CN111289231A - Rotor system health monitoring method and system based on incomplete B-spline data fitting - Google Patents
Rotor system health monitoring method and system based on incomplete B-spline data fitting Download PDFInfo
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Abstract
The invention relates to a rotor system health monitoring method and system based on incomplete B-spline data fitting, wherein monitoring data of a rotor system in normal work is obtained through a rotor system monitoring module, B-spline basis function items with larger error reduction rate are sequentially screened according to a forward regression orthogonal algorithm until the total error of the selected B-spline basis function items meets the fitting precision requirement; determining the control coefficient of each selected B-spline basis function item through least square fitting, and realizing fitting of monitoring data under normal work by establishing an incomplete B-spline baseline model; calculating a tolerance range under a 3 sigma principle when the rotor system normally works based on the established baseline model and the assumption that the deviation obeys normal distribution when the rotor system normally works; formulating a quantitative index for judging the running state of the rotor according to the distribution characteristics of the monitoring data; the operating state of the rotor system is predicted and determined.
Description
Technical Field
The invention belongs to the technical field of rotor system health monitoring, and particularly relates to a rotor system health monitoring method and system based on incomplete B-spline data fitting.
Background
The rotor system is used as an important part of large-scale rotating machinery, and the safety of the whole unit is related to the good and bad running performance of the rotor system. The rotor inevitably generates unbalanced centrifugal force due to manufacturing, material, assembly and other reasons, and the complex alternating load caused by impact load, temperature field change, oil film vortex and the like during the working of the rotor brings great influence to the running stability of the rotor, and causes the rubbing and instability of the rotor, and causes the strong complex vibration of a system and the abrasion, fatigue crack and fracture of the rotor. Therefore, the rotor system is subjected to health monitoring, the unhealthy operation rotor is found as soon as possible to carry out fault diagnosis and maintenance, the service life of the rotor is prolonged, the safety, the reliability and the utilization rate of equipment are improved, and the rotor system has important significance in preventing catastrophic accidents, reducing unplanned shutdown and improving economic benefits.
The vibration signal of the rotor operation contains abundant information, and the characteristic parameters reflecting the system operation state contained in the signal can be obtained through analyzing and processing the vibration signal, so that the change of the operation state of the rotor can be identified and predicted in a fixed manner, diagnosis can be made in time before an accident occurs, and a basis is provided for determining the reason and the position of the vibration fault. Therefore, the rotor system health monitoring method based on the signal processing technology has important engineering application value.
In the fault diagnosis process, a system regression model is often established from data obtained by tests and observation through a data fitting method, and a functional relation between variables is researched to help us to know the internal rules and essential attributes of things, so as to predict other possible states and other important attributes of the system.
The accuracy of the data fitting will directly affect the characterization of the actual system. In the process of modeling an actual system, direct estimation based on a complete variable model leads to the over-complicated model and the identification ill condition of the system; meanwhile, considering the influence of random errors on the observation data, an approximate model which has the minimum overall error and optimally reflects the observation data needs to be searched from the whole situation, namely, an essential item in a structure or a system needs to be determined from a large number of regression items, and then an incomplete regression model of the system is established.
A common method of fitting to discrete data is least squares fitting. In order to improve the accuracy of data fitting, on one hand, more system characteristics need to be added, the order of a polynomial is improved, and a more perfect model is established; on the other hand, the model has better generalization capability, data overfitting caused by too complicated model is avoided, the influence of data noise is reduced, and the stability of the model is ensured. The B-spline basis function has the characteristics of local support and same order of polynomial curve in a non-zero interval, and is an important data fitting tool. The order of the B-spline basis function is an input quantity and does not depend on the number of control points, so that the B-spline baseline model provides more flexible control for data fitting.
Disclosure of Invention
The invention aims to provide a rotor system health monitoring method based on incomplete B-spline data fitting, which is characterized in that under the condition that B-spline node vectors and orders are adjustable, data fitting is carried out on a B-spline baseline model by changing fitting tolerance or iteration times, a tolerance range of a rotor system in normal operation is established, and the health monitoring of an in-service rotor system is realized.
It is another object of the present invention to provide a rotor system health monitoring system based on incomplete B-spline data fitting.
In order to achieve the purpose, the invention provides the following technical scheme:
a rotor system health monitoring method based on incomplete B-spline data fitting comprises the following steps:
acquiring monitoring data of the rotor system during normal work, wherein the monitoring data are running state variables and environment variables of the rotor system, and comprise rotor rotating speed, eccentric mass, load characteristics, system temperature and rotor amplitude; the rotor amplitude y (t) is obtained by sampling a rotor vibration original signal through a sensor and processing the rotor vibration original signal, and is used as a judgment index quantity of the running state of a rotor system, namely a system output quantity; other variables are directly obtained by sampling of a sensor and are used as a system for fitting the vibration amplitude of the rotorInput independent variable x1(t),x2(t),...,xM(t); the specific form of the obtained monitoring data is [ x ]1(t),x2(t),...,xM(t),y(t)]Determining an incomplete B-spline baseline model after fitting by an incomplete B-spline data fitting method based on a forward regression orthogonal algorithm, wherein t is the number of sampling points of monitoring data, and t is 1, 2.. and N is the total number of the sampling points;
and obtaining the tolerance range of the amplitude of the rotor system in normal operation based on the assumption that the amplitude deviation obeys normal distribution and the 3 sigma principle when the rotor system is in normal operation by the incompletely B-spline baseline model obtained by fitting:
calculating the rotor amplitude deviation from the monitored data under normal operation and the baseline model:
and e to N (mu, sigma)2) Wherein y (t) is the amplitude of the sampling point corresponding to the monitoring data,
amplitude deviation e obeys normal distribution N (mu, sigma) for amplitude output response estimation of incomplete B-spline baseline model2) μ is the mean and σ is the standard deviation; make the rotor amplitude tolerance range
Then y (t, e) can cover 99.73% of the rotor deviation value e in normal operation, and participate in establishing a prediction criterion of health monitoring;
from the defined rotor amplitude tolerance range, for monitoring data of in-service rotor operation, a health monitoring criterion is defined: p is Nin/NallIn the formula, NinFor monitoring the amount of data falling within the amplitude range, NallIs the total amount of monitoring data; probability PAs a quantitative index for predicting and judging the running state of the rotor, monitoring data are within a tolerance range, and the rotor system is in a healthy state; otherwise the rotor system is damaged.
In step 1, the determination index amount of the rotor system operating condition is: and the rotor amplitude y (t) is obtained by acquiring a rotor vibration original signal by a piezoelectric acceleration sensor arranged on a rotor system, carrying out signal processing by a system tracking band-pass filter, extracting an effective rotor vibration signal and then obtaining a rotor vibration amplitude by an FFT algorithm and median filtering.
In the step 1, the incomplete B-spline data fitting method based on the forward regression orthogonal algorithm comprises the following steps:
step 1.1, B-spline baseline model general form regression from multivariate data:
in the formula, x1,x2,...,xMIs an independent variable, the subscript M is the number of variables, and y is the output response;
are respectively the ith1,i2,...,iMAbout variable x1,x2,...,xMP times the B-spline basis function of (1),
can be expressed as:
is a B-spline basis function term
Coefficient of (1), MmIs about the variable xmBasis function of
Number, M ═ 1, 2.·, M;
according to the monitored data [ x1(t),x2(t),...,xM(t),y(t)]T is the number of sampling points of the monitoring data, t is 1,2, and N are the total number of the sampling points, namely a group of ordinal column groups taking the sampling time as the sequence, the minimum value and the maximum value of each independent variable are found out to determine the parameter range (x)m,min,xm,max) M1, 2.. times, M, combining the number p of constructed B-spline basis functions and the number L of nodes, constructing a node vector x of each independent variablem＝{xm,0,xm,1,...,xm,LM, B-spline basis function generated by the code-de Boor recursion formula
B-spline basis function terms of constituent variables
Step 1.2, sequentially performing the following steps of all B-spline basis function terms based on a forward regression orthogonal algorithm:
(i1＝1,2,...,M1,...,iM＝1,2,...,MM) B-spline base function items participating in the base line model are screened out, the B-spline base line model of the system is optimized, and an incomplete B-spline base line model is established; the method comprises the following specific steps:
step 1.2.1: constructing a set of auxiliary regression vector W (t) ═ w1(t),...,wS(t)]T is the number of sampling points of the monitored data, t is 1,2, N (N is the total number of sampling points), w1(t),...,wS(t) the auxiliary regression quantities sequentially screened from the B-spline basis function candidates, and S is the number of auxiliary regression quantities meeting the requirement;
for the k-th screening, the residual B-spline basis function terms are subjected to orthogonal decomposition and used as an auxiliary regression wk(t) and calculating the error reduction rate of the respective candidate by constructing an intermediate estimator, namely:
in the formula (I), the compound is shown in the specification,
for the k-th screening of candidates of the auxiliary regression yields,
orthogonal decomposition coefficients, intermediate estimators and error reduction rates, w, of the corresponding auxiliary regression candidatesi(t), i is 1,2,3, k-1 is the selected auxiliary regression,
the residual B-spline basis function terms are used, and y (t) is the amplitude of the corresponding sampling point of the monitoring data;
step 1.2.2: finding out the maximum item of error reduction rate in the candidate items of the auxiliary regression quantity to order
Determining its superscript, wherein M1...MMThen assist the regression
Selected, corresponding B-spline basis function terms
Is selected;
step 1.2.3: until the kth iteration (k < D), the fitting accuracy requirement is met:
or k is equal to D, the maximum iteration times are reached, and the iteration is terminated; wherein e isexpD is the maximum number of iterations for the expected error; after iteration is terminated, screening out auxiliary regression quantities meeting the fitting requirements and corresponding B-spline basis function terms, and performing step 1.3;
step 1.3, determining a control coefficient of the B-spline basis function item screened out in the step 1.2 through least square fitting;
in the formula (I), the compound is shown in the specification,
to control the coefficient, N1(t),N2(t),...,Nk(t) B-spline basis function terms corresponding to the screened auxiliary regression quantities respectively, and y (t) amplitude of sampling points corresponding to the monitoring data;
step 1.4, determining an incomplete B-spline baseline model after fitting according to the B-spline baseline function item corresponding to the auxiliary regression amount screened in the step 1.2 and the control coefficient determined in the step 1.3:
in the formula (I), the compound is shown in the specification,
and (4) estimating the output response of the incomplete B-spline baseline model to the multivariate input as the output prediction of the multivariate input.
A rotor system health monitoring system based on incomplete B-spline data fitting according to the method, the monitoring system comprising: the system comprises a rotor system monitoring module, a health data fitting module, a diagnostic standard establishing module and a health diagnosis module; wherein the content of the first and second substances,
the rotor system monitoring module is used for acquiring monitoring data of the rotor system under normal work;
the rotor system health data fitting module is used for fitting the rotor health data through an incomplete B-spline baseline model based on a forward regression orthogonal algorithm according to the monitoring data of the rotor system obtained by the rotor system monitoring module under the normal work;
the rotor system diagnosis standard establishing module is used for obtaining an incomplete B-spline baseline model of monitoring data under normal work of the rotor system according to fitting of the rotor system health data fitting module, and obtaining a tolerance range of the amplitude of the rotor system under normal work based on the assumption that the amplitude deviation of the rotor system under normal work obeys normal distribution and a 3 sigma diagnosis principle;
and the rotor system health diagnosis module is used for counting the tolerance range of the amplitude of the rotor system during normal work, which is established by the rotor system diagnosis standard establishment module, counting the monitored data distribution condition of the in-service rotor system and speculating and judging the running state of the rotor system.
The rotor system health data fitting module is divided into the following four modules:
the node vector acquisition module is used for constructing the node vectors of the independent variables according to the parameter range, the node number and the B-spline basis function times of the monitoring data of the rotor system under normal work, which are acquired by the rotor system monitoring module;
the B-spline basic function generating module is used for generating a B-spline basic function through a code-de Boor recursion formula through the node vector and the B-spline basic function order of the independent variable constructed by the node vector acquiring module to form a B-spline basic function item of the variable;
the B-spline basic function item screening module is used for screening B-spline basic function items formed by the B-spline basic function generating module, screening B-spline basic function items corresponding to auxiliary regression quantities which greatly contribute to the reduction rate of the fitting error through a forward regression orthogonal algorithm, and participating in building an incomplete B-spline baseline model of the system;
and the incomplete B-spline baseline model determining module is used for determining a control coefficient of the B-spline baseline model through least square fitting according to the B-spline baseline function selected by the B-spline baseline function screening module to obtain the fitted B-spline baseline model.
Compared with the prior art, the invention has the beneficial effects that:
according to the rotor system health monitoring method and system based on incomplete B-spline data fitting, the fitting tolerance of given designated data is met, the B-spline basis function item is increased by increasing the node vector density and changing the B-spline basis function order, the B-spline basis function item form is adjusted, and data fitting is performed on a B-spline baseline model to avoid data under-fitting; screening auxiliary regression quantities corresponding to B-spline basis function items meeting the fitting tolerance through a forward regression orthogonal algorithm, and regulating and controlling the number of the B-spline basis function items participating in the baseline model, so that the fitting efficiency is improved while data overfitting is avoided; the incomplete B-spline baseline model reserves the local support property of the B-spline basis function, can depict the local characteristics of the system, realizes the reproduction characterization of original data, establishes the tolerance range of the rotor system during normal work, and further realizes the health monitoring of the in-service rotor system.
Drawings
FIG. 1 is a flow chart of a rotor system health monitoring method based on incomplete B-spline data fitting of the present invention;
FIG. 2 is a flow chart of an incomplete B-spline data fitting of the present invention;
FIG. 3 is a graph of monitor data fitted according to an embodiment of the present invention;
FIG. 4 is a partial B-spline basis function of an embodiment of the present invention;
FIG. 5 shows the fitting error of the B-spline baseline model for K14 and K45 according to an embodiment of the present invention;
FIG. 6 is a graph of the fit error for the B-spline baseline model and the incomplete B-spline baseline model when K is 45 for an embodiment of the present invention;
FIG. 7 is a graph of a baseline model of a healthy rotor system and a distribution of monitored data over the health of an in-service rotor system;
FIG. 8 is a graph of a baseline model of a healthy rotor system and a distribution of monitored data during in-service rotor system damage;
FIG. 9a is a schematic diagram of a rotor system health monitoring system based on incomplete B-spline data fitting according to the present invention;
FIG. 9b is a schematic diagram of the rotor system health data fitting module according to the present invention.
Detailed Description
The invention is further illustrated with reference to the figures and examples.
The invention provides a rotor system health monitoring method based on incomplete B-spline data fitting, which comprises the steps of obtaining monitoring data of a rotor system during normal work through a rotor system monitoring module, sequentially screening B-spline basic function items with larger error reduction rate according to a forward regression orthogonal algorithm until the total error of the selected B-spline basic function items meets the fitting precision requirement; determining the control coefficient of each selected B-spline basis function item through least square fitting, and realizing fitting of monitoring data under normal work by establishing an incomplete B-spline baseline model; calculating a tolerance range under a 3 sigma principle when the rotor system normally works based on the established baseline model and the assumption that the deviation obeys normal distribution when the rotor system normally works; formulating a quantitative index for judging the running state of the rotor according to the distribution characteristics of the monitoring data; predicting and determining the operating state of the rotor system: the monitoring data is within the tolerance range, and the rotor system is in a healthy state, otherwise the rotor system is likely to be damaged. As shown in fig. 1, the rotor system health monitoring method includes the following steps:
The monitoring data of the rotor system during normal work is obtained through the rotor system monitoring module, and the monitoring data are the running state variables and the environment variables of the rotor system, including the rotor rotating speed, the eccentric mass and the loadLoad characteristics, system temperature, rotor amplitude, etc. The rotor amplitude y (t) is obtained by sampling a rotor vibration original signal through a sensor and processing the rotor vibration original signal, and is used as a judgment index quantity of the running condition of a rotor system, namely a system output quantity; other variables are directly obtained by sampling of a sensor and are used as system input independent variables x of the vibration amplitude of the simulated rotor1(t),x2(t),...,xM(t) of (d). The specific form of the obtained monitoring data is [ x ]1(t),x2(t),...,xM(t),y(t)]And determining a fitted incomplete B-spline baseline model by an incomplete B-spline data fitting method based on a forward regression orthogonal algorithm, wherein t is the number of the monitoring data sampling points, t is 1, 2.
Wherein, the judgment index quantity of the rotor system running state is as follows: and the rotor amplitude y (t) is obtained by acquiring a rotor vibration original signal by a piezoelectric acceleration sensor arranged on a rotor system, carrying out signal processing by a system tracking band-pass filter, extracting an effective rotor vibration signal and then obtaining a rotor vibration amplitude by an FFT algorithm and median filtering.
As shown in fig. 2, the incomplete B-spline data fitting method based on the forward regression orthogonal algorithm includes the following steps:
step 1.1, B-spline baseline model general form regression from multivariate data:
in the formula, x1,x2,...,xMIs an independent variable, the subscript M is the number of variables, and y is the output response;
are respectively the ith1,i2,...,iMAbout variable x1,x2,...,xMP times the B-spline basis function of (1),
can be expressed as:
is a B-spline basis function term
Coefficient of (1), MmIs about the variable xmBasis function of
Number, M ═ 1, 2.·, M;
according to the monitored data [ x1(t),x2(t),...,xM(t),y(t)]T is the number of sampling points of the monitoring data, t is 1,2, and N are the total number of the sampling points, namely a group of ordinal column groups taking the sampling time as the sequence, the minimum value and the maximum value of each independent variable are found out to determine the parameter range (x)m,min,xm,max) M1, 2.. times, M, combining the number p of constructed B-spline basis functions and the number L of nodes, constructing a node vector x of each independent variablem＝{xm,0,xm,1,...,xm,LM, B-spline basis function generated by the code-de Boor recursion formula
B-spline basis function terms of constituent variables
Step 1.2, sequentially performing the following steps of all B-spline basis function terms based on a forward regression orthogonal algorithm:
(i1＝1,2,...,M1,...,iM＝1,2,...,MM) And B-spline basis function items participating in the baseline model are screened out, the B-spline baseline model of the system is optimized, and the incomplete B-spline baseline model is established. The method comprises the following specific steps:
step 1.2.1: constructing a set of auxiliary regression vector W (t) ═ w1(t),...,wS(t)]T is the number of sampling points of the monitored data, and t is 1, 2.N (N is the total number of samples), w1(t),...,wS(t) is the auxiliary regression quantities sequentially screened from the B-spline basis function candidates, and S is the number of auxiliary regression quantities meeting the requirements.
For the k-th screening, the residual B-spline basis function terms are subjected to orthogonal decomposition and used as an auxiliary regression wk(t) and calculating the error reduction rate of the respective candidate by constructing an intermediate estimator, namely:
in the formula (I), the compound is shown in the specification,
for the k-th screening of candidates of the auxiliary regression yields,
orthogonal decomposition coefficients, intermediate estimators and error reduction rates, w, of the corresponding auxiliary regression candidatesi(t), i is 1,2,3, k-1 is the selected auxiliary regression,
the residual B-spline basis function term is used, and y (t) is the amplitude of the corresponding sampling point of the monitored data.
Step 1.2.2: finding errors in candidate terms of auxiliary regression quantitiesMaximum term of differential reduction rate, order
i1＝1,2,...,M1,...,iM＝1,2,...,MMDetermine its superscript, e.g.: m1...MMThen assist the regression
Selected, corresponding B-spline basis function terms
Is selected.
Step 1.2.3: until the kth iteration (k < D), the fitting accuracy requirement is met:
or k equals D, the maximum number of iterations is reached, and the iteration is terminated. Wherein e isexpFor expected error, D is the maximum number of iterations. And after iteration is terminated, screening out the auxiliary regression quantity meeting the fitting requirement and the corresponding B-spline basis function item, and performing step 1.3.
And step 1.3, determining the control coefficient of the B-spline basis function item screened out in the step 1.2 by least square fitting.
In the formula (I), the compound is shown in the specification,
to control the coefficient, N1(t),N2(t),...,NkAnd (t) the B-spline basis function items corresponding to the screened auxiliary regression quantities respectively. And y (t) is the amplitude of the corresponding sampling point of the monitored data.
Step 1.4, determining an incomplete B-spline baseline model after fitting according to the B-spline baseline function item corresponding to the auxiliary regression amount screened in the step 1.2 and the control coefficient determined in the step 1.3:
in the formula (I), the compound is shown in the specification,
the output response estimation of the incomplete B-spline baseline model to the multivariable input can be used as the output prediction of the multivariable input.
Rotor system vibration amplitude is affected by many factors, such as: stiffness and damping of the system, rotor speed, eccentric mass, load characteristics, system temperature, etc. Fig. 3 shows a graph of monitored data of a normal operating curve of a rotor system to be fitted according to an embodiment of the present invention, in which only the rotational speed is used as an independent variable, and the number M of the independent variables is 1. The rotating speed range is 60-100 Hz, the number of the set nodes is L-14, and the corresponding node vector is as follows: x is the number of1＝{x,1,x0,,..1.,1x,K}＝1{6,0,61, 63, 3.6,6.6,6.9,9, 73, 2.7,6.5,7,9.8,8.3,100}8 takes the order p of the B-spline basis function as 3, so that the B-spline basis function is obtained
i11., 17 may be determined by a code-de Boor recursion formula.
FIG. 4 shows a partial B-spline basis function, the coefficients of which can be determined by least squares fitting, the results of which are set forth in Table 1. And B-spline fitting curves of monitoring data under normal work can be obtained through each B-spline basis function and the corresponding control coefficient.
TABLE 1B-spline Baseline model basis function terms and fitting coefficients thereof
| Term of basis function | Coefficient of fit | Term of basis function | Coefficient of fit | Term of basis function | Coefficient of fit | Term of basis function | Coefficient of fit |
| N1,3(x) | 0.3594 | N6,3(x) | 0.9119 | N11,3(x) | 2.1149 | N16,3(x) | 4.9271 |
| N2,3(x) | 0.3486 | N7,3(x) | 0.8010 | N12,3(x) | 2.6904 | N17,3(x) | 4.9661 |
| N3,3(x) | 0.2894 | N8,3(x) | 1.1442 | N13,3(x) | 3.1658 | ||
| N4,3(x) | 0.6451 | N9,3(x) | 1.4619 | N14,3(x) | 4.0309 | ||
| N5,3(x) | 0.3353 | N10,3(x) | 1.7061 | N15,3(x) | 4.7121 |
As the number of nodes increases, the B-spline baseline model fitting data becomes unstable, and when the number of nodes increases to K equal to 45, an overfitting phenomenon occurs, and the final fitting error is much larger than when K equal to 14.
Fig. 5 shows the fitting error of the B-spline curve model when K is 14 and K is 45. When K is 14, the maximum value of the rotor amplitude, the average value and the standard deviation are respectively: 0.1636 μm, 0.0032 μm and 0.0582 μm, indicating that the fitting error is small and negligible; when K is 45, the maximum value of the rotor amplitude, the average value and the standard deviation are respectively: 2.5892 μm, 0.0284 μm and 0.2725 μm, the corrosion of the final data tends to worsen, and the B-spline basis functions increase, the calculation becomes more complicated, and errors accumulate, and the B-spline baseline model cannot be adopted.
The B-spline basis function when K is 45 is recursively screened by the forward orthogonal algorithm, the control coefficient of each selected item is determined by least square estimation, the fitting error of the final improved incomplete B-spline baseline model is given in fig. 6, and the maximum value, the average value and the standard deviation of the rotor amplitude are respectively: 0.1885 μm, 0.0009 μm and 0.0708 μm. As can be seen from the figure, by adopting the curve fitting method, the fitted curve graph has higher copying degree, and the fitting error is well controlled.
And 2, calculating the amplitude tolerance range of the normal work of the rotor system by the baseline model.
And obtaining the tolerance range of the amplitude of the rotor system in normal operation based on the assumption that the amplitude deviation obeys normal distribution and the 3 sigma principle when the rotor system is in normal operation by the incompletely B-spline baseline model obtained by fitting:
calculating the rotor amplitude deviation from the monitored data under normal operation and the baseline model:
and e to N (mu, sigma)2) Wherein y (t) is the amplitude of the sampling point corresponding to the monitoring data,
amplitude deviation e obeys normal distribution N (mu, sigma) for amplitude output response estimation of incomplete B-spline baseline model2) μ is the mean and σ is the standard deviation; make the rotor amplitude tolerance range
Then y (t, e) can cover 99.73% of the rotor deviation value e during normal operation, and participate in establishing the prediction criteria for health monitoring.
And 3, counting the distribution situation of the monitoring data of the in-service rotor system, and speculating and judging the running state of the rotor system.
From the defined rotor amplitude tolerance range, for monitoring data of in-service rotor operation, defining a prediction criterion for health monitoring: p is Nin/NallIn the formula NinFor monitoring the amount of data falling within the amplitude range, NallIs the total amount of monitoring data; the probability P is used as a quantitative index for the prediction and judgment of the running state of the rotor, the reliability of the probability P is directly related to a baseline model of monitoring data fitting under normal work, a more reasonable and efficient method is provided for data fitting based on an incomplete B-spline baseline model of a forward regression orthogonal algorithm, and the reliability of rotor system health monitoring by using the incomplete B-spline baseline model is higher. The monitoring data is within a tolerance range, and the rotor system is in a healthy state, otherwise the rotor system is likely to be damaged.
Fig. 7 and 8 respectively show the monitoring data distribution of the rotor system under different operating states of a certain in-service rotor. For the former, the monitoring data set is distributed in a tolerance range, and P is 81/81 and 100%, the in-service rotor can be presumed to work normally; for the latter, more monitoring data are distributed outside the tolerance band, P is 50/81 is 61.7%, and the active rotor can be presumed to be damaged.
In a second aspect, the present invention provides a rotor system health monitoring system based on incomplete B-spline data fitting, as shown in fig. 9a, the monitoring system comprising: the system comprises a rotor system monitoring module, a health data fitting module, a diagnostic standard establishing module and a health diagnosis module.
And the rotor system monitoring module is used for acquiring monitoring data of the rotor system under normal work.
And the rotor system health data fitting module is used for fitting the rotor health data through an incomplete B-spline baseline model based on a forward regression orthogonal algorithm according to the monitoring data of the rotor system obtained by the rotor system monitoring module under the normal work.
And the rotor system diagnosis standard establishing module is used for obtaining an incomplete B-spline baseline model of monitoring data under normal work of the rotor system according to fitting of the rotor system health data fitting module, and obtaining a tolerance range of the amplitude of the rotor system under normal work based on the assumption that the amplitude deviation of the rotor system under normal work obeys normal distribution and the 3 sigma diagnosis principle.
And the rotor system health diagnosis module is used for counting the tolerance range of the amplitude of the rotor system during normal work, which is established by the rotor system diagnosis standard establishment module, counting the monitored data distribution condition of the in-service rotor system and speculating and judging the running state of the rotor system.
As shown in fig. 9b, the rotor system health data fitting module is divided into the following four modules:
the node vector acquisition module is used for constructing the node vectors of the independent variables according to the parameter range, the node number and the B-spline basis function times of the monitoring data of the rotor system under normal work, which are acquired by the rotor system monitoring module;
the B-spline basic function generating module is used for generating a B-spline basic function through a code-de Boor recursion formula through the node vector and the B-spline basic function order of the independent variable constructed by the node vector acquiring module to form a B-spline basic function item of the variable;
the B-spline basic function item screening module is used for screening B-spline basic function items formed by the B-spline basic function generating module, screening B-spline basic function items corresponding to auxiliary regression quantities which greatly contribute to the reduction rate of the fitting error through a forward regression orthogonal algorithm, and participating in building an incomplete B-spline baseline model of the system;
and the incomplete B-spline baseline model determining module is used for determining a control coefficient of the B-spline baseline model through least square fitting according to the B-spline baseline function selected by the B-spline baseline function screening module to obtain the fitted B-spline baseline model.
The incomplete B-spline-based data fitting method is a multi-variable data regression method, is particularly effective in determining the important items of a regression model and providing final control parameters when the regression model has a plurality of variables and high complexity, can show good stability, high efficiency and excellent profiling capability, and is suitable for the fields of generation of complex curves and curved surfaces in computer drawing, data regression of a system nonlinear model, identification of a brief model of a system with an unknown structure in nonlinear system identification and the like.
In the description of the present invention, numerous specific details are set forth. However, embodiments of the invention may be practiced without these specific details. In embodiments, well-known methods, structures and techniques have not been shown in detail in order not to obscure an understanding of this description.
Finally, it should be noted that: the above examples are only intended to illustrate the technical solution of the present invention, but not to limit it; modifications of the technical solutions described in the above embodiments, or equivalents of some or all technical features may be made, and such modifications or substitutions do not depart from the scope of the technical solutions of the embodiments, and all of the technical solutions should be covered in the claims and the specification of the present invention.
Claims (5)
1. A rotor system health monitoring method based on incomplete B-spline data fitting is characterized by comprising the following steps: the rotor system health monitoring method comprises the following steps:
step 1, fitting an incomplete B-spline baseline model of monitoring data when a rotor system works normally;
acquiring monitoring data of the rotor system during normal work, wherein the monitoring data are running state variables and environment variables of the rotor system, and comprise rotor rotating speed, eccentric mass, load characteristics, system temperature and rotor amplitude; the rotor amplitude y (t) is obtained by sampling a rotor vibration original signal through a sensor and processing the rotor vibration original signal, and is used as a judgment index quantity of the running state of a rotor system, namely a system output quantity; other variables are directly obtained by sampling of a sensor and are used as system input independent variables x for fitting the vibration amplitude of the rotor1(t),x2(t),...,xM(t); the specific form of the obtained monitoring data is [ x ]1(t),x2(t),...,xM(t),y(t)]Determining an incomplete B-spline baseline model after fitting by an incomplete B-spline data fitting method based on a forward regression orthogonal algorithm, wherein t is the number of sampling points of monitoring data, and t is 1, 2.. and N is the total number of the sampling points;
step 2, calculating the amplitude tolerance range of the normal work of the rotor system by the baseline model;
and obtaining the tolerance range of the amplitude of the rotor system in normal operation based on the assumption that the amplitude deviation obeys normal distribution and the 3 sigma principle when the rotor system is in normal operation by the incompletely B-spline baseline model obtained by fitting:
calculating the rotor amplitude deviation from the monitored data under normal operation and the baseline model:
and is
Wherein y (t) is the amplitude of the sampling point corresponding to the monitored data,
amplitude deviation e obeys normal distribution N (mu, sigma) for amplitude output response estimation of incomplete B-spline baseline model2) μ is the mean and σ is the standard deviation; make the rotor amplitude tolerance range
Then y (t, e) can cover 99.73% of the rotor deviation value e in normal operation, and participate in establishing a prediction criterion of health monitoring;
step 3, counting the distribution situation of the monitoring data of the in-service rotor system, and speculating and judging the running state of the rotor system;
from the defined rotor amplitude tolerance range, for monitoring data of in-service rotor operation, a health monitoring criterion is defined: p is Nin/NallIn the formula, NinFor monitoring the amount of data falling within the amplitude range, NallIs the total amount of monitoring data; the probability P is used as a quantitative index for predicting and judging the running state of the rotor, the monitoring data is in a tolerance range, and the rotor system is in a healthy state; otherwise the rotor system is damaged.
2. The method of claim 1, wherein: in step 1, the determination index amount of the rotor system operating condition is: and the rotor amplitude y (t) is obtained by acquiring a rotor vibration original signal by a piezoelectric acceleration sensor arranged on a rotor system, carrying out signal processing by a system tracking band-pass filter, extracting an effective rotor vibration signal and then obtaining a rotor vibration amplitude by an FFT algorithm and median filtering.
3. The method of claim 1, wherein: in the step 1, the incomplete B-spline data fitting method based on the forward regression orthogonal algorithm comprises the following steps:
step 1.1, B-spline baseline model general form regression from multivariate data:
in the formula, x1,x2,...,xMIs an independent variable, the subscript M is the number of variables, and y is the output response;
are respectively the ith1,i2,...,iMAbout variable x1,x2,...,xMP times the B-spline basis function of (1),
can be expressed as:
is a B-spline basis function term
Coefficient of (1), MmIs about the variable xmBasis functions of
Number, M ═ 1, 2.·, M;
according to the monitored data [ x1(t),x2(t),...,xM(t),y(t)]T is the number of sampling points of the monitoring data, t is 1,2, and N are the total number of the sampling points, namely a group of ordinal column groups taking the sampling time as the sequence, the minimum value and the maximum value of each independent variable are found out to determine the parameter range (x)m,min,xm,max) M1, 2.. times, M, combining the number p of constructed B-spline basis functions and the number L of nodes, constructing a node vector x of each independent variablem＝{xm,0,xm,1,...,xm,LM, B-spline basis function generated by Cox-debour recursion formula
B-spline basis function terms of constituent variables
Step 1.2, sequentially performing the following steps of all B-spline basis function terms based on a forward regression orthogonal algorithm:
b-spline base function items participating in the base line model are screened out, the B-spline base line model of the system is optimized, and an incomplete B-spline base line model is established; the method comprises the following specific steps:
step 1.2.1: constructing a set of auxiliary regression vector W (t) ═ w1(t),...,wS(t)]T is the number of sampling point of monitoring data, t1,2, N (N is the total number of samples), w1(t),...,wS(t) the auxiliary regression quantities sequentially screened from the B-spline basis function candidates, and S is the number of the auxiliary regression quantities meeting the requirement;
for the k-th screening, the residual B-spline basis function terms are subjected to orthogonal decomposition and used as auxiliary regression wk(t) and calculating the error reduction rate of the respective candidate by constructing an intermediate estimator, namely:
in the formula (I), the compound is shown in the specification,
for the k-th screening of candidates of the auxiliary regression yields,
orthogonal decomposition coefficients, intermediate estimators and error reduction rates, w, of the corresponding auxiliary regression candidatesi(t), i is 1,2,3, k-1 is the selected auxiliary regression,
is the remaining B-spline basis function term, y (t) is the number monitoredAccording to the amplitude of the corresponding sampling point;
step 1.2.2: finding out the maximum item of error reduction rate in the candidate items of the auxiliary regression quantity to order
Determining its superscript, wherein M1...MMThen assist the regression
Selected, corresponding B-spline basis function terms
Is selected;
step 1.2.3: until the kth iteration (k < D), the fitting accuracy requirement is met:
or k is equal to D, the maximum iteration times are reached, and the iteration is terminated; wherein e isexpD is the maximum number of iterations for the expected error; after iteration is terminated, screening out auxiliary regression quantities meeting the fitting requirements and corresponding B-spline basis function terms, and performing step 1.3;
step 1.3, determining a control coefficient of the B-spline basis function item screened out in the step 1.2 through least square fitting;
in the formula (I), the compound is shown in the specification,
to control the coefficient, N1(t),N2(t),...,Nk(t) B-spline basis function terms corresponding to the screened auxiliary regression quantities respectively, and y (t) amplitude of sampling points corresponding to the monitoring data;
step 1.4, determining an incomplete B-spline baseline model after fitting according to the B-spline basis function item corresponding to the auxiliary regression amount screened in the step 1.2 and the control coefficient determined in the step 1.3:
in the formula (I), the compound is shown in the specification,
and (4) estimating the output response of the incomplete B-spline baseline model to the multivariate input as the output prediction of the multivariate input.
4. A rotor system health monitoring system based on incomplete B-spline data fitting according to the method of any one of claims 1-3, characterized by: the monitoring system includes: the system comprises a rotor system monitoring module, a health data fitting module, a diagnostic standard establishing module and a health diagnosis module; wherein the content of the first and second substances,
the rotor system monitoring module is used for acquiring monitoring data of the rotor system under normal work;
the rotor system health data fitting module is used for fitting the rotor health data through an incomplete B-spline baseline model based on a forward regression orthogonal algorithm according to the monitoring data of the rotor system obtained by the rotor system monitoring module under the normal work;
the rotor system diagnosis standard establishing module is used for obtaining an incomplete B-spline baseline model of monitoring data under normal work of the rotor system according to fitting of the rotor system health data fitting module, and obtaining a tolerance range of the amplitude of the rotor system under normal work based on the assumption that the amplitude deviation of the rotor system under normal work obeys normal distribution and a 3 sigma diagnosis principle;
and the rotor system health diagnosis module is used for counting the tolerance range of the amplitude of the rotor system in normal working according to the tolerance range of the amplitude of the rotor system in normal working, which is established by the rotor system diagnosis standard establishing module, counting the distribution condition of the monitoring data of the in-service rotor system and speculating and judging the running state of the rotor system.
5. The monitoring system of claim 4, wherein: the rotor system health data fitting module is divided into the following four modules:
the node vector acquisition module is used for constructing the node vectors of the independent variables according to the parameter range, the node number and the B-spline basis function times of the monitoring data of the rotor system under normal work, which are acquired by the rotor system monitoring module;
the B-spline basis function generating module is used for generating a B-spline basis function through a code-de Boor recursion formula through the node vector and the B-spline basis function order of the independent variable constructed by the node vector acquiring module to form a B-spline basis function item of the variable;
the B-spline basic function item screening module is used for screening B-spline basic function items formed by the B-spline basic function generating module through a forward regression orthogonal algorithm, screening B-spline basic function items corresponding to auxiliary regression quantities which greatly contribute to the reduction rate of the fitting error, and participating in establishing an incomplete B-spline basic model of the system;
and the incomplete B-spline baseline model determining module is used for determining a control coefficient of the B-spline baseline model through least square fitting according to the B-spline baseline function selected by the B-spline baseline function screening module to obtain the fitted B-spline baseline model.
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