CN104931255A - Method for evaluating whether fault feature parameter of gearbox good or bad - Google Patents

Abstract

The invention relates to a method for evaluating whether a fault feature parameter of a gearbox are good or bad, which comprises the steps of respectively calculating a probability density function of the feature parameter at a normal state and a target fault mode; setting an upper limit and a lower limit of a fault threshold, and extracting 101 values in a interval formed by the upper limit and the lower limit of the fault threshold in an evenly spaced mode to act as fault thresholds; respectively calculating a false alarm rate and a fault detection rate of each fault threshold according to the probability density function of the feature parameter at the normal stage and the probability density function of the feature parameter at the fault mode; fitting according to the acquired false alarm rate and the acquired fault detection rate of each fault threshold by taking the false alarm rate as an independent variable and taking the fault detection rate as a dependent variable to acquire an ROC curve of the feature parameter; carrying out integration on the ROC curve in an interval of (0, 1), and calculating the area below the curve to act as an evaluation index. The method provides a basis for extracting the sensitive and effective fault feature parameter, thereby improving the efficiency and the accuracy in fault diagnosis of the gearbox.

Description

A kind of method for evaluating gearbox fault characteristic parameter quality

Technical field

The invention belongs to fault diagnosis field, be specifically related to one and be applied to the preferred method of gearbox fault characteristic parameter.

Background technology

Gear case is the crucial drive disk assembly such as aircraft, car, complex structure, under being in the rugged surroundings of high speed, alternating overload for a long time, again due to its irredundant design, easy generation fault and damage, its health status is directly connected to aircraft, the safe operation of car and the life security of human pilot.Therefore, occur just to carry out condition monitoring and fault diagnosis to gear case to improve aircraft, car safety in operation and Accident prevention.

Extract the prerequisite that responsive, effective Fault characteristic parameters is Fault Diagnosis of Gear Case, it directly constrains efficiency and the accuracy of Fault Diagnosis of Gear Case.And prior art lacks a kind of effective method to extract suitable Fault characteristic parameters.

Summary of the invention

In order to there be a quantitative evaluation to the quality of each Fault characteristic parameters, thus select the feature to each fault mode sensitivity, goal of the invention of the present invention is to provide a kind of method for evaluating gearbox fault characteristic parameter quality, the probability density function of characteristic parameter under normal condition and target faults pattern is calculated respectively by adopting normal distribution matching, the fault threshold recycled in various degree calculates corresponding false alarm rate and fault detect rate, and fit to ROC curve, finally to ROC curve (0, 1) interval interior integration, below calculated curve, area is as evaluation index, index this characteristic parameter larger is more excellent.

Goal of the invention of the present invention is achieved through the following technical solutions:

For evaluating a method for gearbox fault characteristic parameter quality, comprise the steps:

1) characteristic parameter sample is in normal state extracted, and the probability density function of characteristic parameter under calculating normal condition;

2) extract and step 1) the identical sample of characteristic parameter under target faults pattern, and the probability density function of characteristic parameter under calculating fault mode;

3) upper and lower bound of fault threshold is set, and in the interval that the upper and lower bound of fault threshold is formed, extracts 101 values at equal intervals as fault threshold;

4) according to characteristic parameter probability density function in normal state and probability density function in a failure mode, false alarm rate and the fault detect rate of each fault threshold is calculated respectively;

5) take false alarm rate as independent variable, fault detect rate is dependent variable, the false alarm rate obtained according to each fault threshold and fault detect rate, and matching obtains the ROC curve of characteristic parameter sample;

6) to ROC curve integration in (0,1) is interval, below calculated curve, area is as evaluation index.

According to above-mentioned feature, described characteristic parameter sample Normal Distribution, and adopt the method for some parameter estimation to calculate characteristic parameter sample, obtain average and variance, thus obtain calculating probability density function.

According to above-mentioned feature, obtain after the false alarm rate that described ROC curve negotiating adopts least square quadratic polynomial to obtain each fault threshold and fault detect rate carry out matching.

Accompanying drawing explanation

Fig. 1 is characteristic parameter probability distribution graph under normal condition in embodiment;

Fig. 2 is characteristic parameter probability distribution graph under target faults pattern in embodiment;

Fig. 3 is false alarm rate and fault detect rate result of calculation in embodiment;

Fig. 4 is ROC curve and Index result of calculation;

Fig. 5 is schematic flow sheet of the present invention.

Embodiment

Below in conjunction with the drawings and specific embodiments, the present invention will be further described.

As shown in Figure 5, the invention provides a kind of can the method for quantitative evaluation gearbox fault characteristic parameter quality, have employed the method based on ROC curve, can quantitative description different characteristic parameter to the sensitivity of various fault mode, comprise following steps:

Step one: extract characteristic parameter sample x in normal state ₁, x ₂, L, x _n, x _irepresent the characteristic ginseng value in a certain moment.Suppose the characteristic parameter sample Normal Distribution N (μ under normal condition ₁, σ ₁ ²), adopt the method computation of mean values μ of some parameter estimation ₁and variances sigma ₁ ², computing formula is: thus characteristic parameter probability density function under obtaining normal condition see Fig. 1.

Step 2: extract the sample y of the characteristic parameter identical with step one under target faults pattern ₁, y ₂, L, y _m, y _irepresent the characteristic ginseng value in a certain moment.Suppose characteristic parameter sample Normal Distribution N (μ ₂, σ ₂ ²), adopt the method computation of mean values μ of some parameter estimation ₂and variances sigma ₂ ², computing formula is: thus characteristic parameter probability density function under obtaining target faults pattern $g\left(y\right|{\mathrm{\μ}}_2,{\mathrm{\σ}}_2)=\frac{1}{\sqrt{2\mathrm{\π}}{\mathrm{\σ}}_2}\exp \{-\frac{(y-{\mathrm{\μ}}_2)}{2{\mathrm{\σ}}_2^2}\},$ See Fig. 2.

Step 3: calculate fault threshold upper limit T _max=max ((μ ₁+ 3 × σ ₁), (μ ₂+ 3 × σ ₂)), fault threshold lower limit T _min=min ((μ ₁-3 × σ ₁), (μ ₂-3 × σ ₂)), at interval [T _min, T _max] in extract 101 points at equal intervals $\{T_1,T_2,L,T_{100},T_{101}\}=\{T_{\min },T_{\min }+\frac{1}{100}(T_{\max }-T_{\min }),L,T_{\min }+\frac{99}{100}(T_{\max }-T_{\min }),T_{\max }\}.$

Step 4: for each fault threshold T _i, i=0,1, L, 100, calculate false alarm rate ${\mathrm{FA}}_i={\∫}_{T_i}^{+\∞}f\left(x\right|{\mathrm{\μ}}_1,{\mathrm{\σ}}_1)\mathrm{dx},$ Fault detect rate ${\mathrm{HIT}}_i={\∫}_{T_i}^{+\∞}g\left(y\right|{\mathrm{\μ}}_1,{\mathrm{\σ}}_1)\mathrm{dy},$ See Fig. 3.

Step 5: take false alarm rate as independent variable, fault detect rate is dependent variable, { (FA ₁, HIT ₁), L, (FA ₁₀₁, HIT ₁₀₁) be sample, to following solving equations:

$\left\{\begin{array}{c}{a}_0\×101+a_1\underset{i=1}{\overset{101}{\mathrm{\Σ}}}{\mathrm{FA}}_i+a_2\underset{i=1}{\overset{101}{\mathrm{\Σ}}}{\mathrm{FA}}_i^2=\underset{i=1}{\overset{101}{\mathrm{\Σ}}}{\mathrm{HIT}}_i\\ a_0\underset{i=1}{\overset{101}{\mathrm{\Σ}}}{\mathrm{FA}}_i+a_1\underset{i=1}{\overset{101}{\mathrm{\Σ}}}{\mathrm{FA}}_i^2+a_2\underset{i=1}{\overset{101}{\mathrm{\Σ}}}{\mathrm{FA}}_i^3=\underset{i=1}{\overset{101}{\mathrm{\Σ}}}{\mathrm{FA}}_i\×{\mathrm{HIT}}_i\\ a_0\underset{i=1}{\overset{101}{\mathrm{\Σ}}}{\mathrm{FA}}_i^2+a_1\underset{i=1}{\overset{101}{\mathrm{\Σ}}}{\mathrm{FA}}_i^3+a_2\underset{i=1}{\overset{101}{\mathrm{\Σ}}}{\mathrm{FA}}_i^4=\underset{i=1}{\overset{101}{\mathrm{\Σ}}}{\mathrm{FA}}_i^2\×{\mathrm{HIT}}_i\end{array}\right.$

Obtain ROC curvilinear function parameter value a ₀, a ₁, a ₂, then ROC curvilinear function is HIT=h (FA)=a ₀+ a ₁fA+a ₂fA ², see Fig. 4.

Step 6: calculate characteristic parameter evaluation index index value is larger, illustrates that this characteristic parameter is higher to this fault mode susceptibility, the characteristic parameter i.e. optimal characteristics parameter of this fault mode that Index value is maximum, see Fig. 4.

Be understandable that, for those of ordinary skills, can be equal to according to technical scheme of the present invention and inventive concept thereof and replace or change, and all these change or replace the protection domain that all should belong to the claim appended by the present invention.

Claims (3)

1., for evaluating a method for gearbox fault characteristic parameter quality, it is characterized in that comprising the steps:

1) characteristic parameter sample is in normal state extracted, and the probability density function of characteristic parameter under calculating normal condition;

2) extract and step 1) the identical sample of characteristic parameter under target faults pattern, and the probability density function of characteristic parameter under calculating this target faults pattern;

3) upper and lower bound of fault threshold is set, and in the interval that the upper and lower bound of fault threshold is formed, extracts 101 values at equal intervals as fault threshold;

4) according to characteristic parameter probability density function in normal state and probability density function in a failure mode, false alarm rate and the fault detect rate of each fault threshold is calculated respectively;

5) take false alarm rate as independent variable, fault detect rate is dependent variable, the false alarm rate obtained according to each fault threshold and fault detect rate, and matching obtains the ROC curve of characteristic parameter;

6) to ROC curve integration in (0,1) is interval, below calculated curve, area is as evaluation index.

2. the method for evaluating gearbox fault characteristic parameter quality according to claim 1, it is characterized in that described characteristic parameter Normal Distribution, and adopt the method for some parameter estimation to calculate characteristic parameter, obtain average and variance, thus obtain calculating probability density function.

3. the method for evaluating gearbox fault characteristic parameter quality according to claim 1, is characterized in that the false alarm rate that described ROC curve negotiating adopts least square quadratic polynomial to obtain each fault threshold and fault detect rate obtain after carrying out matching.