CN103697915B - A kind of satellite sensor failure diagnosticability evaluation method of considering interference effect - Google Patents

Abstract

The invention discloses a kind of satellite sensor failure diagnosticability evaluation method of considering interference effect, for the satellite sensor system that comprises the disturbing factor impact such as noise and modeling uncertainty, respectively using " vector distance similitude " and " direction vector similitude " as evaluation index, the deployment scenario of mathematical description, system model and satellite sensor by fault mode, realizes sensor failure and can detect and the quantitatively evaluating of isolability. The present invention, in the situation that not relying on any fault diagnosis algorithm, can advance to the design phase by the diagnosis of satellite sensor failure, and guides distributing rationally of satellite sensor.

Description

A kind of satellite sensor failure diagnosticability evaluation method of considering interference effect

Technical field

The present invention relates to a class and consider the satellite sensor failure diagnosticability evaluation method of interference effect, belong toIn satellite control field.

Background technology

Satellite sensor is the general designation of satellite attitude measurement element, mainly comprises star sensor, infrared earthSensor, gyroscope etc. As the important measuring cell in control system, once satellite sensor occursFault will have a strong impact on the precision of attitude of satellite control, even causes attitude rolling when serious. Along with sensitivityIncreasingly the increase of the integrated scale of device and complexity, and the impact of unpredictable space environment factor, makeIt inevitably breaks down. Be down to minimum and overcome product inherent reliability in order to make fault effectsNot enough shortcoming need be considered the impact of fault, and fault diagnosability is done in sensor design processFor a kind of index is brought in design system for instructing the optimization of sensor configuration. But, existingIn satellite sensor design process, do not consider this index.

Fault diagnosability refers to: fault can the accurate and effective degree that is detected and isolates. Fixed from itIn justice, can find out, fault diagnosability comprises detectability and isolability two parts. Diagnosticability is commentedValency is basis and the prerequisite of fault diagnosis algorithm. Because for fault that can not be detected, what no matter designsPlant diagnosis algorithm and all can not realize detection and the isolation of fault. Diagnosticability evaluation be exactly do not rely on appointWhat, in the situation of fault diagnosis algorithm, for the Mathematical Modeling of system and the configuring condition of sensor, analyzeThe influence degree of specified fault pattern to system.

For the detectability evaluation of control system, technology in the past mainly comprises following three aspects:: 1) baseExistence judgment in fault to transfer function between output; 2) the system energy using fault as a kind of stateObservation is analyzed; 3) existence judgment based on output and input message structure residual error vector. For can be everyFrom property evaluation, achievement in the past mainly comprises following two aspects: 1) based on different faults, output is affectedOtherness is differentiated; 2) incidence matrix based on closing series structure between I/O information and fault entersRow qualitative analysis. Above adopted technology is not all considered the disturbing factor such as noise, modeling uncertaintyImpact; And gained evaluation result is qualitatively, can only illustrate that can fault be detected and be isolated,And can not illustrate that fault is detected and segregate complexity.

Summary of the invention

Technical problem to be solved by this invention is: overcome the deficiencies in the prior art, provide a class to considerThe satellite sensor failure diagnosticability evaluation method of interference effect, can be real in the Control System Design stageThe now quantitatively evaluating to sensor failure, the optimization that and guides sensor to configure.

Technical solution of the present invention is:

A kind of satellite sensor failure diagnosticability evaluation method of considering interference effect comprises that step is as follows:

(1), based on model standardization and equivalent space transform process method, given satellite sensor is enteredRow pretreatment obtains pretreated model;

(2) utilize the pretreated model obtaining in step (1), and employing " vector distance similitude "As detectability evaluation index, carry out the quantitatively evaluating of fault detectability;

(3) whether the quantitative evaluation result that judges detectability fault is 0, if 0 is judged fault notCan be detected, enter step (7); Otherwise judge that fault is detectable failure, enter step (4);

(4) judged whether other detectable failures, entered step (5) if having, otherwise judgement shouldFault can not be isolated, and enters step (7);

(5) utilize the pretreated model obtaining in step (1), and employing " direction vector similitude "As isolability evaluation index, can detect event to the detectability fault obtaining in step (3) and otherBarrier carries out isolability quantitatively evaluating;

(6) whether the quantitative evaluation result that judges isolability fault is 0, if 0 is judged fault notCan be isolated, enter step (7); Otherwise judge that fault is to be isolated fault, enter step (7);

(7) finish.

In described step (1), obtaining pretreated model is:

N_HLz_s=N_HFf_s+N_HEe_s

Wherein, $z_s=\left[\begin{array}{c}y(k-n+1)\\ \·\\ \·\\ \·\\ y\left(k\right)\\ u(k-n+1)\\ \·\\ \·\\ \·\\ u\left(k\right)\end{array}\right],f_s=\left[\begin{array}{c}f(k-n+1)\\ \·\\ \·\\ \·\\ f\left(k\right)\end{array}\right],e_s=\left[\begin{array}{c}w(k-n+1)\\ \·\\ \·\\ \·\\ w\left(k\right)\\ v(k-n+1)\\ \·\\ \·\\ \·\\ v\left(k\right)\end{array}\right];$

N_HFor the left orthogonal basis of matrix H kernel, i.e. N_HH=0；x∈RⁿFor state variable; Y ∈ R^mForOutput quantity; U ∈ R^qFor input quantity; F ∈ R^pFor fault variable; W ∈ R^lWith v ∈ R^tFor disturbing, z_s∈R^(m+q)s、x_s∈R^n(s+1)、f_s∈R^psAnd e_s∈R^(l+t)sRepresent respectively observed quantity, state variable, the fault of pretreated modelWith the time heap stack vector disturbing, s is that length of window is: s=n+1; Rⁿ、R^m、R^q、R^p、R^l、R^t、R^(m+q)s、R^n(s+1)、R^psAnd R^(l+t)sBe respectively n in real number field dimension, m dimension, q dimension, p dimension,L dimension, t dimension, (m+q) s dimension, n (s+1) dimension, ps peacekeeping (l+t) s dimensional vector, n, m, q, p, l andT is positive integer; K is sampling time point; I is unit matrix; A, C, B_u、D_u、B_f、D_f、B_wWithD_vFor the sytem matrix of pretreated model.

Fault detectability evaluation index based on " vector distance similitude " in described step (2) is:

$\mathrm{FD}\left(f_i\right)=\frac{1}{2}{\left|\right|N_H{F}_i{f}_{\mathrm{si}}\left|\right|}^2$

Wherein: f_siRepresent the fault mode of specifying; F_iRepresent fault f_iCorresponding location matrix in F, i is for justInteger.

Fault isolability evaluation index based on " direction vector similitude " in described step (5) is:

Wherein:Be two detectable failure vector f_iAnd f_jBetween angle.

The present invention's beneficial effect is compared with prior art:

(1) fault diagnosis of satellite sensor is advanceed to the design phase by the present invention, diagnosable according to faultProperty evaluation result instruct distributing rationally of sensor, and set it as a kind of index and bring satellite control system intoIn system design system.

(2) the present invention does not need to design any fault diagnosis algorithm, only relies on the mathematical modulo of satellite sensorType and deployment scenario thereof, can realize designated mode fault is carried out detecting and isolability evaluation.

(3) the present invention can realize satellite sensor failure and can detect and the quantitatively evaluating of isolability,Can give to be out of order and can detect and isolable complexity; And can find out the inspection of satellite sensor failureThe weak spot of surveying and isolating, for the design of fault diagnosis algorithm provides theoretical foundation.

Brief description of the drawings

Fig. 1 is fault diagnosability evaluation method flow chart of the present invention.

Detailed description of the invention

Below in conjunction with accompanying drawing, the specific embodiment of the present invention is further described in detail.

The present invention is directed to the satellite sensor mathematics that a class comprises the disturbing factor such as noise, modeling uncertaintyModel, provides a kind of fault can detect and the evaluation method of isolability.

As shown in Figure 1, satellite sensor failure diagnosticability evaluation method of the present invention comprises the steps:

(1), based on model standardization and equivalent space transform process method, given satellite sensor is enteredRow pretreatment obtains pretreated model;

The Mathematical Modeling of satellite sensor is:

$\left\{\begin{array}{c}x(k+1)=\mathrm{Ax}\left(k\right)+B_{u}u\left(k\right)+B_{f}f\left(k\right)+B_{w}w\left(k\right)\\ y\left(k\right)=\mathrm{Cx}\left(k\right)+D_{u}u\left(k\right)+D_{f}f\left(k\right)+D_{v}v\left(k\right)\end{array}\right.$

Wherein: x ∈ RⁿFor state variable; Y ∈ R^mFor output quantity; U ∈ R^qFor input quantity; F ∈ R^pFor faultVariable; W ∈ R^lWith v ∈ R^tFor disturbing, the two is normal distribution, and linearity is uncorrelated mutually; Rⁿ、R^m、R^q、R^p、R^t、R^lFor the n dimension in real number field, m dimension, q dimension, p dimension, t peacekeeping l dimensional vector,N, m, q, p, t and l are positive integer; K is sampling time point; B_u、D_u、A、C、B_f、D_f、B_wAnd D_vFor the location matrix of pretreated model;

According to regular hour window (length of window is: s=n+1), above-mentioned satellite sensor model is carried outIteration, and construct following relational expression:

Lz_s=Hx_s+Ff_s+Ee_s

Wherein: z_s∈R^(m+q)s、x_s∈R^n(s+1)、f_s∈R^psAnd e_s∈R^(l+t)sRepresent respectively pretreated model observed quantity,The time heap stack vector of state variable, fault and interference, R^(m+q)s、R^n(s+1)、R^psAnd R^(l+t)sFor at real number(m+q) s dimension in territory, n (s+1) dimension, ps dimension, (l+t) s dimensional vector; Mathematic(al) representation is:

$z_s=\left[\begin{array}{c}y(k-n+1)\\ \·\\ \·\\ \·\\ y\left(k\right)\\ u(k-n+1)\\ \·\\ \·\\ \·\\ u\left(k\right)\end{array}\right],e_s=\left[\begin{array}{c}w(k-n+1)\\ \·\\ \·\\ \·\\ w\left(k\right)\\ v(k-n+1)\\ \·\\ \·\\ \·\\ v\left(k\right)\end{array}\right],f_s=\left[\begin{array}{c}f(k-n+1)\\ \·\\ \·\\ \·\\ f\left(k\right)\end{array}\right],x_s=\left[\begin{array}{c}x(k-n+1)\\ \·\\ \·\\ \·\\ x(k+1)\end{array}\right];$

L, H, F and E are the coefficient matrix of corresponding dimension, are respectively:

Above-mentioned standardized model is carried out to equivalent space conversion, obtains pretreated model:

N_HLz_s=N_HFf_s+N_HEe_s

In formula: N_HFor the left orthogonal basis of matrix H kernel, i.e. N_HH=0。

Can find according to pretreated model: the model equal sign left side is known input and output amount, equal signThe right comprises the fault of known mode and interference two parts that known probability distributes, when disturbing as normal distributionTime, observed quantity N_HLz_sPhysical meaning be: with N_HFf_sFor average, with N_HEe_sDistribution variance is varianceMultivariate normal distributions; Multivariate normal distributions is converted into standardized normal distribution by the result of pretreated model processing.

(2) utilize the pretreated model obtaining in step (1), and employing " vector distance similitude "As detectability evaluation index, carry out the quantitatively evaluating of fault detectability;

For the difference between the above-mentioned normal distribution of quantificational description, based on the concept of " vector distance similitude ",Analyze by introducing K-L divergence (Kullback – Leiblerdivergence), it calculates publicFormula is:

$D_{\mathrm{KL}}\left(p_i\right|\left|p_j\right)=\underset{\underset{x\∈z_{f_j}}{x\∈z_{f_i}}}{\mathrm{\Σ}}{p}_i\left(x\right)\ln \frac{p_i\left(x\right)}{p_j\left(x\right)}$

In formula: p_iAnd p_jBe respectively polynary distributionWithProbability density function, mathematic(al) representation is respectively:

$p_i\left(x\right)=\frac{1}{{\left|2\mathrm{\π}\right|}^{n/2}}\exp [-\frac{1}{2}{(x-{\mathrm{\μ}}_i)}^T{\mathrm{\Σ}}_i^{-1}(x-{\mathrm{\μ}}_i)]$

$p_j\left(x\right)=\frac{1}{{\left|2\mathrm{\π}\right|}^{n/2}}\exp [-\frac{1}{2}{(x-{\mathrm{\μ}}_j)}^T{\mathrm{\Σ}}_j^{-1}(x-{\mathrm{\μ}}_j)]$

Wherein: μ_iAnd ∑_iBe respectively polynary distributionAverage and variance; μ_jAnd ∑_jBe respectively polynary distribution'sAverage and variance.

Above-mentioned expression formula is updated in K-L divergence computing formula, obtains through deriving:

$D_{\mathrm{KL}}\left(p_i\right|\left|p_j\right)=\frac{1}{2}[\mathrm{tr}\left({\mathrm{\Σ}}_j^{-1}{\mathrm{\Σ}}_i\right)+{({\mathrm{\μ}}_j-{\mathrm{\μ}}_i)}^T{\mathrm{\Σ}}_j^{-1}({\mathrm{\μ}}_j-{\mathrm{\μ}}_i)-n-\ln \left(\right|{\mathrm{\Σ}}_i|/|{\mathrm{\Σ}}_j\left|\right)]$

Because normal distribution is converted to standardized normal distribution by pretreated model, so ∑_i=∑_jWhen=I, above formula letterTurn to:

$D_{\mathrm{KL}}\left(p_i\right|\left|p_j\right)=\frac{1}{2}{({\mathrm{\μ}}_j-{\mathrm{\μ}}_i)}^T({\mathrm{\μ}}_j-{\mathrm{\μ}}_i)=\frac{1}{2}{\left|\right|{\mathrm{\μ}}_i-{\mathrm{\μ}}_j\left|\right|}^2$

The pretreated model obtaining based on step (1), is converted into because meet the interference model of normal distributionStandardized normal distribution, therefore fault f_iDetectability quantitatively evaluating formula be:

$\mathrm{FD}\left(f_i\right)=\min \left(D_{\mathrm{KL}}\left(p_i\right|\left|0\right)\right)=\min \left(\frac{1}{2}{\left|\right|({\mathrm{\μ}}_i-0)\left|\right|}^2\right)=\frac{1}{2}{\left|\right|{\mathrm{\μ}}_i\left|\right|}^2=\frac{1}{2}{\left|\right|N_H{F}_i{f}_{\mathrm{si}}\left|\right|}^2$

Wherein: f_siFor the fault mode of specifying; F_iFor fault f_iThe location matrix of correspondence in F.

From above-mentioned fault detectability judgement schematics, can obviously find out: as FD (f_i)=0 o'clock, showsFault f_iCan not be detected, and FD (f_i) numerical value show more greatly fault vector f_iDistance apart from null vector is got overF_iDetectability higher.

(3) whether the quantitative evaluation result that judges detectability fault is 0, if 0 is judged fault notCan be detected, enter step (7); Otherwise judge that fault is detectable failure, enter step (4);

(4) judged whether other detectable failures, entered step (5) if having, otherwise judgement shouldFault can not be isolated, and enters step (7);

(5) utilize the pretreated model obtaining in step (1), and employing " direction vector similitude "As isolability evaluation index, can detect event to the detectability fault obtaining in step (3) and otherBarrier carries out isolability quantitatively evaluating;

Can not detected fault be not there is isolability; Only there is the fault of detectability,Likely be isolated.

For quantitative analysis has detectability fault f_iAnd f_jBetween can degree of isolation, based on " vector sideTo similitude " concept, by introducing direction vector cosine method, carry out the quantitatively evaluating of Fault Isolation,Its computing formula is:

Wherein:Be two detectable failure vector f_iAnd f_jBetween angle.

Above formula shows: by comparing vector N_HF_if_siAnd N_HF_jf_sjBetween direction cosines, can realize faultf_iAnd f_jBetween the quantitatively evaluating of isolability. ConsiderSpan be [1,1], for ease of commentingValency analysis need be ensured that compared numerical value is positive number. Therefore, direction cosines value is converted to angleValue, and be handled as follows:

Above formula shows: in the time can detecting angle between vector and more approach pi/2, and fault f_iAnd f_jBetween isolateProperty is larger; In the time that its value is 0, f_iAnd f_jCan not be isolated.

(6) whether the quantitative evaluation result that judges isolability fault is 0, if 0 is judged fault notCan be isolated, enter step (7); Otherwise judge that fault is to be isolated fault, enter step (7);

(7) finish.

With a specific embodiment, operation principle of the present invention and concrete steps are described below:

Satellite sensor adopts infrared earth sensor and gyrostatic combination. Wherein, infrared earthSensor is for the attitude angle of instrumented satellite on the axis of rolling and pitch axisAnd θ; Gyroscope is just adopting three axlesHand over and install, respectively the attitude angular velocity of instrumented satellite on rolling, pitching and yaw axisWithExamineConsidering is decoupling zero to attitude of satellite angle/angular speed and rolling and yaw axis on pitch axis, for ease of analyzing,Below will only consider pitch axis.

The Mathematical Modeling of the satellite sensor of infrared earth sensor and gyroscope combination on pitch axis is:

$\left\{\begin{array}{c}\left[\begin{array}{c}\mathrm{\θ}(k+1)\\ d_y(k+1)\\ b_y(k+1)\end{array}\right.=\left[\begin{array}{ccc}1& -\mathrm{dt}& -\mathrm{dt}\\ 0& 1-1/{\mathrm{\τ}}_t\mathrm{dt}& 0\\ 0& 0& 1\end{array}\right]\left[\begin{array}{c}\mathrm{\θ}\left(k\right)\\ d_y\left(k\right)\\ b_y\left(k\right)\end{array}\right]+\left[\begin{array}{c}\mathrm{dt}({\mathrm{\ω}}_0+g_y)\\ 0\\ 0\end{array}\right]+\left[\begin{array}{cc}\mathrm{dt}& 0\\ 0& 0\\ 0& 0\end{array}\right]\left[\begin{array}{c}{f}_{\mathrm{gy}}\left(k\right)\\ f_{\mathrm{h\θ}}\left(k\right)\end{array}\right]+\left[\begin{array}{c}{n}_y\left(k\right)\\ n_{\mathrm{dy}}\left(k\right)\\ n_{\mathrm{by}}\left(k\right)\end{array}\right]\\ \mathrm{\θ}\left(k\right)=\left[\begin{array}{ccc}1& 0& 0\end{array}\right]\left[\begin{array}{c}\mathrm{\θ}\left(k\right)\\ d_y\left(k\right)\\ b_y\left(k\right)\end{array}\right]+\left[\begin{array}{cc}0& 1\\ 0& 0\\ 0& 0\end{array}\right]\left[\begin{array}{c}{f}_{\mathrm{gy}}\left(k\right)\\ f_{\mathrm{h\θ}}\left(k\right)\end{array}\right]+n_{\mathrm{\θ}}\left(k\right)\end{array}\right.$

Wherein: d_yRepresent the correlation of indices drift term of gyroscope on pitch axis; b_yRepresent that gyroscope is at pitch axisOn constant value drift item; Dt represents sampling time interval, and value is dt=0.1s; τ_yFor time constant, getValue is τ_y=1；ω₀Represent satellite orbit angular speed, value is ω₀=0.06rad/s；n_y、n_dy、n_byAnd n_θPointThe white Gaussian noise of Biao Shi not being correlated with, distribution form is followed successively by n_y(k)～N(0,10^-6)、n_dy(k)～N(0,10^-5)、n_by(k)～N(0,10^-4) and n_θ(k)～N(0,10^-4)；f_gyAnd f_hθRepresent respectively gyroscope and infrared earth sensorFault variable on pitch axis.

When fault mode adopts deviation increase type, i.e. f_i(s)=[0.10.30.70.9] T, gained gyroscope andThe fault of infrared earth sensor on pitch axis can detect the quantitative evaluation result with isolability, as tableShown in 1.

As can be seen from Table 1: based on " vector distance similitude ", obtain fault f_gyAnd f_hθExamineThe property surveyed is respectively 0.1334 and 39.9141. This illustrates f_hθCompared with f_gyMore easily be detected, infraredThe deviation increase type fault of earth sensor is stronger compared with the detectability of the similar fault of gyroscope. Based on " vowingAmount directional similarity ", obtain f_gyAnd f_hθBetween isolability be 1.5708. This explanation is by designObserver also makes the spatial direction difference of its residual error vector, can realize infrared earth sensor and gyroThe deviation increase type fault of instrument is isolated.

Table 1 fault diagnosability evaluation result

The unspecified part of the present invention belongs to general knowledge as well known to those skilled in the art.

Claims (1)

1. a satellite sensor failure diagnosticability evaluation method of considering interference effect, its feature existsAs follows in step:

(1) based on model standardization and equivalent space transform process method, to given satellite sensorCarry out pretreatment and obtain pretreated model;

(2) utilize the pretreated model obtaining in step (1), and employing " vector distance similitude "As detectability evaluation index, carry out the quantitatively evaluating of fault detectability;

(3) whether the quantitative evaluation result of failure judgement detectability is 0, if 0 is judged faultCan not be detected and enter step (7); Otherwise judge that fault can detect, enter step (4);

(4) judged whether other detectable failures, entered step (5) if having, otherwise judgement shouldFault can not be isolated, and enters step (7);

(5) utilize the pretreated model obtaining in step (1), and employing " direction vector similitude "As isolability evaluation index, can detect the detectability fault obtaining in step (3) and otherFault is carried out the quantitatively evaluating of isolability;

(6) whether the quantitative evaluation result that judges isolability fault is 0, if 0 is judged faultCan not be isolated, enter step (7); Otherwise judge that fault can be isolated, enter step (7);

(7) finish;

In described step (1), obtaining pretreated model is:

N_HLz_s＝N_HFf_s+N_HEe_s

Wherein, $z_s=\left[\begin{array}{c}y(k-n+1)\\ \·\\ \·\\ \·\\ y\left(k\right)\\ u(k-n+1)\\ \·\\ \·\\ \·\\ u\left(k\right)\end{array}\right],$ $f_s=\left[\begin{array}{c}f(k-n+1)\\ \·\\ \·\\ \·\\ f\left(k\right)\end{array}\right],$ $e_s=\left[\begin{array}{c}w(k-n+1)\\ \·\\ \·\\ \·\\ w\left(k\right)\\ v(k-n+1)\\ \·\\ \·\\ \·\\ v\left(k\right)\end{array}\right];$

N_HFor the left orthogonal basis of matrix H kernel, i.e. N_HH＝0；x∈RⁿFor state variable; Y ∈ R^mFor outputAmount; U ∈ R^qFor input quantity; F ∈ R^pFor fault variable; W ∈ R^lWith v ∈ R^tFor disturbing, z_s∈R^(m+q)s、x_s∈R^n(s+1)、f_s∈R^psAnd e_s∈R^(l+t)sBe respectively pretreated model observed quantity, state variable, fault and dryThe time heap stack vector of disturbing; S is length of window (s=n+1); Rⁿ、R^m、R^q、R^p、R^l、R^t、R^(m+q)s、R^n(s+1)、R^psAnd R^(l+t)sBe respectively n in real number field dimension, m dimension, q dimension, p dimension, l dimension,T dimension, (m+q) s dimension, n (s+1) dimension, ps peacekeeping (l+t) s dimensional vector, n, m, q, p, l and t arePositive integer; K is sampling time point; I is unit matrix; A, C, B_u、D_u、B_f、D_f、B_wAnd D_vFor the sytem matrix of pretreated model;

Fault detectability evaluation index based on " vector distance similitude " in described step (2) is:

$FD\left(f_i\right)=\frac{1}{2}\left|\right|N_H{F}_i{f}_{si}|{|}^2$

Wherein: f_siRepresent the fault mode of specifying; F_iRepresent fault vector f_iThe location matrix of correspondence in F, i isPositive integer, N_HFor the left orthogonal basis of matrix H kernel;

Fault isolability evaluation index based on " direction vector similitude " in described step (5) is:

Wherein:Be two detectable failure vector f_iAnd f_jBetween angle.