A rotating machinery condition monitoring method based on the probability distribution measurement of impact components

Abstract

The present invention discloses a rotating machinery state monitoring method based on the measurement of the probability distribution of the impact component, comprising the following steps: 1) using a regression analysis method to process the vibration data of the rotating machinery operation process to obtain the characteristic parameters of the Alpha stable distribution; 2) using a hypothesis test method to perform a goodness of fit test on the Alpha stable distribution, if the goodness of fit is less than the hypothesis test significance level ζ, then using a parameter correction method to optimize the characteristic parameters of the Alpha stable distribution; 3) setting a measurement criterion for the probability distribution of the impact component to quantify the fluctuation value of the probability distribution of the impact component; 4) analyzing the fluctuation value of the probability distribution of the impact component at different operating moments of the rotating machinery and equipment to determine the operating state of the rotating machinery and equipment. The present invention establishes an Alpha stable distribution model through regression analysis and parameter correction optimization strategy to comprehensively and accurately characterize the statistical characteristics of the operating process of the rotating machinery and equipment.

Description

Technical Field

[0001] The present invention relates to the field of health monitoring and intelligent operation and maintenance of mechanical equipment, and in particular to a rotating machinery state monitoring method based on impact component probability distribution measurement. Background Art

[0002] Rotating machinery equipment is widely used in various fields of national economy and people's livelihood, and its operating health directly determines whether the production process is stable and reliable. Unexpected production shutdowns caused by rotating machinery equipment failures will not only bring great economic losses, but also directly threaten people's lives. Therefore, accurate and sensitive status monitoring of rotating machinery equipment has become very important.

[0003] However, as the operating conditions of rotating machinery and equipment become increasingly complex, it has become very difficult to establish a reliable condition monitoring system that can accurately reflect its degradation trend. On the one hand, transient interference during the operation of rotating machinery and equipment causes traditional measurement indicators to fluctuate violently, and cannot accurately reflect its health status and degradation trend; on the other hand, increasingly complex operating conditions require more powerful state feature extraction methods to fully characterize the operating status of rotating machinery and equipment.

[0004] In response to the above problems, experts and scholars have conducted research on rotating machinery condition monitoring methods from multiple perspectives and proposed a variety of condition monitoring indicator systems. According to different construction strategies and implementation methods, current condition monitoring indicators can be divided into two categories: monitoring indicators based on statistics and signal processing, and monitoring indicators based on machine learning. From the perspective of construction, monitoring indicators based on statistics and signal processing have clear physical meanings and are relatively easy to calculate, such as root mean square (RMS), kurtosis, Gini index, and other high-order statistics, which are widely used in the industrial field. However, since this type of indicator only considers part of the statistical information, the characterization ability of the operating state of rotating machinery equipment at different degradation stages is limited. In addition, this type of indicator is greatly affected by transient interference, which leads to non-ideal and violent fluctuations in the condition monitoring results; monitoring indicators based on machine learning overcome the problem of limited characterization ability of a single indicator, and conduct more comprehensive condition monitoring of rotating machinery equipment through the fusion of multi-source indicators. However, machine learning related algorithms do not have good physical interpretability, and their strict data sample requirements and long time-consuming problems still need further in-depth research and optimization.

[0005] From the above analysis, it can be seen that the research and establishment of a rotating machinery condition monitoring index system with high accuracy, strong robustness and clear physical meaning has a very urgent industrial application demand and broad application prospects. Summary of the invention

[0006] The object of the present invention is to provide a rotating machinery state monitoring method based on the probability distribution measurement of the impact component, comprising the following steps:

[0007] 1) Use sensors to collect vibration data during the operation of rotating machinery.

[0008] 2) The vibration data of the rotating machinery during operation is processed using the regression analysis method to obtain the characteristic parameters of the Alpha stable distribution used to characterize the impact characteristics of the vibration data of the rotating machinery;

[0009] The characteristic parameters of the Alpha stable distribution include a characteristic index α, a dispersion coefficient γ, a symmetry parameter β and a position parameter δ.

[0010] The steps of obtaining characteristic parameters of the Alpha stable distribution for describing the impact characteristics of the rotating machinery vibration data include:

[0011] 2.1) Establish the Alpha stable distribution characteristic function φ(t), that is:

[0012] φ(t)=exp{jδt-γ|t| α ·[1+jβsgn(t)ω(t,α)]} (1)

[0013] Wherein, α is the characteristic index, and 0<α≤2, which is used to characterize the significance of the signal impact characteristics; β is the symmetry parameter, and -1≤β≤1; δ is the location parameter; γ is the dispersion coefficient, and γ>0, which is used to characterize the dispersion degree of the Alpha stable distribution around the location parameter; j is the imaginary unit; t is the time;

[0014] Among them, the parameters ω(t,α) and the parameters sgn(t) are as follows:

[0015]

[0016]

[0017] 2.2) Convert formula (1) into a linear expression, namely:

[0018] log(-log|φ(t)| 2 )=log(2γ)+αlog|t (4)

[0019] 2.3) For the regression operator y(t) = log[-log|φ(t)| 2 ] A regression analysis is performed on the parameter ψ(t)=log|t| as shown in formula (5), thereby obtaining estimated values ​​of the characteristic index α and the dispersion coefficient γ;

[0020] y k(t) = log(2γ) + αψ k (t)+ε k (5)

[0021] In the formula, ε k is the error term after the kth iteration; the subscript k is the number of regression analysis iterations;

[0022] 2.4) For the regression operator z(u i )=g(u i )+πk(u i ) about the real number u i and parameter sgn(u i )|u i | α Perform regression analysis as shown in formula (6) to obtain the estimated values ​​of the symmetry parameter β and the location parameter δ; k(u i ) is about u i Function of

[0023]

[0024] Where η i is the error term after the i-th iteration, u i is a real number;

[0025] Among them, the inverse tangent function g(u i ) is as follows:

[0026] g(u i )=arctan{Im[φ(u i )] / Re[φ(u i )]} (7)

[0027] In the formula, Re[φ(u i )] and Im[φ(u i )] are the functions φ(u i )'s real and imaginary parts.

[0028] 3) Use the hypothesis test method to perform a goodness of fit test on the Alpha stable distribution. If the goodness of fit is less than the hypothesis test significance level ζ, use the parameter correction method to optimize the characteristic parameters of the Alpha stable distribution, update the Alpha stable distribution, and repeat step 3); if the goodness of fit is greater than or equal to the hypothesis test significance level ζ, proceed to step 4);

[0029] The steps of using hypothesis testing method to test the goodness of fit of Alpha stable distribution include:

[0030] 3.1) Establish hypothesis test based on Alpha stable distribution, namely:

[0031]

[0032] In the formula, is the probability distribution function of the collected vibration data x; is the probability distribution function of the corresponding Alpha stable distribution estimated by the characteristic parameters; H 0 and H 1 represent the null hypothesis and the alternative hypothesis respectively.

[0033] 3.2) Resample the data B times according to the Alpha stable distribution to obtain the sample signal sequence Each signal contains N sampling points; is the sample signal obtained by the B-th data resampling;

[0034] 3.3) Establish the test statistic T(X), and calculate the vibration data x and the resampled signal X respectively * The test statistic values ​​of R (x) and B is the number of data resampling based on the Alpha stable distribution;

[0035] 3.4) Calculate the goodness of fit of the Alpha stable distribution Right now:

[0036]

[0037] Among them, the activation function κ(x) is as follows:

[0038]

[0039] 3.5) Set the significance level ζ of the hypothesis test to judge the goodness of fit Is it less than the significance level ζ of the hypothesis test? If so, the parameter correction method is used to optimize the characteristic parameters of the Alpha stable distribution, thereby updating the Alpha stable distribution. The resampled signal obtained based on the Alpha stable distribution The length of is consistent with the length of the vibration data x.

[0040] The steps of optimizing the characteristic parameters of the Alpha stable distribution using the parameter correction method include:

[0041] 3.5.1) Reduce the parameter search step size and expand the parameter search space to optimize the regression operator y(t) = log[-log|φ(t)| 2 ], and then update the estimated values ​​of the characteristic index α and the dispersion coefficient γ;

[0042] 3.5.2) Use the same parameter search step size and parameter search space as step 1) to optimize the regression operator z(ui )=g(u i )+πk(u i ), and then update the estimated values ​​of the symmetry parameter β and location parameter δ.

[0043] 4) Setting the measurement criteria for the probability distribution of the impact component, comparing the Alpha stable distribution of the rotating machinery at the current moment with that at the initial moment, and quantifying the fluctuation value of the probability distribution of the impact component;

[0044] The steps of quantifying the fluctuation value of the probability distribution of the impact component include:

[0045] 4.1) Align the Alpha stable distribution corresponding to the current moment and the initial moment through translation transformation, that is:

[0046] Δμ=μ c -μ 0 (11)

[0047] In the formula, μ c and μ 0 They represent the symmetric center of the Alpha stable distribution obtained at the current moment and the initial moment respectively; Δμ is the center offset;

[0048] 4.2) Set the probability distribution criterion of the impact component f(x,h), that is:

[0049]

[0050] Where h is the amplitude boundary of the impact component; p c and p 0 Represent the probability density functions of the current moment and the initial moment respectively, and ε is the set minimum value.

[0051] 4.3) Calculate the fluctuation value Θ(x,h) of the probability distribution of the impact component, that is:

[0052] Θ(x,h)=f c (x,h)-f 0 (x,h) (13)

[0053] In the formula, f c (x,h) and f 0 (x,h) are the impact probability distribution functions at the current moment and the initial moment respectively.

[0054] 5) Analyze the fluctuation values ​​of the probability distribution of the impact component of the rotating machinery at different operating times to determine the operating status of the rotating machinery.

[0055] The operating status of the rotating mechanical equipment includes normal and abnormal; when the fluctuation value Θ(x, h) of the impact component probability distribution is less than or equal to the preset fluctuation threshold 3σ, the operating status of the rotating mechanical equipment is normal; when the fluctuation value Θ(x, h) of the impact component probability distribution is greater than the preset fluctuation threshold 3σ, the operating status of the rotating mechanical equipment is abnormal.

[0056] When the operating status of the rotating machinery is abnormal, the square envelope spectrum analysis method is used to analyze the vibration data of the rotating machinery and verify the operating status of the rotating machinery.

[0057] The method for verifying abnormal state monitoring results using the square envelope spectrum analysis method includes: performing square envelope spectrum analysis on abnormal state vibration data, and if the fault characteristic frequency and its frequency multiple components of the rotating mechanical equipment parts appear in the square envelope spectrum, the corresponding parts are faulty.

[0058] The technical effect of the present invention is undoubted, and the beneficial effects of the present invention are as follows:

[0059] Aiming at the operation process of rotating machinery and equipment, the present invention provides a rotating machinery state monitoring method based on the probability distribution measurement of the impact component. The Alpha stable distribution model is established through regression analysis and parameter correction optimization strategy to comprehensively and accurately characterize the statistical characteristics of the operation process of rotating machinery and equipment, and thus a probability distribution measurement criterion of the impact component is proposed to quantitatively evaluate the degradation state of rotating machinery and equipment at different stages. Based on the statistical characteristics of probability distribution, the method provided by the present invention can comprehensively and accurately reflect the degradation state of rotating machinery and equipment, overcome the problem of limited characterization ability of traditional indicators, and has a clear physical meaning; secondly, the method does not require a large number of data samples for training, and has good computational efficiency and convenience; in addition, since the probability distribution model of vibration data is established from the overall perspective, the method is more robust to transient interference. The technical effect of the present invention is significant, and it has good engineering application value and application prospects. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] Figure 1 It is an execution logic diagram of a rotating machinery state monitoring method based on the probability distribution measurement of the impact component according to the present invention;

[0061] Figure 2 It is a data collection test bench for the entire life cycle of a rolling bearing in an embodiment of the present invention;

[0062] Figure 3 It is the time domain waveform of the rolling bearing vibration data collected in the embodiment of the present invention;

[0063] Figure 4 is the goodness of fit test result in the embodiment of the present invention;

[0064] Figure 5 The rolling bearing state monitoring result based on the probability distribution measurement of the impact component in the embodiment of the present invention;

[0065] Figure 6 (a)-(d) are the results of square envelope spectrum analysis of vibration data of data file 531, data file 532, data file 533, and data file 534 in an embodiment of the present invention;

[0066] Figure 7 (a)-(h) are the comparison results of kurtosis, root mean square, Hoyer index, L2 / L1 norm, negative entropy, smoothing index, Gini coefficient, and state monitoring curve of the method in the embodiment of the present invention;

[0067] Figure 8 It is the trend comparison result of various indicator status monitoring in the embodiment of the present invention. DETAILED DESCRIPTION

[0068] The present invention is further described below in conjunction with the embodiments, but it should not be understood that the above subject matter of the present invention is limited to the following embodiments. Without departing from the above technical ideas of the present invention, various substitutions and changes are made according to the common technical knowledge and customary means in the art, which should all be included in the protection scope of the present invention.

[0069] Embodiment 1:

[0070] See also Figures 1 to 8 , a rotating machinery state monitoring method based on impact component probability distribution measurement, comprising the following steps:

[0071] 1) Use sensors to collect vibration data during the operation of rotating machinery.

[0072] 2) The vibration data of the rotating machinery during operation is processed using the regression analysis method to obtain the characteristic parameters of the Alpha stable distribution used to characterize the impact characteristics of the vibration data of the rotating machinery;

[0073] The characteristic parameters of the Alpha stable distribution include a characteristic index α, a dispersion coefficient γ, a symmetry parameter β and a position parameter δ.

[0074] The steps of obtaining characteristic parameters of the Alpha stable distribution for describing the impact characteristics of the rotating machinery vibration data include:

[0075] 2.1) Establish the Alpha stable distribution characteristic function φ(t), that is:

[0076] φ(t)=exp{jδt-γ|t| α ·[1+jβsgn(t)ω(t,α)]} (1)

[0077] Wherein, α is the characteristic index, and 0<α≤2, which is used to characterize the significance of the signal impact characteristics; β is the symmetry parameter, and -1≤β≤1; δ is the location parameter; γ is the dispersion coefficient, and γ>0, which is used to characterize the dispersion degree of the Alpha stable distribution around the location parameter; j is the imaginary unit; t is the time;

[0078] Among them, the parameters ω(t,α) and the parameters sgn(t) are as follows:

[0079]

[0080]

[0081] 2.2) Convert formula (1) into a linear expression, namely:

[0082] log(-log|φ(t)| 2 )=log(2γ)+αlog|t| (4)

[0083] 2.3) For the regression operator y(t) = log[-log|φ(t)| 2 ] A regression analysis is performed on the parameter ψ(t)=log|t| as shown in formula (5), thereby obtaining estimated values ​​of the characteristic index α and the dispersion coefficient γ;

[0084] y k (t) = log(2γ) + αψ k (t)+ε k (5)

[0085] In the formula, ε k is the error term after the kth iteration; the subscript k is the number of regression analysis iterations;

[0086] 2.4) For the regression operator z(u i )=g(u i )+πk(u i ) about the real number u i and parameter sgn(u i )|u i | α Perform regression analysis as shown in formula (6) to obtain the estimated values ​​of the symmetry parameter β and the location parameter δ; k(u i ) is about u i Function of

[0087]

[0088] Where η i is the error term after the i-th iteration, u i is a real number;

[0089] Among them, the inverse tangent function g(u i ) is as follows:

[0090] g(u i )=arctan{Im[φ(u i )] / Re[φ(u i )]} (7)

[0091] In the formula, Re[φ(u i )] and Im[φ(u i )] are the functions φ(u i )'s real and imaginary parts.

[0092] 3) Use the hypothesis test method to perform a goodness of fit test on the Alpha stable distribution. If the goodness of fit is less than the hypothesis test significance level ζ, use the parameter correction method to optimize the characteristic parameters of the Alpha stable distribution, update the Alpha stable distribution, and repeat step 3); if the goodness of fit is greater than or equal to the hypothesis test significance level ζ, proceed to step 4);

[0093] The steps of using hypothesis testing method to test the goodness of fit of Alpha stable distribution include:

[0094] 3.1) Establish hypothesis test based on Alpha stable distribution, namely:

[0095]

[0096] In the formula, is the probability distribution function of the collected vibration data x; is the probability distribution function of the corresponding Alpha stable distribution estimated by the characteristic parameters; H 0 and H 1 represent the null hypothesis and the alternative hypothesis respectively.

[0097] 3.2) Resample the data B times according to the Alpha stable distribution to obtain the sample signal sequence Each signal contains N sampling points; is the sample signal obtained by the B-th data resampling;

[0098] 3.3) Establish the test statistic T(X), and calculate the vibration data x and the resampled signal X respectively * The test statistic values ​​of R (x) and B is the number of data resampling based on the Alpha stable distribution;

[0099] 3.4) Calculate the goodness of fit of the Alpha stable distribution Right now:

[0100]

[0101] Among them, the activation function κ(x) is as follows:

[0102]

[0103] 3.5) Set the significance level ζ of the hypothesis test to judge the goodness of fit Is it less than the significance level ζ of the hypothesis test? If so, the parameter correction method is used to optimize the characteristic parameters of the Alpha stable distribution, thereby updating the Alpha stable distribution. The resampled signal obtained based on the Alpha stable distribution The length of is consistent with the length of the vibration data x.

[0104] The steps of optimizing the characteristic parameters of the Alpha stable distribution using the parameter correction method include:

[0105] 3.5.1) Reduce the parameter search step size and expand the parameter search space to optimize the regression operator y(t) = log[-log|φ(t)| 2 ], and then update the estimated values ​​of the characteristic index α and the dispersion coefficient γ;

[0106] 3.5.2) Use the same parameter search step size and parameter search space as step 1) to optimize the regression operator z(u i )=g(u i )+πk(u i ), and then update the estimated values ​​of the symmetry parameter β and location parameter δ.

[0107] 4) Setting the measurement criteria for the probability distribution of the impact component, comparing the Alpha stable distribution of the rotating machinery at the current moment with that at the initial moment, and quantifying the fluctuation value of the probability distribution of the impact component;

[0108] The steps of quantifying the fluctuation value of the probability distribution of the impact component include:

[0109] 4.1) Align the Alpha stable distribution corresponding to the current moment and the initial moment through translation transformation, that is:

[0110] Δμ=μ c -μ 0 (11)

[0111] In the formula, μ c and μ 0 They represent the symmetric center of the Alpha stable distribution obtained at the current moment and the initial moment respectively; Δμ is the center offset;

[0112] 4.2) Set the probability distribution criterion of the impact component f(x,h), that is:

[0113]

[0114] Where h is the amplitude boundary of the impact component; p c and p 0 Represent the probability density functions of the current moment and the initial moment respectively, and ε is the set minimum value.

[0115] 4.3) Calculate the fluctuation value Θ(x,h) of the probability distribution of the impact component, that is:

[0116] Θ(x,h)=f c (x,h)-f 0 (x,h) (13)

[0117] In the formula, f c (x,h) and f 0 (x,h) are the impact probability distribution functions at the current moment and the initial moment respectively.

[0118] 5) Analyze the fluctuation values ​​of the probability distribution of the impact component of the rotating machinery at different operating times to determine the operating status of the rotating machinery.

[0119] The operating status of the rotating mechanical equipment includes normal and abnormal; when the fluctuation value Θ(x, h) of the impact component probability distribution is less than or equal to the preset fluctuation threshold 3σ, the operating status of the rotating mechanical equipment is normal; when the fluctuation value Θ(x, h) of the impact component probability distribution is greater than the preset fluctuation threshold 3σ, the operating status of the rotating mechanical equipment is abnormal.

[0120] When the operating status of the rotating machinery is abnormal, the square envelope spectrum analysis method is used to analyze the vibration data of the rotating machinery and verify the operating status of the rotating machinery.

[0121] The method for verifying abnormal state monitoring results using the square envelope spectrum analysis method includes: performing square envelope spectrum analysis on abnormal state vibration data, and if the fault characteristic frequency and its frequency multiple components of the rotating mechanical equipment parts appear in the square envelope spectrum, the corresponding parts are faulty.

[0122] Embodiment 2:

[0123] A rotating machinery state monitoring method based on impact component probability distribution measurement comprises the following steps:

[0124] 1) Use sensors to collect vibration data during the operation of rotating machinery.

[0125] 2) The vibration data of the rotating machinery during operation is processed using the regression analysis method to obtain the characteristic parameters of the Alpha stable distribution used to characterize the impact characteristics of the vibration data of the rotating machinery;

[0126] 3) Use the hypothesis test method to perform a goodness of fit test on the Alpha stable distribution. If the goodness of fit is less than the hypothesis test significance level ζ, use the parameter correction method to optimize the characteristic parameters of the Alpha stable distribution, update the Alpha stable distribution, and repeat step 3); if the goodness of fit is greater than or equal to the hypothesis test significance level ζ, proceed to step 4);

[0127] 4) Setting the measurement criteria for the probability distribution of the impact component, comparing the Alpha stable distribution of the rotating machinery at the current moment with that at the initial moment, and quantifying the fluctuation value of the probability distribution of the impact component;

[0128] 5) Analyze the fluctuation values ​​of the probability distribution of the impact component of the rotating machinery at different operating times to determine the operating status of the rotating machinery.

[0129] Embodiment 3:

[0130] A rotating machinery state monitoring method based on the probability distribution measurement of the impact component, the main steps are shown in Example 2, wherein the characteristic parameters of the Alpha stable distribution include the characteristic index α, the dispersion coefficient γ, the symmetry parameter β and the position parameter δ.

[0131] Embodiment 4:

[0132] A method for monitoring the state of a rotating machine based on the probability distribution measurement of an impact component, the main steps of which are shown in Example 2, wherein the step of obtaining characteristic parameters of an Alpha stable distribution for characterizing the impact characteristics of vibration data of the rotating machine comprises:

[0133] 1) Establish Alpha stable distribution characteristic function:

[0134] φ(t)=exp{jδt-γ|t| α ·[1+jβsgn(t)ω(t,α)]} (1)

[0135] Wherein, α is the characteristic index, and 0<α≤2, which is used to characterize the significance of the signal impact characteristics; β is the symmetry parameter, and -1≤β≤1; δ is the location parameter; γ is the dispersion coefficient, and γ>0, which is used to characterize the dispersion degree of the Alpha stable distribution around the location parameter; j is the imaginary unit; t is the time;

[0136] Among them, the parameters ω(t,α) and the parameters sgn(t) are as follows:

[0137]

[0138]

[0139] 2) Convert formula (1) into a linear expression, namely:

[0140] log(-log|φ(t)| 2 )=log(2γ)+αlog|t| (4)

[0141] 3) For the regression operator y(t)=log[-log|φ(t)| 2 ] A regression analysis is performed on the parameter ψ(t)=log|t| as shown in formula (5), thereby obtaining estimated values ​​of the characteristic index α and the dispersion coefficient γ;

[0142] y k (t) = log(2γ) + αψ k (t)+ε k (5)

[0143] In the formula, ε k is the error term after the kth iteration;

[0144] 4) For the regression operator z(u i )=g(u i )+πk(u i ) about the real number u i and parameter sgn(u i )|u i | α Perform a regression analysis as shown in formula (6) to obtain estimated values ​​of the symmetry parameter β and the location parameter δ;

[0145]

[0146] Where η i is the error term after the i-th iteration, u i is a real number;

[0147] Among them, the inverse tangent function g(u i ) is as follows:

[0148] g(u i )=arctan{Im[φ(u i )] / Re[φ(u i )]} (7)

[0149] In the formula, Re[φ(u i )] and Im[φ(u i )] are the functions φ(u i )'s real and imaginary parts.

[0150] Embodiment 5:

[0151] A rotating machinery state monitoring method based on the probability distribution measurement of the impact component, the main steps are shown in Example 2, wherein the step of using the hypothesis testing method to perform a goodness of fit test on the Alpha stable distribution includes:

[0152] 1) Establish a hypothesis test based on the Alpha stable distribution, namely:

[0153]

[0154] In the formula, is the probability distribution function of the collected vibration data x; is the probability distribution function of the corresponding Alpha stable distribution estimated by the characteristic parameters; H 0 and H 1 represent the null hypothesis and the alternative hypothesis respectively.

[0155] 2) Resample the data B times according to the Alpha stable distribution to obtain the sample signal sequence Each signal contains N sampling points;

[0156] 3) Establish the test statistic T(X) and calculate the vibration data x and the resampled signal X respectively * The test statistic values ​​of R (x) and B is the number of data resampling based on the Alpha stable distribution;

[0157] 4) Calculate the goodness of fit of the Alpha stable distribution Right now:

[0158]

[0159] Among them, the activation function κ(x) is as follows:

[0160]

[0161] 5) Set the significance level ζ of the hypothesis test to judge the goodness of fit Is it less than the significance level ζ of the hypothesis test? If so, the parameter correction method is used to optimize the characteristic parameters of the Alpha stable distribution, thereby updating the Alpha stable distribution.

[0162] Embodiment 6:

[0163] A rotating machinery state monitoring method based on the probability distribution measurement of the impact component, the main steps are shown in Example 2, wherein the resampled signal obtained according to the Alpha stable distribution The length of is consistent with the length of the vibration data x.

[0164] Embodiment 7:

[0165] A method for monitoring the state of a rotating machine based on the probability distribution measurement of an impact component, the main steps of which are shown in Example 2, wherein the step of optimizing the characteristic parameters of the Alpha stable distribution by using a parameter correction method comprises:

[0166] 1) Reduce the parameter search step size and expand the parameter search space to optimize the regression operator y(t) = log[-log|φ(t)| 2 ], and then update the estimated values ​​of the characteristic index α and the dispersion coefficient γ;

[0167] 2) Use the same parameter search step size and parameter search space as step 1) to optimize the regression operator z(u i )=g(u i )+πk(u i ), and then update the estimated values ​​of the symmetry parameter β and location parameter δ.

[0168] Embodiment 8:

[0169] A method for monitoring the state of a rotating machine based on the measurement of the probability distribution of an impact component, the main steps of which are shown in Example 2, wherein the step of quantifying the fluctuation value of the probability distribution of the impact component comprises:

[0170] 1) Align the Alpha stable distribution corresponding to the current moment and the initial moment through translation transformation, that is:

[0171] Δμ=μ c -μ 0 (1)

[0172] In the formula, μ c and μ 0 Represent the symmetric center of the Alpha stable distribution obtained at the current moment and the initial moment respectively;

[0173] 2) Set the probability distribution criterion of the impact component, namely:

[0174]

[0175] Where h is the amplitude boundary of the impact component; p c and p 0 Represent the probability density functions of the current moment and the initial moment respectively, and ε is the set minimum value.

[0176] 3) Calculate the fluctuation value of the probability distribution of the impact component, that is:

[0177] Θ(x,h)=f c (x,h)-f 0(x,h) (3)

[0178] In the formula, f c (x,h) and f 0 (x,h) are the impact probability distribution functions at the current moment and the initial moment respectively.

[0179] Embodiment 9:

[0180] A method for monitoring the state of rotating machinery based on the measurement of the probability distribution of impact components, the main steps of which are shown in Example 2, wherein the operating state of the rotating machinery equipment includes normal and abnormal; when the fluctuation value Θ(x, h) of the probability distribution of the impact component is less than or equal to the preset fluctuation threshold 3σ, the operating state of the rotating machinery equipment is normal, and when the fluctuation value Θ(x, h) of the probability distribution of the impact component is greater than the preset fluctuation threshold 3σ, the operating state of the rotating machinery equipment is abnormal.

[0181] Embodiment 10:

[0182] A method for monitoring the state of rotating machinery based on the probability distribution measurement of impact components, the main steps of which are shown in Example 2, wherein when the operating state of the rotating machinery equipment is abnormal, the vibration data of the rotating machinery equipment is analyzed by a square envelope spectrum analysis method to verify the operating state of the rotating machinery equipment.

[0183] Embodiment 11:

[0184] A method for monitoring the state of rotating machinery based on the probability distribution measurement of impact components, the main steps of which are shown in Example 2, wherein the method of verifying the abnormal state monitoring results using the square envelope spectrum analysis method includes: performing square envelope spectrum analysis on the abnormal state vibration data, and if the fault characteristic frequency and its frequency multiple components of the rotating machinery equipment parts appear in the square envelope spectrum, then the corresponding parts are faulty.

[0185] Embodiment 12:

[0186] See also Figures 1 to 8 , a rotating machinery state monitoring method based on impact component probability distribution measurement, comprising the following steps:

[0187] 1) Using sensors to collect vibration data during the operation of the rotating machinery.

[0188] 2) A regression analysis method is used to obtain the Alpha stable distribution characteristic parameters used to characterize the impact characteristics of the rotating machinery vibration data.

[0189] The steps of obtaining the characteristic parameters of the Alpha stable distribution using the regression analysis method include:

[0190] 2.1) Establish Alpha stable distribution characteristic function:

[0191] φ(t)=exp{jδt-γ|t| α ·[1+jβsgn(t)ω(t,α)]} (1)

[0192] In the formula, α is the characteristic index, and 0<α≤2, representing the significance of the signal impact characteristics; β is the symmetry parameter, and -1≤β≤1; δ is the location parameter; γ is the dispersion coefficient, and γ>0, representing the dispersion degree of the Alpha stable distribution around the location parameter; j is the imaginary unit. In addition, ω(t,α) and sgn(t) are expressed as:

[0193]

[0194]

[0195] 2.2) Convert formula (1) into a linear expression, namely:

[0196] log(-log|φ(t)| 2 )=log(2γ)+αlog|t| (4)

[0197] 2.3) By y(t)=log[-log|φ(t)| 2 ] The following regression analysis can be performed on ψ(t) = log|t| to estimate α and γ

[0198] y k (t) = log(2γ) + αψ k (t)+ε k (5)

[0199] In the formula, ε k is the error term after the kth iteration.

[0200] 2.4) After obtaining the estimated values ​​of α and γ, we can calculate z(u i )=g(u i )+πk(u i )About u i and sgn(u i )|u i | α By performing regression analysis as shown in formula (6), we can estimate β and δ

[0201]

[0202] Where η i is the error term after the i-th iteration, u i is a real number, g(u i ) is the inverse tangent function, expressed as:

[0203] g(u i )=arctan{Im[φ(u i )] / Re[φ(u i )]} (7)

[0204] In the formula, Re[φ(u i )] and Im[φ(u i )] are the functions φ(u i )'s real and imaginary parts.

[0205] Using the above regression analysis method, the characteristic parameters (α, β, γ, δ) of the Alpha stable distribution can be estimated.

[0206] 3) Perform a goodness of fit test on the Alpha stable distribution by hypothesis testing method.

[0207] The steps of testing the goodness of fit of the established Alpha stable distribution by hypothesis testing method include:

[0208] 3.1) Establish hypothesis test based on Alpha stable distribution estimated by characteristic parameters:

[0209]

[0210] In the formula, is the probability distribution function of the collected vibration data x, is the probability distribution function of the corresponding Alpha stable distribution estimated by the characteristic parameters, H 0 and H 1 represent the null hypothesis and the alternative hypothesis respectively.

[0211] 3.2) According to the above Alpha stable distribution, the data is resampled B times to obtain the sample signal sequence Each signal contains N sampling points.

[0212] 3.3) Establish the test statistic T(X), and calculate the observed sample x and the resampled signal X respectively * The test statistic value of R (x) and

[0213] 3.4) Use the above test statistic to calculate the p-value under the hypothesis test condition to characterize the goodness of fit of the Alpha stable distribution:

[0214]

[0215] Where B is the number of data resampling based on the Alpha stable distribution, k = 1, 2, ..., B, and the expression of the activation function κ(x) is:

[0216]

[0217] 3.5) Set the significance level ζ of the hypothesis test. If the p-value obtained by formula (9) is greater than ζ, then accept the null hypothesis H 0 Otherwise, H is rejected 0 .

[0218] 4) For the Alpha stable distribution whose goodness of fit is lower than the set threshold, the characteristic parameters of the Alpha stable distribution are optimized through the parameter correction strategy.

[0219] The steps of optimizing the characteristic parameters of the Alpha stable distribution whose goodness of fit is lower than the set threshold through the parameter correction strategy include:

[0220] 4.1) Optimize the regression operator y(t) = log[-log|φ(t)| by reducing the parameter search step size and expanding the parameter search space at the same time. 2 ], thereby obtaining more accurate characteristic parameters α and γ.

[0221] 4.2) Fix the above feature parameters α and γ, adopt the same parameter search step and search space optimization strategy, and obtain more accurate feature parameters β and δ.

[0222] 4.3) Use the optimized characteristic parameters (α, β, γ, δ) to update the original Alpha stable distribution model and perform the goodness of fit test again.

[0223] 4.4) If the optimized Alpha stable distribution meets the goodness-of-fit test threshold requirement, the parameter correction optimization process is terminated, otherwise continue with steps 4.1) to 4.3).

[0224] 5) Set the measurement criteria for the probability distribution of the impact component, compare the Alpha stable distribution of the rotating machinery at the current moment with the initial moment, and quantify the fluctuation value of the probability distribution of the impact component.

[0225] The solution to the fluctuation value of the probability distribution of the impact component includes the following steps:

[0226] 5.1) Align the Alpha stable distribution corresponding to the current moment and the initial moment through translation transformation, that is:

[0227] Δμ=μ c -μ 0 (11)

[0228] In the formula, μ c and μ 0 Represent the symmetric center of the Alpha stable distribution obtained at the current moment and the initial moment respectively. Δμ is the center offset;

[0229] 5.2) Set the probability distribution criterion of the impact component:

[0230]

[0231] Where h is the amplitude boundary of the impact component, p c and p 0 Represent the probability density functions of the current moment and the initial moment respectively, and ε is the set minimum value.

[0232] 5.3) According to the above shock component probability distribution measurement criteria, the fluctuation value of the shock component probability distribution can be obtained, that is:

[0233] Θ(x,h)=f c (x,h)-f 0 (x,h) (13)

[0234] In the formula, f c (x,h) and f 0 (x,h) are the cumulative impact probability distribution functions at the current moment and the initial moment respectively.

[0235] 6) By analyzing the fluctuation value of the probability distribution of the impact component, the operating status of the rotating mechanical equipment can be judged.

[0236] The steps of judging the operating state of the rotating mechanical equipment according to the fluctuation value of the probability distribution of the impact component include:

[0237] 6.1) Collect N continuous vibration data samples during the initial stable operation stage of the rotating machinery equipment, calculate the fluctuation value of the probability distribution of the impact component according to formula (13), and set the 3σ threshold accordingly.

[0238] 6.2) Collect the vibration data of the rotating mechanical equipment at the current moment and calculate the probability distribution fluctuation value of its impact component. If it does not exceed the set 3σ threshold, its operating status is normal, otherwise it is abnormal.

[0239] The vibration data of the rotating machinery equipment determined to be in an abnormal state is analyzed to verify the accuracy of the state monitoring results. The method includes: performing square envelope spectrum analysis on the abnormal state vibration data. If the fault characteristic frequency and its frequency multiple components of the rotating machinery parts appear in the square envelope spectrum, it is determined that the parts are faulty.

[0240] Embodiment 13:

[0241] A rotating machinery state monitoring method based on impact component probability distribution measurement, the specific steps are as follows:

[0242] Step 1: Use sensors to collect vibration data during the operation of rotating machinery;

[0243] Step 2: Using the regression analysis method on the collected vibration data, obtain the Alpha stable distribution characteristic parameters used to characterize its impact characteristics;

[0244] Step 3: Use hypothesis testing method to verify the goodness of fit of the established Alpha stable distribution;

[0245] Step 4: For the Alpha stable distribution whose goodness of fit is lower than the set threshold, the characteristic parameters of the Alpha stable distribution are optimized through the parameter correction strategy;

[0246] Step 5: Set the measurement criteria for the probability distribution of the impact component, compare the Alpha stable distribution of the rotating machinery at the current moment with that at the initial moment, and quantify the fluctuation value of the probability distribution of the impact component;

[0247] Step 6: Determine the operating status of the rotating machinery by analyzing the fluctuation value of the probability distribution of the impact component.

[0248] The step 2 specifically includes the following steps:

[0249] Step 201: Establish Alpha stable distribution characteristic function:

[0250] φ(t)=exp{jδt-γ|t| α ·[1+jβsgn(t)ω(t,α)]} (1)

[0251] In the formula, α is the characteristic index, and 0<α≤2, representing the significance of the signal impact characteristics; β is the symmetry parameter, and -1≤β≤1; δ is the location parameter; γ is the dispersion coefficient, and γ>0, representing the dispersion degree of the Alpha stable distribution around the location parameter; j is the imaginary unit. In addition, ω(t,α) and sgn(t) are expressed as:

[0252]

[0253]

[0254] Step 202: Convert formula (1) into a linear expression, namely:

[0255] log(-log|φ(t)| 2 )=log(2γ)+αlog|t| (4)

[0256] Step 203: By y(t)=log[-log|φ(t)| 2 ] The following regression analysis can be performed on ψ(t) = log|t| to estimate α and γ

[0257] y k (t) = log(2γ) + αψ k (t)+ε k (5)

[0258] In the formula, ε k is the error term after the kth iteration.

[0259] Step 204: After obtaining the estimated values ​​of α and γ, z(u i )=g(u i )+πk(u i )About u i and sgn(u i )|u i | α By performing regression analysis as shown in formula (6), we can estimate β and δ

[0260]

[0261] Where η i is the error term after the i-th iteration, u i is a real number, g(u i ) is the inverse tangent function, expressed as:

[0262] g(u i )=arctan{Im[φ(u i )] / Re[φ(u i )]} (7)

[0263] In the formula, Re[φ(u i )] and Im[φ(u i )] are the functions φ(u i )'s real and imaginary parts.

[0264] The step 3 specifically comprises the following steps:

[0265] Step 301: Establish a hypothesis test based on the Alpha stable distribution estimated by the characteristic parameters:

[0266]

[0267] In the formula, is the probability distribution function of the collected vibration data x, is the probability distribution function of the corresponding Alpha stable distribution estimated by the characteristic parameters, H 0 and H 1 represent the null hypothesis and the alternative hypothesis respectively.

[0268] Step 302: Perform B data resampling according to the above Alpha stable distribution to obtain a sample signal sequence Each signal contains N sampling points.

[0269] Step 303: Establish the test statistic T(X), and calculate the observed sample x and the resampled signal X respectively. * The test statistic value of R (x) and

[0270] Step 304: Calculate the p-value under the hypothesis test condition using the above test statistic to characterize the goodness of fit of the Alpha stable distribution:

[0271]

[0272] Where B is the number of data resampling based on the Alpha stable distribution, k = 1, 2, ..., B, and the expression of the activation function κ(x) is:

[0273]

[0274] Step 305: Set the significance level ζ of the hypothesis test. If the p-value obtained by formula (9) is greater than ζ, then accept the null hypothesis H 0 Otherwise, H is rejected 0 .

[0275] The step 4 specifically comprises the following steps:

[0276] Step 401: Optimize the regression operator y(t)=log[-log|φ(t)| by reducing the parameter search step size and expanding the parameter search space at the same time. 2 ], thereby obtaining more accurate characteristic parameters α and γ.

[0277] Step 402: fix the above characteristic parameters α and γ, adopt the same parameter search step and search space optimization strategy, and obtain more accurate characteristic parameters β and δ.

[0278] Step 403: Use the optimized characteristic parameters (α, β, γ, δ) to update the original Alpha stable distribution model and perform a goodness of fit test again.

[0279] Step 404: If the optimized Alpha stable distribution meets the goodness-of-fit test threshold requirement, the parameter correction optimization process is terminated, otherwise, steps 401 to 403 are continued.

[0280] The step 5 specifically comprises the following steps:

[0281] Step 501: Align the Alpha stable distribution corresponding to the current moment and the initial moment through translation transformation, that is:

[0282] Δμ=μ c -μ 0 (11)

[0283] In the formula, μ c and μ 0 Represent the symmetric center of the Alpha stable distribution obtained at the current moment and the initial moment respectively.

[0284] Step 502: Setting the impact component probability distribution metric:

[0285]

[0286] Where h is the amplitude boundary of the impact component, p c and p 0 Represent the probability density functions of the current moment and the initial moment respectively, and ε is the set minimum value.

[0287] Step 503: According to the above shock component probability distribution measurement criteria, the fluctuation value of the shock component probability distribution can be obtained, that is:

[0288] Θ(x,h)=f c (x,h)-f 0 (x,h) (13)

[0289] In the formula, f c (x,h) and f 0 (x,h) are the cumulative impact probability distribution functions at the current moment and the initial moment respectively.

[0290] The step 6 specifically comprises the following steps:

[0291] Step 601: Collect N continuous vibration data samples during the initial stable operation stage of the rotating mechanical equipment, calculate the fluctuation values ​​of the probability distribution of the impact components according to formula (13), and set the 3σ threshold accordingly.

[0292] Step 602: Collect vibration data of the rotating mechanical equipment at the current moment, calculate the probability distribution fluctuation value of its impact component, and if it does not exceed the set 3σ threshold, its operating state is normal, otherwise it is abnormal.

[0293] Step 603: Perform square envelope spectrum analysis on the detected abnormal state data to verify the accuracy of the state monitoring.

[0294] Embodiment 14:

[0295] This embodiment is based on a rolling bearing full life cycle data set publicly provided by the Intelligent Operation and Maintenance System Center of the University of Cincinnati, USA, to verify the effectiveness of the method provided by the present invention in rolling bearing condition monitoring.

[0296] Step 1: Rolling bearing vibration data collection.

[0297] Data acquisition test bench for rolling bearing full life cycle test Figure 2 As shown in the figure, during the test, the spindle speed is 2000 rpm, the sampling frequency is set to 20kHz, each data file contains 20480 data points, and data is collected every 10 minutes during the test. Finally, 984 data files are generated. The time domain waveform is as follows Figure 3 shown.

[0298] Step 2: For each vibration data sample collected, the regression analysis method as described above is used to calculate and obtain the characteristic parameters of the Alpha stable distribution used to characterize its impact characteristics.

[0299] Step 3: Use the hypothesis test method to verify the goodness of fit of the established Alpha stable distribution. The specific process is: establish a hypothesis test as shown in formula (8), where H 0 is the null hypothesis, H 1 is the alternative hypothesis; based on the established Alpha stable distribution used to characterize the impact characteristics of rolling bearings at the current stage, 200 data resamplings are performed, and 20480 data points are obtained each time; a test statistic is established, and the test statistic values ​​of the currently collected vibration data samples and the resampled data are calculated respectively, and the p-value is calculated accordingly; the significance level of the hypothesis test is set to 0.05, and if the p-value is greater than the significance level threshold, the null hypothesis H is accepted. 0 , it is considered that the goodness of fit meets the requirements, otherwise H 0 .

[0300] Step 4: For the Alpha stable distribution whose goodness of fit is lower than the set significance level threshold, the characteristic parameters of the Alpha stable distribution are optimized through the parameter correction strategy. The specific operation is: optimize the regression operator by reducing the parameter search step size and expanding the parameter search space at the same time, thereby re-estimating and updating the characteristic parameters. The goodness of fit test results after parameter optimization are as follows: Figure 4 shown.

[0301] Step 5: According to formula (12), the impact component probability distribution measurement criteria are set, and the Alpha stable distribution of the rolling bearing at the current moment is compared with that at the initial moment. The fluctuation value of the impact component probability distribution is quantified and used as the state monitoring indicator during the operation of the rolling bearing. The results are as follows: Figure 5 shown.

[0302] Step 6: By analyzing the fluctuation value of the probability distribution of the impact component, the operating status of the rotating mechanical equipment is determined. The specific steps are as follows:

[0303] The first 200 probability distribution fluctuation values ​​of the impact components are selected as the monitoring results of the rolling bearing under normal conditions, and the 3σ threshold interval is set. The results are as follows: Figure 5 According to the 3σ criterion, the running state of the rolling bearing showed abnormal fluctuations in the 533rd data collection period, and the impact component increased, indicating that the rolling bearing may have an early failure at this time.

[0304] In order to verify the accuracy of the above condition monitoring results, the square envelope spectrum analysis method is used to analyze the rolling bearing vibration data samples of the 533rd and adjacent periods. The results are as follows: Figure 6 As shown. Figure 6 (c) It can be seen that starting from the 533rd data collection period, the characteristic frequency f of the outer ring fault of the rolling bearing o and its double frequency components begin to appear in the square envelope spectrum, indicating that the rolling bearing has already experienced an early local fault. This verifies that the rotating machinery state monitoring method based on the impact component probability distribution measurement provided by the present invention has a strong sensitivity to early faults.

[0305] In order to verify the condition monitoring performance of the method provided by the present invention, it is compared with the currently more commonly used condition monitoring indicators such as kurtosis, root mean square, Hoyer index, L2 / L1 norm, negative entropy, smoothness index and Gini coefficient. The rolling bearing degradation curves depicted by the above different indicators are shown in Figure 2. Figure 7 As shown, when a local fault occurs in the rolling bearing and gradually intensifies, the above-mentioned comparison indicators all experience violent fluctuations to varying degrees, and the degradation curve shows a trend of first rising and then falling, which is unfavorable for the subsequent remaining service life prediction based on the state indicators and the formulation of operation and maintenance plans. The degradation curve obtained by the method provided by the present invention has an obvious trend, which can provide favorable conditions for the subsequent failure prediction of rolling bearings. In addition, in order to verify the sensitivity of the above-mentioned different indicators to the early failure of rolling bearings, the indicator calculation results of the first 200 data samples are used to set the 3σ threshold interval, and the fault initial point detection results are shown in Table 1. The fault initial point detection results of the method provided by the present invention are the same as the root mean square, and are better than the detection results of other comparison indicators, which verifies its effectiveness in rolling bearing state monitoring.

[0306] Table 1 Fault initial points detected by different methods

[0307]

[0308] In addition to verifying the sensitivity of different indicators to early failure of rolling bearings, Figure 7 The trend of rolling bearing degradation curves obtained by different monitoring indicators is quantitatively analyzed. The results are as follows Figure 8 It can be seen that the rolling bearing state monitoring result obtained by the rotating machinery state monitoring method based on the probability distribution measurement of the impact component provided by the present invention has excellent predictable trend, which can provide favorable conditions for the subsequent prediction of the remaining service life of the rolling bearing based on the state index and the formulation of the operation and maintenance plan.

Claims

1. A rotating machinery state monitoring method based on the probability distribution measurement of the impact component, characterized in that: The following steps are involved: 1) Use sensors to collect vibration data during the operation of rotating machinery; 2) The vibration data of the rotating machinery during operation is processed using the regression analysis method to obtain the characteristic parameters of the Alpha stable distribution used to characterize the impact characteristics of the vibration data of the rotating machinery; 3) Use the hypothesis test method to perform a goodness of fit test on the Alpha stable distribution. If the goodness of fit is less than the hypothesis test significance level ζ, use the parameter correction method to optimize the characteristic parameters of the Alpha stable distribution, update the Alpha stable distribution, and repeat step 3); if the goodness of fit is greater than or equal to the hypothesis test significance level ζ, proceed to step 4); 4) Setting the measurement criteria for the probability distribution of the impact component, comparing the Alpha stable distribution of the rotating machinery at the current moment with that at the initial moment, and quantifying the fluctuation value of the probability distribution of the impact component; 5) Analyze the probability distribution fluctuation value of the impact component of the rotating machinery at different operating times to determine the operating status of the rotating machinery; The characteristic parameters of the Alpha stable distribution include characteristic index α, dispersion coefficient γ, symmetry parameter β and position parameter δ; The operating state of the rotating machinery includes normal and abnormal; when the fluctuation value Θ(x, h) of the probability distribution of the impact component is less than or equal to the preset fluctuation threshold 3σ, the operating state of the rotating machinery is normal; when the fluctuation value Θ(x, h) of the probability distribution of the impact component is greater than the preset fluctuation threshold 3σ, the operating state of the rotating machinery is abnormal; When the rotating machinery is in an abnormal operating state, the square envelope spectrum analysis method is used to analyze the rotating machinery vibration data and verify the rotating machinery operating state; The method for verifying abnormal state monitoring results using the square envelope spectrum analysis method includes: performing square envelope spectrum analysis on abnormal state vibration data, and if the fault characteristic frequency and its frequency multiple components of the rotating machinery parts appear in the square envelope spectrum, the corresponding parts are faulty.

2. A rotating machinery state monitoring method based on impact component probability distribution measurement according to claim 1, characterized in that: The steps of obtaining characteristic parameters of the Alpha stable distribution for describing the impact characteristics of the rotating machinery vibration data include: 1) Establish the Alpha stable distribution characteristic function φ(t), that is: φ(t)=exp{jδt-γ|t| α ·[1+jβsgn(t)ω(t,α)]} (1) Wherein, α is the characteristic index, and 0<α≤2, which is used to characterize the significance of the signal impact characteristics; β is the symmetry parameter, and -1≤β≤1; δ is the location parameter; γ is the dispersion coefficient, and γ>0, which is used to characterize the dispersion degree of the Alpha stable distribution around the location parameter; j is the imaginary unit; t is the time; Among them, the parameters ω(t,α) and the parameters sgn(t) are as follows: 2) Convert formula (1) into a linear expression, namely: log(-log|φ(t)| 2 )=log(2γ)+αlog|t| (4) 3) For the regression operator y(t)=log[-log|φ(t)| 2 ] A regression analysis is performed on the parameter ψ(t)=log|t| as shown in formula (5), thereby obtaining estimated values ​​of the characteristic index α and the dispersion coefficient γ; y k (t)=log(2γ)+αψ k (t)+e k (5) In the formula, ε k is the error term after the kth iteration; the subscript k is the number of regression analysis iterations; 4) For the regression operator z(u i )=g(u i )+πk(u i ) about the real number u i and parameter sgn(u i )|u i | α Perform regression analysis as shown in formula (6) to obtain the estimated values ​​of the symmetry parameter β and the location parameter δ; k(u i ) is about u i Function of Where η i is the error term after the i-th iteration, u i is a real number; Among them, the inverse tangent function g(u i ) is as follows: g(u i )=arctan{Im[φ(u i )] / Re[φ(u i )]} (7) In the formula, Re[φ(u i )] and Im[φ(u i )] are the functions φ(u i )'s real and imaginary parts.

3. The rotating machinery state monitoring method based on the probability distribution measurement of the impact component according to claim 1 is characterized in that: The steps of using hypothesis testing method to test the goodness of fit of Alpha stable distribution include: 1) Establish a hypothesis test based on the Alpha stable distribution, namely: In the formula, is the probability distribution function of the collected vibration data x; is the probability distribution function of the corresponding Alpha stable distribution estimated by the characteristic parameters; H0 and H1 represent the null hypothesis and the alternative hypothesis respectively; 2) Resample the data B times according to the Alpha stable distribution to obtain the sample signal sequence Each signal contains N sampling points; is the sample signal obtained by the B-th data resampling; 3) Establish the test statistic T(X) and calculate the vibration data x and the resampled signal X respectively * The test statistic values ​​of R (x) and B is the number of data resampling based on the Alpha stable distribution; 4) Calculate the goodness of fit of the Alpha stable distribution Right now: Among them, the activation function κ(x) is as follows: 5) Set the significance level ζ of the hypothesis test to judge the goodness of fit Is it less than the significance level ζ of the hypothesis test? If so, the parameter correction method is used to optimize the characteristic parameters of the Alpha stable distribution, thereby updating the Alpha stable distribution.

4. A rotating machinery state monitoring method based on impact component probability distribution measurement according to claim 3, characterized in that: Resampled signal obtained according to Alpha stable distribution The length of is consistent with the length of the vibration data x.

5. The rotating machinery state monitoring method based on the probability distribution measurement of the impact component according to claim 1 is characterized in that: The steps of optimizing the characteristic parameters of the Alpha stable distribution using the parameter correction method include: 1) Reduce the parameter search step size and expand the parameter search space to optimize the regression operator y(t) = log[-log|φ(t)| 2 ], and then update the estimated values ​​of the characteristic index α and the dispersion coefficient γ; 2) Use the same parameter search step size and parameter search space as step 1) to optimize the regression operator z(u i )=g(u i )+πk(u i ), and then update the estimated values ​​of the symmetry parameter β and location parameter δ.

6. The rotating machinery state monitoring method based on the probability distribution measurement of the impact component according to claim 1 is characterized in that: The steps of quantifying the fluctuation value of the probability distribution of the impact component include: 1) Align the Alpha stable distribution corresponding to the current moment and the initial moment through translation transformation, that is: Dm=m c -μ0 (11) In the formula, μ c and μ0 represent the symmetric center of the Alpha stable distribution obtained at the current moment and the initial moment respectively; 2) Set the probability distribution criterion of the impact component f(x,h), that is: Where h is the amplitude boundary of the impact component; p c and p0 represent the probability density functions at the current time and the initial time respectively, and ε is the set minimum value; 3) Calculate the fluctuation value Θ(x,h) of the probability distribution of the impact component, that is: Θ(x,h)=f c (x,h)-f0(x,h) (13) In the formula, f c (x,h) and f0(x,h) are the impact probability distribution functions at the current moment and the initial moment respectively.

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