CN103697915A - Diagnostic evaluation method considering disturbing influence for satellite sensor fault - Google Patents

Abstract

The invention discloses a diagnostic evaluation method considering disturbing influence for a satellite sensor fault. The diagnostic evaluation method comprises the following steps: aiming at a satellite sensor system influenced by interference factors such as noise and modeling nondeterminacy, respectively taking vector distance similarity and vector direction similarity as evaluation indexes to realize the detection and isolability quantitative evaluation of the sensor fault through deploying conditions of mathematical description, system model and a satellite sensor of a fault mode. The diagnostic evaluation method provided by the invention can bring the fault diagnosis of the satellite sensor forward to a design stage on the condition of not depending on any fault diagnosis algorithm, and guide the optimal configuration of the satellite sensor.

Description

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

Technical field

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

Background technology

Satellite sensor is the general designation of satellite attitude measurement element, mainly comprises star sensor, infrared earth sensor, gyroscope etc.As the important measuring sensor in control system, once the precision that satellite sensor breaks down and controls having a strong impact on the attitude of satellite even causes attitude rolling when serious.Along with the increase increasingly of the integrated scale of sensor and complicacy, and the impact of unpredictable space environment factor, it is inevitably broken down.In order to make fault effects, be down to minimum and overcome the shortcoming of product inherent reliability deficiency, need in sensor design process, consider the impact of fault, and using fault diagnosability as a kind of index, bring in design system for instructing the optimization of sensor configuration.Yet, in existing 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.From its definition, can find out, fault diagnosability comprises detectability and isolability two parts.Diagnosticability evaluation is basis and the prerequisite of fault diagnosis algorithm.Because for fault that can not be detected, design detection and isolation which kind of diagnosis algorithm all can not be realized fault.Diagnosticability evaluation is exactly in the situation that not relying on any fault diagnosis algorithm, for the mathematical model of system and the configuring condition of sensor, analyzes the influence degree of specified fault pattern to system.

For the detectability evaluation of control system, technology in the past mainly comprises following three aspects:: the 1) existence judgment to transport function between output based on fault; 2) the system observability using fault as a kind of state is analyzed; 3) existence judgment based on output and input message structure residual error vector.For isolability evaluation, achievement in the past mainly comprises following two aspects: 1) based on different faults, the otherness of output impact is differentiated; 2) incidence matrix based on closing series structure between I/O information and fault carries out qualitative analysis.Above adopted technology is not all considered the impact of the disturbing factors such as noise, modeling uncertainty; And gained evaluation result is qualitatively, can only illustrates that can fault be detected and be isolated, and can not illustrate that fault is detected and segregate complexity.

Summary of the invention

Technical matters to be solved by this invention is: overcome the deficiencies in the prior art, provide a class to consider the satellite sensor failure diagnosticability evaluation method of disturbing effect, in the Control System Design stage, can realize the quantitatively evaluating to sensor failure, and guide the optimization of sensor configuration.

Technical solution of the present invention is:

A kind ofly consider that the satellite sensor failure diagnosticability evaluation method of disturbing effect comprises that step is as follows:

(1), based on model standardization and equivalent space transform process method, given satellite sensor is carried out to pre-service and obtain pretreated model;

(2) utilize the pretreated model obtaining in step (1), and adopt " vector distance similarity " 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 that fault can not be detected, enters step (7); Otherwise judge that fault is detectable failure, enter step (4);

(4) judge whether other detectable failures, if having, entered step (5), otherwise judged that this fault can not be isolated, entered step (7);

(5) utilize the pretreated model obtaining in step (1), and adopt " direction vector similarity " as isolability evaluation index, the detectability fault and other detectable failures that in step (3), obtain are carried out to isolability quantitatively evaluating;

(6) whether the quantitative evaluation result that judges isolability fault is 0, if 0 is judged that fault can not be isolated, enters 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 ∈ R ⁿfor state variable; Y ∈ R ^mfor output 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) s}the time heap stack vector that represents respectively observed quantity, state variable, fault and the interference of pretreated model, s is that length of window is: s=n+1; R ⁿ, R ^m, R ^q, R ^p, R ^l, R ^t, R ^{(m+q) s}, R ^{n (s+1)}, R ^psand R ^{(l+t) s}be respectively n 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 in real number field, n, m, q, p, l and t are positive integer; K is sampling time point; I is unit matrix; A, C, B _u, D _u, B _f, D _f, B _wand D _vsystem matrix for pretreated model.

Fault detectability evaluation index based on " vector distance similarity " 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 _sithe fault mode that represents appointment; F _irepresent fault f _ithe location matrix of correspondence in F, i is positive integer.

Fault isolability evaluation index based on " direction vector similarity " 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) the present invention advances to the design phase by the fault diagnosis of satellite sensor, according to fault diagnosability evaluation result, instructs distributing rationally of sensor, and it is brought in satellite control system design system as a kind of index.

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

(3) the present invention can realize satellite sensor failure and can detect the quantitatively evaluating with isolability, can provide fault and can detect and isolable complexity; And can find out that satellite sensor failure detects and the thin spot of isolation, for the design of fault diagnosis algorithm provides theoretical foundation.

Accompanying drawing explanation

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

Embodiment

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 mathematical model that a class comprises the disturbing factors such as noise, modeling uncertainty, provide a kind of fault can detect the evaluation method with 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 carried out to pre-service and obtain pretreated model;

The mathematical model 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 ∈ R ⁿfor state variable; Y ∈ R ^mfor output quantity; U ∈ R ^qfor input quantity; F ∈ R ^pfor fault variable; W ∈ R ^lwith v ∈ R ^tfor disturbing, the two is normal distribution, and linearity is uncorrelated mutually; R ⁿ, 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 _vlocation matrix for pretreated model;

According to regular hour window (length of window is: s=n+1) above-mentioned satellite sensor model is carried out to iteration, 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) s}the time heap stack vector that represents respectively observed quantity, state variable, fault and the interference of pretreated model, R ^{(m+q) s}, R ^{n (s+1)}, R ^psand R ^{(l+t) s}for (m+q) s dimension in real number field, 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 matrix of coefficients 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.

According to pretreated model, can find: the model equal sign left side is known input and output amount, equal sign the right comprises the fault of known mode and interference two parts that known probability distributes, when disturbing as normal distribution, and observed quantity N _hlz _sphysical meaning be: with N _hff _sfor average, with N _hee _sdistribution variance is the multivariate normal distribution of variance; The result that pretreated model is processed is converted into standardized normal distribution by multivariate normal distribution.

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

For the difference between the above-mentioned normal distribution of quantificational description, the concept based on " vector distance similarity ", by introducing K-L divergence (Kullback – Leibler divergence), to analyze, its computing formula 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 distribution

with

probability 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 distribution

average and variance; μ _jand ∑ _jbe respectively polynary distribution average and variance.

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

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

Because pretreated model is converted to standardized normal distribution by normal distribution, so ∑ _i=∑ _jduring=I, above formula is reduced 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 standardized normal distribution because meet the interference model of normal distribution, so 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 _sifault mode for appointment; 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, shows fault f _ican not be detected, and FD (f _i) numerical value show more greatly fault vector f _idistance apart from null vector is far away, i.e. f _idetectability higher.

(3) whether the quantitative evaluation result that judges detectability fault is 0, if 0 is judged that fault can not be detected, enters step (7); Otherwise judge that fault is detectable failure, enter step (4);

(4) judge whether other detectable failures, if having, entered step (5), otherwise judged that this fault can not be isolated, entered step (7);

(5) utilize the pretreated model obtaining in step (1), and adopt " direction vector similarity " as isolability evaluation index, the detectability fault and other detectable failures that in step (3), obtain are carried out to isolability quantitatively evaluating;

Can not detected fault be not there is isolability; The fault only with detectability, is just likely isolated.

For quantitative analysis has detectability fault f _iand f _jbetween can degree of isolation, based on " direction vector similarity " 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 cosine, can realize fault f _iand f _jbetween the quantitatively evaluating of isolability.Consider

span be [1,1], for ease of evaluation analysis, need be guaranteed that compared numerical value is positive number.Therefore, direction cosine value is converted to angle value, and is 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 isolability larger; When 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 that fault can not be isolated, enters step (7); Otherwise judge that fault is to be isolated fault, enter step (7);

(7) finish.

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

Satellite sensor adopts infrared earth sensor and gyrostatic array mode.Wherein, infrared earth sensor is for the attitude angle of instrumented satellite on the axis of rolling and pitch axis

and θ; Gyroscope adopts three axle quadratures to install, respectively the attitude angular velocity of instrumented satellite on rolling, pitching and yaw axis

with

consider that attitude of satellite angle/angular velocity and rolling and yaw axis are decoupling zeros on pitch axis, for ease of analyzing, below will only consider pitch axis.

The mathematical model 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 the constant value drift item of gyroscope on pitch axis; Dt represents sampling time interval, and value is dt=0.1s; τ _yfor time constant, value is τ _y=1; ω ₀represent satellite orbit angular velocity, value is ω ₀=0.06rad/s; n _y, n _dy, n _byand n _θrepresent respectively relevant white Gaussian noise, 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 _{h θ}represent respectively gyroscope and the infrared earth sensor fault variable on pitch axis.

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

As can be seen from Table 1: based on " vector distance similarity ", obtain fault f _gyand f _{h θ}detectability be respectively 0.1334 and 39.9141.This illustrates f _{h θ}compared with f _gymore easily be detected, the deviation increase type fault of infrared earth sensor is stronger compared with the detectability of the similar fault of gyroscope.Based on " direction vector similarity ", obtain f _gyand f _{h θ}between isolability be 1.5708.This explanation is by design observer and make the spatial direction of its residual error vector different, can realize infrared earth sensor and gyrostatic deviation increase type fault are 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 (4)

1. a satellite sensor failure diagnosticability evaluation method of considering disturbing effect, is characterized in that step is as follows:

(1), based on model standardization and equivalent space transform process method, given satellite sensor is carried out to pre-service and obtain pretreated model;

(2) utilize the pretreated model obtaining in step (1), and adopt " vector distance similarity " 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 that fault can not be detected and enters step (7); Otherwise judge that fault can detect, enter step (4);

(4) judge whether other detectable failures, if having, entered step (5), otherwise judged that this fault can not be isolated, entered step (7);

(5) utilize the pretreated model obtaining in step (1), and adopt " direction vector similarity " as isolability evaluation index, the quantitatively evaluating that the detectability fault obtaining in step (3) and other detectable failures are carried out to isolability;

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

(7) finish.

2. a kind of satellite sensor failure diagnosticability evaluation method of considering disturbing effect according to claim 1, is characterized in that: 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 ∈ R ⁿfor state variable; Y ∈ R ^mfor output 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) s}be respectively the time heap stack vector of pretreated model observed quantity, state variable, fault and interference; S is length of window (s=n+1); R ⁿ, R ^m, R ^q, R ^p, R ^l, R ^t, R ^{(m+q) s}, R ^{n (s+1)}, R ^psand R ^{(l+t) s}be respectively n 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 in real number field, n, m, q, p, l and t are positive integer; K is sampling time point; I is unit matrix; A, C, B _u, D _u, B _f, D _f, B _wand D _vsystem matrix for pretreated model.

3. a kind of satellite sensor failure diagnosticability evaluation method of considering disturbing effect according to claim 1, is characterized in that: the fault detectability evaluation index based on " vector distance similarity " 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 _sithe fault mode that represents appointment; F _irepresent fault f _ithe location matrix of correspondence in F, i is positive integer.

4. a kind of satellite sensor failure diagnosticability evaluation method of considering disturbing effect according to claim 1, is characterized in that: the fault isolability evaluation index based on " direction vector similarity " in described step (5) is:

Wherein:

be two detectable failure vector f _iand f _jbetween angle.

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