CN104678989B - The state aware optimization method of fault diagnosability is improved under a kind of noise circumstance - Google Patents

Abstract

The state aware optimization method of fault diagnosability is improved under a kind of noise circumstance, the fault diagnosability energy index that process noise and observation noise influence are quantified is considered first；Then genetic algorithm fitness function is set up by optimization aim of cost Least-cost needed for measuring point arrangement, being finally based on binary strings genetic algorithm carries out state aware selection, completion status sensing and optimizing process, the focus for improving system fault diagnosis ability is advanced to the design phase, ensure that the stability of stochastic linear dynamical system and the accuracy of design, the quantity of state aware can be greatly reduced simultaneously, such that it is able to reduce the configuration quantity of satellite control system sensor, the design cost of satellite control system is reduced.

Description

The state aware optimization method of fault diagnosability is improved under a kind of noise circumstance

Technical field

The present invention relates to a kind of state aware optimization method for improving fault diagnosability, under particularly a kind of noise circumstance The state aware optimization method of fault diagnosability is improved, belongs to Aerospace Control field.

Background technology

Increasingly increase with the fast development and people of modern control technology to system performance requirements so that control system The structure and scale of system is increasing, function is increasingly sophisticated.There is failure miscellaneous unavoidably in complicated system, so as to cause to be System hydraulic performance decline, even collapses completely when serious.In satellite control system, a small failure is just possible to cause huge Disaster, bring beyond measure loss.Therefore, it is the running quality of Guarantee control system, it is necessary to which the failure for improving system is examined Disconnected and disposal ability, it is ensured that after failure generation, failure is detected in time, be accurately positioned the source of trouble, and adopt an effective measure and make Fault impact is minimized, and this is to overcome product inherent reliability not enough from system level, improves control system operational reliability With prolong long-life effective means.

In order to improve the trouble diagnosibility of satellite control system, it is necessary first to which the state to sensory perceptual system optimizes cloth Office, to improve the trouble diagnosibility of system, and for fault diagnosis subsystem provides diagnostic message as much as possible.But due to weight The constraints such as amount, volume, up-downgoing data volume be numerous so that satellite control system can not possibly be to all fault modes and state All perceived.Therefore, layout need to be optimized to the state of system, it is provided on the premise of constraints is met Failure diagnosis information as much as possible.However, in the research in the existing field, do not consider ambient noise influence (including： Process noise and observation noise etc.).In fact, ambient noise can have a strong impact on fault diagnosis system is realizing detection and isolation just True property, this is mainly reflected in：So that the output bias that ambient noise causes are mistakened as making troubleshooting；The deviation quilt that failure causes Do not considered as noise, the small fault that particularly dynamical system early stage occurs usually is submerged in noise.And it is current, Not yet consider to optimize layout for the state perception system for improving fault diagnosability in the design process of satellite control system, The selection of diagnostic message relies primarily on the experience of designer, and this causes the diagnosticability of satellite control system poor.

The content of the invention

Technology solve problem of the invention is：Overcome the deficiencies in the prior art, there is provided one kind improves fault diagnosability State perception system layout optimization method, optimize layout process in take into full account process noise and observation noise etc. interference because The influence of element, state aware optimization is carried out using genetic algorithm, and the focus for improving system fault diagnosis ability is advanced to Design phase, it is ensured that the stability of stochastic linear dynamical system and the accuracy of design.

Technical solution of the invention is：The state aware optimization side of fault diagnosability is improved under a kind of noise circumstance Method, step is as follows：

(1) process noise and observation noise are considered, the separate manufacturing firms model according to satellite control system is quantified Fault diagnosability energy index；

The separate manufacturing firms model of the satellite control system is by formula：

Be given, in formula：x∈RⁿIt is the state variable of satellite control system；y∈R^mIt is the output of satellite control system；u∈ R^qIt is the input of satellite control system；f∈R^pBe the fault vector of satellite control system, the failure include actuator failures and Sensor failure；w∈R^lWith v ∈ R^tRespectively process noise and observation noise；Rⁿ、R^m、R^q、R^p、R^lAnd R^tIt is illustrated respectively in real number N dimensions, m dimensions in domain, q dimensions, p dimensions, l peacekeeping t dimensional vectors, n, m, q, p, l and t are positive integer；K is sampling time point；A、B_u、 B_f、B_w、C、D_u、D_fAnd D_vIt is the sytem matrix of corresponding dimension；

(2) with required cost Least-cost as optimization aim, the fitness function of genetic algorithm is set up；

The fitness function of the genetic algorithm is：

Wherein：c_senSensor configuration cost needed for representing a state aware, the sensor configuration cost is by sensing The price and weight of device are quantified；n_sen(χ) represents the state aware number of configuration；M represents the set of state aware, and χ is M Subset；F(q_i,q_j,n_sen) represent that the detectable performance indications of quantization or the isolability of quantization of satellite control system can refer to Mark；λ represents coefficient factor, and its span is [0,1], r_kIt is penalty factor, r_k>0, and during k →+∞, r_k→+∞；

(3) using the set of all state awares as population set, population scale N1, the crossover probability of genetic algorithm are determined P1, mutation probability P2, maximum evolutionary generation N2 and fitness function threshold value N3；

(4) genetic algorithm parameter determined in the genetic algorithm fitness function and step (3) that are determined using step (2), State aware selection is carried out based on binary strings genetic algorithm, judge state aware in population fitness function value whether more than etc. In fitness function threshold value N3, if being more than or equal to fitness function threshold value N3, into step (5)；Otherwise reenter step (4)；

(5) state aware selected in output step (4), completion status sensing and optimizing.

The detectable performance indications of the quantization in the step (1) are by formula：

Be given, wherein FD (f_i) it is failure f_iThe detectable performance indications for quantifying, FD (f_i) span be [0,1], FD (f_i) closer to 1, f_iDetectability it is higher；Conversely, FD (f_i) closer to 0, f_iDetectability it is lower；p(N_HF_if_si| H) table Fault vector N when showing that fault-free occurs_HF_if_siProbability density function, H represent satellite control system fault-free occur, F_iRepresent Failure f_iFfault matrix, i is positive integer, f_siRepresent fault mode set in advance.

Failure f in the step (1)_iWith f_jBetween quantify isolability energy index by：

Be given, wherein FI (f_i,f_j) it is failure f_iWith f_jBetween quantify isolability energy index；FI(f_i,f_j) value model Enclose is [0,1], FI (f_i,f_j) closer to 1, represent f_iWith f_jBetween isolability can be stronger；FI(f_i,f_j) closer to 0, can be every It is weaker from performance.

Compared with the prior art, the invention has the advantages that：

(1) present invention carries out the optimization of satellite control system fault diagnosability state aware using genetic algorithm, can obtain Do well the globally optimal solution of perception, it is to avoid other traditional optimized algorithms are easily trapped into the deficiency of local optimum, improve star The accuracy of control system fault diagnosability state aware optimum results；

(2) can be with the quantizating index of isolability energy, and base The present invention gives satellite control system fault detectability The fitness function of genetic algorithm is given in fault detectability energy index and isolability energy index, is to defend under noise circumstance The optimization of star control system fault diagnosability state aware provides accurate Mathematical Modeling；

(3) present invention has taken into full account that process noise and observation are made an uproar during fault diagnosability energy index is calculated The disturbing factors such as sound to diagnosticability can influence, the accurate description fault diagnosability energy of satellite control system, so as to carry The accuracy and robustness of fault diagnosability state aware optimum results under noise circumstance high；

(4) fault diagnosis of satellite control system is advanceed to the design phase by the present invention, and by satellite control system event Barrier state aware optimization realizes the engineering objective of the diagnosis of raising system on-orbit fault and disposal ability；

(5) method in the present invention can greatly reduce the quantity of state aware, be passed such that it is able to reduce satellite control system The configuration quantity of sensor, reduces the design cost of satellite control system.

Brief description of the drawings

Fig. 1 is flow chart of the present invention；

Fig. 2 is the FB(flow block) of genetic Optimization Algorithm used by the present invention；

Fig. 3 distributes figure rationally for present invention gained measuring point.

Specific embodiment

Specific embodiment of the invention is further described in detail below in conjunction with the accompanying drawings.

Fig. 1 is the FB(flow block) of the inventive method, and as shown in Figure 1, step of the invention is as follows：

(1) process noise and observation noise are considered, the separate manufacturing firms model according to satellite control system is quantified Fault diagnosability energy index；

Satellite control system can be described with state-space model as follows：

In formula：x∈RⁿIt is state variable；y∈R^mIt is output；u∈R^qIt is input；f∈R^pIt is fault vector, including performs Device failure and sensor failure；w∈R^lWith v ∈ R^tRespectively process noise and observation noise, can be described as system interference；Rⁿ、 R^m、R^q、R^p、R^lAnd R^tIt is illustrated respectively in n dimensions, m dimensions, q dimensions, p dimensions, l peacekeeping t dimensional vectors, n, m, q, p, l and t in real number field It is positive integer；K is sampling time point；A、B_u、B_f、B_w、C、D_u、D_fAnd D_vIt is the sytem matrix of corresponding dimension.

Above-mentioned satellite control system model is iterated according to time window length s=n+1, and constructs following standard Change model：

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)sThe respectively observation of standardized model, state The time heap stack vector of variable, failure and interference, mathematic(al) representation is：

L, H, F and E are the coefficient matrix of corresponding dimension, respectively (wherein, I represents unit matrix)：

Equivalent space conversion is carried out to above-mentioned standard model, following statistical model is obtained：

N_HLz_s=N_HFf_s+N_HEe_s

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

Due to failure f_iDetectability and p (r=N_HF_if_si| H) numerical value be inversely proportional, obtaining following detectability can refer to Mark：

Wherein：FD(f_i) it is failure f_iDetectability energy, that is, represent failure f_iThe complexity being detected；It takes Value scope is [0,1], and the numerical value is closer to 1, f_iDetectability it is higher；Conversely, the numerical value is closer to 0, f_iDetectability get over It is low；p(N_HF_if_si| H) fault vector N when representing that fault-free occurs_HF_if_siProbability density function, F_iRepresent failure f_iIn failure Corresponding position in matrix F, i is positive integer, f_siThe fault mode that expression is specified.

According to the Fault Isolation principle in fixed residual error direction, to realize failure f_iFrom f_jMiddle isolation/distinguish, needs Meet following formula：

In formula：q_i=N_HF_if_si；q_j=N_HF_jf_sj；R=N_HLz_s；Symbol " " represents dot-product operation；| | represent absolute Value；| | | | represent vector norm；F_jRepresent failure f_jThe corresponding position in matrix F, j is positive integer, f_sjWhat expression was specified Fault mode.

Work as rq_i>0 and rq_j>When 0, on above formula both sides with multiplying | | r | | and by r=q_i+e_i(e_i=N_HE_ie_si) substitute into, warp Cross and be derived by：

In formula：n_iAnd n_jQ is represented respectively_iAnd q_jUnit vector.

Work as rq_i>0 and rq_j<When 0, can obtain：

Similarly, can obtain working as rq_i<0 and rq_j<0 and rq_i<0 and rq_j>In the case of 0 two kinds | | q_i| | value. In sum, to by f_iFrom f_jMiddle isolation, need to meet following requirement：

In formula：||N_HF_if_si||_cRepresent failure f_iFrom f_jFault vector N needed for middle isolation_HF_if_siThe critical value of norm.

Knowable to from above formula：Failure f_iWith f_jBetween isolability it is higher, it is required | | N_HF_if_si||_cNumerical value it is smaller, i.e., f_iWith f_jBetween isolability with | | N_HF_if_si||_cIt is inversely proportional.

Therefore, failure f_iWith f_jBetween quantify isolability energy index be：

Wherein：FI(f_i,f_j) it is failure f_iWith f_jBetween isolability energy, that is, represent failure f_iFrom f_jMiddle differentiation/isolation Complexity out；Its span is [0,1], and the numerical value represents f closer to 1_iWith f_jBetween isolability it is stronger；Should Numerical value is closer to 0, and isolability is weaker.

(2) with required cost Least-cost as optimization aim, the fitness function of genetic algorithm is set up：

In formula：c_senRepresent cost needed for one measuring point of configuration；n_sen(χ) represents the measuring point number of configuration；M represents all surveys The set of point, χ is the subset of M；F(q_i,q_j,n_sen) represent above-mentioned FD (f_i) and FI (f_i,f_j) computing formula；F_req(q_i,q_j, n_sen) represent the diagnosable performance indications specified；λ represents coefficient factor, and its span is [0,1].

To eliminate above-mentioned inequality constraints, using following object function：

Wherein：r_kIt is penalty factor, r_k>0 and r_k→+∞(k→+∞)。

(3) using the set of all state awares as population set, population scale N1, the crossover probability of genetic algorithm are determined P1, mutation probability P2, maximum evolutionary generation N2 and fitness function threshold value N3；The span of N1：20~50；P1's and P2 takes Value scope is：[0,1]；The span of N2 is：100~300；The span of N3 is：0.5~1；

(4) genetic algorithm parameter determined in the genetic algorithm fitness function and step (3) that are determined using step (2), Based on binary strings genetic algorithm, (Li Min is waited write by force《The basic theories of genetic algorithm and application》Page 17 to 74) carry out state Selection is perceived, whether the fitness function value of state aware in population is judged more than or equal to fitness function threshold value N3, if being more than Equal to fitness function threshold value N3, then into step (5)；Otherwise reenter step (4)；The flow of binary strings genetic algorithm Figure, as shown in Figure 2.

(5) state aware selected in output step (4), completion status sensing and optimizing.

Embodiment

For the satellite attitude control system of 3 axles stabilization, its state-space model can be described as：

In formula： θ and ψ represent the rolling of satellite relative orbit coordinate system respectively Angle, the angle of pitch and yaw angle, ω_x、ω_yAnd ω_zRepresent projection of the measuring satellite angular velocities vector on 3 principal moments axles；U=[T_x T_y T_z]^T, T_x、T_yAnd T_zRepresent control moment along 3 components of principal moments axle；f_aRepresent momenttum wheel failure；W (k) and v (k) obey as follows respectively Normal distribution w (t)~N (0_6×1,2.25×10^-10I_6×6) and 0 and I represents the null matrix and unit matrix of corresponding dimension respectively；

I_x、I_yAnd I_zSatellite is represented in 3 rotary inertias of the principal axis of inertia, value is I_x=12.50kgm²、I_y= 13.70kg·m²And I_z=15.90kgm², ω₀Orbit angular velocity is represented, value is ω₀=0.001rad/s, dt represent sampling Time interval, value is dt=0.01s；B_J=diag { 1/I_x 1/I_y 1/I_z, B_dt=diag { dt dt dt}；B_w=I_6×6。

Matrix C is state aware matrix to be optimized.When fault mode uses deviation increase type, i.e. f_si=[0.1 0.3 0.5 0.7 0.9 1.1 1.3]^T, relevant parameter is set in genetic algorithm：Population scale 20, crossover probability 0.7, variation is general Rate 0.3, maximum evolutionary generation 100.By the way that after optimization, the system only needs observer state variable ω_x、ω_yAnd ω_z, you can meet dynamic The detectable and isolable performance requirement of amount wheel failure.Therefore the concrete form of optimization gained Matrix C is：

Relation between measuring point number and diagnosable performance indications, as shown in figure 3, as can be seen from Figure 3, according in embodiment Matrix C carries out state aware optimization, it is only necessary to observer state variable ω_x、ω_yAnd ω_z, you can reach satellite control system failure The 98% of diagnosticability energy, it can be seen that, the method in the present invention can greatly reduce the quantity of state aware, such that it is able to reduce The configuration quantity of satellite control system sensor, reduces the design cost of satellite control system.

By the specific embodiment of the invention as can be seen that raising failure can under a kind of noise circumstance provided by the present invention Diagnostic state aware optimization method takes full advantage of the own characteristic of satellite control system structure, it is ensured that optimum results Reliability and stability, considerably increase optimal speed, are conducive to being obtained in time in practical engineering application the state sense of system Know optimization information.And, the method is equally applicable to satellite control system, and state aware information is less under pattern in orbit Situation.

The content not being described in detail in description of the invention belongs to the known technology of professional and technical personnel in the field.

Claims (3)

1. the state aware optimization method of fault diagnosability is improved under a kind of noise circumstance, it is characterised in that step is as follows：

(1) process noise and observation noise, the event that the separate manufacturing firms model according to satellite control system is quantified are considered Hinder diagnosable performance indications；

The separate manufacturing firms model of the satellite control system is by formula：

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

Be given, in formula：x∈RⁿIt is the state variable of satellite control system；y∈R^mIt is the output of satellite control system；u∈R^qFor The input of satellite control system；f∈R^pIt is the fault vector of satellite control system, the failure includes actuator failures and sensitivity Device failure；w∈R^lWith v ∈ R^tRespectively process noise and observation noise；Rⁿ、R^m、R^q、R^p、R^lAnd R^tIt is illustrated respectively in real number field N dimension, m dimension, q dimension, p dimension, l peacekeeping t dimensional vectors, n, m, q, p, l and t be positive integer；K is sampling time point；A、B_u、B_f、 B_w、C、D_u、D_fAnd D_vIt is the sytem matrix of corresponding dimension；

(2) with required cost Least-cost as optimization aim, the fitness function of genetic algorithm is set up；

The fitness function of the genetic algorithm is：

$\underset{\mathrm{\&chi;}\&SubsetEqual;M}{\min }l(\mathrm{\&chi;},r_k)$

$l(\mathrm{\&chi;},r_k)=c_{sen}{n}_{sen}\left(\mathrm{\&chi;}\right)+r_k\underset{i,j}{\&Sigma;}{\{\min \&lsqb;0,F(q_i,q_j,n_{sen})-{\mathrm{\&lambda;F}}_{req}(q_i,q_j,n_{sen})\&rsqb;\}}^2$

Wherein：c_senSensor configuration cost needed for representing a state aware, the sensor configuration cost is by sensor Price and weight are quantified；n_sen(χ) represents the state aware number of configuration；M represents the set of state aware, and χ is the son of M Collection；F(q_i,q_j,n_sen) represent satellite control system quantization detectable performance indications or the isolability energy index of quantization；λ Coefficient factor is represented, its span is [0,1], r_kIt is penalty factor, r_k>0, and during k →+∞, r_k→+∞；

Wherein, F_req(q_i,q_j,n_sen) represent the diagnosable performance indications specified；q_i=N_HF_if_si；q_j=N_HF_jf_sj；N_HRepresenting matrix The left orthogonal basis of H kernels, F_iRepresent failure f_iFfault matrix, i is positive integer, f_siRepresent fault mode set in advance；

(3) using the set of all state awares as population set, determine the population scale N1 of genetic algorithm, crossover probability P1, Mutation probability P2, maximum evolutionary generation N2 and fitness function threshold value N3；

(4) genetic algorithm parameter determined in the genetic algorithm fitness function and step (3) that are determined using step (2), is based on Whether binary strings genetic algorithm carries out state aware selection, judge the fitness function value of state aware in population more than or equal to suitable Response function threshold N3, if being more than or equal to fitness function threshold value N3, into step (5)；Otherwise reenter step (4)；

(5) state aware selected in output step (4), completion status sensing and optimizing.

2. the state aware optimization method of fault diagnosability is improved under a kind of noise circumstance according to claim 1, It is characterized in that：The detectable performance indications for quantifying are by formula：

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

Be given, wherein FD (f_i) it is failure f_iThe detectable performance indications for quantifying, FD (f_i) span be [0,1], FD (f_i) Closer to 1, f_iDetectability it is higher；Conversely, FD (f_i) closer to 0, f_iDetectability it is lower；p(N_HF_if_si| H) indicate without Fault vector N when failure occurs_HF_if_siProbability density function, H represent satellite control system fault-free occur.

3. the state aware optimization method of fault diagnosability is improved under a kind of noise circumstance according to claim 1, It is characterized in that：The isolability energy index of quantization is by formula：

$FI(f_i,f_j)=\frac{1}{\left|\right|N_H{F}_i{f}_{si}|{|}_c+1}$

Be given, wherein FI (f_i,f_j) it is failure f_iWith f_jBetween quantify isolability energy index；FI(f_i,f_j) span is [0,1], FI (f_i,f_j) closer to 1, represent f_iWith f_jBetween isolability can be stronger；FI(f_i,f_j) closer to 0, isolability Can be weaker.