for predicting inertial navigation system faults based on a confidence rule base of the present invention realizes navigation error prediction using the pulse data of the laser inertial navigation system; the expert system based on the confidence rule base can effectively process various uncertain information and can handle inertial navigation system fault prediction problems in complex environments; the method provides an effective way to predict faults of laser inertial navigation system by predicting the navigation error and setting the navigation error threshold to judge the fault state.

Description

Technical Field

[0001] The present invention belongs to the field of fault prediction of inertial navigation devices, and in particular relates to an inertial navigation device fault prediction method based on a confidence rule base for determining an inertial navigation device state by predicting navigation accuracy. Background Art

[0002] With the development of modern aerospace technology, the performance requirements for aircraft are getting higher and higher, and the requirements for navigation systems that control flight accuracy are also getting higher and higher. Inertial devices, as the core part of the navigation system, mainly include components such as gyroscopes and accelerometers, and play a very critical role in navigation. Whether the inertial devices can work normally is directly related to whether the navigation is accurate. The laser inertial group is an optical inertial device developed with the laser technology. Compared with traditional inertial devices, optical inertial devices have high precision, strong anti-interference ability, long life and good reliability. Therefore, laser inertial groups are often used in rockets, drones, etc.

[0003] The working environment of most navigation systems is complex, which has a great impact on inertial devices. Due to the complex manufacturing process and the lack of analysis of the internal mechanism of the laser inertial group and the knowledge related to the health management of the laser inertial group, the fault analysis of the laser inertial group is not clear enough so far, and it is impossible to achieve accurate modeling of the internal mechanism of the inertial group. The analysis of its fault state cannot be completely analyzed from the mechanism of the laser inertial group, so the fault state of the laser inertial group is not discovered in time. Therefore, in order to improve the accuracy of the navigation system, it is particularly important to determine the fault state of the inertial group. Summary of the invention

[0004] The present invention aims to provide an inertial group fault prediction method based on a confidence rule base for determining the inertial group state by predicting navigation accuracy.

[0005] The inertial group fault prediction method based on the confidence rule base described in the present invention establishes a confidence rule base model with the accumulated pulse amount per unit time as input and the navigation error as output through static testing of the laser inertial group; then the navigation error per unit time is used to reflect the fault state of the laser inertial group, and the fault threshold of the navigation accuracy is set to reflect the fault state of the laser inertial group, thereby realizing the fault prediction of the laser inertial group.

[0006] The inertial group fault prediction method based on the confidence rule base of the present invention performs static tests on the laser inertial group in various environments, obtains the pulse amounts of the X-axis, Y-axis and Z-axis of the gyroscope and accelerometer in the laser inertial group from the test data; processes the pulse amount data to obtain the cumulative pulse amount; selects the cumulative pulse amount per unit time as feature information; then performs Monte Carlo simulation (MC) on the feature information to simulate various states that different laser inertial groups may reach during the test, establishes a confidence rule base model with the cumulative pulse amount per unit time as input and the navigation error per unit time as output, finally optimizes and adjusts the parameters of the confidence rule base model, sets a fault threshold for the output navigation error, and then reflects the fault state of the laser inertial group, and realizes the fault prediction of the laser inertial group through the pulse amount of the navigation information.

[0007] The inertial group fault prediction method based on the confidence rule base of the present invention comprises the following steps:

[0008] Step 1: Attribute input information selection and Monte Carlo simulation;

[0009] Firstly, the laser inertial group pulse data of the test is differentially processed to obtain the differential component of the pulse data, and the feature of the differential component is extracted to select the feature quantity that best reflects the differential component information of the navigation error. According to the actual test and expert knowledge, the cumulative pulse quantity is selected as the feature quantity as the model input; the differential components per unit time of each axis of the gyroscope and accelerometer are accumulated to obtain the cumulative pulse quantity, and the cumulative pulse quantity per unit time is used as the model input; the input of the model is the cumulative pulse increment per unit time of the X-axis, Y-axis, and Z-axis of the gyroscope and accelerometer;

[0010] The input data is converted into acceleration and angular velocity of analog quantity, and the trend of acceleration and angular velocity is analyzed through Monte Carlo simulation. The probability distribution of the system analog quantity is analyzed by random sampling method, and the various states that the analog quantity in the system may reach are simulated, so as to reflect the uncertainty of the output;

[0011] Step 2: Construction of the inertial navigation error prediction model;

[0012] According to the input of step 1, a navigation error prediction model based on a confidence rule base is established; the expression of the kth confidence rule in the confidence rule base is as follows:

[0013]

[0014] In formula (1), t is the unit time; Indicates the i-th premise attribute x in the k-th rule i The reference value set is given by experts based on the specific environment and internal working mechanism; L represents the number of rules; M represents the number of premise attributes; θk represents the rule weight of the Kth rule; δ i represents the weight of the i-th premise attribute in the rule, which reflects the importance of the i-th premise attribute relative to other premise attributes; β j,k Indicates the jth output result D relative to the output part in the Kth rule j Confidence level; D j Indicates the evaluation level of the output reference value;

[0015] First, input information x i Converted to reference value Confidence

[0016]

[0017] α i j represents the matching degree of the i-th input attribute in the j-th rule, x i represents the input of the attribute, γ ik Indicates the attribute reference value of the Kth rule;

[0018] In order to obtain the matching degree α i j Then the evidence reasoning algorithm (ER) is used to combine the rules and calculate the output. First, the activation weight must be calculated, and the activation weight is expressed as:

[0019]

[0020] Where 0≤w k ≤1, k=1,…,L; L is the number of activated rules; is the relative attribute weight, which indicates the relative importance of the attribute.

[0021] The reasoning of ER algorithm is divided into iterative algorithm and analytical algorithm. The calculation of analytical algorithm is simple and its expression is

[0022]

[0023] where β i Represents the confidence of the Nth result in the output, and 0≤β i ≤1, The output of BRB is expressed as

[0024] Z(x i )={(D n ,β n )},n=1,2,...,N (6)

[0025]

[0026] Z(x i ) represents the output result based on BRB, u(D n ) represents the evaluation result D n The utility of The results of the prediction model;

[0027] Step 3: Model training and optimization;

[0028] Since the initial parameters of the prediction model are all given by experts, when the confidence rule base system is relatively complex, it is difficult for experts to determine the exact values ​​of these parameters, so it is necessary to optimize the initial parameters, and randomly select 50% of the optimized data as training data, and the remaining data as test data to detect the accuracy of the prediction model;

[0029] Step 4: Fault diagnosis;

[0030] Based on the confidence rule base prediction model established in step 3, the accumulated pulse amount of the laser inertial group is used as input and the navigation error is used as output. According to expert knowledge, a threshold of the navigation error per unit time based on the fault state of the laser inertial group is given. When the navigation error per unit time of the laser inertial group is greater than the threshold, the laser inertial group is considered to be in a faulty state.

[0031] In the inertial group fault prediction method based on the confidence rule base of the present invention, the process of initial parameter optimization in step 3 is: the optimization algorithm optimizes the model parameters using the projection covariance matrix adaption evolution strategy (P-CMA-ES) based on the projection operator;

[0032] The confidence rule base parameter optimization model is expressed as

[0033] minf(V)

[0034] stA(V)=0,B(V)≥0

[0035] f(V) represents the objective function; V represents the vector composed of the parameters of the confidence rule base; A(V) represents the equality constraint; B(V) represents the inequality constraint;

[0036] The initial values ​​of the optimization parameters are given by experts, and the constraints that the parameters should satisfy during optimization are:

[0037] 1) Rule weights. After standardization, the rule weights should satisfy the following requirements:

[0038] 0≤θ k ≤1,k=1,2,…,L

[0039] 2) Attribute weights. After being standardized, attribute weights should satisfy:

[0040]

[0041] 3) Confidence of initial rule output:

[0042] 0≤β n，k ≤1, n=1,…,N,k=1,2,…,L

[0043] 4) If the kth rule is complete, then the sum of all confidences output by the rule is 1; otherwise, the sum of the confidences is less than 1, as expressed as follows:

[0044]

[0045] Mean square error (MSE) is used to indicate the accuracy of the model, and its expression is as follows:

[0046]

[0047] in, represents the output value of the model; y(t) is the true value of the output; T is the number of data; V represents the vector composed of the parameters that need to be optimized by the confidence rule base.

[0048] The inertial group fault prediction method based on the confidence rule base described in the present invention has the following advantages: (1) the navigation error prediction is realized by using the pulse data of the laser inertial group; (2) the expert system based on the confidence rule base can effectively process various uncertain information and can handle the inertial group fault prediction problem in complex environments; (3) this method predicts the navigation error, sets the navigation error threshold to judge the fault state, and provides an effective way to predict the fault of the laser inertial group. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 It is a flow chart of the method for predicting inertial group faults based on the confidence rule base of the present invention;

[0050] Figure 2 It is a schematic diagram for comparing and explaining the inertial group fault prediction method based on the confidence rule base described in the present invention. DETAILED DESCRIPTION

[0051] The inertial group fault prediction method based on the confidence rule base of the present invention is described in detail below through the accompanying drawings and embodiments.

[0052] The inertial group fault prediction method based on the confidence rule base of the present invention performs static tests on the laser inertial group in various environments, obtains the pulse amounts of the X-axis, Y-axis and Z-axis of the gyroscope and accelerometer in the laser inertial group from the test data; processes the pulse amount data to obtain the cumulative pulse amount; selects the cumulative pulse amount per unit time as characteristic information; and then performs Monte Carlo simulation on the characteristic information to simulate the uncertainty of complex environments and sensors in measurement, simulates various states that different laser inertial groups may reach during the test, and establishes a confidence rule base model with the cumulative pulse amount per unit time as input and the navigation error per unit time as output; since all the parameters in the initial model are given by expert knowledge, in order to increase the accuracy of the expert knowledge, the confidence rule base model is finally optimized and adjusted, and a fault threshold is set for the output navigation error, thereby reflecting the fault state of the laser inertial group, and realizing the fault prediction of the laser inertial group through the pulse amount of the navigation information.

[0053] like Figure 1 As shown, the inertial group fault prediction method based on the confidence rule base of the present invention mainly includes the following steps:

[0054] Step 1: Attribute input information selection and Monte Carlo simulation

[0055] Taking into account the principles of universality and completeness of attribute selection, and combining with the working principle of the laser inertial group, starting from actual testing, based on the data analysis and test process analysis of the laser inertial group and combined with expert knowledge, the accumulated pulse amount of the three axes of the gyroscope and accelerometer is selected as the input information of the attribute.

[0056] In this embodiment, in order to simulate the state of the laser inertial navigation system in a complex environment, tests under room temperature, low temperature and ultra-low temperature environments are selected. The test data of the laser inertial navigation system is a pulse signal, and the sampling frequency of the pulse signal is 5ms. The navigation data is differentiated to obtain pulse increment data. According to the actual situation combined with expert knowledge, the cumulative pulse amount is used as the characteristic information of the pulse increment data to establish a prediction model for the navigation error. The 6,000,000 groups of data measured in the experiment are grouped, and every 60,000 groups of data (i.e., 5 minutes) are divided into a group. One group of input data corresponds to one navigation error output. The first 60,000 groups of data are used for aiming, and the next 60,000 groups of data are used for one navigation. The navigation error corresponding to each 60,000 groups of data is used as the navigation error per unit time (i.e., 5 minutes). The data is subjected to Monte Carlo simulation, and a total of 98 groups of navigation error data are obtained.

[0057] A total of 98 sets of data were obtained in the tests under room temperature, low temperature and ultra-low temperature environments.

[0058] X input (t i )=x 60000i+1+x 60000i+2 +...+x 60000i+60000 (i=1,2…98) (10)

[0059] where x k represents the Kth pulse increment data, X input (t i ) represents the accumulated pulse quantity of the i-th one.

[0060] Table 1 shows the input of the premise attributes of the system:

[0061] Table 1 Attribute input

[0062]

[0063] Step 2: Construction of the laser inertial navigation accuracy prediction model;

[0064] In establishing the prediction confidence rule base model, the expression of the Kth rule is:

[0065]

[0066] Then y(t)is{(D1,β 1，k ), (D2, β 2，k ), (D3, β 3，k ), (D4, β 4，k )}

[0067] With rule weight θ k , attribute weight δ1, δ2, δ3, δ4, δ5, δ6

[0068] Where T x T y T z J x J y J z Respectively represent the accumulated pulses of the gyroscope X-axis, Y-axis, and Z-axis and the accelerometer X-axis, Y-axis, and Z-axis. is a set of reference values ​​of premise attributes, where the reference value levels of the attributes are represented by S and L, respectively, and D i is the set of reference values ​​for output. The reference values ​​of output navigation accuracy are represented by S, M, SL, and L respectively. The attribute weight δ i With the rule weight θ k The parameters are given by experts.

[0069] The reference values ​​and reference levels of attribute input are shown in Tables 2 to 7, the reference values ​​and reference levels of navigation accuracy as output are shown in Table 8, and the attribute weights, rule weights and initial confidence distribution are shown in Table 9.

[0070] Table 2 Gyroscope X-axis reference value definition

[0071]

[0072] Table 3 Gyroscope Y-axis reference value definition

[0073]

[0074] Table 4 Gyroscope Z-axis reference value definition

[0075]

[0076] Table 5 Gyroscope X-axis reference value definition

[0077]

[0078] Table 6 Gyroscope Y-axis reference value definition

[0079]

[0080] Table 7 Gyroscope Z-axis reference value definition

[0081]

[0082] Table 8 Definition of navigation error reference value

[0083]

[0084] Table 9 Navigation accuracy initial prediction model

[0085]

[0086] Step 3: Navigation accuracy prediction model optimization

[0087] After the navigation accuracy prediction model based on the BRB confidence rule base is constructed, due to the large number of initial parameters and the uncertainty of expert knowledge, the predicted value of the initial parameters of the model will have a certain deviation from the actual true value, affecting the accuracy of the prediction model. The initial parameters need to be optimized to improve the accuracy of the prediction model.

[0088] In this embodiment, a total of 98 sets of data were measured, 50% of which were extracted as training data to optimize the initial parameters of the prediction model; the remaining data were used as test data to detect the accuracy of the optimized model. The optimization algorithm uses the projection covariance matrix adaptation evolution strategy (P-CMA-ES) based on the projection operator to optimize the model parameters.

[0089] Table 10 shows the prediction model after navigation accuracy optimization;

[0090] Table 10 Prediction model after navigation accuracy optimization

[0091]

[0092] Depend on Figure 2 From the results, we can see that the unoptimized prediction model has a large error and cannot predict the problem, while the accuracy of the optimized prediction model has been greatly improved and can effectively handle the prediction problem.

[0093] Since the optimization algorithm based on P-CMA-ES has a certain degree of randomness, the optimized BRB model was tested. A set of MSEs were obtained after 50 tests, ranging from 1.5523 to 2.1012. The MSE of the unoptimized BRB model was 22.5608. Table 11 is a comparison chart of MSEs before and after optimization.

[0094] Table 11 Comparison of MSE before and after optimization

[0095]

[0096] Through comparative tests, it can be seen that the MSE of the optimized BRB has been greatly reduced compared with that before optimization, and the model accuracy has been improved, indicating that the optimized BRB can improve the prediction of the actual laser inertial group test navigation accuracy and further solve the laser inertial group fault prediction problem in complex environments.

[0097] Step 4: Setting the fault threshold

[0098] Combining expert knowledge with actual tests, a fault threshold based on the change in unit navigation error was set. In this test, the fault threshold was set to 16m. When the navigation error was greater than 16m, it indicated a laser inertial group fault.

[0099] Depend on Figure 2 It can be seen that there is a certain error between the predicted value of the BRB model before optimization and the true value of the navigation error, and the model has omissions, with an overall false alarm rate of 14.63%. The difference between the predicted value of the optimized BRB model and the true value of the navigation error is significantly reduced, with an overall false alarm rate of 2.44%. The improved accuracy shows that the optimized BRB model has certain prediction capabilities.

Claims

1. A method for predicting inertial group faults based on a confidence rule base, characterized in that: Through static testing of the laser inertial group, a confidence rule base model is established with the accumulated pulse quantity per unit time as input and the navigation error as output; then the navigation error per unit time is used to reflect the fault state of the laser inertial group, and the fault threshold of navigation accuracy is set to reflect the fault state of the laser inertial group, so as to realize the fault prediction of the laser inertial group; specifically, by static testing the laser inertial group in various environments, the pulse quantity of the X-axis, Y-axis and Z-axis of the gyroscope and accelerometer in the laser inertial group is obtained from the test data; the pulse quantity data is processed to obtain the accumulated pulse quantity; The accumulated pulse quantity per unit time is selected as characteristic information; Then, a Monte Carlo simulation is performed on the characteristic information to simulate the various states that different laser inertial navigation systems may reach during the test, and a confidence rule base model is established with the accumulated pulse amount per unit time as input and the navigation error per unit time as output. Finally, the parameters of the confidence rule base model are optimized and adjusted, and a fault threshold is set for the output navigation error to reflect the fault state of the laser inertial navigation system, and the fault prediction of the laser inertial navigation system is achieved through the pulse amount of the navigation information.

2. The inertial group fault prediction method based on the confidence rule base according to claim 1 is characterized in that The following steps are involved: Step 1: Attribute input information selection and Monte Carlo simulation; Firstly, the laser inertial group pulse data of the test is differentially processed to obtain the differential component of the pulse data, and the feature of the differential component is extracted. Combined with expert knowledge, the cumulative pulse quantity is selected as the feature quantity as the model input; The unit time difference components of each axis of the gyroscope and accelerometer are accumulated to obtain the cumulative pulse increment, and the cumulative pulse amount per unit time is used as the model input; The input data is converted into acceleration and angular velocity of analog quantity, and the trend of acceleration and angular velocity is analyzed through Monte Carlo simulation. The probability distribution of the system analog quantity is analyzed by random sampling method, and the various states that the analog quantity in the system may reach are simulated, so as to reflect the uncertainty of the output; Step 2: Construction of the inertial navigation error prediction model; According to the input of step 1, a navigation error prediction model based on a confidence rule base is established; the expression of the kth confidence rule in the confidence rule base is as follows: In formula (1), t is the unit time; Indicates the i-th premise attribute x in the k-th rule i The reference value set is given by experts based on the specific environment and internal working mechanism; L represents the number of rules; M represents the number of premise attributes; θ k represents the rule weight of the Kth rule, which reflects the importance of the Kth rule; δ i represents the weight of the i-th premise attribute in the rule, β j,k Indicates the jth output result D relative to the output part in the Kth rule j Confidence level; D j Indicates the evaluation level of the output reference value; First, input information x i Converted to reference value Confidence In the formula represents the matching degree of the i-th input attribute in the j-th rule, x i represents the input of the attribute, γ ik Indicates the attribute reference value of the Kth rule; In seeking matching The rules are then integrated and calculated using the evidence reasoning algorithm. When the system has input, some rules based on the confidence rule base are activated, and the weight calculation method of the activated rules is: Where 0≤w k ≤1, k=1,…,L; L is the number of activated rules; is the matching degree of the input relative to the premise attribute in the corresponding rule, i = 1,…,m; θ k is the rule weight; δ i is the attribute weight; is the relative attribute weight; The ER parsing algorithm is expressed as β i Represents the confidence of the Nth result in the output, and 0≤β i ≤1, The output of the confidence rule base is expressed as S(x i )={(D n ,b n )},n=1,2,...,N (7) S(x i ) represents a nonlinear model built based on a confidence rule base, which transforms the final output into the expected effect: u(D n ) represents the evaluation result D n The utility of It represents the expected effect of the prediction model and is also the expected output result; Step 3: Model training and optimization; Since the initial parameters of the prediction model are all given by experts, when the confidence rule base system is relatively complex, it is difficult for experts to determine the exact values ​​of these parameters, so it is necessary to optimize the initial parameters, and randomly select 50% of the optimized data as training data, and the remaining data as test data to detect the accuracy of the prediction model; Step 4: Fault diagnosis; Based on the confidence rule base prediction model established in step 3, the accumulated pulse amount of the laser inertial group is used as input and the navigation error is used as output. According to expert knowledge, a threshold of the navigation error per unit time based on the fault state of the laser inertial group is given. When the navigation error per unit time of the laser inertial group is greater than the threshold, the laser inertial group is considered to be in a faulty state.

3. The inertial group fault prediction method based on the confidence rule base according to claim 2 is characterized in that The process of initial parameter optimization described in step 3 is as follows: the optimization algorithm optimizes the model parameters using a covariance matrix adaptive optimization strategy based on considering the projection operator; The confidence rule base parameter optimization model is expressed as minf(V) stA(V)=0,B(V)≥0 f(V) represents the objective function; V represents the vector composed of the parameters of the confidence rule base; A(V) represents the equality constraint; B(V) represents the inequality constraint; The initial values ​​of the optimization parameters are given by experts, and the constraints that the parameters should satisfy during optimization are: 1) Rule weights. After standardization, the rule weights should satisfy the following requirements: 0≤θ k ≤1,k=1,2,…,L 2) Attribute weights. After being standardized, attribute weights should satisfy: 3) Confidence of initial rule output: <h2 style=";text-align:left;direction:ltr">0≤β<h2 style=";text-align:left;direction:ltr"> n，k <h2 style=";text-align:left;direction:ltr"> ≤1, n = 1,…, N, k = 1, 2,…, L 4) If the kth rule is complete, then the sum of all confidences output by the rule is 1; otherwise, the sum of the confidences is less than 1, as expressed as follows: The mean square error is used to indicate the accuracy of the model, and its expression is as follows: in, represents the output value of the model; y(t) is the true value of the output; T is the number of data; V represents the vector composed of the parameters that need to be optimized by the confidence rule base.

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