WO2020118512A1 - 一种基于lft的航空发动机传感器及执行机构故障诊断方法 - Google Patents
一种基于lft的航空发动机传感器及执行机构故障诊断方法 Download PDFInfo
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- WO2020118512A1 WO2020118512A1 PCT/CN2018/120243 CN2018120243W WO2020118512A1 WO 2020118512 A1 WO2020118512 A1 WO 2020118512A1 CN 2018120243 W CN2018120243 W CN 2018120243W WO 2020118512 A1 WO2020118512 A1 WO 2020118512A1
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B64—AIRCRAFT; AVIATION; COSMONAUTICS
- B64F—GROUND OR AIRCRAFT-CARRIER-DECK INSTALLATIONS SPECIALLY ADAPTED FOR USE IN CONNECTION WITH AIRCRAFT; DESIGNING, MANUFACTURING, ASSEMBLING, CLEANING, MAINTAINING OR REPAIRING AIRCRAFT, NOT OTHERWISE PROVIDED FOR; HANDLING, TRANSPORTING, TESTING OR INSPECTING AIRCRAFT COMPONENTS, NOT OTHERWISE PROVIDED FOR
- B64F5/00—Designing, manufacturing, assembling, cleaning, maintaining or repairing aircraft, not otherwise provided for; Handling, transporting, testing or inspecting aircraft components, not otherwise provided for
- B64F5/60—Testing or inspecting aircraft components or systems
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- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B23/00—Testing or monitoring of control systems or parts thereof
- G05B23/02—Electric testing or monitoring
- G05B23/0205—Electric testing or monitoring by means of a monitoring system capable of detecting and responding to faults
- G05B23/0218—Electric testing or monitoring by means of a monitoring system capable of detecting and responding to faults characterised by the fault detection method dealing with either existing or incipient faults
- G05B23/0243—Electric testing or monitoring by means of a monitoring system capable of detecting and responding to faults characterised by the fault detection method dealing with either existing or incipient faults model based detection method, e.g. first-principles knowledge model
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- G—PHYSICS
- G07—CHECKING-DEVICES
- G07C—TIME OR ATTENDANCE REGISTERS; REGISTERING OR INDICATING THE WORKING OF MACHINES; GENERATING RANDOM NUMBERS; VOTING OR LOTTERY APPARATUS; ARRANGEMENTS, SYSTEMS OR APPARATUS FOR CHECKING NOT PROVIDED FOR ELSEWHERE
- G07C5/00—Registering or indicating the working of vehicles
- G07C5/08—Registering or indicating performance data other than driving, working, idle, or waiting time, with or without registering driving, working, idle or waiting time
- G07C5/0808—Diagnosing performance data
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- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B2219/00—Program-control systems
- G05B2219/30—Nc systems
- G05B2219/45—Nc applications
- G05B2219/45071—Aircraft, airplane, ship cleaning manipulator, paint stripping
Definitions
- the invention belongs to the field of aircraft engine fault diagnosis, and in particular relates to a LFT-based aircraft engine sensor and actuator failure diagnosis method.
- An aero engine is an important part of an aircraft.
- the health of the flight state depends directly on the health of the aero engine.
- the sensor of the aero engine is used as the bottom information collection platform of the aero engine, which can accurately measure the state information of the components and the system in the process of the aero engine, thereby constructing an effective control system. If the aero-engine sensor fails, it is impossible to provide accurate performance and status parameters to the control system, and accurate control cannot be achieved.
- the aero-engine actuator is an important link between the aero-engine and the control system. According to the control instructions given by the control system, the actuator drives the actual control variable to control the working state of the aero-engine.
- the present invention monitors the performance of aero-engine sensors and actuators and has real-time diagnosis and warning of fault conditions, which is of great significance.
- the existing literature shows that, first of all, the research direction of the fault diagnosis technology of the existing aero-engine sensors and actuators is mainly focused on the fault detection, that is, only the aero-engine sensor and the actuators can be judged whether the fault occurs, and the fault There are few studies on signal estimation methods. Specifically, different fault modes of sensors and actuators correspond to different fault handling measures. For the sensor failure of the aero engine, the actual failure is mainly drift. If the sensor drifts, the sensor measurement information can be corrected by the controller design. The failure of the aero engine actuator includes degradation, drift and stuck. If the actuator is degraded or drifted, the controller can be designed to keep the aero engine working normally; if the actuator is stuck, the actuator needs to be switched. To the redundant mode, perform actuator maintenance after the flight is completed.
- the aero engine can be described as a typical LPV (linear variable parameter) system.
- the literature shows that the fault estimation methods of LPV systems have been divided into two major categories in recent years: one is the observer-based method, but this type of method is not robust to the disturbance in the system and the model uncertainty, that is, the system is subjected to Errors caused by external disturbances and modeling will seriously affect the observation results of the observer; the other is the fault estimation method based on H ⁇ optimization technology.
- This method can improve the robustness of the system, but the fault estimation research based on this technology It is still in its infancy, and there are still many issues worthy of in-depth discussion.
- the present invention provides an LFT-based aero-engine sensor and actuator fault diagnosis method, which can According to the changes in the parameters of the aeroengine LPV model, adaptively adjust the parameters of the fault estimator to achieve rapid detection of faults in the system, and accurately reconstruct the fault signal, promptly propose repairs, and provide better control for subsequent fault tolerance The basic guarantee.
- An LFT-based aero-engine sensor and actuator fault diagnosis method includes the following steps:
- Step 1 The method of combining small disturbance method and linear fitting method to establish aero-engine state variable model
- Step 2 Establish a linear variable parameter (LPV) model of the aero engine dependent on affine parameters
- Step 3 Transform the aeroengine LPV model dependent on the affine parameters of disturbances and sensor and actuator failures into an LFT structure, and establish an H ⁇ integrated framework of the aeroengine LPV fault estimator;
- Step 4 Solve a set of linear matrix inequalities LMIs to obtain the solution condition of the fault estimator
- Step 5 Design the fault estimator in combination with the LFT structure to realize the fault diagnosis of aero-engine sensors and actuators.
- the step 1 includes the following steps:
- Step 1.1 Input the oil pressure p f at the steady-state operating point to the aero engine, and after the relative conversion speed n h of the aero engine high pressure turbine reaches the corresponding stable state, input the oil pressure step signal U pf1 with an amplitude of 0.01 p f To the aero engine, collect the aero engine output high-pressure turbine relative conversion speed response Y nh1 and low-pressure turbine relative conversion speed response Y nl1 respectively ;
- Step 1.3 Taking the oil pressure step signal U pfi as the input variable, the high-pressure turbine relative conversion speed response Y nhi and the low-pressure turbine relative conversion speed response Y nli as the state variables, the aero-engine under each steady-state operating point is solved according to the linear fitting method Discrete small deviation state variable model;
- Step 1.4 According to the sampling period T, convert the discrete small deviation state variable model of the aero engine at each steady-state operating point into a continuous small deviation state variable model to obtain the aero engine state variable model;
- the step 2 includes the following steps:
- Step 2.2 Express the system matrix A p ( ⁇ ) and control matrix B p ( ⁇ ) of the aero engine continuous small deviation state variable model as affine parameter dependent forms, as follows:
- a 0 , A 1 , B 0 , and B 1 respectively represent coefficient matrices to be sought.
- I is the identity matrix
- [I ⁇ I] + is the Moore-Penrose pseudo-inverse of [I ⁇ I], that is, the system matrix A p ( ⁇ ) and the control matrix B p ( ⁇ ) of the aeroengine LPV model dependent on the affine parameters are obtained;
- Step 2.3 Establish LPV model of aero-engines dependent on affine parameters
- step 3 establishes the H ⁇ synthesis framework of the aeroengine LPV fault estimator including the following steps:
- Step 3.1 Represent the aero-engine LPV model P(s, ⁇ ) with disturbances and sensor and actuator failure affine parameter dependence as
- d ⁇ R q is the disturbance signal
- f ⁇ R l fault signals including actuators and sensor failure fault
- R q, R l each dimension is represented by q, l the set of real numbers
- E p, F p, G p and H p are system state space matrices
- the upper LFT structure of P(s, ⁇ ) is expressed as
- Step 3.2 Let the fault estimator K(s, ⁇ ) be of the form
- a K , B K1 , B K ⁇ , C K1 , C K ⁇ , D K11 , D K1 ⁇ , D K ⁇ 1 , D K ⁇ are the system state space matrix
- Step 3.3 change portion ⁇ ( ⁇ ) according to the time aeroengine LPV model P (s, ⁇ ) and fault estimator K (s, ⁇ ) when the change portion ⁇ K ( ⁇ ), H ⁇ LPV fault estimator Comprehensive
- the framework is expressed as
- the step 4 obtains the solvable condition for the existence of the fault estimator including the following steps:
- Step 4.1 Obtain the solution condition for the existence of the fault estimator K(s, ⁇ ), namely
- X is positive definite symmetric matrix, full block scalar matrix It is a symmetric matrix, and ⁇ >0 is the performance index; Q, S, and R represent the sub-scalar matrix blocks of P, respectively.
- Step 4.2 Block the positive definite symmetric matrix X and its inverse matrix X -1
- L, M, E respectively represent the matrix block of X
- J, N respectively represent the sub-matrix block of X -1 .
- Q 1 , Q 2 and Q 3 respectively represent the sub-matrix blocks of Q
- S 1 , S 2 , S 3 and S 4 respectively represent the sub-matrix blocks of S
- R 1 , R 2 and R 3 respectively represent the sub-sub-blocks of R Matrix block, Respectively Sub-matrix block of, Respectively Sub-matrix block of, Respectively Sub-matrix block of, Respectively Of sub-matrix blocks.
- N L and N J represent [C 2 D 2 ⁇ D 21 ] and The base of nuclear space;
- Step 4.3 Solve linear matrix inequalities (15)-(18) to obtain matrix solutions L, J, Q 3 , S 4 ,
- the step 5 combined with the LFT structural design fault estimator includes the following steps:
- Step 5.1 According to the obtained matrix solution L, J, Q 3 , S 4 , Find the positive definite symmetric matrix X, the full block scalar matrix P and its inverse matrix from equations (13) and (14)
- Step 5.2 According to Schur's complement theorem, express the linear matrix inequality (11) as
- Step 5.3 Obtain the state space matrix of the fault estimator K(s, ⁇ )
- the beneficial effects of the present invention are: through the aero-engine sensor and actuator fault diagnosis method designed by the present invention, the aero-engine LPV model and the fault estimator are converted into a time-invariant part and a time-varying part LFT structure, in which the time-varying The part changes with the change of the time-varying parameter vector, so that the fault estimator has gain scheduling characteristics, which can realize the accurate estimation of the fault signal under the influence of uncertain conditions such as external disturbances and modeling errors, so that it is convenient to understand the type of fault, Generate information such as time and severity.
- the present invention reduces the conservativeness of the fault estimator design through the S process.
- Figure 3 shows the upper LFT structure of the aeroengine LPV model P(s, ⁇ ).
- Figure 4 is a system structure diagram under the LFT framework.
- Figure 5 shows the H ⁇ synthesis framework of the LPV fault estimator.
- Figure 6(a) and Figure 6(b) are the simulation results of catastrophic failure estimation.
- Fig. 7(a) and Fig. 7(b) are the simulation results of the slowly varying fault estimation.
- Figures 8(a) and 8(b) are the simulation results of intermittent fault estimation.
- FIG. 9 is a schematic flowchart of the present invention.
- Step 1.1 Input the oil pressure p f at the steady-state operating point to the aero engine, and after the relative conversion speed n h of the aero engine high pressure turbine reaches the corresponding stable state, input the oil pressure step signal U pf1 with an amplitude of 0.01 p f To the aero-engine, collect the aero-engine output high-pressure turbine relative conversion speed response Y nh1 and low-pressure turbine relative conversion speed response Y nl1 respectively .
- fi high pressure turbine in response to the relative rotational speed converted Y nhi
- Step 1.3 Taking the oil pressure step signal U pfi as the input variable, the high-pressure turbine relative conversion speed response Y nhi and the low-pressure turbine relative conversion speed response Y nli as the state variables, then the aerospace engine discrete small deviation state variable model is expressed as
- the state variable x p [Y nl Y nh ] T ⁇ R n
- the input variable u U pf ⁇ R t
- the output variable y p Y nh ⁇ R m
- i 1, 2, 3, ..., 13
- Subscripts k, k+1 are the corresponding sampling times
- E i , F i , G i , H i are the system space matrix of the appropriate dimension
- R n , R t , R m represent the dimension n, respectively Set of real numbers of t and m
- T means transpose the matrix.
- Step 2.2 Express the system matrix A p ( ⁇ ) and the control matrix B p ( ⁇ ) of the aero engine continuous small deviation state variable model system as affine parameter dependent forms, as follows:
- a 0 , A 1 , B 0 , and B 1 respectively represent the coefficient matrix to be sought.
- I is the identity matrix
- Step 2.3 Establish LPV model of aero-engines dependent on affine parameters
- Step 3.1 Represent the aero-engine LPV model P(s, ⁇ ) with disturbances and sensor and actuator failure affine parameter dependence as
- d ⁇ R q is the disturbance signal
- the Gaussian white noise with a standard deviation of 0.001 is taken
- f ⁇ R l is the fault signal, including sensor fault and actuator fault
- the mutation fault, slow-change fault and intermittent fault are taken respectively
- R q , R l represents the set of real numbers with dimensions q and l respectively
- G p 0.2
- H p 1.
- Fu represents the upper LFT structure
- P′ represents the time-invariant part of P(s, ⁇ )
- the sum of the dimension t of u, the dimension q of the disturbance signal d and the dimension l of the fault signal f; the system state space matrix is
- Step 3.2 Let the fault estimator K(s, ⁇ ) be of the form
- xK ⁇ R k is the state variable of the fault estimator K(s, ⁇ )
- a K ( ⁇ ), B K ( ⁇ ), C K ( ⁇ ), D K ( ⁇ ) is the system state space matrix.
- K(s, ⁇ ) as the following LFT structure, as follows:
- K′ represents the time-invariant part of K(s, ⁇ )
- a K , B K1 , B K ⁇ , C K1 , C K ⁇ , D K11 , D K1 ⁇ , D K ⁇ 1 , and D K ⁇ are system state space matrices of appropriate dimensions.
- Step 3.3 The system connection diagram under the LFT framework is shown in Figure 4, then the state space expression of system P 1 in Figure 4 is
- system matrix A A p
- system matrix B ⁇ B p ⁇
- system matrices B 1 B pw
- the system matrix B 2 0 n ⁇ l
- the system matrix C ⁇ C p ⁇
- the system matrix D ⁇ D p ⁇
- the system matrix D ⁇ 1 D p ⁇ w
- the system matrix D ⁇ 2 0 r ⁇ l
- the system matrix C 1 0 p1 ⁇ n
- the system matrix D 1 ⁇ 0 p1 ⁇ r
- system matrix System matrix System matrix System matrix System matrix System matrix System matrix System matrix D 22 0 p2 ⁇ l
- n represents the dimension of the state variable x p of the aeroengine
- r represents the output variable w ⁇ of the time-varying part ⁇ ( ⁇ ) and the output variable w K of the time-varying part ⁇ K ( ⁇ ) dimension.
- H ⁇ integrated framework LPV fault estimator may represent The following formula, as shown in Figure 5
- Is the fault estimation error that is, the output variable of the H ⁇ synthesis frame of the LPV fault estimator
- the system matrix System matrix System matrix System matrix System matrix System matrix System matrix System matrix System matrix Fault estimator matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix matrix
- Step 4.1 If there is a symmetric positive definite matrix X, symmetric matrix So that equation (37) and equation (38) are established,
- the closed-loop system (36) is asymptotically stable, and the L 2 induced norm of the closed-loop transfer function from the external input w to the fault estimation error e f is less than the performance index ⁇ ( ⁇ >0). That is, the solvable conditions for the existence of the fault estimator K(s, ⁇ ) are Equation (37) and Equation (38). Among them, Q, S, R respectively represent the sub-matrix block of P.
- Step 4.2 Block the positive definite symmetric matrix X and its inverse matrix X -1
- L, M, E respectively represent the matrix block of X
- J, N respectively represent the sub-matrix block of X -1 .
- Q 1 , Q 2 and Q 3 respectively represent the sub-matrix blocks of Q
- S 1 , S 2 , S 3 and S 4 respectively represent the sub-matrix blocks of S
- R 1 , R 2 and R 3 respectively represent the sub-sub-blocks of R Matrix block, Respectively Sub-matrix block of, Respectively Sub-matrix block of, Respectively Sub-matrix block of, Respectively Of sub-matrix blocks.
- the linear matrix inequality (37) is organized as
- Step 4.3 The linear matrix inequality (42) is organized as
- U ⁇ and V ⁇ are the basis of the nuclear space of U T and V, respectively.
- N L and N J represent [C 2 D 2 ⁇ D 21 ] and The base of the nuclear space.
- Step 4.4 Use the LMI toolbox in MATLAB to solve the linear matrix inequalities (40), (44), (47), (48), and obtain the optimal ⁇ value of 0.21, and the corresponding matrix solutions L, J, Q 3 . S 4 ,
- Step 5.1 According to the obtained matrix solution L, J, Q 3 , S 4 , Find the positive definite symmetric matrix X, the full block scalar matrix P and its inverse matrix from equations (39) and (41)
- Step 5.2 According to Schur complement theorem, the linear matrix inequality (37) is expressed as
- Step 5.3 Obtain the state space matrix of the fault estimator K(s, ⁇ )
- the simulation results show that the fixed parameter fault estimator designed by the standard H ⁇ method cannot cope well with the change of variable parameters, and the LPV fault estimator designed by the present invention can quickly detect the fault in the system and accurately reconstruct the fault signal, Has obvious performance advantages.
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Abstract
一种基于LFT的航空发动机传感器及执行机构故障诊断方法,包括以下步骤:采用小扰动法与线性拟合法相结合的方法建立航空发动机状态变量模型,并基于此模型建立仿射参数依赖的航空发动机LPV模型;将带有扰动信号及传感器与执行机构故障信号的航空发动机LPV模型转化为LFT结构,得到LPV故障估计器的H ∞综合框架;通过求解一组线性矩阵不等式LMIs获得故障估计器存在的有解条件;结合LFT结构设计故障估计器,实现航空发动机传感器及执行机构的故障诊断。所述诊断方法根据航空发动机参数的变化,自适应地调整故障估计器的参数,迅速地检测传感器及执行机构故障,准确重构故障信号,为后续的主动容错控制提供基础。
Description
本发明属于航空发动机故障诊断领域,具体涉及一种基于LFT的航空发动机传感器及执行机构故障诊断方法。
航空发动机是飞机的重要部件,飞行状态健康与否直接取决于航空发动机的健康状态。其中,航空发动机的传感器作为航空发动机的底层信息采集平台,能够准确测量航空发动机工作过程中的部件和系统状态信息,从而构建出有效的控制系统。若航空发动机传感器发生故障,则无法给控制系统提供精确的性能和状态参数,无法实现精确的控制。而航空发动机的执行机构是连接航空发动机和控制系统的重要环节,执行机构根据控制系统给定的控制指令,驱动实际控制量变化,从而控制航空发动机的工作状态。若航空发动机执行机构发生故障,则会给控制系统提供错误的信息,从而给飞机的安全带来隐患,有可能引发灾难性的后果。因此,本发明针对航空发动机传感器及执行机构的性能进行监测,对故障状态实时诊断、告警,具有重要的意义。
已有文献表明,首先,现有的航空发动机传感器及执行机构的故障诊断技术的研究方向主要集中在故障检测方面,即只能对航空发动机传感器及执行机构是否发生故障给出判断,而针对故障信号进行估计方法的研究较少。具体的,传感器及执行机构不同的故障模式对应的故障处理措施不同。对于航空发动机的传感器故障,实际故障以漂移为主,若传感器发生漂移,则可通过控制器设计对传感器测量信息进行校正。航空发动机的执行机构故障包括退化、漂移与卡死等状态,若执行机构发生退化或漂移,则可通过控制器设计使航空发动机保持正常工作;若执行机构发生卡死,则需要进行执行机构切换到冗余模式,待飞行完成后进行执行机构维护。因此,只对故障检测进行研究,即判断是否发生故障,不利于航空发动机的安全运行与维护。而对故障程度可靠的估计,可实现航空发动机传感器及执行机构状态的准确判断,同时降低航空发动机的维修成本。此外,航空发动机可以描述为一种典型的LPV(线性变参数)系统。文献表明,LPV系统的故障估计方法近年来主要分为两大类:一是基于观测器的方法,但是这类方法对系统中的扰动以及模型不确定性鲁棒性不强,即系统受到的外界扰动和建模带来的误差会严重影响观测器的观测结果;另一类是基于H
∞优化技术的故障估计方法,该方法可以提高系统的鲁棒性,但基于该技术的故障估计研究仍处于刚刚起步的阶段,还有许多问题值得深入地探讨。
发明内容
针对现有航空发动机传感器及执行机构故障诊断技术中无法实现外界干扰及建模误差下对故障信号进行准确估计的问题,本发明提供一种基于LFT的航空发动机传感器及执行机构故障诊断方法,能够根据航空发动机LPV模型中参数的变化,自适应地调整故障估计器的参数,实现迅速地检测系统中的故障,并准确地重构故障信号,及时提出维修建议,为之后的容错控制提供更好的基础保障。
为实现上述目的,本发明采用的技术方案步骤如下:
一种基于LFT的航空发动机传感器及执行机构故障诊断方法,包括以下步骤:
步骤1:采用小扰动法与线性拟合法相结合的方法建立航空发动机状态变量模型;
步骤2:建立仿射参数依赖的航空发动机线性变参数(LPV)模型;
步骤3:将存在扰动及传感器与执行机构故障的仿射参数依赖的航空发动机LPV模型转化为LFT结构,建立航空发动机LPV故障估计器的H
∞综合框架;
步骤4:求解一组线性矩阵不等式LMIs,获得故障估计器存在的有解条件;
步骤5:结合LFT结构设计故障估计器,实现航空发动机传感器及执行机构的故障诊断。
所述步骤1包括以下步骤:
步骤1.1:向航空发动机输入稳态工作点下的油压p
f,待航空发动机高压涡轮相对换算转速n
h达到相应稳定状态后,将幅值为0.01p
f的油压阶跃信号U
pf1输入到航空发动机中,分别采集航空发动机输出高压涡轮相对换算转速响应Y
nh1和低压涡轮相对换算转速响应Y
nl1;
步骤1.2:重复步骤1的过程N次,分别采集得到给定油压p
fi下的高压涡轮相对换算转速响应Y
nhi和低压涡轮相对换算转速响应Y
nli,i=1,2,3,…,N;
步骤1.3:以油压阶跃信号U
pfi为输入变量,高压涡轮相对换算转速响应Y
nhi和低压涡轮相对换算转速响应Y
nli为状态变量,根据线性拟合法求解各稳态工作点下的航空发动机离散小偏差状态变量模型;
步骤1.4:根据采样周期T,将各稳态工作点下的航空发动机离散小偏差状态变量模型转换为连续小偏差状态变量模型,得到航空发动机状态变量模型;
其中,状态变量x
p=[Y
nl
T Y
nh
T]
T∈R
n,
表示x
p的一阶导数,输入变量u=U
pf∈R
t,输出变量y
p=Y
nh∈R
m,A
pi、B
pi、C
pi、D
pi是系统状态空间矩阵,且C
pi=C
p=[0 1]、D
pi=D
p=0;R
n、R
t、R
m分别表示维数为n、t、m的实数集,T表示对矩阵进行转置。
所述步骤2包括以下步骤:
步骤2.1:设航空发动机高压涡轮相对换算转速n
hi为调度参数θ(i),i=1,2,3,…,N;
步骤2.2:将航空发动机连续小偏差状态变量模型的系统矩阵A
p(θ)和控制矩阵B
p(θ)表述成仿射参数依赖形式,如下:
A
p(θ)=A
0+θA
1,B
p(θ)=B
0+θB
1 (2)
其中,A
0、A
1、B
0、B
1分别表示待求的系数矩阵。
将式(2)改写为
其中,I是单位矩阵。
则有
其中,[I θI]
+为[I θI]的Moore-Penrose伪逆,即求得仿射参数依赖的航空发动机LPV模型的系统矩阵A
p(θ)和控制矩阵B
p(θ);
步骤2.3:建立仿射参数依赖的航空发动机LPV模型
所述步骤3建立航空发动机LPV故障估计器的H
∞综合框架包括以下步骤:
步骤3.1:将存在扰动及传感器与执行机构故障的仿射参数依赖的航空发动机LPV模型P(s,θ)表示为
其中,d∈R
q为扰动信号,f∈R
l为故障信号,包括传感器故障及执行机构故障,R
q、R
l分别表示维数为q、l的实数集;E
p、F
p、G
p、H
p是系统状态空间矩阵,P(s,θ)的上LFT结构表示为
其中,外部输入变量w=[u
T d
T f
T]
T∈R
p1,w
θ∈R
r为时变部分Δ(θ)=θI的输出变量,z
θ∈R
r为时变部分Δ(θ)=θI的输入变量,A
p、B
pθ、B
pw、C
pθ、C
pw、D
pθθ、D
pθw、D
pwθ、D
pww是系统状态空间矩阵;R
p1、R
r分别表示维数为p1、r的实数集,且有p1=t+q+l,即外部输入变量w的维数p1等于航空发动机的输入变量u的维数t、扰动信号d的维数q和故障信号f的维数l之和。
步骤3.2:设故障估计器K(s,θ)形式如下
其中,x
K∈R
k为故障估计器K(s,θ)的状态变量,
表示x
K的一阶导数,R
k表示维数为k的实数集;u
K=[u
T y
p
T]
T∈R
p2为K(s,θ)的输入变量,p2=t+m,即K(s,θ)的输入变量u
K的维数p2等于航空发动机的输入变量u的维数t和航空发动机的输出变量y
p的维数m之和;
的输出变量,即故障信号f的估计值,A
K(θ)、B
K(θ)、C
K(θ)、D
K(θ)是系统状态空间矩阵,将K(s,θ)表示成下LFT结构,如下:
其中,w
K∈R
r为时变部分Δ
K(θ)=θI的输出变量,z
K∈R
r为时变部分Δ
K(θ)=θI的输入 变量,A
K、B
K1、B
Kθ、C
K1、C
Kθ、D
K11、D
K1θ、D
Kθ1、D
Kθθ是系统状态空间矩阵;
步骤3.3:根据航空发动机LPV模型P(s,θ)中时变部分Δ(θ)和故障估计器K(s,θ)中时变部分Δ
K(θ),LPV故障估计器的H
∞综合框架表示为
其中,
为故障估计误差,系统矩阵
系统矩阵
系统矩阵
系统矩阵
系统矩阵
系统矩阵
系统矩阵
系统矩阵
系统矩阵
故障估计器矩阵
矩阵
矩阵
矩阵
矩阵
矩阵
矩阵
矩阵
矩阵
矩阵
矩阵
矩阵
矩阵
矩阵
矩阵
矩阵D
04=D
11,矩阵A=A
p,矩阵B
θ=B
pθ,矩阵B
1=B
pw,矩阵B
2=0
n×l,矩阵C
θ=C
pθ,矩阵D
θθ=D
pθθ,矩阵D
θ1=D
pθw,矩阵D
θ2=0
r×l,矩阵C
1=0
p1×n,矩阵D
1θ=0
p1×r,矩阵
矩阵
矩阵
矩阵
矩阵
矩阵D
22=0
p2×l;n表示航空发动机的状态变量x
p的维数,r表示时变部分Δ(θ)的输出变量w
θ和时变部分Δ
K(θ)的输出变量w
K的维数,k表示故障估计器K(s,θ)的状态变量x
K的维数。
所述步骤4得到故障估计器存在的有解条件包括以下步骤:
步骤4.1:得到故障估计器K(s,θ)存在的有解条件,即
步骤4.2:对正定对称矩阵X及其逆矩阵X
-1进行分块
其中,L、M、E分别表示X的矩阵块,J、N、F分别表示X
-1的子矩阵块。
其中,Q
1、Q
2、Q
3分别表示Q的子矩阵块,S
1、S
2、S
3、S
4分别表示S的子矩阵块,R
1、R
2、R
3分别表示R的子矩阵块,
分别表示
的子矩阵块,
分别表示
的子矩阵块,
分别表示
的子矩阵块,
分别表示
的子矩阵块。
化简故障估计器K(s,θ)存在的有解条件,即
R>0,Q=-R,S+S
T=0 (18)
所述步骤5结合LFT结构设计故障估计器包括以下步骤:
步骤5.2:根据Schur补定理,将线性矩阵不等式(11)表示为
求解线性矩阵不等式(19),得到故障估计器矩阵Ω;
步骤5.3:得到故障估计器K(s,θ)的状态空间矩阵
本发明的有益效果为:通过本发明设计的航空发动机传感器及执行机构故障诊断方法,将航空发动机LPV模型和故障估计器分别转化为时不变部分和时变部分组成的LFT结构,其中时变部分随着时变参数向量的变化而变化,因而使故障估计器具有增益调度特性,可以实现外界扰动和建模误差等不确定性条件影响下故障信号的准确估计,从而方便了解故障的类型、产生时间以及严重程度等信息。此外,本发明通过S过程,降低了故障估计器设计的保守性。
图1为H=0,Ma=0,n
2=90%工作状态下航空发动机状态空间模型的高压涡轮相对换算转速响应Y
nh与试验数据对比曲线。
图2为H=0,Ma=0,n
2=90%工作状态下航空发动机LPV模型的高压涡轮相对换算转速响应Y
nh与试验数据对比曲线。
图3为航空发动机LPV模型P(s,θ)的上LFT结构图。
图4为LFT框架下的系统结构图。
图5为LPV故障估计器的H
∞综合框架。
图6(a)和图6(b)为突变故障估计仿真结果。
图7(a)和图7(b)为缓变故障估计仿真结果。
图8(a)和图8(b)为间歇故障估计仿真结果。
图9为本发明的流程示意图。
下面结合附图及技术方案对本发明实施例做进一步详细说明。
本发明的流程示意图如图9所示,具体步骤如下:
步骤1.1:向航空发动机输入稳态工作点下的油压p
f,待航空发动机高压涡轮相对换算转速n
h达到相应稳定状态后,将幅值为0.01p
f的油压阶跃信号U
pf1输入到航空发动机中,分别采集航空发动机输出高压涡轮相对换算转速响应Y
nh1和低压涡轮相对换算转速响应Y
nl1。
步骤1.2:重复上述过程13次,即在(H=0,Ma=0,n
h=88%、89%、…、100%)13个工况的平衡点处分别采集得到给定油压p
fi下的高压涡轮相对换算转速响应Y
nhi和低压涡轮相对换算转速响应Y
nli,i=1,2,3,…,13。
步骤1.3:以油压阶跃信号U
pfi为输入变量,高压涡轮相对换算转速响应Y
nhi和低压涡轮相对换算转速响应Y
nli为状态变量,则航空发动机离散型小偏差状态变量模型表示为
其中,状态变量x
p=[Y
nl Y
nh]
T∈R
n,输入变量u=U
pf∈R
t,输出变量y
p=Y
nh∈R
m,i=1,2,3,…,13,下标k、k+1为对应的采样时刻,E
i、F
i、G
i、H
i是适当维数的系统状态空间矩阵;R
n、R
t、R
m分别表示维数为n、t、m的实数集,T表示对矩阵进行转置。根据拟合法基本思想,针对式(21)建立线性最小二乘问题,利用MATLAB中的lsqnonlin函数求解其系统矩阵E
i,F
i,G
i,H
i。
步骤1.4:根据采样周期T=25ms,将各稳态工作点下的航空发动机离散小偏差状态变量模型转换为连续小偏差状态变量模型,得到航空发动机状态变量模型;
其中A
pi、B
pi、C
pi、D
pi是适当维数的系统状态空间矩阵,且C
pi=C
p=[0 1]、D
pi=D
p=0,给出在工作点H=0,Ma=0,n
2=90%处的状态空间模型的高压涡轮相对换算转速响应Y
nh曲线,如图1所示,其与试验数据的平均相对误差为0.26%。
步骤2.1:设航空发动机高压涡轮相对换算转速n
hi为调度参数θ(i),i=1,2,3,…,13。
步骤2.2:将航空发动机连续小偏差状态变量模型系统矩阵A
p(θ)和控制矩阵B
p(θ)表述成仿射参数依赖形式,如下:
其中A
0、A
1、B
0、B
1分别表示待求的系数矩阵。
将式(23)改写为
其中,I是单位矩阵。
则有
步骤2.3:建立仿射参数依赖的航空发动机LPV模型
给出在工作点H=0,Ma=0,n
2=90%处航空发动机LPV模型的高压涡轮相对换算转速响应Y
nh曲线,如图2所示,其与试验数据的平均相对误差为2.51%。
步骤3.1:将存在扰动及传感器与执行机构故障的仿射参数依赖的航空发动机LPV模型P(s,θ)表示为
其中,d∈R
q为扰动信号,取标准差0.001的高斯白噪声,f∈R
l为故障信号,包括传感器故障及执行器故障,分别取突变故障、缓变故障和间歇故障,R
q、R
l分别表示维数为q、l的实数集;
G
p=0.2,H
p=1。
P(s,θ)的上LFT结构可表示为下式,具体的如图3所示,
其中,F
u表示上LFT结构,P′表示P(s,θ)中时不变部分,Δ(θ)=θI表示P(s,θ)中时变部分,即
其中,外部输入变量w=[u
T d
T f
T]
T∈R
p1,w
θ∈R
r为时变部分Δ(θ)=θI的输出变量,z
θ∈R
r为时变部分Δ(θ)=θI的输入变量;R
p1、R
r分别表示维数为p1、r的实数集,且有p1=t+q+l,即外部输入变量w的维数p1等于航空发动机的输入变量u的维数t、扰动信号d的维数q和故障信号f的维数l之和;系统状态空间矩阵为
步骤3.2:设故障估计器K(s,θ)形式如下
其中,xK∈R
k为故障估计器K(s,θ)的状态变量,u
K=[u
T y
p
T]
T∈R
p2为K(s,θ)的输入变量,p2=t+m,即K(s,θ)的输入变量u
K的维数p2等于航空发动机的输入变量u的维数t和航空发动机的输出变量y
p的维数m之和;
为K(s,θ)的输出变量,即故障信号f的估计值,A
K(θ)、B
K(θ)、C
K(θ)、D
K(θ)是系统状态空间矩阵。将K(s,θ)表示成下LFT结构,如下:
其中,F
l表示下LFT结构,K′表示K(s,θ)中时不变部分,Δ
K(θ)=θI表示K(s,θ)中时变部分,即
其中,w
K∈R
r为时变部分Δ
K(θ)=θI的输出变量,z
K∈R
r为时变部分Δ
K(θ)=θI的输入变量,A
K、B
K1、B
Kθ、C
K1、C
Kθ、D
K11、D
K1θ、D
Kθ1、D
Kθθ是适当维数的系统状态空间矩阵。
步骤3.3:LFT框架下的系统连接图如图4所示,则图4中系统P
1的状态空间表达式为
其中,系统矩阵A=A
p,系统矩阵B
θ=B
pθ,系统矩阵B
1=B
pw,系统矩阵B
2=0
n×l,系统矩阵C
θ=C
pθ,系统矩阵D
θθ=D
pθθ,系统矩阵D
θ1=D
pθw,系统矩阵D
θ2=0
r×l,系统矩阵C
1=0
p1×n,系统矩阵D
1θ=0
p1×r,系统矩阵
系统矩阵
系统矩阵
系统矩阵
系统矩阵
D
22=0
p2×l;n表示航空发动机的状态变量x
p的维数,r表示时变部分Δ(θ)的输出变量w
θ和时变部分Δ
K(θ)的输出变量w
K的维数。
根据航空发动机LPV模型P(s,θ)中时变部分Δ(θ)和故障估计器K(s,θ)中时变部分Δ
K(θ),LPV故障估计器的H
∞综合框架可表示为下式,具体的如图5所示
其中,
为故障估计误差,即LPV故障估计器的H
∞综合框架的输出变量,系统矩阵
系统矩阵
系统矩阵
系统矩阵
系统矩阵
系统矩阵
系统矩阵
系统矩阵
系统矩阵
故障估计器矩阵
矩阵
矩阵
矩阵
矩阵
矩阵
矩阵
矩阵
矩阵
矩阵
矩阵
矩阵
矩阵
矩阵
矩阵
矩阵D
04=D
11。
则闭环系统(36)渐进稳定,并且从外部输入w到故障估计误差e
f的闭环传递函数的L
2诱导范数小于性能指标γ(γ>0)。即故障估计器K(s,θ)存在的有解条件为式(37)、式(38)。其中,Q、S、R分别表示P的子矩阵块。
步骤4.2:对正定对称矩阵X及其逆矩阵X
-1进行分块
其中,L、M、E分别表示X的矩阵块,J、N、F分别表示X
-1的子矩阵块。
由于X为正定对称矩阵,可得
其中,Q
1、Q
2、Q
3分别表示Q的子矩阵块,S
1、S
2、S
3、S
4分别表示S的子矩阵块,R
1、R
2、R
3分别表示R的子矩阵块,
分别表示
的子矩阵块,
分别表示
的子矩阵块,
分别表示
的子矩阵块,
分别表示
的子矩阵块。
线性矩阵不等式(37)整理为
因此,令Q=-R,S+S
T=0。即式(38)可整理为
R>0,Q=-R,S+S
T=0 (44)
综上所述,故障估计器K(s,θ)存在的有解条件转化为式(40)、式(42)、式(44)。
步骤4.3:线性矩阵不等式(42)整理为
其中,U
⊥和V
⊥分别是U
T和V的核空间的基。
经过简单计算,线性矩阵不等式(45)、(46)化简为
步骤5.2:根据Schur补定理,线性矩阵不等式(37)表示为
将闭环系统(36)中的值代入,可得
求解线性矩阵不等式(50),得到故障估计器矩阵Ω。
步骤5.3:得到故障估计器K(s,θ)的状态空间矩阵
在工作点H=0km,Ma=0,n
2=90%处的仿真结果如图6(a)和图6(b)、图7(a)和图7(b)、图8(a)和图8(b)所示,并与标准H
∞方法进行比较。仿真结果表明标准H
∞方法设计的固定参数故障估计器不能很好地应对变参数的变化,而本发明设计的LPV故障估计器可以迅速地检测系统中的故障,并准确地重构故障信号,具有明显的性能优势。
Claims (1)
- 一种基于LFT的航空发动机传感器及执行机构故障诊断方法,其特征在于,包括以下步骤:步骤1:采用小扰动法与线性拟合法相结合的方法建立航空发动机状态变量模型;步骤1.1:向航空发动机输入稳态工作点下的油压p f,待航空发动机高压涡轮相对换算转速n h达到相应稳定状态后,将幅值为0.01p f的油压阶跃信号U pf1输入到航空发动机中,分别采集航空发动机输出高压涡轮相对换算转速响应Y nh1和低压涡轮相对换算转速响应Y nl1;步骤1.2:重复步骤1的过程N次,分别采集得到给定油压p fi下的高压涡轮相对换算转速响应Y nhi和低压涡轮相对换算转速响应Y nli,i=1,2,3,…,N;步骤1.3:以油压阶跃信号U pfi为输入变量,高压涡轮相对换算转速响应Y nhi和低压涡轮相对换算转速响应Y nli为状态变量,根据线性拟合法求解各稳态工作点下的航空发动机离散小偏差状态变量模型;步骤1.4:根据采样周期T,将各稳态工作点下的航空发动机离散小偏差状态变量模型转换为连续小偏差状态变量模型,得到航空发动机状态变量模型;其中,状态变量x p=[Y nl T Y nh T] T∈R n, 表示x p的一阶导数,输入变量u=U pf∈R t,输出变量y p=Y nh∈R m,A pi、B pi、C pi、D pi是系统状态空间矩阵,且C pi=C p=[0 1]、D pi=D p=0;R n、R t、R m分别表示维数为n、t、m的实数集,T表示对矩阵进行转置;步骤2:建立仿射参数依赖的航空发动机LPV模型;步骤2.1:设航空发动机高压涡轮相对换算转速n hi为调度参数θ(i),i=1,2,3,…,N;步骤2.2:将航空发动机连续小偏差状态变量模型的系统矩阵A p(θ)和控制矩阵B p(θ)表述成仿射参数依赖形式,如下:A p(θ)=A 0+θA 1,B p(θ)=B 0+θB 1 (2)其中,A 0、A 1、B 0、B 1分别表示待求的系数矩阵;将式(2)改写为其中,I是单位矩阵;则有其中,[I θI] +为[I θI]的Moore-Penrose伪逆,即求得仿射参数依赖的航空发动机LPV模型的系统矩阵A p(θ)和控制矩阵B p(θ);步骤2.3:建立仿射参数依赖的航空发动机LPV模型步骤3:将存在扰动及传感器与执行机构故障的仿射参数依赖的航空发动机LPV模型转化为LFT结构,建立航空发动机LPV故障估计器的H ∞综合框架;步骤3.1:将存在扰动及传感器与执行机构故障的仿射参数依赖的航空发动机LPV模型P(s,θ)表示为其中,d∈R q为扰动信号,f∈R l为故障信号,包括传感器故障及执行机构故障,R q、R l分别表示维数为q、l的实数集;E p、F p、G p、H p是系统状态空间矩阵,P(s,θ)的上LFT结构表示为其中,外部输入变量w=[u T d T f T] T∈R p1,w θ∈R r为时变部分Δ(θ)=θI的输出变量,z θ∈R r为时变部分Δ(θ)=θI的输入变量,A p、B pθ、B pw、C pθ、C pw、D pθθ、D pθw、D pwθ、D pww是系统状态空间矩阵;R p1、R r分别表示维数为p1、r的实数集,且有p1=t+q+l,即外部输入变量w的维数p1等于航空发动机的输入变量u的维数t、扰动信号d的维数q和故障信号f的维数l之和;步骤3.2:设故障估计器K(s,θ)形式如下其中,x K∈R k为故障估计器K(s,θ)的状态变量, 表示x K的一阶导数,R k表示维数为k的实数集;u K=[u T y p T] T∈R p2为K(s,θ)的输入变量,p2=t+m,即K(s,θ)的输入变量u K的维数p2等于航空发动机的输入变量u的维数t和航空发动机的输出变量y p的维数m之和; 为K(s,θ)的输出变量,即故障信号f的估计值,A K(θ)、B K(θ)、C K(θ)、D K(θ)是系统状态空间矩阵,将K(s,θ)表示成下LFT结构,如下:其中,w K∈R r为时变部分Δ K(θ)=θI的输出变量,z K∈R r为时变部分Δ K(θ)=θI的输入变量,A K、B K1、B Kθ、C K1、C Kθ、D K11、D K1θ、D Kθ1、D Kθθ是系统状态空间矩阵;步骤3.3:根据航空发动机LPV模型P(s,θ)中时变部分Δ(θ)和故障估计器K(s,θ)中时变部分Δ K(θ),LPV故障估计器的H ∞综合框架表示为其中, 为故障估计误差,系统矩阵 系统矩阵 系统矩阵 系统矩阵 系统矩阵 系统矩阵 系统矩阵 系统矩阵 系统矩阵 故障估计器矩阵 矩阵 矩阵 矩阵 矩阵 矩阵 矩阵 矩阵 矩阵 矩阵 矩阵 矩阵 矩阵 矩阵 矩阵 矩阵D 04=D 11,矩阵A=A p,矩阵B θ=B pθ,矩阵B 1=B pw,矩阵B 2=0 n×l,矩阵C θ=C pθ,矩阵D θθ=D pθθ,矩阵D θ1=D pθw,矩阵D θ2=0 r×l,矩阵C 1=0 p1×n,矩阵D 1θ=0 p1×r,矩阵 矩阵 矩阵 矩阵 矩阵 D 22=0 p2×l;n表示航空发动机的状态变量x p的维数,r表示时变部分Δ(θ)的输出变量w θ和时变部分Δ K(θ)的输出变量w K的维数,k表示故障估计器K(s,θ)的状态变量x K的维数;步骤4:求解一组线性矩阵不等式LMIs,获得故障估计器存在的有解条件;步骤4.1:得到故障估计器K(s,θ)存在的有解条件,即步骤4.2:对正定对称矩阵X及其逆矩阵X -1进行分块其中,L、M、E分别表示X的矩阵块,J、N、F分别表示X -1的子矩阵块;其中,Q 1、Q 2、Q 3分别表示Q的子矩阵块,S 1、S 2、S 3、S 4分别表示S的子矩阵块,R 1、R 2、R 3分别表示R的子矩阵块, 分别表示 的子矩阵块, 分别表示 的子矩阵块, 分别表示 的子矩阵块, 分别表示 的子矩阵块;化简故障估计器K(s,θ)存在的有解条件,即R>0,Q=-R,S+S T=0 (18)步骤5:结合LFT结构设计故障估计器,实现航空发动机传感器及执行机构的故障诊断;步骤5.2:根据Schur补定理,将线性矩阵不等式(11)表示为求解线性矩阵不等式(19),得到故障估计器矩阵Ω;步骤5.3:得到故障估计器K(s,θ)的状态空间矩阵
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