CN111105153A - Satellite health state multi-stage fuzzy evaluation method based on AHP-entropy weight method - Google Patents

Satellite health state multi-stage fuzzy evaluation method based on AHP-entropy weight method Download PDF

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CN111105153A
CN111105153A CN201911282950.7A CN201911282950A CN111105153A CN 111105153 A CN111105153 A CN 111105153A CN 201911282950 A CN201911282950 A CN 201911282950A CN 111105153 A CN111105153 A CN 111105153A
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张超
张越程
吕刚明
谭炜
张海威
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Abstract

The invention discloses a satellite health state multi-level fuzzy evaluation method based on an AHP-entropy weight method, which comprises the steps of constructing a system weight system comprising subjective weight, objective weight and comprehensive weight, providing accurate comprehensive weight for the fuzzy comprehensive evaluation method by adopting an analytic hierarchy process and an entropy weight method, providing subjective weight by the analytic hierarchy process, providing objective weight by the entropy weight method, and obtaining the comprehensive weight combining subjective and objective by the subjective and objective weight through an optimization function; and constructing a system evaluation system comprising a factor domain, a comment set, a membership function, an evaluation matrix and multi-stage fuzzy evaluation, comprehensively evaluating the service state of the on-orbit satellite, evaluating each layer of elements according to the membership principle of the fuzzy comprehensive evaluation, and then sequentially evaluating the overall health state from bottom to top by adopting a multi-stage fuzzy comprehensive evaluation method. The invention improves the safety and reliability of the satellite system, reduces the effective life cycle operation cost and ensures the smooth completion of the on-orbit satellite task.

Description

Satellite health state multi-stage fuzzy evaluation method based on AHP-entropy weight method
Technical Field
The invention belongs to the technical field of health assessment of the use state of an on-orbit satellite, and particularly relates to a satellite health state multi-stage fuzzy evaluation method based on an AHP-entropy weight method.
Background
Due to the complexity of the satellite system itself and the uncertainty of the outer space environment, it is difficult to ensure that the satellite does not fail during the service life, and the subsystems of the satellite system are coupled, so that once a component fails, the system is likely to be broken down, therefore, the evaluation of the satellite system health is more and more important, the satellite system health evaluation is a powerful tool for reducing the satellite operation faults and guaranteeing the safe operation of the satellite, the satellite system health evaluation is scientific evaluation on the satellite operation state and the health degree by utilizing the telemetering parameters, then the expert makes scientific and effective health management strategy for the satellite through the analysis of the evaluation result, the satellite system health assessment is a key tool for improving the safety and reliability of the satellite system, reducing the operating cost of the on-orbit satellite and guaranteeing the normal operation of the satellite.
At present, the methods for evaluating the health state of a loss-of-function satellite are mainly divided into the following methods:
1. the method based on data mining comprises the following steps: k-means algorithm, orthogonal segmentation clustering and unary correlation vector machine method. The method mainly comprises the steps of extracting a data set under a normal condition by using a clustering-based method, and then calculating the variance of the distance between a real-time data vector and a normal-state data vector to be used as a characteristic quantity to carry out satellite health assessment. The method is only suitable for single-stage health assessment, and cannot reflect the influence of components in a multi-stage system on the health state of the system.
2. A health assessment method based on Bayes network is a method for synthesizing prior information of unknown parameters and sample information, obtaining posterior information according to Bayesian formula, and inferring the unknown parameters according to the posterior information. The method has the disadvantages that the Bayes network is often lack of prior knowledge and data support in the establishing process, the complete Bayes network is difficult to establish, and the multistage satellite system is difficult to apply and lack of practicability.
3. A multilevel health assessment method based on hierarchical reasoning comprises the following steps: analytic hierarchy process, weighted average synthesis process, state number process. The method mainly divides the satellite system into a plurality of layers according to the relationship among the influence factors of the satellite system, converts the complex multi-target and multi-criterion problem into a simple single-target and multi-layer problem, and has strong practicability. The method has the defects of high redundancy and reconfigurable characteristics of the satellite, and the weight parameters of the evaluation model depend on subjective judgment and expert experience too much, so that subjective assumption is easy to cause.
Disclosure of Invention
The invention aims to solve the technical problem of providing a satellite health state multi-stage fuzzy evaluation method based on an AHP-entropy weight method aiming at the defects in the prior art, accurately evaluating the health state of a satellite, making scientific and effective health management decisions for the satellite according to the evaluation result, and being an effective method for improving the safety and reliability of a satellite system, reducing the effective life cycle operation cost and further ensuring the smooth completion of an on-orbit satellite task.
The invention adopts the following technical scheme:
the satellite health state multi-stage fuzzy evaluation method based on the AHP-entropy weight method comprises the following steps:
s1, constructing a system weight system comprising subjective weight, objective weight and comprehensive weight, providing accurate comprehensive weight for a fuzzy comprehensive evaluation method by adopting an analytic hierarchy process and an entropy weight method, providing subjective weight by adopting the analytic hierarchy process, providing objective weight by adopting the entropy weight method, and obtaining the comprehensive weight combining subjective and objective by using the subjective and objective weight through an optimization function;
s2, constructing a system evaluation system comprising a factor domain, a comment set, a membership function, an evaluation matrix and multi-level fuzzy evaluation, comprehensively evaluating the use state of the on-orbit satellite, evaluating each layer of elements according to the membership principle of the fuzzy comprehensive evaluation, and then sequentially recurrently evaluating the overall health state from bottom to top by adopting a multi-level fuzzy comprehensive evaluation method.
Specifically, in step S1, the subjective weight is specifically constructed as follows:
s1011, constructing a hierarchical structure, wherein an evaluation target forms a target layer, and an evaluation factor forms a factor layer;
s1012, constructing a judgment matrix, and establishing a judgment matrix R (R) of each layerij)n×nWherein r isijTwo influencing factors r of the componentiAnd rjThe compared importance degree is given by 1-9 scales;
s1013, detecting by adopting a consistency index CI, and judging that the consistency of the matrix R can be accepted when the CI is less than 0.1; when the CI is greater than 0.1, comparing every two to establish an interpretation matrix R again, and automatically adjusting by a matrix conversion method;
and S1014, obtaining the weight value accurately in an iterative mode by taking the weight obtained by the root method as an initial value.
Further, step S1013 is specifically:
constructing an antisymmetric matrix B of the judgment matrix R:
bij＝lgrij
constructing an optimal transfer matrix C of the matrix B:
Figure BDA0002317259080000031
constructing a pseudo-optimal uniform transfer matrix R of a matrix C*：
Figure BDA0002317259080000032
And converting the optimal transfer matrix into a pseudo-optimal transfer matrix R meeting the consistency.
Specifically, step S1014 specifically includes:
calculating the geometric mean value of row elements of the judgment matrix R:
Figure BDA0002317259080000033
obtaining approximate feature vectors
Figure BDA0002317259080000041
Normalizing it:
Figure BDA0002317259080000042
get the rough weight vector W ═ W (W)1,w2,w3,...,wn)TThen taking X(0)＝(w1,w2,...,wn) As an initial value, using an iterative formula:
X(k)＝X(k-1)R
calculating X(k)For a given precision ε, if:
|X(k)-X(k-1)|<ε
to X(k)Normalization processing is the obtained optimal weight, and iteration is finished; otherwise with X(k)And the initial value is set, and the iteration is carried out again until the initial value is met.
Specifically, in step S1, the objective weight is constructed by:
constructing an attribute matrix p of each layer of index of the satellite according to historical data of the indexij；
Entropy processing the attribute matrix information as follows: :
Figure BDA0002317259080000043
Figure BDA0002317259080000044
the objective weight of β ═ β was obtained1,β2....βn)。
Specifically, in step S1, in the step of solving the comprehensive weight by the optimization function, the optimization function is:
Figure BDA0002317259080000045
the constraint conditions are as follows:
Figure BDA0002317259080000046
wherein u isiIs a subjective proportion, siIs an integrated weight, wiAs subjective weight, βiIs an objective weight.
Specifically, in step S2, the construction of the factor domain and comment set specifically includes:
factor domain U of each layer formed by indexes of each layer in satellite hierarchical structurei＝{u1,u2,u3,...,um}，uiIs the ith index of the ith layer; the grade division of each index by the decision maker forms a comment set Vi＝{v1,v2,v3,...,vm}。
Specifically, in step S2, constructing the membership function and the evaluation matrix specifically includes:
Figure BDA0002317259080000051
wherein, XiIs an actual measurement value of the index, V2Is the j-th level upper limit value, V, of the index i1Is the j-th lower limit of the index i, MiIs the maximum value of index i, miIs the minimum value of the index i, rijIs a membership function with index i at level j.
Specifically, in step S2, the multi-stage blur evaluation specifically includes:
s2031, substituting the bottom-layer factor domain index into a membership function to obtain a bottom-layer fuzzy matrix R, performing fuzzy operation according to the fuzzy matrix R and the weight W thereof to obtain a fuzzy vector S of the index of the previous layer, performing matrix operation according to the index fuzzy vector S and a corresponding grade health degree matrix H to obtain the health degree M of the index, and simultaneously obtaining the grade and the state of the index according to the maximum membership degree principle;
s2032, the fuzzy matrix of the layer is formed by the fuzzy vectors of the indexes obtained in the step S2031, then the fuzzy vectors of the layer are obtained by fuzzy operation with the weight, then the fuzzy vectors and the corresponding grade health degree matrix are subjected to matrix operation to obtain the health degree and the state of the indexes, and simultaneously the grade and the state of the indexes are obtained according to the maximum membership degree principle;
s2033, repeating the step S2032, and sequentially recurrently progressing from the lowest layer to the highest layer of the hierarchical structure of the satellite to obtain the running states of the index, the subsystem and the whole satellite.
Further, the specific fuzzy operation according to the fuzzy matrix R and the weight W thereof is as follows:
Figure BDA0002317259080000061
the index health degree M is:
M＝S*H。
compared with the prior art, the invention has at least the following beneficial effects:
according to the satellite health state multi-stage fuzzy evaluation method based on the AHP-entropy weight method, each layer of elements are evaluated according to the membership degree principle of fuzzy comprehensive evaluation, and then the overall health state is successively and recurrently evaluated by adopting the multi-stage fuzzy comprehensive evaluation method from bottom to top, so that the influence of components in a multi-stage system on the health state of the system can be overcome, and the defect that the weighted average method mainly adopted by the multi-stage health evaluation method of the current satellite excessively depends on subjective judgment and expert experience can be avoided. The analytic hierarchy process can solve the complexity of the satellite system, and the fuzzy comprehensive evaluation process can solve the problems of fuzzy and difficult quantization of the satellite system indexes; meanwhile, aiming at the problem of rough weight of the fuzzy comprehensive evaluation method, a method of combining an Analytic Hierarchy Process (AHP) and an entropy weight method is adopted to provide accurate weight for the fuzzy comprehensive evaluation method, and meanwhile, the defect that the weight is easy to subjectively assume only by adopting the AHP is avoided, so that the defect that the entropy weight method lacks subjective factors is overcome.
Furthermore, the subjective weight utilizes the abundant knowledge and experience of experts to measure the degree of influence of each index on the system state, so as to make up for the defect that the objective weight lacks the objective factual basis.
Furthermore, the objective weight is to measure the degree of influence of each index on the system state by mining index history, so as to make up for the defect that subjective assumption is easily caused by subjective weight.
Furthermore, the subjective weight and the objective weight are subjected to an optimization function to obtain a comprehensive function, and an accurate weight which accords with subjective and objective facts is provided for a multi-stage fuzzy comprehensive evaluation method.
Further, the factor universe is a set formed by indexes influencing the system state, and is an index for evaluating the system state. The comment set is an evaluation standard set which is made by experts from good to bad for the index state in the factor domain, and provides evaluation standards for index grade division and state.
Furthermore, the membership function can be used for quantitative evaluation of indexes difficult to quantify, the indexes in the factor domain construct the degrees of membership to each standard in the comment set through the membership function, the magnitude of the membership degree forms evaluation vectors of the indexes, then the evaluation vectors of the indexes influencing the system state form an evaluation matrix of the system, and theoretical basis is provided for evaluating the system state.
Furthermore, the multi-stage fuzzy evaluation process is to solve the defect that the single-stage fuzzy evaluation method is easy to generate the super-fuzzy phenomenon when the indexes influencing the system state are too many, a plurality of layers are divided for the indexes influencing the system state, then more accurate evaluation is obtained in a mode of recursion from a bottom layer to a high layer, and meanwhile, accurate quantitative evaluation for the indexes which are difficult to quantify is also solved.
In conclusion, the method solves the problem that the satellite system is too complex and difficult to evaluate, and can also solve the defect that partial influence indexes of the satellite system are difficult to quantitatively evaluate due to ambiguity and uncertainty; the multi-stage fuzzy comprehensive evaluation method based on the combination of the AHP and the entropy weight method can solve the problem of rough weight of the fuzzy comprehensive evaluation method and avoid the defect that the weighted average method mainly adopted by the multi-stage health evaluation method of the current satellite excessively depends on subjective judgment and expert experience.
The technical solution of the present invention is further described in detail by the accompanying drawings and embodiments.
Drawings
FIG. 1 is a schematic diagram of satellite system features and solutions;
FIG. 2 is a schematic diagram of a multi-stage fuzzy comprehensive evaluation method based on an analytic hierarchy process and an entropy weight method;
FIG. 3 is a flow chart of determining weights;
FIG. 4 is a flow chart of the analytic hierarchy process for determining subjective weights;
FIG. 5 is a schematic diagram of a subsystem of an actuator;
FIG. 6 is a flow chart of a multi-stage fuzzy comprehensive evaluation method;
FIG. 7 is a diagram of a hierarchical fuzzy comprehensive evaluation process;
FIG. 8 is a schematic view of the health of the X-axis momentum wheel;
FIG. 9 is a schematic diagram of health of a subsystem of an actuator.
Detailed Description
Referring to fig. 1, a satellite system has the characteristics of complexity, uncertainty, ambiguity, hierarchy and the like, so that the invention establishes a comprehensive evaluation index system with a hierarchical structure, researches problems existing in fuzzy comprehensive evaluation and hierarchical analysis and provides an improved method, and provides a multi-stage fuzzy comprehensive evaluation method based on the combination of hierarchical analysis and an entropy weight method on the basis of the comprehensive evaluation index system, so as to comprehensively evaluate the use state of the in-orbit satellite.
Referring to fig. 2, the invention relates to a satellite health status multi-stage fuzzy evaluation method based on an AHP-entropy weight method, which includes the following steps:
s1, constructing a system weight system;
referring to fig. 3, the system weight system is constructed by subjective weight construction, objective weight construction, and comprehensive weight construction.
The method combining the Analytic Hierarchy Process (AHP) and the entropy weight method is adopted to provide accurate comprehensive weight for the fuzzy comprehensive evaluation method, the defect that the weight is easy to assume subjectively by adopting the AHP is overcome, and the defect that the entropy weight method lacks subjective factors is overcome, wherein the Analytic Hierarchy Process (AHP) provides subjective weight, the entropy weight method provides objective weight, and then the subjective and objective weight is subjected to an optimization function to obtain the comprehensive weight combining subjectivity and objectivity.
S101, index subjective weight construction;
referring to fig. 4, the determination of subjective weights by the analytic hierarchy process mainly includes four steps: establishing a hierarchical structure, establishing a judgment matrix, checking consistency and solving subjective weight.
S1011, constructing a hierarchical structure
Referring to fig. 5, the hierarchical decomposition model is generally composed of elements such as an evaluation target (target layer), evaluation factors (factor layer), and a design to be evaluated (solution layer). And the evaluation target constitutes a target layer, the evaluation factor constitutes a factor layer and the design scheme to be evaluated constitutes a scheme layer. When calculating the factor weight, the scheme layer is omitted, and only the factor layer and the target layer are considered.
S1012, constructing a judgment matrix
The basic information of AHP is to give judgment to the relative importance of each element in each layer and repeatedly answer the element C of the above layerkAs a guideline, two elements ri，rjWhich is more important, how much is important? Establishing a judgment matrix R ═ R (R) of each layerij)n×nWherein r isijTwo influencing factors r of the componentiAnd rjThe magnitude of the compared importance degrees is given by 1-9 scales, and is shown in the following table:
AHP proportional Scale
Figure BDA0002317259080000091
S1013, checking consistency of judgment matrix
The requirement for complete consistency of the judgment matrix is impractical, but the requirement for substantial consistency of the judgment is generally contrary to common sense, for example, judgment that A is extremely important than B, and judgment that B is extremely important than C and C is extremely important than A occurs. A chaotic and unsuppressed decision matrix may cause decision errors, and when the decision matrix deviates too much from consistency, the reliability of the result of any sort of ordered vector estimation method is questionable, so that the consistency of the decision matrix needs to be detected.
Generally, a consistency index CI is adopted for detection, when CI is less than 0.1, the consistency of a judgment matrix R is acceptable, when CI is greater than 0.1, the judgment matrix R needs to be established by pairwise comparison again, but when indexes are too much, the CI is difficult to meet the requirement that CI is less than 0.1, artificial adjustment often has subjective blindness, and therefore automatic adjustment is achieved through a matrix conversion method, and the method specifically comprises the following steps:
firstly, constructing an antisymmetric matrix B of a judgment matrix R by formula (1):
bij＝lgrij(1)
then, an optimal transfer matrix C of the matrix B is constructed by formula (2):
Figure BDA0002317259080000101
finally, a pseudo-optimal consistent transfer matrix R of the matrix C is constructed through a formula (3)*：
Figure BDA0002317259080000102
And converting the judgment matrix R into a pseudo-optimal transfer matrix R which accords with consistency through the optimal transfer matrix, so that the difficulty in judging consistency is avoided.
S1014, solving the judgment matrix R
Usually, a root method is used for solving the judgment matrix R, but the weight precision obtained in this way is low, so that the weight obtained by the root method is used as an initial value, and a more accurate weight value is obtained in an iterative manner, specifically:
firstly, solving the geometric mean value of row elements of a judgment matrix R:
Figure BDA0002317259080000103
obtaining approximate feature vectors
Figure BDA0002317259080000104
Normalizing it:
Figure BDA0002317259080000105
get the rough weight vector W ═ W (W)1,w2,w3,...,wn)TThen taking X(0)＝(w1,w2,...,wn) As an initial value, using an iterative formula:
X(k)＝X(k-1)R (6)
x is calculated by the formula (6)(k)For a given precision ε, if:
|X(k)-X(k-1)|<ε (7)
to X(k)Normalization processing is the obtained optimal weight, and iteration is finished; otherwise with X(k)For the initial value, iterate again until equation (7) is satisfied.
S102, establishing an index objective weight;
the entropy weight method is to determine objective weight of an index according to the discrete degree of data, according to the explanation of the basic principle of information theory, information is a measure of the system order degree, entropy is a measure of the system order degree, if the information entropy of the index is smaller, the amount of information provided by the index is larger, the larger the information entropy of the index is, the higher the weight is in the comprehensive evaluation, specifically:
firstly, an attribute matrix p of each layer of index of the satellite is constructed according to historical data of the indexij；
The attribute matrix information is then entropy processed as shown in equation (8):
Figure BDA0002317259080000111
Figure BDA0002317259080000112
the objective weight of β ═ β was obtained1,β2....βn)。
S103, solving comprehensive weight by an optimization function;
in order to take the preference of a decision maker into consideration with information contained in the subjective and objective weighting methods, comprehensive weight is obtained by optimally combining the subjective and objective weights, and an optimization function is shown as a formula (9):
Figure BDA0002317259080000113
the constraint conditions are as follows:
Figure BDA0002317259080000121
wherein u isiFor subjective proportion, the comprehensive weight s can be seen from the optimization functioniIs compared with the subjective weight wiWith little difference from the objective weight βiThe difference is small, indicating the composite weight siThe subjective and objective weight information is integrated.
S2, constructing a system evaluation system;
referring to fig. 6, a multi-level fuzzy comprehensive evaluation method adopted for system evaluation system construction is mainly divided into three parts, namely construction of factor domains and comment sets, construction of membership functions and evaluation matrices, and a multi-level fuzzy evaluation process;
s201, constructing a factor domain and a comment set;
each layer of indexes in the satellite hierarchical structure form a factor domain U of each layeri＝{u1,u2,u3,...,um}，uiIs the ith index of the ith layer. The grade division of each index by the decision maker forms a comment set Vi＝{v1,v2,v3,...,vm}。
In general, the number p of comment levels is an integer in [3,7 ]; if p is too large, the choice comment is difficult to describe and the grade attribution is not easy to judge; if p is too small, the quality requirement of fuzzy comprehensive judgment is not met; in general, p is an odd number, and may have an intermediate rank to facilitate determination of rank assignment of an object to be evaluated.
The specific grade is agreed by an evaluation expert according to the content of an evaluation object, proper language description is adopted, and the evaluation economic benefit is V ═ good, general, poor or poor }; and V is taken as { high, general, low and low } for evaluating the living standard of residents.
Referring to fig. 8, the present invention divides the factors affecting the satellite state into a device level, a system level and a satellite level, and then divides each index into five levels from good to bad.
Figure BDA0002317259080000122
Figure BDA0002317259080000131
S202, constructing a membership function and an evaluation matrix;
after the factor domain and the comment set are constructed, a membership function is required to be constructed to measure the factor domain index uiBelonging to a corresponding grade v in the comment setiDegree of (r)ijThe constructed membership functions are as follows:
Figure BDA0002317259080000141
wherein, XiIs an actual measurement value of the index, V2Is the j-th level upper limit value, V, of the index i1Is the j-th lower limit of the index i, MiIs the maximum value of index i, miIs the minimum value of the index i, rijIs a membership function with index i at level j.
Element u in the factorial domainiSubstituting into membership function to obtain fuzzy matrix R, i.e. evaluation matrix R, wherein RijFactor u of expressioniBelonging to the comment set viTo the extent of (c). An object to be evaluated is under a certain factor uiThe aspect performance is characterized by the row vector of the fuzzy matrix R, and in other evaluation methods, the aspect performance is mostly characterized by an evaluation index actual value. From this point of view, therefore, fuzzy comprehensive evaluation requires more information.
S203, multi-stage fuzzy evaluation;
please refer to fig. 7, which specifically includes:
s2031, substituting the indexes of the bottom factor domain into a membership function formula (10) to obtain a bottom fuzzy matrix R, carrying out fuzzy operation according to the formula (11) fuzzy matrix R and the weight W thereof to obtain a fuzzy vector S of the index of the previous layer, carrying out matrix operation according to the formula (12) fuzzy vector S of the index and a corresponding grade health degree matrix H to obtain the health degree M of the index, and simultaneously obtaining the grade and the state of the index according to a maximum membership degree principle;
Figure BDA0002317259080000142
M＝S*H (12)
s2032, the fuzzy vectors of the indexes obtained in the step S2031 form a fuzzy matrix of the layer, then fuzzy operation is carried out on the fuzzy matrix and the weight to obtain the fuzzy vector of the layer, then matrix operation is carried out on the fuzzy vector and the corresponding grade health degree matrix to obtain the health degree and the state of the indexes, and the grade and the state of the indexes can be obtained according to the maximum membership degree principle;
s2033, repeating the step S2032, and sequentially recurrently progressing from the lowest layer to the highest layer of the hierarchical structure of the satellite to obtain the running states of the index, the subsystem and the whole satellite.
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. The components of the embodiments of the present invention generally described and illustrated in the figures herein may be arranged and designed in a wide variety of different configurations. Thus, the following detailed description of the embodiments of the present invention, presented in the figures, is not intended to limit the scope of the invention, as claimed, but is merely representative of selected embodiments of the invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The invention discloses a satellite health state multilevel fuzzy evaluation method based on an AHP-entropy weight method, which takes an execution mechanism subsystem under a satellite attitude control system as an example, and a hierarchy mechanism of the execution mechanism subsystem is shown in figure 5. according to a method for establishing a weight system by using a previous hierarchy analysis method and an entropy weight method, the weight system of the execution mechanism subsystem is obtained and is shown in table 1:
TABLE 1 actuator subsystem weight hierarchy
Figure BDA0002317259080000151
Figure BDA0002317259080000161
As shown in table 1 above, since the indexes of the momentum wheel assembly have substantially the same functions, the subjective weight difference is very small, but in an actual system, the indexes are often more and more important under the condition of deterioration, so that the entropy weight method is adopted to make up for the deficiency of the analytic hierarchy process, and a more accurate weight system is obtained.
Referring to fig. 8, the health degree of the X-axis momentum wheel in the normal state under the momentum wheel assembly can be seen to be maintained at a high level in the normal state, the green line indicates the health degree of the X-axis momentum wheel in the fault state, and it can be seen that the health degree of the X-axis momentum wheel is reduced due to the fault of the X-axis momentum wheel in about 250s, which is consistent with the reality.
Referring to fig. 9, according to the evaluation result of the execution mechanism subsystem obtained by the AHP-multi-stage fuzzy comprehensive evaluation model, the health degree of the X-axis momentum wheel is rapidly decreased due to the failure of the X-axis momentum wheel in about 250s, and the health degree of the upper index momentum wheel component is decreased due to the influence of the X-axis momentum wheel, so that the health degree of the target layer execution mechanism subsystem is decreased, which is consistent with the reality, thereby proving the reliability of the evaluation method of the present invention.
The above-mentioned contents are only for illustrating the technical idea of the present invention, and the protection scope of the present invention is not limited thereby, and any modification made on the basis of the technical idea of the present invention falls within the protection scope of the claims of the present invention.

Claims (10)

1. The satellite health state multi-stage fuzzy evaluation method based on the AHP-entropy weight method is characterized by comprising the following steps of:
s1, constructing a system weight system comprising subjective weight, objective weight and comprehensive weight, providing accurate comprehensive weight for a fuzzy comprehensive evaluation method by adopting an analytic hierarchy process and an entropy weight method, providing subjective weight by adopting the analytic hierarchy process, providing objective weight by adopting the entropy weight method, and obtaining the comprehensive weight combining subjective and objective by using the subjective and objective weight through an optimization function;
s2, constructing a system evaluation system comprising a factor domain, a comment set, a membership function, an evaluation matrix and multi-level fuzzy evaluation, comprehensively evaluating the use state of the on-orbit satellite, evaluating each layer of elements according to the membership principle of the fuzzy comprehensive evaluation, and then sequentially recurrently evaluating the overall health state from bottom to top by adopting a multi-level fuzzy comprehensive evaluation method.
2. The AHP-entropy weight method-based satellite health state multi-stage fuzzy evaluation method as claimed in claim 1, wherein in step S1, the subjective weight is specifically constructed as follows:
s1011, constructing a hierarchical structure, wherein an evaluation target forms a target layer, and an evaluation factor forms a factor layer;
s1012, constructing a judgment matrix, and establishing a judgment matrix R (R) of each layerij)n×nWherein r isijTwo influencing factors r of the componentiAnd rjThe compared importance degree is given by 1-9 scales;
s1013, detecting by adopting a consistency index CI, and judging that the consistency of the matrix R can be accepted when the CI is less than 0.1; when the CI is greater than 0.1, comparing every two to establish an interpretation matrix R again, and automatically adjusting by a matrix conversion method;
and S1014, obtaining the weight value accurately in an iterative mode by taking the weight obtained by the root method as an initial value.
3. The AHP-entropy weight method-based satellite health state multi-stage fuzzy evaluation method as claimed in claim 2, wherein step S1013 specifically comprises:
constructing an antisymmetric matrix B of the judgment matrix R:
bij＝lgrij
constructing an optimal transfer matrix C of the matrix B:
Figure FDA0002317259070000021
constructing a pseudo-optimal uniform transfer matrix R of a matrix C*：
Figure FDA0002317259070000022
And converting the optimal transfer matrix into a pseudo-optimal transfer matrix R meeting the consistency.
4. The AHP-entropy weight method-based satellite health state multi-stage fuzzy evaluation method as claimed in claim 1, wherein step S1014 specifically comprises:
calculating the geometric mean value of row elements of the judgment matrix R:
Figure FDA0002317259070000023
obtaining approximate feature vectors
Figure FDA0002317259070000024
Normalizing it:
Figure FDA0002317259070000025
get the rough weight vector W ═ W (W)1,w2,w3,...,wn)TThen taking X(0)＝(w1,w2,...,wn) As an initial value, using an iterative formula:
X(k)＝X(k-1)R
calculating X(k)For a given precision ε, if:
|X(k)-X(k-1)|<ε
to X(k)Normalization processing is the obtained optimal weight, and iteration is finished; otherwise with X(k)And the initial value is set, and the iteration is carried out again until the initial value is met.
5. The AHP-entropy weight method based satellite health state multi-stage fuzzy evaluation method as claimed in claim 1, wherein in step S1, objective weight is constructed specifically as follows:
constructing an attribute matrix p of each layer of index of the satellite according to historical data of the indexij；
Entropy processing the attribute matrix information as follows: :
Figure FDA0002317259070000031
Figure FDA0002317259070000032
the objective weight of β ═ β was obtained1,β2....βn)。
6. The AHP-entropy weight method based satellite health state multi-stage fuzzy evaluation method as claimed in claim 1, wherein in step S1, in the step of solving the comprehensive weight by the optimization function, the optimization function is:
Figure FDA0002317259070000033
the constraint conditions are as follows:
Figure FDA0002317259070000034
wherein u isiIs a subjective proportion, siIs an integrated weight, wiAs subjective weight, βiIs an objective weight.
7. The AHP-entropy weight method based satellite health state multi-stage fuzzy evaluation method as claimed in claim 1, wherein in step S2, constructing factor discourse domain and comment set specifically comprises:
factor domain U of each layer formed by indexes of each layer in satellite hierarchical structurei＝{u1,u2,u3,...,um}，uiIs the ith index of the ith layer; the grade division of each index by the decision maker forms a comment set Vi＝{v1,v2,v3,...,vm}。
8. The AHP-entropy weight method-based satellite health state multi-stage fuzzy evaluation method as claimed in claim 1, wherein in step S2, constructing a membership function and an evaluation matrix specifically comprises:
Figure FDA0002317259070000041
wherein, XiIs an actual measurement value of the index, V2Is the j-th level upper limit value, V, of the index i1Is the j-th lower limit of the index i, MiIs the maximum value of index i, miIs the minimum value of the index i, rijIs a membership function with index i at level j.
9. The AHP-entropy weight method based satellite health state multi-stage fuzzy evaluation method as claimed in claim 1, wherein in step S2, the multi-stage fuzzy evaluation specifically comprises:
s2031, substituting the bottom-layer factor domain index into a membership function to obtain a bottom-layer fuzzy matrix R, performing fuzzy operation according to the fuzzy matrix R and the weight W thereof to obtain a fuzzy vector S of the index of the previous layer, performing matrix operation according to the index fuzzy vector S and a corresponding grade health degree matrix H to obtain the health degree M of the index, and simultaneously obtaining the grade and the state of the index according to the maximum membership degree principle;
s2032, the fuzzy matrix of the layer is formed by the fuzzy vectors of the indexes obtained in the step S2031, then the fuzzy vectors of the layer are obtained by fuzzy operation with the weight, then the fuzzy vectors and the corresponding grade health degree matrix are subjected to matrix operation to obtain the health degree and the state of the indexes, and simultaneously the grade and the state of the indexes are obtained according to the maximum membership degree principle;
s2033, repeating the step S2032, and sequentially recurrently progressing from the lowest layer to the highest layer of the hierarchical structure of the satellite to obtain the running states of the index, the subsystem and the whole satellite.
10. The AHP-entropy weight method based satellite health state multi-stage fuzzy evaluation method as claimed in claim 9, wherein the fuzzy operation according to the fuzzy matrix R and its weight W is specifically:
Figure FDA0002317259070000042
the index health degree M is:
M＝S*H。
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