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CN109543357B - A Quantitative Evaluation Method of Failure Degree for Optimization of Multiple Regression Models - Google Patents

A Quantitative Evaluation Method of Failure Degree for Optimization of Multiple Regression Models Download PDF

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CN109543357B
CN109543357B CN201910024090.0A CN201910024090A CN109543357B CN 109543357 B CN109543357 B CN 109543357B CN 201910024090 A CN201910024090 A CN 201910024090A CN 109543357 B CN109543357 B CN 109543357B
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谭晓栋
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University of Electronic Science and Technology of China
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Abstract

The invention discloses a fault degree quantitative evaluation method for multivariate regression model optimization, which comprises fault degree evaluation modeling and fault degree calculation by using optimized measuring points, a fault evaluation model and fault degree indexes. The method calculates the fault degree evaluation result of the test sample; calculating a fault degree evaluation root-mean-square matrix of the test sample; and carrying out fault degree evaluation by using the optimized evaluation model and the fault degree index, wherein the optimally selected fault degree evaluation model can synthesize the relationship among the source of fault data acquisition, the extraction of the fault degree index and the fault degree to ensure that the root mean square error is evaluated to be minimum.

Description

Fault degree quantitative evaluation method for multivariate regression model optimization
Technical Field
The invention belongs to the field of quantitative evaluation of fault degree, and particularly relates to a fault degree quantitative evaluation method for multivariate regression model optimization. The method is mainly applied to typical mechanical parts in electromechanical systems, such as bearings, gears, shafts and the like.
Background
The fault degree evaluation refers to analyzing and extracting fault characteristics according to the collected data information, and evaluating the severity degree or severity level of the fault by adopting an intelligent algorithm. The timely and accurate evaluation result can effectively trigger a maintenance decision mechanism, so that the aggravation of the fault degree or the occurrence of secondary faults is avoided, and the method has important significance for reducing the probability of the occurrence of the functional failure of the equipment. In practical engineering, for a system with good encapsulation performance, it is difficult to directly measure the severity of a fault (such as crack length and pitting width) through a detection instrument or equipment, and abnormal signals such as noise, vibration, temperature, output drift, oil and the like caused by the fault can only be collected through detection equipment or sensors and the like deployed on the equipment.
Currently, the known methods have the following problems:
first, in the prior art, the effectiveness of data on evaluation is not analyzed from the source of a fault degree signal, so that a useful fault signal is not used, a useless signal is strongly interfered, and the evaluation accuracy and efficiency are directly reduced.
Secondly, the influence of the data source, the index and the model on the fault degree evaluation is not comprehensively analyzed in the prior art, so that the evaluation accuracy which depends on the index and the model is low.
Disclosure of Invention
In order to solve the above problems in the prior art, the present invention aims to provide a method for quantitatively evaluating a failure degree of multivariate regression model optimization.
The technical scheme adopted by the invention is as follows:
a fault degree quantitative evaluation method for multivariate regression model optimization comprises fault degree evaluation modeling and fault degree calculation by using optimized measuring points, a fault evaluation model and fault degree indexes, wherein the fault degree evaluation modeling comprises the following steps:
s1.1, fault degree simulation and injection: simulating components carrying faults of different severity degrees, installing the components into a system, and operating the system to generate fault signals;
s1.2, collecting multivariate data: a plurality of measuring points are arranged inside and outside the system, abnormal signals caused by fault propagation are monitored, and fault signal sets monitored by the measuring points under different fault degrees are obtained;
s1.3, constructing a fault degree index vector;
s1.4, setting a fault degree evaluation model;
s1.5, calculating a fault degree evaluation model coefficient matrix corresponding to the training sample, and then calculating a fault degree evaluation result of the test sample;
s1.6, calculating the fault degree of the test sample to evaluate the root mean square error;
s1.7, optimizing and selecting a measuring point, a fault evaluation model and a fault degree index.
Preferably, the implementation process of S1.3 is: adopting a time-frequency statistical index extraction method, and constructing a fault degree index vector by using a formula (1):
Figure BDA0001941833450000021
in the formula, FnN is more than or equal to 1 and less than or equal to N as the nth fault degree index vectorF，NFFor the total number of selectable fault level indicators, fiIs a calculation function of the ith fault degree index, N is the total number of samples, NTTotal number of stations deployed, ojkJ is more than or equal to 1 and less than or equal to N, k is more than or equal to 1 and less than or equal to N for the data collected at the kth measuring point in the jth sampleT。
Preferably, the time-frequency statistical indicator extraction method includes a mean value, a root mean square amplitude, an absolute mean value, a skewness, a kurtosis, a variance, a peak value, a standard deviation, a peak-peak value, an average power, a waveform indicator, a peak indicator, a pulse indicator, a margin indicator, a skewness indicator, a kurtosis indicator or a mean frequency.
Preferably, the implementation process of S1.4 is: an alternative multiple regression evaluation model is set using equation (2) depending on the number of measurements:
Figure BDA0001941833450000031
in the formula (f)iIs a calculation function of the ith fault degree index, N is the total number of samples, NTTotal number of stations deployed, ojkJ is more than or equal to 1 and less than or equal to N, k is more than or equal to 1 and less than or equal to N for the data collected at the kth measuring point in the jth sampleT，
Figure BDA0001941833450000036
To evaluate the model coefficients.
Preferably, in S1.5, a calculation formula for calculating a fault degree evaluation model coefficient matrix corresponding to the training sample is as follows:
Figure BDA0001941833450000032
in the formula (B)ij)trainTo use the ith modelAn evaluation model coefficient matrix (X) corresponding to the training sample obtained by the indexij)trainFor a training sample observation matrix calculated using the jth index for the ith model, YtrainTrue fault level vector for training sample
Figure BDA0001941833450000035
NtrainIs the total number of training samples.
Preferably, in S1.5, the calculation formula for calculating the evaluation result of the fault degree of the test sample is as follows:
Figure BDA0001941833450000033
in the formula (I), the compound is shown in the specification,
Figure BDA0001941833450000034
to use a fault level model MiAnd a failure degree index FjEvaluating the fault degree vector of the obtained test sample, (B)ij)trainFor the evaluation model coefficient matrix obtained using the training samples, the (X) is calculated by equation (3)ij)trainTo a fault degree model MiAnd a failure degree index FjA matrix of calculated test sample observations.
Preferably, the implementation process of S1.6 is:
s1.6.1, calculating N using equation (5)MUnder one model, N is adoptedFCalculating the fault degree of each index to evaluate a root mean square error matrix:
Figure BDA0001941833450000041
in the formula, R is a root mean square matrix for evaluating the fault degree of the test sample, the row of R corresponds to a fault degree model, the column corresponds to a fault degree index, and NMEvaluating the total number of models for the degree of failure, rijDefining Using a Fault level model MiAnd a failure degree index FjDegree of lower faultThe root mean square error of the evaluation;
s1.6.2, r is calculated by equation (6)ij：
Figure BDA0001941833450000042
In the formula, NtestIn order to test the total number of samples,
Figure BDA0001941833450000043
to use a fault level model MiAnd a failure degree index FjThe result of the evaluation of the degree of failure of (a) is calculated by the formula (4), YtestTo test the true fault level vector of the sample,
Figure BDA0001941833450000045
preferably, the implementation process of S1.7 is: and (3) optimally selecting an evaluation model and a fault degree index corresponding to the minimum root mean square error of the fault evaluation by using an equation (7):
Figure BDA0001941833450000044
in the formula, M*、F*Respectively evaluating the model corresponding to the minimum root mean square error and the fault degree index for the fault degree, and calculating the minimum root mean square error according to the model M*The expression of (A) determines the optimal measurement point set T*And model parameters B*。
Preferably, the process of calculating the fault degree by using the optimized measuring point, the fault evaluation model and the fault degree index includes:
s2.1, measuring point set T optimized by using formula (7)*Collecting data O in the current statec；
S2.2, fault degree index F optimized by using formula (7)*Extracting the fault degree index of the data in the current state, and constructing an observed value vector matrix Xc；
S2.3, calculating the fault degree under the current state by using an equation (8):
Figure BDA0001941833450000051
in the formula, XcAs a vector matrix of observations, B*And (4) optimal model parameters.
The invention has the beneficial effects that:
the method calculates the fault degree evaluation result of the test sample; calculating a fault degree evaluation root-mean-square matrix of the test sample; and carrying out fault degree evaluation by using the optimized evaluation model and the fault degree index, wherein the optimally selected fault degree evaluation model can synthesize the relationship among the source of fault data acquisition, the extraction of the fault degree index and the fault degree to ensure that the root mean square error is evaluated to be minimum.
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FIG. 1 is a flow chart of a method of an embodiment of the present invention.
Fig. 2 is a graph of the original waveforms for four levels of severity of an inner loop fault in accordance with an embodiment of the present invention.
FIG. 3 is an embodiment T of the present invention*And original waveform diagrams of the current state are acquired by the two middle measuring points.
Detailed Description
The invention is further described with reference to the following figures and specific embodiments.
Example (b):
as shown in fig. 1, in the method for quantitatively evaluating the failure degree of multivariate regression model optimization according to this embodiment, firstly, multivariate test point data is divided into training samples and testing samples, different failure degrees and indexes are constructed using the training samples to describe multivariate regression failure degree evaluation models, the testing samples are used to compare the root mean square error evaluated by each evaluation model under different indexes, and then an optimal failure degree evaluation model and a failure degree index are selected.
On the basis, the optimal data source, the fault degree index and the evaluation model are integrated to realize accurate fault degree evaluation, and finally, the evaluation precision and efficiency are ensured to be improved.
A fault degree quantitative evaluation method for multivariate regression model optimization is specifically realized by the following steps:
firstly, evaluating and modeling fault degree.
S1.1, simulating and injecting fault degree. Simulating components carrying faults of different severity degrees in modes of software simulation or hardware processing and the like, installing the components with the faults into a system, and operating the system to generate fault signals.
S1.2, collecting multivariate data. According to the monitoring requirements of the system, a plurality of measuring points are arranged inside and outside the system, abnormal signals caused by fault propagation are monitored, and fault signal sets monitored by the measuring points under different fault degrees are obtained.
And S1.3, constructing a fault degree index vector. Adopting a time-frequency statistical index extraction method commonly used in engineering, such as a mean value, a root mean square value, a square root amplitude value, an absolute mean value, skewness, kurtosis, a variance, a peak value, a standard deviation, a peak-peak value, average power, a waveform index, a peak index, a pulse index, a margin index, a skewness index, a kurtosis index, a mean frequency and the like, and constructing a fault degree index vector by using an equation (1):
Figure BDA0001941833450000061
in the formula, FnN is more than or equal to 1 and less than or equal to N as the nth fault degree index vectorF，NFFor the total number of selectable fault level indicators, fiIs a calculation function of the ith fault degree index, N is the total number of samples, NTTotal number of stations deployed, ojkJ is more than or equal to 1 and less than or equal to N, k is more than or equal to 1 and less than or equal to N for the data collected at the kth measuring point in the jth sampleT。
And S1.4, setting a fault degree evaluation model. An alternative multiple regression evaluation model is set using equation (2) depending on the number of measurements.
Figure BDA0001941833450000071
In the formula (f)iIs a calculation function of the ith fault degree index, N is the total number of samples, NTTotal number of stations deployed, ojkJ is more than or equal to 1 and less than or equal to N, k is more than or equal to 1 and less than or equal to N for the data collected at the kth measuring point in the jth sampleT，
Figure BDA0001941833450000075
To evaluate the model coefficients.
And S1.5, calculating a fault degree evaluation result of the test sample.
S1.5.1, calculating a fault degree evaluation model coefficient matrix corresponding to the training sample by using the formula (3):
Figure BDA0001941833450000072
in the formula (B)ij)trainFor the evaluation model coefficient matrix corresponding to the training sample obtained by using the jth index of the ith model, (X)ij)trainFor a training sample observation matrix calculated using the jth index for the ith model, YtrainTrue fault level vector for training sample
Figure BDA0001941833450000076
NtrainIs the total number of training samples.
S1.5.2, calculating the fault degree evaluation result of the test sample by using the formula (4):
Figure BDA0001941833450000073
in the formula (I), the compound is shown in the specification,
Figure BDA0001941833450000074
to use a fault level model MiAnd a failure degree index FjEvaluating the fault degree vector of the obtained test sample, (B)ij)trainFor the evaluation model coefficient matrix obtained using the training samples, the (X) is calculated by equation (3)ij)trainTo a fault degree model MiAnd a failure degree index FjA matrix of calculated test sample observations.
And S1.6, calculating the fault degree of the test sample to evaluate the root mean square error. Calculation of N Using equation (5)MUnder one model, N is adoptedFAnd calculating the fault degree of each index to evaluate a root mean square error matrix.
Figure BDA0001941833450000081
In the formula, the rows outside the brackets represent characteristic vectors, the columns outside the brackets represent model numbers, R is a fault degree evaluation root-mean-square matrix of a test sample, the rows of R correspond to fault degree models, the columns correspond to fault degree indexes, and N isMEvaluating the total number of models for the degree of failure, rijDefining Using a Fault level model MiAnd a failure degree index FjThe root mean square error of the lower fault degree evaluation is calculated by using an equation (6) to obtain rij：
Figure BDA0001941833450000082
In the formula, NtestIn order to test the total number of samples,
Figure BDA0001941833450000083
to use a fault level model MiAnd a failure degree index FjThe result of the evaluation of the degree of failure of (a) is calculated by the formula (4), YtestTo test the true fault level vector of the sample,
Figure BDA0001941833450000085
s1.7, optimizing and selecting a measuring point, a fault evaluation model and a fault degree index. And (3) optimally selecting an evaluation model and a fault degree index corresponding to the minimum root mean square error of the fault evaluation by using an equation (7):
Figure BDA0001941833450000084
in the formula, M*、F*Respectively evaluating the model corresponding to the minimum root mean square error and the fault degree index for the fault degree, and calculating the minimum root mean square error according to the model M*The expression of (A) determines the optimal measurement point set T*And model parameters B*。
And secondly, evaluating the fault degree.
S2.1, measuring point set T optimized by using formula (7)*Collecting data O in the current statec。
S2.2, fault degree index F optimized by using formula (7)*Extracting the fault degree index of the data in the current state, and constructing an observed value vector matrix Xc。
S2.3, calculating the fault degree under the current state by using an equation (8):
Figure BDA0001941833450000091
in the formula, XcAs a vector matrix of observations, B*And (4) optimal model parameters.
The main idea of the invention is elaborated by taking a rolling bearing fault simulation experiment table as an example:
firstly, evaluating and modeling fault degree.
S1.1, simulating and injecting fault degree.
The rolling bearing fault simulation experiment table comprises a 2hp motor (1hp ═ 746w), a torque sensor, an indicator and an electric control device. The experimental bearing is a 6205-2RS JEMSKF type deep groove ball bearing, the power of the motor is 746W, and the rotating speed of the input shaft is 1772 r/min. The bearing inner ring faults with 4 severity degrees are machined by using electric sparks, the severity degrees of the faults are divided into 0 inch, 0.007 inch, 0.014 inch and 0.021 inch, and the bearings carrying the 4 severity faults are respectively installed on a test bed to run.
S1.2, collecting multivariate data.
The upper parts of bearing seats at the motor driving end and the fan end of the test bed are respectively provided withOne measurement point, i.e. a set of measurement points t1,t2}, total number of measurement points NT2, vibration data corresponding to 4 severity faults are collected using accelerometers mounted at 2 stations, 3 sets of data are collected for each fault condition, and 12 sets of data are summed, as shown in fig. 2 for the original waveforms for 4 severity faults in the inner ring. Selecting 2 groups of data as training samples for each fault state, namely the total number N of training samplestrainTraining the true fault level vector Y of the sample 8train(000.0070.0070.0140.0140.0210.021); the remaining 1 set of data for each state totaled 4 sets of data as test samples, i.e. the total number of test samples NtestTest sample true failure level vector Y, 4test＝(0 0.007 0.014 0.021)。
And S1.3, constructing a fault degree index vector.
10 time frequency statistical index extraction methods commonly used in engineering, namely the total number N of fault degree indexesF10, respectively correspond to the mean value (F)1) Root mean square value (F)2) Root of square amplitude (F)3) Absolute mean (F)4) Skewness (F)5) Kurtosis (F)6) Variance (F)7) Peak value (F)8) Standard deviation (F)9) Peak to peak value (F)10) Constructing a fault degree index vector, and adopting a square root amplitude index (F) as the following formula3) The fault degree index vector of the established training sample is as follows:
Figure BDA0001941833450000101
and S1.4, setting a fault degree evaluation model. Due to the total number N of measuring pointsT2, the following 6 multiple regression models can be set:
M1：y＝b0+b1x1；
M2：y＝b0+b1x2；
Figure BDA0001941833450000102
Figure BDA0001941833450000103
Figure BDA0001941833450000104
M6：y＝b0+b1x1+b2x2。
based on the model, setting observation value vectors corresponding to 8 training samples:
Figure BDA0001941833450000111
Figure BDA0001941833450000112
Figure BDA0001941833450000113
Figure BDA0001941833450000114
the method for solving the observed value matrix of the training samples adopting other 9 indexes is similar, and is not repeated herein.
And S1.5, calculating a fault degree evaluation result of the test sample. Calculating a fault degree evaluation model coefficient B corresponding to 8 training samples by using an equation (3):
Figure BDA0001941833450000121
Figure BDA0001941833450000122
using fault level indicator F3(i.e., the square root amplitude) a vector of observed values of 4 test samples under the above 6 evaluation models was established:
Figure BDA0001941833450000123
use index F3And establishing an observation value matrix of 4 test samples by the 6 evaluation models:
Figure BDA0001941833450000124
Figure BDA0001941833450000125
Figure BDA0001941833450000126
the observed value matrix solving method of the test sample under other 9 indexes is similar, and is not repeated herein.
The index F can be calculated by using the formula (4)3The following and 6 evaluation models above described the results of the evaluation of the degree of failure of the test samples:
Figure BDA0001941833450000131
Figure BDA0001941833450000132
Figure BDA0001941833450000133
Figure BDA0001941833450000134
Figure BDA0001941833450000135
Figure BDA0001941833450000136
the evaluation results of the fault degrees of the test samples under other 9 indexes are similar, and are not repeated here.
And S1.6, calculating the fault degree of the 4 test samples to evaluate the root mean square error. The root mean square error matrix for fault degree evaluation using 10 fault degree indexes under 6 models was calculated using equation (5).
As described above, the true fault level vectors for the 4 test samples,
Ytest＝(0 0.007 0.014 0.021)。
the root mean square error values of the 6 evaluation models under index 1 were calculated using equation (6).
r13＝0.3508×10-4,r23＝0.5902×10-4,r33＝0.3074×10-4,
r43＝0.0617×10-4,r53＝0.0383×10-4,r63＝0.1524×10-4
From the root mean square error comparison of the above evaluations, it can be seen that at the failure level index F3The root mean square error for the evaluation using model 5 was 0.0383 × 10 min-4. Similarly, the root mean square is evaluated by calculating the fault degrees of the test samples of the other 9 indexes under the 6 evaluation models by using the formulas (5) and (6), which is not repeated herein.
And S1.7, selecting an optimized fault evaluation model and a fault degree index by using an equation (7) according to the solving result, and carrying out comparative analysis according to the calculating result. In the root mean square error matrix under 6 evaluation models and 10 fault degree indexes, the model corresponding to the minimum evaluation root mean square error is M5Hehe fingerMarked F2(i.e. root mean square), i.e. (M)*,F*)＝(M5,F2)。
By comparative analysis, model M5 is expressed as: y is b0+b1f1+b2f1 2+b3f2+b4f2 2I.e. indicating the severity of the fault and the measured point t1And t2In a binary quadratic polynomial relationship, the corresponding optimized model coefficient B ═ B52＝(0.0035 0.2617 -0.2999 -0.2834 0.3436)T. According to model M5It can be known that the optimized measuring point set T*＝{t1，t2}。
And secondly, evaluating the fault degree.
S2.1, use optimization measuring point T*Two measuring points t in1And t2Collecting data O in the current statec，
As shown in FIG. 3 as T*And original waveforms of the current state are acquired by the two middle measuring points.
S2.2, use optimization index F*＝{F2Extracting indexes of the current unknown state (namely, the indexes are corresponding to root mean square), and constructing an observed value vector matrix Xc＝(1 0.0005 0.00052 0.0002 0.00022)。
S2.3, evaluating the fault degree in the current state by using an equation (8)
Figure BDA0001941833450000141
(in inches).
The invention is not limited to the above alternative embodiments, and any other various forms of products can be obtained by anyone in the light of the present invention, but any changes in shape or structure thereof, which fall within the scope of the present invention as defined in the claims, fall within the scope of the present invention.

Claims (8)

1.一种多元回归模型优化的故障程度量化评估方法，其特征在于：包括故障程度评估建模，以及利用优化的测点、故障评估模型及故障程度指标进行故障程度计算，故障程度评估建模包括如下步骤：1. A method for quantifying the degree of failure for multiple regression model optimization, which is characterized in that: including the evaluation and modeling of the degree of failure, and using the optimized measurement points, the evaluation model for the failure and the degree of failure index to calculate the degree of failure, and the evaluation and modeling of the degree of failure. It includes the following steps: S1.1、故障程度模拟与注入：模拟携带不同严重程度故障的部件并安装进系统，运行系统产生故障信号；S1.1. Fault degree simulation and injection: simulate components carrying faults of different severity and install them into the system, and the operating system generates fault signals; S1.2、采集多元数据：系统内外部设置多个测点，监测故障传播引起的异常信号，获得不同故障程度下各个测点监测的故障信号集；S1.2. Collect multivariate data: set up multiple measuring points inside and outside the system to monitor abnormal signals caused by fault propagation, and obtain the set of fault signals monitored by each measuring point under different fault degrees; S1.3、构建故障程度指标向量；S1.3. Construct the failure degree index vector; S1.4、设定故障程度评估模型；S1.4. Set the failure degree evaluation model; S1.5、计算训练样本对应的故障程度评估模型系数矩阵，然后计算测试样本的故障程度评估结果；S1.5. Calculate the coefficient matrix of the failure degree evaluation model corresponding to the training sample, and then calculate the failure degree evaluation result of the test sample; S1.6、计算测试样本的故障程度评估均方根误差；S1.6. Calculate the root mean square error of the failure degree evaluation of the test sample; S1.7、优化选择测点、故障评估模型及故障程度指标；S1.7. Optimal selection of measuring points, fault assessment models and fault degree indicators; 所述S1.3的实现过程为：采用时频统计指标提取方法，使用式(1)构建故障程度指标向量：The implementation process of S1.3 is as follows: adopt the time-frequency statistical index extraction method, and use the formula (1) to construct the failure degree index vector:
Figure FDA0002585581280000011
Figure FDA0002585581280000011
 式中，Fn为第n个故障程度指标向量，1≤n≤NF，NF为可供选择的故障程度指标总数，fi为第i个故障程度指标的计算函数，N为故障程度指标样本总数，NT为部署的测点总数，ojk为在第j个样本中第k个测点采集的数据，1≤j≤N，1≤k≤NT。In the formula, F n is the nth failure degree index vector, 1≤n≤N F , NF is the total number of optional failure degree indicators, f i is the calculation function of the ith failure degree index, and N is the failure degree The total number of index samples, N T is the total number of deployed measurement points, o jk is the data collected at the kth measurement point in the jth sample, 1≤j≤N, 1≤k≤NT . 2.根据权利要求1所述的一种多元回归模型优化的故障程度量化评估方法，其特征在于：所述时频统计指标提取方法包括均值、均方根值、方根幅值、绝对均值、偏斜度、峭度、方差、峰值、标准差、峰峰值、平均功率、波形指标、峰值指标、脉冲指标、裕度指标、偏斜度指标、峭度指标或均值频率。2. The method for quantifying the degree of failure optimized by a multiple regression model according to claim 1, characterized in that: the method for extracting time-frequency statistical indicators comprises mean value, root mean square value, root square amplitude value, absolute mean value, Skewness, kurtosis, variance, peak value, standard deviation, peak-to-peak value, mean power, waveform index, peak index, pulse index, margin index, skewness index, kurtosis index, or mean frequency. 3.根据权利要求1所述的一种多元回归模型优化的故障程度量化评估方法，其特征在于：所述S1.4的实现过程为：根据测点的数目使用式(2)设定可供选择的多元回归评估模型：3. The method for quantifying the degree of failure of multiple regression model optimization according to claim 1, characterized in that: the implementation process of described S1.4 is: according to the number of measuring points, use formula (2) to set available Selected multiple regression evaluation model:
Figure FDA0002585581280000021
Figure FDA0002585581280000021
 式中，fi为第i个故障程度指标的计算函数，N为故障程度指标样本总数，NT为部署的测点总数，ojk为在第j个样本中第k个测点采集的数据，1≤j≤N，1≤k≤NT，
Figure FDA0002585581280000022
为评估模型系数。In the formula, f i is the calculation function of the ith failure degree index, N is the total number of samples of the failure degree index, N T is the total number of deployed measuring points, and o jk is the data collected at the kth measuring point in the jth sample. , 1≤j≤N, 1≤k≤N T ,
Figure FDA0002585581280000022
to evaluate the model coefficients. 4.根据权利要求3所述的一种多元回归模型优化的故障程度量化评估方法，其特征在于：所述S1.5中，计算训练样本对应的故障程度评估模型系数矩阵的计算公式为：4. The fault degree quantification evaluation method optimized by a multiple regression model according to claim 3 is characterized in that: in said S1.5, the calculation formula for calculating the fault degree evaluation model coefficient matrix corresponding to the training sample is:
Figure FDA0002585581280000023
Figure FDA0002585581280000023
 式中，(Bij)train为使用第i个模型第j个指标获得的训练样本对应的评估模型系数矩阵，(Xij)train为针对第i个模型使用第j个指标计算的训练样本观测值矩阵，Ytrain为训练样本真实的故障程度向量
Figure FDA0002585581280000024
Ntrain为训练样本的总数。In the formula, (B ij ) train is the evaluation model coefficient matrix corresponding to the training sample obtained by using the j-th indicator of the i-th model, and (X ij ) train is the training sample observation calculated using the j-th indicator for the i-th model Value matrix, Y train is the true failure degree vector of the training sample
Figure FDA0002585581280000024
N train is the total number of training samples. 5.根据权利要求4所述的一种多元回归模型优化的故障程度量化评估方法，其特征在于：所述S1.5中，计算测试样本的故障程度评估结果的计算公式为：5. The method for quantifying the degree of failure of a multiple regression model optimization according to claim 4, wherein: in the S1.5, the calculation formula for calculating the evaluation result of the degree of failure of the test sample is:
Figure FDA0002585581280000031
Figure FDA0002585581280000031
 式中，
Figure FDA0002585581280000032
为使用故障程度模型Mi和故障程度指标Fj评估得到的测试样本的故障程度向量，(Bij)train为使用训练样本获得的评估模型系数矩阵，通过式(3)计算，(Xij)train为针对故障程度模型Mi和故障程度指标Fj计算的测试样本观测值矩阵。In the formula,
Figure FDA0002585581280000032
is the failure degree vector of the test sample obtained by evaluating the failure degree model Mi and the failure degree index F j , (B ij ) train is the evaluation model coefficient matrix obtained by using the training sample, calculated by formula (3), (X ij ) train is the test sample observation value matrix calculated for the fault degree model Mi and the fault degree index F j . 6.根据权利要求5所述的一种多元回归模型优化的故障程度量化评估方法，其特征在于：所述S1.6的实现过程为：6. The fault degree quantification evaluation method of a kind of multiple regression model optimization according to claim 5, is characterized in that: the realization process of described S1.6 is: S1.6.1、使用式(5)计算NM个模型下采用NF个指标计算故障程度评估均方根误差矩阵：S1.6.1. Use formula (5) to calculate the root mean square error matrix of failure degree evaluation under N M models using N F indicators:
Figure FDA0002585581280000033
Figure FDA0002585581280000033
 式中，R为测试样本的故障程度评估均方根矩阵，R的行对应故障程度模型，列对应故障程度指标，NM为故障程度评估模型总数，rij定义使用故障程度模型Mi和故障程度指标Fj下故障程度评估的均方根误差；In the formula, R is the root mean square matrix of the failure degree evaluation of the test sample, the row of R corresponds to the failure degree model, the column corresponds to the failure degree index, N M is the total number of failure degree evaluation models, and r ij defines the use of the failure degree model Mi and the failure degree model. The root mean square error of the failure degree evaluation under the degree index F j ; S1.6.2、使用式(6)计算得到rij：S1.6.2, use formula (6) to calculate r ij :
Figure FDA0002585581280000034
Figure FDA0002585581280000034
 式中，Ntest为测试样本总数，
Figure FDA0002585581280000035
为使用故障程度模型Mi和故障程度指标Fj的故障程度评估结果，通过式(4)计算得出，Ytest为测试样本真实的故障程度向量，
Figure FDA0002585581280000036
In the formula, N test is the total number of test samples,
Figure FDA0002585581280000035
In order to use the failure degree model Mi and the failure degree index F j to evaluate the failure degree, it is calculated by formula (4), Y test is the real failure degree vector of the test sample,
Figure FDA0002585581280000036
 7.根据权利要求6所述的一种多元回归模型优化的故障程度量化评估方法，其特征在于：所述S1.7的实现过程为：使用式(7)优化选择故障评估均方根误差最小对应的评估模型和故障程度指标：7. The method for quantifying failure degree optimization of a multiple regression model according to claim 6, characterized in that: the implementation process of S1.7 is: using formula (7) to optimize the selection of failure evaluation root mean square error minimum Corresponding evaluation model and failure degree indicators:
Figure FDA0002585581280000041
Figure FDA0002585581280000041
 式中，M*、F*分别为故障程度评估均方根误差最小对应的模型和故障程度指标，根据模型M*的表达式确定最优的测点集合T*和模型参数B*。In the formula, M * and F * are the model corresponding to the minimum root mean square error of the fault degree evaluation and the fault degree index, respectively, and the optimal measurement point set T * and the model parameter B * are determined according to the expression of the model M* . 8.根据权利要求7所述的一种多元回归模型优化的故障程度量化评估方法，其特征在于：所述利用优化的测点、故障评估模型及故障程度指标进行故障程度计算过程为：8. The method for quantifying the degree of failure of a kind of multiple regression model optimization according to claim 7, it is characterized in that: described utilizing optimized measuring point, fault evaluation model and fault degree index to carry out the fault degree calculation process as follows: S2.1、使用式(7)优化的测点集合T*采集当前状态下的数据Oc；S2.1, use the measurement point set T * optimized by formula (7) to collect data O c under the current state; S2.2、使用式(7)优化的故障程度指标F*提取当前状态下的数据的故障程度指标，构建观测值向量矩阵Xc；S2.2, using the optimized failure degree index F * of formula (7) to extract the failure degree index of the data in the current state, and construct the observation value vector matrix X c ; S2.3、使用式(8)计算当前状态下的故障程度：S2.3. Use formula (8) to calculate the fault degree in the current state:
Figure FDA0002585581280000042
Figure FDA0002585581280000042
 式中，Xc为观测值向量矩阵，B*最优的模型参数。In the formula, X c is the observed value vector matrix, and B * the optimal model parameters.
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