CN111259551A - Inertial measurement unit fault prediction method based on confidence rule base - Google Patents
Inertial measurement unit fault prediction method based on confidence rule base Download PDFInfo
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Abstract
An inertial measurement unit fault prediction method based on a confidence rule base belongs to the field of fault prediction of inertial navigation devices and is characterized in that: establishing a confidence rule base model which takes accumulated pulse quantity in unit time as input and takes navigation error as output through static test of the laser inertial measurement unit; and then reflecting the fault state of the laser inertial measurement unit by using the navigation error of unit time, setting a fault threshold value of navigation precision, reflecting the fault state of the laser inertial measurement unit, and realizing the fault prediction of the laser inertial measurement unit. The inertial measurement unit fault prediction method based on the confidence rule base realizes navigation error prediction by using pulse data of a laser inertial measurement unit; an expert system based on a confidence rule base can effectively process various information with uncertainty and can process the inertial measurement unit fault prediction problem in a complex environment; according to the method, the navigation error is predicted, the navigation error threshold is set to judge the fault state, and an effective way is provided for the fault prediction of the laser inertial measurement unit.
Description
Technical Field
The invention belongs to the field of fault prediction of inertial navigation devices, and particularly relates to an inertial measurement unit fault prediction method based on a confidence rule base, which is used for judging an inertial measurement unit state through navigation precision prediction.
Background
With the development of modern aerospace technology, the performance requirements on an aircraft are higher and higher, the requirements on a navigation system for controlling flight precision are also higher and higher, an inertial device is used as a core part of the navigation system and mainly comprises a gyroscope, an accelerometer and other elements, the inertial device plays a very critical role in navigation, whether the navigation is accurate or not can be directly related to the normal work of the inertial device, a laser inertial unit is an optical inertial device developed along with a laser technology, and compared with the traditional inertial device, the optical inertial device is high in precision, strong in anti-interference capability, long in service life and good in reliability, so that the laser inertial unit is commonly used for rockets, unmanned planes and the like.
Most navigation systems have complex working environments and generate large influence on inertial devices, and due to the fact that manufacturing processes are complex and the analysis of internal mechanisms of the laser inertial measurement unit and the knowledge related to the health management of the laser inertial measurement unit are lacked, the fault analysis of the laser inertial measurement unit is not clear at present, accurate modeling of the internal mechanisms of the inertial measurement unit cannot be achieved, the analysis of fault states of the laser inertial measurement unit cannot be completely analyzed from the mechanisms of the laser inertial measurement unit, and therefore the fault states of the laser inertial measurement unit cannot be found timely. Therefore, in order to improve the accuracy of the navigation system, it is important to determine the fault state of the inertial measurement unit.
Disclosure of Invention
The invention aims to provide an inertial measurement unit fault prediction method based on a confidence rule base, which judges the inertial measurement unit state through predicting navigation precision.
The invention relates to an inertial measurement unit fault prediction method based on a confidence rule base, which comprises the steps of establishing a confidence rule base model by taking accumulated pulse quantity in unit time as input and navigation error as output through static test of a laser inertial measurement unit; and then reflecting the fault state of the laser inertial measurement unit by using the navigation error of unit time, setting a fault threshold value of navigation precision, reflecting the fault state of the laser inertial measurement unit, and realizing the fault prediction of the laser inertial measurement unit.
According to the inertial measurement unit fault prediction method based on the confidence rule base, the laser inertial measurement unit is subjected to static test in various environments, and pulse quantities of an X axis, a Y axis and a Z axis of a gyroscope and an accelerometer in the laser inertial measurement unit are obtained from test data; processing the data of the pulse quantity to obtain an accumulated pulse quantity; selecting the accumulated pulse quantity in unit time as characteristic information; and then carrying out Monte Carlo simulation (MC) on the characteristic information, simulating various states which can be reached by different laser inertial units in the test, establishing a confidence rule base model which takes the accumulated pulse quantity in unit time as input and takes the navigation error in unit time as output, finally carrying out optimization parameter adjustment on the confidence rule base model, setting a fault threshold value for the output navigation error, further reflecting the fault state of the laser inertial units, and realizing the fault prediction of the laser inertial units through the pulse quantity of the navigation information.
The invention discloses an inertial measurement unit fault prediction method based on a confidence rule base, which comprises the following steps:
step 1: selecting attribute input information and performing Monte Carlo simulation;
firstly, carrying out differential processing on tested laser inertial measurement unit pulse data to obtain a differential quantity of the pulse data, carrying out feature extraction on the differential quantity, selecting a feature quantity of differential quantity information which can reflect navigation errors most, and selecting an accumulated pulse quantity as the feature quantity to be used as model input according to actual test and expert knowledge; accumulating the unit time difference components of the gyroscope and the accelerometer in each axial direction to obtain an accumulated pulse quantity, and taking the accumulated pulse quantity of the unit time as model input; the input of the model is the accumulated pulse increment of the gyroscope, the accelerometer in unit time of X axis, Y axis and Z axis;
converting input data into acceleration and angular velocity of analog quantity, analyzing the trend of the acceleration and the angular velocity through Monte Carlo simulation, analyzing probability distribution in the analog quantity of the system by adopting a random sampling method, and simulating each state which the analog quantity in the system can possibly reach so as to reflect the uncertainty of output;
step 2: constructing an inertial navigation error prediction model;
according to the input of the 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 shown as follows:
in formula (1), t is a unit time;
denotes the ith precondition attribute x in the kth ruleiThe set of reference values of (a), which may be given by an expert in connection with the specific environment and internal working mechanism; l represents the number of rules; m represents the number of the premise attributes; thetakA rule weight representing a Kth rule; deltaiRepresenting the weight of the ith prerequisite attribute in the rule, which reflects the importance of the ith prerequisite attribute relative to other prerequisite attributes, βj,kDenotes the jth output result D relative to the output section in the Kth rulejThe confidence of (2); djAn evaluation level indicating an output reference value;
firstly, input information xiConversion to relative reference value
Degree of confidence of
in finding the degree of matching
Then, the rule is fused and calculated by an Evidence Reasoning (ER) algorithm and is output; first, an activation weight is calculated, and the activation weight can be expressed as:
wherein w is more than or equal to 0k1, k is equal to or less than 1 … L; l is the number of activated rules;
is a relative attribute weight, representing the relative importance of an attribute.
The reasoning of the ER algorithm is divided into an iterative algorithm and an analytic algorithm, wherein the analytic algorithm is simple and convenient to calculate, and the expression is
β thereiniRepresents the confidence of the Nth result in the output, an
The output result of the BRB can be expressed as
Z(xi)＝{(Dn,βn)},n＝1,2,...,N (6)
Z(xi) Represents the output result based on BRB, u (D)n) For evaluation result DnThe effectiveness of (a) of (b),
predicting the outcome of the model;
and step 3: training and optimizing the model;
because the initial parameters of the prediction model are all given by experts, when a confidence rule base system is complex, the experts are difficult to determine the accurate values of the parameters, so the initial parameters need to be optimized, 50% of data are randomly taken out from the obtained optimized data to be used as training data, and the rest data are used as test data to detect the accuracy of the prediction model;
and 4, step 4: judging a fault;
and (3) based on the confidence rule base prediction model established in the step (3), setting a threshold value of the unit time navigation error based on the fault state of the laser inertial unit according to expert knowledge by taking the accumulated pulse quantity of the laser inertial unit as input and the navigation error as output, and when the navigation error of the laser inertial unit in unit time is greater than the threshold value, determining that the laser inertial unit is in the fault state.
The invention discloses an inertial measurement unit fault prediction method based on a confidence rule base, wherein the initial parameter optimization process in step 3 is as follows: the optimization algorithm optimizes The model parameters by using a covariance matrix adaptive optimization strategy (P-CMA-ES) based on a projection operator;
the confidence rule base parameter optimization model can be expressed as
min f(V)
s.t.A(V)＝0,B(V)≥0
(v) represents an objective function; v represents a vector consisting of confidence rule base parameters; a (V) represents an equality constraint; b (V) represents an inequality constraint;
the initial value of the optimized parameter is given by an expert, and the constraint condition which the parameter should meet during optimization is
1) And (3) rule weight, wherein the rule weight meets the following requirements after being standardized:
0≤θk≤1,k＝1,2,...L
2) and (3) attribute weight, wherein after the attribute weight is standardized, the following conditions are satisfied:
3) confidence of initial rule output:
0≤βn,k≤1,n＝1,..,N,k＝1,2,...L
4) if the kth rule is complete, then the sum of all confidence levels output by the rule is 1; otherwise, the confidence sum is less than 1, and the expression is as follows:
mean Square Error (MSE) can be used to represent the accuracy of the model, expressed as follows:
wherein the content of the first and second substances,
an output value representing the model; y (t) is the true value of the output; t is the number of data; v denotes a vector consisting of the parameters that the confidence rule base needs to optimize.
The inertial measurement unit fault prediction method based on the confidence rule base has the following advantages: (1) the navigation error prediction is realized by using the pulse data of the laser inertial measurement unit; (2) an expert system based on a confidence rule base can effectively process various information with uncertainty and can process the inertial measurement unit fault prediction problem in a complex environment; and (3) the method sets a navigation error threshold value to judge the fault state through the prediction of the navigation error, and an effective way is provided for the fault prediction of the laser inertial measurement unit.
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FIG. 1 is a schematic flow chart of an inertial measurement unit fault prediction method based on a confidence rule base according to the present invention;
FIG. 2 is a schematic diagram illustrating a comparison of the inertial measurement unit fault prediction method based on the confidence rule base according to the present invention.
Detailed Description
The inertial measurement unit fault prediction method based on the confidence rule base is described in detail below through the accompanying drawings and embodiments.
According to the inertial measurement unit fault prediction method based on the confidence rule base, the laser inertial measurement unit is subjected to static test in various environments, and pulse quantities of an X axis, a Y axis and a Z axis of a gyroscope and an accelerometer in the laser inertial measurement unit are obtained from test data; processing the data of the pulse quantity to obtain an accumulated pulse quantity; selecting the accumulated pulse quantity in unit time as characteristic information; in order to simulate the uncertainty of a complex environment and a sensor in measurement, then carrying out Monte Carlo simulation on characteristic information, simulating various states which can be reached by different laser inertial measurement units in the test, and establishing a confidence rule base model which takes the accumulated pulse quantity in unit time as input and takes the navigation error in unit time as output; because the parameters in the initial model are all given by expert knowledge, in order to increase the accuracy of the expert knowledge, the parameter is optimized and adjusted on the belief rule base model, the fault threshold value is set for the output navigation error, the fault state of the laser inertial measurement unit is further reflected, and the fault prediction of the laser inertial measurement unit is realized through the pulse quantity of the navigation information.
As shown in fig. 1, the inertial measurement unit fault prediction method based on the confidence rule base mainly includes the following steps:
step 1: attribute input information selection and Monte Carlo simulation
Considering the universality principle and the completeness principle of attribute selection, combining the working principle of the laser inertial measurement unit, starting from actual test, and selecting the triaxial accumulated pulse quantity of the gyroscope and the accelerometer as the input information of the attribute according to data analysis and test flow analysis of the laser inertial measurement unit and expert knowledge.
In this embodiment, in order to simulate the state of the laser inertial measurement unit in a complex environment, tests in room temperature, low temperature, and very low temperature environments are selected, the test data of the laser inertial measurement unit is a pulse signal, the sampling frequency of the pulse signal is 5ms, the navigation data is differentiated to obtain pulse incremental data, establishing a prediction model of navigation errors by taking accumulated pulse quantity as characteristic information of pulse increment data according to actual combination with expert knowledge, grouping 6000000 groups of data which are tested, dividing every 60000 groups of data (namely 5 minutes) into one group, outputting a group of input data corresponding to one navigation error, using the first 60000 group of data for aiming, using the next 60000 groups of data for one-time navigation, taking the navigation error corresponding to every 60000 groups of data as the navigation error of one unit time (namely 5 minutes), and carrying out Monte Carlo simulation on the data to obtain 98 groups of navigation error data.
98 groups of data are tested in the environment of room temperature, low temperature and extremely low temperature. Laser inertial measurement unit with extremely low temperature
Xinput(ti)＝x60000i+1+x60000i+2+…+x60000i+60000(i＝1,2…98) (10)
Wherein xkRepresenting the K-th pulse increment data, Xinput(ti) The cumulative pulse amount of the ith pulse is shown.
Table 1 shows the input of the prerequisite attributes of the system:
table 1 Attribute entry
Step 2: constructing a laser inertial navigation accuracy prediction model;
in the establishment of a model of a prediction confidence rule base, the expression mode of the Kth rule is
Then y(t)is{(D1，β1，k)，(D2，β2，k)，(D3，β3，k)，(D4，β4，k)}
With rule weight θkattribute weight δ1，δ2，δ3，δ4，δ5，δ6
Wherein T isxTyTzJxJyJzRespectively represent the accumulated pulse quantities of the X axis, the Y axis and the Z axis of the gyroscope and the X axis, the Y axis and the Z axis of the accelerometer,
is a set of precondition attribute reference values, wherein the reference value of the attribute is ranked small and large and is represented by S, L, DiFor the set of the output reference values, the small, medium, large and large reference values for outputting the navigation precision are respectively expressed by S, M, SL and L; attribute weight δiAnd a rule weight θkIs given by an expert.
The reference values and reference levels of attribute inputs are shown in tables 2 to 7, the reference values and reference levels of navigation accuracy outputs are shown in table 8, and the attribute weights, rule weights, and initial reliability distributions are shown in table 9.
TABLE 2 Gyroscope X-axis reference value definition
TABLE 3 Gyroscope Y-axis reference value definition
TABLE 4 Gyroscope Z-axis reference value definition
TABLE 5 Gyroscope X-axis reference value definition
TABLE 6 Gyroscope Y-axis reference definition
TABLE 7 Gyroscope Z-axis reference value definition
TABLE 8 navigation error reference value definition
TABLE 9 initial prediction model for navigation accuracy
And step 3: navigation accuracy prediction model optimization
After the navigation accuracy prediction model of the confidence rule base based on the BRB is constructed, due to the fact that the number of initial parameters is large, due to the fact that the number of the initial parameters is influenced by the uncertainty of expert knowledge, the predicted value of the initial parameters of the model is deviated from the actual true value to a certain extent, and the accuracy of the prediction model is influenced. Initial parameters need to be optimized to improve the accuracy of the prediction model.
In the embodiment, 98 groups of data are measured, 50% of data are extracted as training data, and initial parameters of a prediction model are optimized; the remaining data serves as test data to check the accuracy of the optimization model. The optimization algorithm optimizes model parameters using a covariance matrix adaptive optimization strategy (P-CMA-ES) based on considering projection operators.
Table 10 shows the prediction model after the navigation accuracy is optimized;
TABLE 10 prediction model after optimization of navigation accuracy
From the results of fig. 2, it can be seen that the problem that the unoptimized prediction model has a large error and cannot be predicted, and the accuracy of the optimized prediction model is greatly improved, so that the prediction problem can be effectively processed.
Because the optimization algorithm based on the P-CMA-ES has certain randomness, the optimized BRB model is tested for 50 times to obtain a group of MSEs (mean square errors), the size of the MSEs changes from 1.5523 to 2.1012, and the size of the MSEs of the unoptimized BRB model is 22.5608; table 11 is a MSE plot before and after optimization.
TABLE 11 comparison of MSE before and after optimization
Compared with the prior art, the MSE of the optimized BRB is greatly reduced, the model precision is improved, and the prediction of the actual laser inertial measurement unit test navigation precision can be improved by the optimized BRB, so that the problem of laser inertial measurement unit fault prediction in a complex environment is further solved.
And 4, step 4: setting of fault threshold
And setting a fault threshold value based on unit navigation error change by combining expert knowledge and actual test, setting the fault threshold value to be 16m in the test, and indicating the laser inertial measurement unit fault when the navigation error is greater than 16 m.
As can be seen from fig. 2, the predicted value of the BRB model before optimization has a certain error compared with the true value of the navigation error, the model has a condition of missing report, the overall false alarm rate is 14.63%, the difference between the predicted value of the BRB model after optimization and the true value of the navigation error is significantly reduced, the overall false alarm rate is 2.44%, and the improvement in precision indicates that the BRB model after optimization has a certain prediction capability.
Claims (4)
1. An inertial measurement unit fault prediction method based on a confidence rule base is characterized by comprising the following steps: establishing a confidence rule base model which takes accumulated pulse quantity in unit time as input and takes navigation error as output through static test of the laser inertial measurement unit; and then reflecting the fault state of the laser inertial measurement unit by using the navigation error of unit time, setting a fault threshold value of navigation precision, reflecting the fault state of the laser inertial measurement unit, and realizing the fault prediction of the laser inertial measurement unit.
2. The inertial measurement unit fault prediction method based on the confidence rule base according to claim 1, wherein: the method comprises the steps that static test is conducted on a laser inertial measurement unit under various environments, and pulse quantities of an X axis, a Y axis and a Z axis of a gyroscope and an accelerometer in the laser inertial measurement unit are obtained from test data; processing the data of the pulse quantity to obtain an accumulated pulse quantity; selecting the accumulated pulse quantity in unit time as characteristic information; then carrying out Monte Carlo simulation on the characteristic information, simulating various states which can be reached by different laser inertial measurement units in the test, and establishing a confidence rule base model which takes the accumulated pulse quantity in unit time as input and takes the navigation error in unit time as output; and finally, optimizing and adjusting parameters of the belief rule base model, setting a fault threshold value for the output navigation error, further reflecting the fault state of the laser inertial measurement unit, and realizing the fault prediction of the laser inertial measurement unit through the pulse quantity of the navigation information.
3. The inertial measurement unit fault prediction method based on the confidence rule base according to claim 2, characterized by comprising the following steps:
step 1: selecting attribute input information and performing Monte Carlo simulation;
firstly, carrying out differential processing on the tested laser inertial measurement unit pulse data to obtain a differential quantity of the pulse data, carrying out feature extraction on the differential quantity, and selecting the accumulated pulse quantity as the feature quantity by combining expert knowledge to be used as model input; accumulating the unit time difference components of the gyroscope and the accelerometer in each axial direction to obtain an accumulated pulse increment, and taking the accumulated pulse quantity of the unit time as model input;
converting input data into acceleration and angular velocity of analog quantity, analyzing the trend of the acceleration and the angular velocity through Monte Carlo simulation, analyzing probability distribution in the analog quantity of the system by adopting a random sampling method, and simulating each state which the analog quantity in the system can possibly reach so as to reflect the uncertainty of output;
step 2: constructing an inertial navigation error prediction model;
according to the input of the 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 shown as follows:
in formula (1), t is a unit time;
denotes the ith precondition attribute x in the kth ruleiThe set of reference values of (a), which may be given by an expert in connection with the specific environment and internal working mechanism; l represents the number of rules; m represents the number of the premise attributes; thetakA rule weight representing the Kth rule, which reflects the importance degree of the Kth rule; deltaiWeight representing the ith prerequisite Attribute in the rule, βj,kDenotes the jth output result D relative to the output section in the Kth rulejThe confidence of (2); djAn evaluation level indicating an output reference value; firstly, input information xiConversion to relative reference value
Degree of confidence of
In the formula
Indicates the degree of matching, x, of the ith input attribute in the jth ruleiInput representing an attribute, γikAn attribute reference value representing a kth rule;
in finding the degree of matching
Then, the rules are fused, calculated and output by an 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 as follows:
wherein w is more than or equal to 0k1, k is equal to or less than 1 … L; l is the number of activation rules;
inputting the matching degree of the input relative to the precondition attributes in the corresponding rule; thetakIs the rule weight; deltaiIs the attribute weight;
is a relative attribute weight; the expression of the ER analytic algorithm is
βiRepresents the confidence of the Nth result in the output, an
The output result of the confidence rule base can be expressed as
S(xi)＝{(Dn,βn)},n＝1,2,...,N (7)
S(xi) Representing a non-linear model built based on a confidence rule baseThe final output is converted to the desired effect
u(Dn) For evaluation result DnThe effectiveness of (a) of (b),
represents the desired effect of the prediction model, and is also the result of the desired output;
and step 3: training and optimizing the model;
because the initial parameters of the prediction model are all given by experts, when a confidence rule base system is complex, the experts are difficult to determine the accurate values of the parameters, so the initial parameters need to be optimized, 50% of the obtained optimized data are randomly taken out to be used as training data, and the rest data are used as test data to detect the accuracy of the prediction model;
and 4, step 4: judging a fault;
and (3) based on the confidence rule base prediction model established in the step (3), setting a threshold value of the unit time navigation error based on the fault state of the laser inertial unit according to expert knowledge by taking the accumulated pulse quantity of the laser inertial unit as input and the navigation error as output, and when the navigation error of the laser inertial unit in unit time is greater than the threshold value, determining that the laser inertial unit is in the fault state.
4. The inertial measurement unit fault prediction method based on the confidence rule base according to claim 3, wherein the initial parameter optimization process in step 3 is as follows: the optimization algorithm optimizes the model parameters by using a covariance matrix adaptive optimization strategy based on a projection operator;
the confidence rule base parameter optimization model can be expressed as
minf(V)
s.t.A(V)＝0,B(V)≥0
(v) represents an objective function; v represents a vector consisting of confidence rule base parameters; a (V) represents an equality constraint; b (V) represents an inequality constraint;
the initial value of the optimized parameter is given by an expert, and the constraint condition which the parameter should meet during optimization is as follows:
1) and (3) rule weight, wherein the rule weight meets the following requirements after being standardized:
0≤θk≤1,k＝1,2,...L
2) and (3) attribute weight, wherein after the attribute weight is standardized, the following conditions are satisfied:
3) confidence of initial rule output:
0≤βn,k≤1,n＝1,..,N,k＝1,2,...L
4) if the kth rule is complete, then the sum of all confidence levels output by the rule is 1; otherwise, the confidence sum is less than 1, and the expression is as follows:
the mean square error can be used to represent the accuracy of the model, expressed as follows:
wherein the content of the first and second substances,
an output value representing the model; y (t) is the true value of the output; t is the number of data; v denotes a vector consisting of the parameters that the confidence rule base needs to optimize.
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