CN111597655B - Product health judging method based on fault occurrence probability - Google Patents
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- CN111597655B CN111597655B CN202010423177.8A CN202010423177A CN111597655B CN 111597655 B CN111597655 B CN 111597655B CN 202010423177 A CN202010423177 A CN 202010423177A CN 111597655 B CN111597655 B CN 111597655B
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Abstract
The invention provides a product health judging method based on failure occurrence probability, which can be used for carrying out statistic limit distribution analysis by converting data into probability distribution density function when large data are not available. The invention converts time series data obtained in the test into probability distribution density functions, constructs a statistic, determines the limit distribution of the statistic, and judges whether two probability distribution density functions come from the same parent body according to the limit distribution under a certain significance level, so that the technical problem in the health monitoring detection field can be solved by means of research results from the statistical field, fault probability calculation is completed without depending on big data, a large amount of test cost and test time are saved, and the method can achieve the same effect only by two tests (one normal product and one fault product) and has very obvious economic benefit.
Description
Technical Field
The invention belongs to the technical field of time series data processing, and particularly relates to a product health judging method based on fault occurrence probability.
Background
The solid rocket engine has the characteristics of simple structure, reliable operation, simple maintenance, convenient use and the like, and is widely applied to the military field. However, since the engine has the specificity of long-term storage, disposable use and no-test during storage, the engine health monitoring is of great significance.
According to the research results at home and abroad, ultrasonic guided wave is one of stress waves, and the guided wave detection has a series of advantages of a wave information detection method, and has the characteristics of long detection distance, high detection efficiency, high speed and the like. The composite material is not influenced by low-frequency vibration of surrounding environment, is applicable to various types, and can generate stronger response to defects such as debonding, layering, cracks and the like which are common in a multi-layer bonding structure (such as a solid rocket engine: comprising a metal/composite material shell, a heat insulating layer, a grain structure and the like).
When the solid engine is subjected to product health traitor through ultrasonic guided waves, the obtained time series data (namely, the time series data) of the signal change along with time is needed to be processed, and then the failure occurrence rate of the product is obtained. However, the existing time series data processing is mainly characterized by converting the time series data into a frequency domain through methods such as Fourier analysis and wavelet analysis, and the like, and can only be applied to time series data with relatively long response time, the response time of the time series data obtained by an ultrasonic guided wave monitoring mode is very short (1 ms), and the response of the natural frequency of a product can not be activated, so that effective frequency domain information can not be obtained, and therefore, the health judgment of the product can not be effectively carried out.
In addition, in the research process, the difficulty of judging whether the product is healthy is the test number if the short time domain information is adopted, if the test number is enough, the distribution of parameters under normal conditions can be judged by adopting a big data method, and then whether a certain product has faults or not can be judged according to the significance level, but the method is not applicable to the research occasion, mainly because the test number is very small in the research occasion, only two rounds of tests are carried out, the test number is not enough to carry out statistical analysis at all, and the statistical requirement is that whether the product is healthy or not is necessarily judged by adopting a probability method.
Disclosure of Invention
In view of the above, the present invention provides a method for judging product health based on probability of occurrence of failure, which can be used for judging product health by converting data into probability distribution density function and then performing statistic limit distribution analysis when there is no big data.
In order to achieve the above object, the product health judging method based on the fault occurrence probability of the present invention is as follows:
two groups of time series data are obtained by measuring a normal product and a fault product at the same measuring point by the same test method; acquiring a distribution density function f of two sets of time series data 1 And f 2 ；
Calculating the distance d (f) between two distribution density functions 1 ,f 2 ) The probability of occurrence of failure at the measurement point P (d (f) 1 ,f 2 ) N), wherein n is the equivalent degree of freedom;
according to P (d (f) 1 ,f 2 ),n)＝P 0 Solving the equivalent degree of freedom n at this time, where P 0 Is a known probability of failure occurrence;
solving d according to the required fault occurrence probability P and P (d, n) =p, wherein d is a distance critical value when the fault occurrence probability is P;
obtaining time series data of the product to be tested and a distribution density function f of the time series data at the same measuring point by using the same test method 3 Calculate d (f 1 ,f 3 )；
When d (f) 1 ,f 3 )>d, the probability of the product being a fault is larger than the normal probability of the product; when d (f) 1 ,f 3 )<The probability of the product being normal is larger than the probability of the product failure; d (f) 1 ,f 3 ) At=d, the probability of failure and normal is half of each.
Wherein the product is a solid rocket engine.
Wherein, a distribution density function f of two groups of time series data is obtained 1 And f 2 The specific mode of (a) is as follows:
the two groups of time series data are subjected to zero drift correction;
then calculating the envelope curves of the two groups of data after the zero drift correction processing, and then carrying out normalization processing on the envelope curves of the two groups of data to obtain a distribution density function f 1 And f 2 。
Wherein, the liquid crystal display device comprises a liquid crystal display device,
when P (d (f) 1 ,f 2 ),n))＝χ 2 (d(f 1 ,f 2 ) N); where τ represents time and T represents the termination time of the health monitoring time series data.
The product health monitoring time series data are obtained through ultrasonic guided wave monitoring.
The beneficial effects are that:
a qualified product is found to carry out a health monitoring test to obtain time series data under normal conditions, and then a unqualified product is found to carry out the health monitoring test to obtain time series data under fault conditions, at the moment, the test quantity is too small to carry out statistical analysis.
The method is not only suitable for time series data obtained by ultrasonic guided wave monitoring, but also suitable for processing test data obtained by various short-time vibration tests and short-time strain tests carried out on the surfaces of the product shells or the part components, so long as the method can be used for judging whether the product shells or the part components are abnormal or not according to the time series data obtained by various short-time test tests on the surfaces of the product shells or the part components.
Drawings
FIG. 1 is a graph showing the results of an engine charge test of the present invention;
FIG. 2 is a graph showing engine blank test results of the present invention;
FIG. 3 is a graph showing the results of the engine charge zero drift correction of the present invention;
FIG. 4 is a graph showing the results of the engine blank zero drift correction according to the present invention;
FIG. 5 is a graph showing the results and envelope of the engine charge zero drift correction of the present invention;
FIG. 6 is a graph showing the results and envelope of the engine blank zero drift correction according to the present invention;
FIG. 7 is a normalized engine charge result of the present invention;
FIG. 8 is a normalized result of the engine blank according to the present invention.
FIG. 9 is a flow chart of obtaining distance threshold according to the present invention.
Detailed Description
The invention will now be described in detail by way of example with reference to the accompanying drawings.
The invention uses the technology of statistical statistic limit distribution to judge health, and grafts two research achievements in the originally irrelevant field into a new method, which is used for solving the technical problems that big data are not available but a probability method is needed to judge whether the product is healthy.
The embodiment provides a method for testing products in a normal state and a fault state by ultrasonic guided wave and the like, two groups of time series data are obtained, the two groups of time series data are processed to obtain the distance between the two groups of time series data, then a critical value of the distance is obtained, and the probability of faults of the products to be tested can be calculated by comparing the critical value with the critical value.
The product health judging method based on the fault occurrence probability of the embodiment specifically comprises the following steps:
step 1, obtaining two groups of time series data under normal state and fault state products;
the normal state and the fault state products refer to two products with the same technical state, and can also refer to the same product in different time periods.
In the normal state product in this embodiment, an ultrasonic guided wave excitation signal of a specific frequency and waveform is generated by a waveform generator at the signal excitation, and the signal is received at the signal reception.
In a fault state product, the excitation signal is generated at the same frequency and waveform at the same signal excitation as in a normal state product, and the signal is received at the same signal reception.
And 2, performing zero drift correction processing on the two groups of data.
And step 3, calculating the envelope curves of the two groups of data after zero drift correction.
Step 4, normalizing the envelope curves of the two groups of data, wherein the data can be regarded as a distribution density function f after normalization 1 And f 2 ；
Step 5, according to a distance calculation formula
Calculating the distance between two distribution density functions, according to the research result of probability theory, its limit distribution is identical to log likelihood ratio function and is χ 2 (d(f 1 ,f 2 ) N), i.e. the probability of failure at the test point is χ 2 (d(f 1 ,f 2 ) N), where n is the equivalent degree of freedom.
Step 6, according to χ 2 (d(f 1 ,f 2 ),n)＝P 0 Solving the equivalent degree of freedom n at this time, where P 0 The probability of occurrence of a fault under the condition that the fault is known is that the theoretical value is 1, but 1 cannot be calculated, so that data close to 1 needs to be found, and P can be recommended for a certain agreed value 0 0.99.
Step 7, according to the required fault occurrence probability P and χ 2 (d, n) =p, solveD is obtained, wherein d is the distance critical value when the probability of occurrence of the fault is P. P=0.5 is typically taken. A flowchart for obtaining the distance threshold is shown in fig. 9.
Step 8, obtaining time series data of the product to be detected at the same measuring point, and obtaining a distribution density function f of the time series data of the product to be detected in the same way as in the steps 1-4 3 Calculate d (f 1 ,f 3 )；
When d (f) 1 ,f 3 )>d, the probability of the product being a fault is larger than the normal probability of the product; when d (f) 1 ,f 3 )<The probability of the product being normal is larger than the probability of the product failure; d (f) 1 ,f 3 ) When=d, this means that each half of the possibilities of failure and normal should generally be handled as a failure.
Wherein f 1 And f 2 And (3) respectively normalizing functions of a normal product and a fault product, wherein tau represents time, and T represents the termination time of the health monitoring time series data.
In this embodiment, the product is health monitored by an ultrasonic guided wave method, and time series data is obtained.
Specific cases: the data processing method is described by taking test data under two extreme states (charged and empty (i.e. not charged)) of a solid rocket engine as an example. The solid rocket engine in two states is tested through the same method and the same measuring point, wherein the excitation signal is a sinusoidal signal of 50kHz, and the sampling time is long: [ -100.5 μs,899.4 μs ], for 1ms, the test results are shown in FIGS. 1 and 2.
The data processing process is as follows:
1) Zero drift correction processing of data
For test data, wherein, let
Then
y 1 (t)＝y(t)-y 0 (2)
Thus, the results of the engine charge and the empty case after zero drift correction are shown in fig. 3 and 4.
2) Calculating envelope curves of all groups of data by Hilbert method
For data y 1 (t) performing a Hibert transform:
the envelope is
y 2 (t)＝|y 1 (t)+iH[y 1 (t)]| (4)
The envelope of the engine charge and the empty casing is shown in fig. 5 and 6.
4) Normalizing each group of data
After normalization, the data can be considered as a distribution density function.
The results of the normalization process of the engine charge and the empty case are shown in fig. 7 and 8.
5) And calculating the distance between the two distribution density functions, defining the distance between the two distribution density functions, if the distance value is small, proving that the two curves are relatively close, and considering that the two curves have no difference or small difference, and if the distance value is large, proving that the two curves have large difference.
The distance is defined as follows:
wherein f 1 And f 2 Normalized functions of the charge engine and the empty engine, respectively.
d(f 1 ,f 2 ) Having the same limit distribution as the log-likelihood function as χ 2 Distribution, which demonstrates the process as follows: handle f 1 ,f 2 Seen as being from a certain distribution family Γ (Θ) The distribution density function of (2) then exists an n-dimensional parameter θ 1 ,θ 2 E theta, such that
f 1 (t)＝f(t；θ 1 )；f 2 (t)＝f(t；θ 2 )
Handle theta 1 Regarded as true value, and θ 2 Regarded as theta 1 The maximum likelihood estimation value of (a) whose properties conform to the various properties of the maximum likelihood estimation is known as χ for the progressive distribution of the log-likelihood ratio function 2 Distribution, degree of freedom n, should be
Wherein the degree of freedom n is an unknown parameter.
Calculated distance between the empty shell and the charge engine was 0.915, note χ 2 (0.915,1) =0.661 is maximum, and thus the degree of freedom n=1.
For a given allowed failure probability P, the threshold d satisfies χ 2 (d, 1) =p, from which d can be calculated. For p=0.5, there is d=0.455.
6) Arranging measuring points on the outer surface of an engine to be tested, and then performing a test to obtain a response curve under a specified excitation frequency;
7): preprocessing the data according to 1) to 4) to obtain f (t) curve, and calculating to obtain
Then at the measuring point d (f 1 ,f*)>The probability of failure is greater than normal at 0.455 when d (f 1 ,f*)<The probability of normal at 0.455 is greater than the probability of failure.
In summary, the above embodiments are only preferred embodiments of the present invention, and are not intended to limit the scope of the present invention. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (5)
1. Based on fault occurrence probabilityThe product health judging method is characterized in that two groups of time series data are obtained by measuring a normal product and a fault product at the same measuring point by the same testing method; acquiring a distribution density function f of two sets of time series data 1 And f 2 ；
Calculating the distance d (f) between two distribution density functions 1 ,f 2 ) The probability of occurrence of failure at the measurement point P (d (f) 1 ,f 2 ) N), wherein n is the equivalent degree of freedom;
according to P (d (f) 1 ,f 2 ),n)＝P 0 Solving the equivalent degree of freedom n at this time, where P 0 Is a known probability of failure occurrence;
solving d according to the required fault occurrence probability P and P (d, n) =p, wherein d is a distance critical value when the fault occurrence probability is P;
obtaining time series data of the product to be tested and a distribution density function f of the time series data at the same measuring point by using the same test method 3 Calculate d (f 1 ,f 3 )；
When d (f) 1 ,f 3 )>d, the probability of the product being a fault is larger than the normal probability of the product; when d (f) 1 ,f 3 )<The probability of the product being normal is larger than the probability of the product failure; d (f) 1 ,f 3 ) At=d, the probability of failure and normal is half of each.
2. The method for judging the health of a product based on the probability of occurrence of a fault as claimed in claim 1, wherein the product is a solid rocket engine.
3. The method for judging health of a product based on probability of occurrence of failure as set forth in claim 1, wherein a distribution density function f of two sets of time-series data is obtained 1 And f 2 The specific mode of (a) is as follows:
the two groups of time series data are subjected to zero drift correction;
calculating the envelope curves of the two groups of data after the zero drift correction treatment, and then carrying out normalization on the envelope curves of the two groups of dataPerforming a normalization process to obtain a distribution density function f 1 And f 2 。
4. The method for judging health of a product based on probability of occurrence of failure according to claim 1, wherein,
when P (d (f) 1 ,f 2 ),n))＝χ 2 (d(f 1 ,f 2 ) N); where τ represents time and T represents the termination time of the health monitoring time series data.
5. The method for judging product health based on probability of occurrence of a fault as claimed in claim 1, wherein the product health monitoring time series data is obtained by ultrasonic guided wave monitoring.
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| US7571347B2 (en) * | 2006-03-20 | 2009-08-04 | Sun Microsystems, Inc. | Method and apparatus for providing fault-tolerance in parallel-processing systems |
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| CN102411106A (en) * | 2011-11-18 | 2012-04-11 | 广东电网公司广州供电局 | Fault monitoring method and device for power transformer |
| CN105894027A (en) * | 2016-03-31 | 2016-08-24 | 华北电力科学研究院有限责任公司 | Principal element degree of association sensor fault detection method and apparatus based on density clustering |
| CN107132310A (en) * | 2017-03-28 | 2017-09-05 | 浙江大学 | Transformer equipment health status method of discrimination based on gauss hybrid models |
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