CN114563016B - Redundant inertial measurement unit fault detection method based on Granges causal analysis - Google Patents
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Abstract
A redundant inertial unit fault detection method based on Granges causal analysis comprises (1) obtaining nominal value data of inertial unit and actual measurement value data of multiple redundant inertial units; (2) Constructing a TVAR model by using the nominal value of the inertial measurement unit, and carrying out model parameter identification and model reconstruction; (3) The following is performed for each of the multiple redundant inertial groups: (a) Constructing a TVAR model aiming at the measured value of the current inertial measurement unit, and carrying out model parameter identification and model reconstruction; (b) Taking the nominal value of the inertial measurement unit as output, taking the measured value of the current inertial measurement unit as input to construct an exogenous input time-varying autoregressive characterization model, and carrying out model parameter identification and model reconstruction; (c) Taking the measured value of the current inertial measurement unit as output, taking the nominal value of the inertial measurement unit as input, constructing a time-varying autoregressive characterization model of exogenous input, and carrying out model parameter identification and model reconstruction; (d) Calculating an interaction glaring cause and effect index, and calculating an error of the interaction glaring cause and effect index between each inertial group and the nominal value of the inertial group; (4) And setting an evaluation principle, and evaluating whether each inertial measurement unit has faults or not.
Description
Technical Field
The invention relates to a redundant inertial measurement unit fault detection method based on a Granges causal analysis, and belongs to the technical field of biological crossing and intelligent information processing.
Background
The inertial measurement device (inertial group) is usually a key single machine of an aircraft control system and is used for sensing angular speed and visual acceleration information in the flight process of an aircraft, and sending the information to a flight control computer for navigation, guidance and control, wherein the accuracy of the information is directly related to success or failure of a flight mission. Therefore, in the aircraft with high reliability requirements, the inertial measurement unit mostly adopts a redundancy design manner. However, the influence of the inconsistency of the space and the ground on the stability of the inertial measurement unit can cause the inertial measurement unit to malfunction, and the navigation control precision of the aircraft is directly influenced. The current online fault detection of the redundant inertial measurement unit generally needs to manually set threshold parameters, seriously depends on experience of designers, and has the problem of poor expansibility. Therefore, the research on the accurate and effective redundant inertial measurement unit online fault identification method plays a vital role in improving the reliability of the aircraft.
Disclosure of Invention
The technical solution of the invention is as follows: aiming at the difficult problem of redundant inertial measurement unit fault detection under a complex background, the method provides a data-driven inertial measurement unit fault accurate identification method, which starts from inertial measurement unit measurement data acquired in real time, constructs a time-varying nonlinear dynamic model of the actual measurement data and nominal information of the redundant inertial measurement unit, calculates a complex dynamic causal correlation characterization index of interaction between an actual measurement value and the nominal value of an inertial measurement unit measurement device based on the time-varying nonlinear dynamic model, and therefore achieves real-time dynamic monitoring and fault detection of the redundant inertial measurement unit measurement data.
The technical scheme of the invention is as follows: a redundant inertial unit fault detection method based on a Grangel causal analysis comprises the following steps:
(1) Acquiring nominal value data of an inertial measurement unit and actual measurement value data of multiple redundant inertial measurement units;
(2) Constructing a time-varying autoregressive model by using the nominal value of the inertial measurement unit, and carrying out model parameter identification and model reconstruction to obtain a reconstructed TVAR model;
(3) The following is performed for each of the multiple redundant inertial groups:
(a) Constructing a time-varying autoregressive model aiming at the measured value of the current inertial measurement unit, and carrying out model parameter identification and model reconstruction to obtain a reconstructed TVAR model of the measured value;
(b) Taking the nominal value of the inertial measurement unit as output, taking the measured value of the current inertial measurement unit as input to construct an exogenous input time-varying autoregressive characterization model, and carrying out model parameter identification and model reconstruction to obtain a reconstructed TVARX model;
(c) Taking the measured value of the current inertial measurement unit as output, taking the nominal value of the inertial measurement unit as input, constructing a exogenous input time-varying autoregressive characterization model, and carrying out model parameter identification and model reconstruction to obtain a reconstructed TVARX model;
(d) Calculating an interaction gracile causal index by using the constructed nominal value of the inertial unit and the reconstructed TVAR model and the reconstructed TVARX model of the current inertial unit, wherein the interaction gracile causal index is used for representing interaction time-varying dynamic gracile causal association of the nominal value of the inertial unit and the measured value of the current inertial unit;
(4) Calculating the error of the interactive glaring cause and effect index between each inertial group and the nominal value of the inertial group;
(5) And setting an evaluation principle, and evaluating whether each inertial measurement unit has faults or not according to the errors.
Preferably, the measured value data of the multi-redundancy inertial measurement unit is measured values of all redundancy inertial measurement units acquired in the flight process according to a given nominal value of the inertial measurement unit and aiming at the flight characteristics and the flight task requirements of the aircraft.
Preferably, the model parameter identification uses a basis function expansion algorithm to convert the parameter to be identified from a time-varying parameter to a time-invariant parameter, and then uses a generalized linear fitting algorithm to identify the model parameter.
Preferably, the in-base function expansion algorithm in the model parameter identification in step (2) utilizes wavelet base function expansion.
Preferably, the basis function used in the basis function expansion algorithm in the model parameter identification in (a) is a multi-wavelet basis function with multiple resolutions.
Preferably, the basis function used in the basis function expansion algorithm in the model parameter identification in (b) is a multi-wavelet basis function with multiple resolutions.
Preferably, the basis function used in the basis function expansion algorithm in the model parameter identification in (c) is a multi-wavelet basis function with multiple resolutions.
Preferably, the interactive gladhand cause and effect index is calculated by: calculating variance var (Y|Y) of reconstructed TVAR model of inertial group nominal value - )；
Calculating the variance of the reconstructed TVARX model obtained by taking the nominal value of the inertial measurement unit as output and the measured value of the current inertial measurement unit as inputThe time-varying dynamic glaring cause and effect index of inertial group to nominal value of inertial group +.>Expressed as:
calculating variance of reconstructed TVAR model of current inertial measurement unit measurement value
Calculating the variance of the reconstructed TVARX model obtained by taking the measured value of the current inertial measurement unit as output and the nominal value of the inertial measurement unit as input
Time-varying dynamic glaring cause and effect index of inertial set nominal value versus current inertial set measurement valueExpressed as:
preferably, the glaring cause and effect index is a time-varying glaring cause and effect index.
Preferably, the error is the mean square error of the interactive glabellar causal index; the evaluation criterion is that the interactive glaring causal mean square error between the redundant inertial set and the nominal value of the inertial set exceeds 50%.
Compared with the prior art, the invention has the beneficial effects that:
(1) Compared with the traditional manual inertial unit fault method, the redundant inertial unit fault detection method based on the Granges causal analysis can effectively monitor the working conditions of all redundant inertial units of the aircraft in real time, automatically identify the fault inertial unit, accurately position specific fault parameters and has higher accuracy and robustness.
(2) The invention applies the data-driven intelligent information analysis means to the field of redundant inertial measurement unit fault monitoring and identification, breaks through the traditional manual fault monitoring mode which is seriously dependent on the experience of operators, and provides a new idea for inertial measurement unit fault monitoring from the basic theoretical level.
(3) The method for detecting the redundant inertial measurement unit faults based on the Granges causal analysis can provide a new technical path for a novel aircraft redundant sensing device fault detection theory.
Drawings
FIG. 1 is a flow chart of the present invention;
fig. 2 is an inertial group fault detection example.
Detailed Description
The invention is further illustrated with reference to figures 1-2 and examples.
As shown in fig. 1, a flowchart of the method of the present invention is shown, and the specific steps are as follows:
(1) And acquiring nominal value data of the inertial measurement unit and multi-redundancy actual measurement value data of the inertial measurement unit.
Aiming at the flight characteristics and the flight mission requirements of the aircraft, carrying out a flight test according to a given nominal value of the inertial measurement unit, and acquiring measured value data of all redundant inertial measurement units in the flight process.
(2) And constructing a time-varying autoregressive model (time-varying autoregressive, TVAR) by using the nominal value of the inertial measurement unit, and carrying out model parameter identification and model reconstruction to obtain a reconstructed model.
Let the nominal value of the inertial set be y= { Y (t) } t=1, 2, …, N, where N is the data length. The TVAR model of the inertial set nominal value can be expressed as:
wherein ε 1 (t) represents a white noise sequence, n y Is the model order of Y, representing the maximum number of relevant hysteretic observations, b i And (t) identifying the model coefficients by using a basis function expansion algorithm and a generalized linear fitting algorithm, wherein the time-varying autoregressive model coefficients to be estimated are obtained.
Wavelet theory demonstrates that a square-scalar signal f can be approximated by multi-resolution wavelet basis function decomposition, as follows:
wherein the method comprises the steps ofSum phi j，k (x)＝2 j/2 ψ(2 j x-k)，j 0 J, k ε Z (Z represents an integer) is the translational and expansion form of the scale function φ (x) and the mother wavelet ψ (x), +.>And beta j，k Representing the wavelet expansion coefficients. Furthermore, when the scale function->When the resolution scale of (2) is large enough, i.e. there is an integer J, then equation (2) can be reduced to:
thus, a set of multi-wavelet basis functions { pi } with tight support and good generalization ability is selected μ (t): μ=1, 2, …, L } pair of time-varying autoregressive model coefficients b to be estimated in equation (1) i (t) performing expansion:
where L represents the maximum number of multi-wavelet basis functions. Therefore, the time-varying autoregressive model coefficient estimation problem is converted into a time-invariant coefficient estimation problem based on a basis function; and then estimating the unfolded time-invariant coefficient by using a generalized linear fitting algorithm. Reconstruction of time-varying autoregressive model coefficients using estimated time-invariant coefficients and multi-wavelet basis functionsThereby obtaining a reconstructed time-varying autoregressive model of the nominal value of the inertial measurement unit.
(3) And constructing a TVAR model by using the measured value of the inertial measurement unit 1, and carrying out model parameter identification and model reconstruction to obtain a reconstructed model.
Let the measurement value of the inertial measurement unit 1 be X 1 ＝{x 1 (t) } t=1, 2, …, N, where N is the data length. The inertial measurement unit 1 measurement TVAR model can be expressed as:
wherein ε 2 (t) represents a white noise sequence, n x1 Is X 1 Represents the maximum number of relevant hysteretic observations. a, a i (t) is a time-varying autoregressive model coefficient to be estimated, the model coefficient is identified by utilizing a basis function expansion algorithm and a generalized linear fitting algorithm, and likewise, a multi-wavelet basis function with tight support and good generalization capability is selected for the time-varying autoregressive model coefficient a to be estimated i (t) expanding, converting an original time-varying model into a time-invariant model, and simultaneously converting a time-varying autoregressive model coefficient estimation problem into a time-invariant coefficient estimation problem based on a basis function; and then estimating the unfolded time-invariant coefficient by using a generalized linear fitting algorithm. Reconstruction of time-varying autoregressive model coefficients using estimated time-invariant coefficients and multi-wavelet basis functionsThereby obtaining a reconstructed time-varying autoregressive model of the inertial mass 1.
(4) And taking the nominal value of the inertial unit as output, taking the measured value of the inertial unit 1 as input to construct an exogenous input time-varying autoregressive characterization model (time-varying autoregressive with exogenous, TVARX), and carrying out model parameter identification and model reconstruction to obtain a reconstruction model.
Taking the nominal value Y= { Y (t) } of the inertial measurement unit as output, and measuring the value X of the inertial measurement unit 1 1 ＝{x 1 (t) } building a TVARX model for the input:
wherein ε 3 (t) represents a white noise sequence,and n y Is X 1 And a model order of Y, representing the maximum number of relevant hysteretic observations. b 1i (t) and b 2i And (t) identifying the model coefficients by using a basis function expansion algorithm and a generalized linear fitting algorithm, wherein the t is the time-varying autoregressive model coefficients of exogenous input to be estimated. Using a multi-wavelet basis function { pi ] μ (t): mu=1, 2, …, L } versus the time-varying coefficient { b } of the TVARX model 1i (t),b 2i (t) } performing expansion:
therefore, the TVARX model coefficient estimation problem is converted into a time-invariant coefficient estimation problem based on a basis function; and then estimating the unfolded time-invariant coefficient by using a generalized linear fitting algorithm. Reconstructing TVARX model coefficients by using estimated time-invariant coefficients and multi-wavelet basis functionsThereby obtaining a reconstructed TVARX model taking the nominal value of the inertial group as output and the measured value of the inertial group 1 as input.
(5) And taking the measured value of the inertial measurement unit 1 as output, taking the nominal value of the inertial measurement unit as input to construct a characterization model, and carrying out model parameter identification and model reconstruction to obtain a reconstructed model.
By measurement X of inertial measurement unit 1 1 ＝{x 1 (t) } is the output, and the inertial nominal value y= { Y (t) } is the input to construct a time-varying autoregressive characterization model of the exogenous input as follows:
wherein ε 4 (t) represents a white noise sequence,and n y Is X 1 And a model order of Y, representing the maximum number of relevant hysteretic observations. a, a 1i (t) and a 2i (t) is a time-varying autoregressive model coefficient of exogenous input to be estimated, identifying the model coefficient by utilizing a basis function expansion algorithm and a generalized linear fitting algorithm, and selecting a multi-wavelet basis function with tight support and good generalization capability to be estimated to obtain a TVARX model coefficient { a } 1i (t),a 2i (t) } expanding, converting the original time-varying model into a time-invariant model, and simultaneously converting the TVARX model coefficient estimation problem into a time-invariant coefficient estimation problem based on a basis function; and then estimating the unfolded time-invariant coefficient by using a generalized linear fitting algorithm. Reconstructing TVARX model coefficients by using the estimated time-invariant coefficients and the multi-wavelet basis function>Thereby obtaining a reconstructed TVARX model taking the measured value of the inertial measurement unit 1 as output and the nominal value of the inertial measurement unit as input.
(6) Calculating the Grandigo causal index by using the reconstructed models in the step (2) and the step (5), and acquiring the interactive dynamic causal relation between the nominal value of the inertial unit and the measured value of the inertial unit 1.
Complicated time-varying dynamic systems can change with time due to the complex environment, etc., so that it is necessary to track and identify the time-varying characteristics of the system. In recent years, there has been an increasing interest in the mechanism of potential correlation between large-scale multi-source factors in time-varying systems. One of the classical methods of detecting such effects is to determine undirected connectivity, including correlation and mutual information. However, determining the directionality of the interaction is critical to understanding the dynamic relationship between complex large-scale time-varying systems. The grange causal (Granger Causality, GC) relationship is an effective method for describing direct causal relationships and can be used for detecting dynamic changes of multi-source factor correlations of complex time-varying systems.
According to the general definition of the cause and effect of glaring, if the variance of the prediction error for predicting the a signal is reduced by including the B signal past information, it can be said that B results in a in the sense of glaring. Thus, time-varying glaring cause and effect (TVGC B-A ) And time-invariant glabellar cause and effect (TVGC A-B ) May be defined by the logarithmic ratio of the error variance from the TVARX model, respectively:
wherein B is - And A - Representing the past information of B and a, respectively. Furthermore, var (A|A - ) And var (B|B) - ) Representing the variance of the prediction error based on the TVAR model, i.e., depending only on its own history information; var (A|A) - ,B - ) And var (B|B) - ,A - ) Representing the variance based on the TVARX model, where both B and a historical observations are taken into account.
It follows that the time-varying dynamic glabellar causal index of the reconstructed TVAR model and TVARX model obtained based on the inertial set nominal value and the measured value of inertial set 1 can be expressed as:
wherein var (Y|Y - ) Representing the variance of the reconstructed TVAR model obtained using the inertial set nominal values, var (y|y - ) Representation of the use of inertiaVariance of the reconstructed TVAR model obtained by the set nominal value;representing the variance of the reconstructed TVARX model obtained by taking the nominal value of the inertial unit as output and the measured value of the inertial unit 1 as input; />Representing the variance of the reconstructed TVAR model obtained using the inertial measurement unit 1 measurements; />The variance of the reconstructed TVARX model obtained by taking the measured value of the inertial unit 1 as output and the nominal value of the inertial unit as input is represented. />Time-varying dynamic glaring cause and effect index representing inertial group 1 versus nominal value of inertial group, +.>Representing the time-varying dynamic glaring cause and effect index of the nominal value of the inertial group versus the inertial group 1.
(7) And (3) respectively constructing a TVAR model and a TVARX model between the TVAR model and an inertial measurement unit nominal value for the redundant inertial measurement units 2-N according to the steps (3) to (6), carrying out parameter identification and model reconstruction, and calculating the interactive time-varying dynamic Granger causal relationship between the corresponding inertial measurement unit measured value and the inertial measurement unit nominal value.
Respectively constructing TVAR models for redundant inertial measurement units 2-N according to the step (3), constructing interactive TVARX models between the TVARX models and the nominal values of the inertial measurement units according to the step (4) and the step (5), identifying and reconstructing the models, and calculating interactive time-varying dynamic Granger causal association indexes between the current inertial measurement units and the nominal values of the inertial measurement units according to the step (6), namely
(8) And calculating the error of the interactive time-varying dynamic Granger causal index between the redundant inertial units 1-N and the nominal value of the inertial unit.
Separately calculating the mean square error between each set of interactive gracile causal indices, i.eAnd-> And->… … as an error in the interactive gladhand cause and effect index.
(9) Setting an evaluation principle, evaluating whether each inertial measurement unit fails or not, and positioning failure parameters.
And (3) setting 50% of a mean square error threshold value of the redundant inertial unit as an evaluation principle for judging that the inertial unit fails on the basis of the mean square error of the interactive glaring causal index between the redundant inertial units 1-N calculated in the step (8) and the nominal value of the inertial unit, namely, when the mean square error of a certain redundant closed unit and the nominal value of the inertial unit is larger than the threshold value, indicating that the inertial unit fails.
The invention is not described in detail in part as being common general knowledge to a person skilled in the art.
Claims (10)
1. A redundant inertial unit fault detection method based on a Grangel causal analysis is characterized by comprising the following steps:
(1) Acquiring nominal value data of an inertial measurement unit and actual measurement value data of multiple redundant inertial measurement units;
(2) Constructing a time-varying autoregressive model by using the nominal value of the inertial measurement unit, and carrying out model parameter identification and model reconstruction to obtain a reconstructed TVAR model;
(3) The following is performed for each of the multiple redundant inertial groups:
(a) Constructing a time-varying autoregressive model aiming at the measured value of the current inertial measurement unit, and carrying out model parameter identification and model reconstruction to obtain a reconstructed TVAR model of the measured value;
(b) Taking the nominal value of the inertial measurement unit as output, taking the measured value of the current inertial measurement unit as input to construct an exogenous input time-varying autoregressive characterization model, and carrying out model parameter identification and model reconstruction to obtain a reconstructed TVARX model;
(c) Taking the measured value of the current inertial measurement unit as output, taking the nominal value of the inertial measurement unit as input, constructing a exogenous input time-varying autoregressive characterization model, and carrying out model parameter identification and model reconstruction to obtain a reconstructed TVARX model;
(d) Calculating an interactive glaring causal index by using the constructed nominal value of the inertial unit and the reconstructed TVAR model of the current inertial unit obtained in the step (2) and the reconstructed TVARX model of the step (c), wherein the interactive glaring causal index is used for representing interactive time-varying dynamic glaring causal association of the nominal value of the inertial unit and the measured value of the current inertial unit;
(4) Calculating an error of an interaction glaring cause and effect index between each inertial group of the multiple redundant inertial groups and a nominal value of the inertial group;
(5) And setting an evaluation principle, and evaluating whether each inertial measurement unit has faults or not according to the errors.
2. The method according to claim 1, characterized in that: the measured value data of the multi-redundancy inertial measurement unit are measured values of all the redundancy inertial measurement units acquired in the flight process according to the nominal value of the given inertial measurement unit aiming at the flight characteristics and the flight task requirements of the aircraft.
3. The method according to claim 1, characterized in that: the model parameter identification utilizes a basis function expansion algorithm to convert parameters to be identified from time-varying parameters to time-invariant parameters, and then utilizes a generalized linear fitting algorithm to identify the model parameters.
4. A method according to claim 3, characterized in that: the basis function expansion algorithm in the model parameter identification in the step (2) utilizes wavelet basis function expansion.
5. A method according to claim 3, characterized in that: (a) The basis functions used in the basis function expansion algorithm in the model parameter identification in (a) are multi-wavelet basis functions with multiple resolutions.
6. A method according to claim 3, characterized in that: (b) The basis functions used in the basis function expansion algorithm in the model parameter identification in (a) are multi-wavelet basis functions with multiple resolutions.
7. A method according to claim 3, characterized in that: (c) The basis functions used in the basis function expansion algorithm in the model parameter identification in (a) are multi-wavelet basis functions with multiple resolutions.
8. The method according to claim 1, characterized in that: the interactive gladhand cause and effect index is calculated by: calculating variance var (Y|Y) of reconstructed TVAR model of inertial group nominal value - )；
Calculating variance var (Y|Y) of the reconstructed TVARX model obtained by taking the nominal value of the inertial measurement unit as output and the current inertial measurement unit as input - ,X 1 - ) The method comprises the steps of carrying out a first treatment on the surface of the Then the inertial set versus nominal time-varying dynamic glaring cause and effect index for the inertial setExpressed as:
calculating variance of reconstructed TVAR model of current inertial measurement unit measurement value
Calculating the variance of the reconstructed TVARX model obtained by taking the measured value of the current inertial measurement unit as output and the nominal value of the inertial measurement unit as input
Inertial measurement of the nominal value of the inertial measurement unit against the current inertial measurement unitTime-varying dynamic gladhand causal index of magnitudeExpressed as:
9. the method according to claim 1 or 8, characterized in that: the Grangel causal index is time-varying Grangel causal index.
10. The method according to claim 8, wherein: the error is the mean square error of the interactive gracile causal index; the evaluation criterion is that the interactive glaring causal mean square error between the redundant inertial set and the nominal value of the inertial set exceeds 50%.
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