CN115758260B - Mechanical equipment state detection method based on Gaussian mixture model - Google Patents

Mechanical equipment state detection method based on Gaussian mixture model Download PDF

Info

Publication number
CN115758260B
CN115758260B CN202310012418.3A CN202310012418A CN115758260B CN 115758260 B CN115758260 B CN 115758260B CN 202310012418 A CN202310012418 A CN 202310012418A CN 115758260 B CN115758260 B CN 115758260B
Authority
CN
China
Prior art keywords
model
state
gaussian mixture
parameters
mixture model
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Active
Application number
CN202310012418.3A
Other languages
Chinese (zh)
Other versions
CN115758260A (en
Inventor
靳亚强
饶猛
刘立斌
左明健
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Qingdao Mingsiwei Technology Co ltd
Original Assignee
Qingdao Mingsiwei Technology Co ltd
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Qingdao Mingsiwei Technology Co ltd filed Critical Qingdao Mingsiwei Technology Co ltd
Priority to CN202310012418.3A priority Critical patent/CN115758260B/en
Publication of CN115758260A publication Critical patent/CN115758260A/en
Application granted granted Critical
Publication of CN115758260B publication Critical patent/CN115758260B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T90/00—Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation

Landscapes

  • Testing Of Devices, Machine Parts, Or Other Structures Thereof (AREA)

Abstract

The invention relates to the technical field of equipment state detection, in particular to a mechanical equipment state detection method based on a Gaussian mixture model, which comprises the following steps: the method comprises the steps of firstly, carrying out RMS on a vibration signal section of the whole life of mechanical equipment to obtain a sample of a model; step two: performing mixed Gaussian distribution modeling; step three: estimating model parameters; step four: determining the distribution number in the Gaussian mixture model; step five: the parameters of the GMM model and the number of the distributions thereof are analyzed, the detection of the partition for determining the mechanical health state and the health state thereof is realized, the health threshold is calculated by utilizing the degradation characteristic distribution form from the statistical viewpoint, and the defect of poor universality of the traditional calculation method is overcome.

Description

Mechanical equipment state detection method based on Gaussian mixture model
Technical Field
The invention relates to the technical field of equipment state detection, in particular to a mechanical equipment state detection method based on a Gaussian mixture model.
Background
Currently, industrial scenes are driven by reduced cost and reduced time requirements. Failure to degrade mechanical equipment typically results in downtime of the overall system, thereby reducing the reliability and availability of the system. This in turn increases production downtime, with significant economic loss and even possible worker safety risks. In this context, it is extremely important to perform effective intelligent operation and maintenance, state monitoring and fault diagnosis on the mechanical equipment.
State monitoring techniques based on vibration signal analysis have irreplaceable advantages over other state detection techniques such as acoustic analysis, thermal imaging analysis, etc., such as well known signal vibration characteristics, sophisticated signal processing techniques, and various commercial sensor supports that may be used for different operating conditions. Based on ISO 10816 file guidance, the health status of a mechanical device may be divided into four regions according to the vibration of the mechanical device itself: zone a (where vibrations of newly serviced machines typically fall), zone B (where vibrations are typically long-term operation without restriction), zone C (where long-term continuous operation is not satisfactory, maintenance is required for a suitable time), zone D (where continued operation is severe enough to cause damage to the machine). It is a problem how to reliably calculate the threshold for different devices to achieve the health zone division.
Disclosure of Invention
The invention aims to solve the technical problems that: the method for detecting the state of the mechanical equipment based on the Gaussian mixture model is provided for overcoming the defects of the prior art.
The invention adopts the technical proposal for solving the technical problems that: the method for detecting the state of the mechanical equipment based on the Gaussian mixture model comprises the following steps:
the method comprises the steps of firstly, carrying out RMS on a vibration signal section of the whole life of mechanical equipment to obtain a sample of a model;
step two: performing mixed Gaussian distribution modeling;
step three: estimating model parameters;
step four: determining the distribution number in the Gaussian mixture model;
step five: and analyzing parameters and the distribution number of the GMM model to realize detection of the partition and the health state of the machine.
In the first step, the formula of the RMS sequence is as follows:
Figure 931548DEST_PATH_IMAGE001
wherein Y (t, n) is a device lifetime time domain segmented signal, t is a time index, t=1, 2,3 … … L; n is a segment index, n=1, 2,3 … … N; l, N are natural numbers.
The second step comprises the following substeps:
2-1: sequence RMS n The probability density of (2) is modeled into a mixed Gaussian model, and a joint probability density function is calculated
Figure 966369DEST_PATH_IMAGE002
；
2-2: calculate the set C of all RMSs for the same health state k Probability density function below
Figure 360441DEST_PATH_IMAGE003
；
2-3: representing parameters in the model as theta, and calculating Gaussian mixture modelLog likelihood function
Figure 319170DEST_PATH_IMAGE004
；
2-4: calculating the cause
Figure 803503DEST_PATH_IMAGE004
Maximum individual parameters
Figure 822275DEST_PATH_IMAGE005
。
The joint probability density function in the 2-1
Figure 703643DEST_PATH_IMAGE006
The calculation formula is as follows:
Figure 653013DEST_PATH_IMAGE007
in the method, in the process of the invention,
Figure 569017DEST_PATH_IMAGE008
is a coefficient of the hybrid model, and
Figure 227531DEST_PATH_IMAGE009
k=1, 2,3 … … K, K being a natural number,
Figure 541401DEST_PATH_IMAGE010
for the set of all RMS under the kth state of health, probability density function under each state of health
Figure 841933DEST_PATH_IMAGE011
Belonging to the same gaussian distribution.
The set C of all RMSs of the same health state in the 2-2 k Probability density function below
Figure 64973DEST_PATH_IMAGE012
The calculation formula is as follows:
Figure 159968DEST_PATH_IMAGE013
in the method, in the process of the invention,
Figure 15928DEST_PATH_IMAGE014
is the average of all samples in the kth state of health,
Figure 808566DEST_PATH_IMAGE015
is a health state set
Figure 168003DEST_PATH_IMAGE010
Standard deviation of all samples.
Three parameters are included in the 2-3 model
Figure 699479DEST_PATH_IMAGE016
Expressed as
Figure 229686DEST_PATH_IMAGE017
Log likelihood function of gaussian mixture model
Figure 340861DEST_PATH_IMAGE018
Expressed as:
Figure 820384DEST_PATH_IMAGE020
where p is the probability.
The third step comprises the following substeps:
3-1: initializing a parameter theta;
3-2: estimating new parameters after the mth iteration
Figure 270564DEST_PATH_IMAGE021
；
3-3: judging whether the convergence criterion is met, if yes, entering a step four, otherwise, returning to the step 3-2 to calculate parameters
Figure 835537DEST_PATH_IMAGE022
。
In 3-2, parameters after the mth iteration
Figure 219245DEST_PATH_IMAGE021
The formula is as follows:
Figure 802542DEST_PATH_IMAGE023
Figure 675820DEST_PATH_IMAGE024
Figure 728090DEST_PATH_IMAGE025
。
in 3-3, the convergence criterion is to calculate whether the difference between two adjacent log likelihood functions is smaller than a preset threshold thr, and the formula is as follows:
Figure 400642DEST_PATH_IMAGE026
。
in the fourth step, the BIC criterion is used to determine the optimal distribution number, the calculation formula is as follows,
Figure 854757DEST_PATH_IMAGE027
。
compared with the prior art, the invention has the following beneficial effects:
the invention provides a mechanical equipment state detection method based on a Gaussian mixture model, which is used for GMM modeling on probability density of a specific time domain index. For each index value, the probability of fit for different classes can be calculated, with the data in the same class having the same gaussian parameters, representing the same state. In this way, the fault can be detected by the occurrence of a second gaussian, and the health status can be partitioned by the gaussian distribution parameter and the gaussian number. Therefore, the health threshold is calculated by utilizing the degradation characteristic distribution form from the statistical viewpoint, and the defect of poor universality of the traditional calculation method is overcome.
Drawings
FIG. 1 is a schematic diagram of device health zone partitioning based on a Gaussian mixture model.
FIG. 2 is a flow chart of a device health area threshold calculation based on a Gaussian mixture model of the present invention.
FIG. 3 shows the number of model distributions at minimum BIC values.
Detailed Description
Embodiments of the present invention are further described below with reference to the accompanying drawings.
Examples
As shown in fig. 1 to 3, the method for detecting the state of the mechanical equipment based on the gaussian mixture model comprises the following steps:
the method comprises the steps of firstly, carrying out RMS on a vibration signal section of the whole life of mechanical equipment to obtain a sample of a model;
in the first step, the formula of the RMS sequence is as follows:
Figure 633357DEST_PATH_IMAGE001
wherein Y (t, n) is a device lifetime time domain segmented signal, t is a time index, t=1, 2,3 … … L; n is a segment index, n=1, 2,3 … … N; l, N are natural numbers. RMS (root mean square) n The value may be considered as N samples. Other features that may characterize degradation of the mechanical device are also possible.
Step two: performing mixed Gaussian distribution modeling; the second step comprises the following substeps:
2-1: sequence RMS n Is modeled as a mixture Gaussian model combining probability density functions
Figure 891032DEST_PATH_IMAGE002
The method is characterized by comprising the following steps:
Figure 413280DEST_PATH_IMAGE007
in the method, in the process of the invention,
Figure 987481DEST_PATH_IMAGE008
is a coefficient of the hybrid model, and
Figure 159486DEST_PATH_IMAGE009
k=1, 2,3 … … K, K being a natural number,
Figure 920769DEST_PATH_IMAGE010
for the set of all RMS under the kth state of health, probability density function under each state of health
Figure 449970DEST_PATH_IMAGE011
Belongs to the same Gaussian distribution;
2-2: calculate the set C of all RMSs for the same health state k Probability density function below
Figure 862366DEST_PATH_IMAGE012
The calculation formula is as follows:
Figure 248348DEST_PATH_IMAGE013
wherein, the liquid crystal display device comprises a liquid crystal display device,
Figure 965768DEST_PATH_IMAGE014
is the average of all samples in the kth state of health,
Figure 580551DEST_PATH_IMAGE015
is a health state set
Figure 598186DEST_PATH_IMAGE010
Standard deviation of all samples;
2-3: representing parameters in the model as theta, and calculating log-likelihood function of Gaussian mixture model
Figure 420648DEST_PATH_IMAGE004
The method comprises the steps of carrying out a first treatment on the surface of the In particular, there are in the modelThree parameters
Figure 156523DEST_PATH_IMAGE028
Expressed as
Figure 276795DEST_PATH_IMAGE029
Log likelihood function of gaussian mixture model
Figure 414515DEST_PATH_IMAGE018
Expressed as:
Figure 142300DEST_PATH_IMAGE030
in the above formula, p is a probability.
2-4: calculating the cause
Figure 582115DEST_PATH_IMAGE031
Maximum individual parameters
Figure 787968DEST_PATH_IMAGE005
The method comprises the following steps:
Figure 232725DEST_PATH_IMAGE032
。
step three: estimating model parameters; because of the log-likelihood function
Figure 131411DEST_PATH_IMAGE004
In the logarithm, the summation symbol is provided, and the non-derivation is performed
Figure 841878DEST_PATH_IMAGE033
And (5) estimating. We now define the desired maximum algorithm (EM algorithm) from the initial parameters in an iterative manner
Figure 851422DEST_PATH_IMAGE034
And (4) until the likelihood function value changes are within a preset stopping parameter, the convergence can be considered.
The third step comprises the following substeps:
3-1: initializing the parameter θ, a common method of initialization is random allocation, but ensuring non-negativity of the parameter, i.e
Figure 917730DEST_PATH_IMAGE035
The method comprises the steps of carrying out a first treatment on the surface of the Sum-and-sum constraint, i.e.
Figure 721738DEST_PATH_IMAGE036
。
3-2: estimating new parameters after the mth iteration
Figure 919501DEST_PATH_IMAGE021
The formula is as follows:
Figure 982003DEST_PATH_IMAGE023
Figure 948822DEST_PATH_IMAGE024
Figure 923732DEST_PATH_IMAGE025
；
in the method, in the process of the invention,
Figure 577434DEST_PATH_IMAGE037
the posterior probability, specifically, refers to the probability that the RMS value belongs to the kth gaussian distribution; each gaussian represents a set of RMS, representing a state of health.
3-3: judging whether the convergence criterion is met, if yes, entering a step four, otherwise, returning to the step 3-2 to calculate the parameters
Figure 928781DEST_PATH_IMAGE022
。
In 3-3, the convergence criterion is to calculate whether the difference between two adjacent log likelihood functions is smaller than a preset threshold thr, and the formula is as follows:
Figure 15686DEST_PATH_IMAGE026
；
the present embodiment sets the value of thr to
Figure DEST_PATH_IMAGE038
。
Step four: determining the distribution number in a Gaussian mixture model (namely a GMM model); the number of GMM hybrid distributions corresponds to the number of machine states, i.e. the number of damaged phases of the working life of the measured machine system, and therefore the number of distributions must be chosen to describe the data distribution as accurately as possible. In real-time monitoring of the mechanical state, we cannot determine the optimal parameter K. The optimal GMM parameters thus obtained are locally optimal.
In the fourth step, the optimal distribution number is determined by using the BIC criterion (namely the bayesian information criterion), the calculation formula is as follows,
Figure 348447DEST_PATH_IMAGE027
；
in the method, in the process of the invention,
Figure DEST_PATH_IMAGE039
representing log likelihood probabilities. The BIC function increases with the number of model parameters and maximizes the variance error between the likelihood function and the true distribution. Thus, a lower BIC value indicates that the model is more appropriate for the data under consideration. The lower the BIC value, the better. BIC is a function of K, and I gate selects an optimal K to minimize BIC globally. This K value is then the K value we want to find-here "low" is a relative concept, finding the lowest at different K values. The lowest BIC value indicates that K at this time is the optimal K.
Step five: and analyzing parameters of the GMM model and the number of the distribution of the parameters, finding out K with the minimum BIC value as the number of the final health areas, and detecting the subareas for determining the health state of the machine and the health state of the subareas.
Referring to fig. 1, the partitioning of device health areas based on a gaussian mixture model is illustrated. The steps are as follows from left to right: histogram of degradation index, GMM model probability distribution of degradation index and full life degradation index trend. The dashed line of threshold 1 in fig. 1 is the intersection of the first gaussian component and the second gaussian component, and the dashed line of threshold 2 represents the intersection of the second gaussian component and the third gaussian component.
As shown in fig. 3, the optimum K value sequence obtained after modeling the bearing vibration signal full life RMS value density GMM, when k=2, indicates that the RMS value distribution form has begun to appear as a second gaussian component, which indicates that the machine has entered a second healthy area, and may indicate that the machine has vibration abnormality and has failed. When the machine continues to operate, when k=3, indicating that the RMS value distribution pattern has deviated from the second healthy zone, a third state is started.

Claims (8)

1. A method for detecting the state of a mechanical device based on a gaussian mixture model, comprising the steps of:
the method comprises the steps of firstly, carrying out RMS on a vibration signal section of the whole life of mechanical equipment to obtain a sample of a model;
step two: performing mixed Gaussian distribution modeling; the second step comprises the following substeps:
2-1: sequence RMS n The probability density of (2) is modeled into a mixed Gaussian model, and a joint probability density function is calculated
Figure QLYQS_1
；
2-2: calculate the set C of all RMSs for the same health state k Probability density function below
Figure QLYQS_2
；
2-3: representing parameters in the model as theta, and calculating log-likelihood function of Gaussian mixture model
Figure QLYQS_3
；
2-4: calculating the cause
Figure QLYQS_4
Maximum individual parameters->
Figure QLYQS_5
；
Step three: estimating model parameters; the third step comprises the following substeps:
3-1: initializing a parameter theta;
3-2: estimating new parameters after the mth iteration
Figure QLYQS_6
；
3-3: judging whether the convergence criterion is met, if yes, entering a step four, otherwise, returning to the step 3-2 to calculate the parameters
Figure QLYQS_7
；
Step four: determining the distribution number in the Gaussian mixture model; in the fourth step, determining the optimal distribution number by using a BIC criterion;
step five: and analyzing parameters and the distribution number of the GMM model to realize detection of the partition and the health state of the machine.
2. The method of claim 1, wherein in the first step, the RMS sequence is formulated as follows:
Figure QLYQS_8
wherein Y (t, n) is a device lifetime time domain segmented signal, t is a time index, t=1, 2,3 … … L; n is a segment index, n=1, 2,3 … … N; l, N are natural numbers.
3. The method for detecting the state of mechanical equipment based on Gaussian mixture model according to claim 2, wherein the joint probability density function in 2-1
Figure QLYQS_9
The calculation formula is as follows:
Figure QLYQS_10
in the method, in the process of the invention,
Figure QLYQS_11
is a coefficient of the hybrid model, and +.>
Figure QLYQS_12
K=1, 2,3 … … K, K being a natural number,
Figure QLYQS_13
for the set of all RMS under the kth state of health, probability density function under each state of health
Figure QLYQS_14
Belonging to the same gaussian distribution.
4. A method for detecting states of mechanical devices based on Gaussian mixture model according to claim 3, wherein the set C of all RMSs of the same health state in 2-2 k Probability density function below
Figure QLYQS_15
The calculation formula is as follows:
Figure QLYQS_16
in the method, in the process of the invention,
Figure QLYQS_17
is the mean value of all samples in the kth health state,/->
Figure QLYQS_18
Is health status set->
Figure QLYQS_19
Standard deviation of all samples.
5. The method for detecting the state of mechanical equipment based on Gaussian mixture model according to claim 4, wherein the model in the 2-3 model has three parameters
Figure QLYQS_20
Expressed as->
Figure QLYQS_21
Log likelihood function of gaussian mixture model +.>
Figure QLYQS_22
Expressed as:
Figure QLYQS_23
where p is the probability.
6. The method for detecting the state of mechanical equipment based on Gaussian mixture model according to claim 5, wherein in 3-2, parameters after the mth iteration
Figure QLYQS_24
The formula is as follows:
Figure QLYQS_25
。
7. the method for detecting the state of a mechanical device based on a gaussian mixture model according to claim 6, wherein in 3-3, the convergence criterion is to calculate whether the difference between two adjacent log likelihood functions is smaller than a preset threshold thr, and the formula is as follows:
Figure QLYQS_26
。
8. the method for detecting the state of mechanical equipment based on a Gaussian mixture model according to claim 7, wherein the optimal distribution number is determined by using BIC criteria in the fourth step, the calculation formula is as follows,
Figure QLYQS_27
。
CN202310012418.3A 2023-01-05 2023-01-05 Mechanical equipment state detection method based on Gaussian mixture model Active CN115758260B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202310012418.3A CN115758260B (en) 2023-01-05 2023-01-05 Mechanical equipment state detection method based on Gaussian mixture model

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202310012418.3A CN115758260B (en) 2023-01-05 2023-01-05 Mechanical equipment state detection method based on Gaussian mixture model

Publications (2)

Publication Number Publication Date
CN115758260A CN115758260A (en) 2023-03-07
CN115758260B true CN115758260B (en) 2023-07-04

Family

ID=85348192

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202310012418.3A Active CN115758260B (en) 2023-01-05 2023-01-05 Mechanical equipment state detection method based on Gaussian mixture model

Country Status (1)

Country Link
CN (1) CN115758260B (en)

Family Cites Families (8)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN102768115B (en) * 2012-06-27 2016-04-20 华北电力大学 A kind of gearbox of wind turbine health status real-time dynamic monitoring method
CN104702378B (en) * 2013-12-06 2018-03-09 华为技术有限公司 The method for parameter estimation and device of Gaussian mixtures
CN105335759B (en) * 2015-11-12 2019-07-16 南方电网科学研究院有限责任公司 A kind of transformer fault detection method based on generating probability model
CN106127300A (en) * 2016-07-04 2016-11-16 哈尔滨理工大学 A kind of rotating machinery health status Forecasting Methodology
CN107132310B (en) * 2017-03-28 2019-04-30 浙江大学 Transformer equipment health status method of discrimination based on gauss hybrid models
JP7040851B2 (en) * 2018-03-09 2022-03-23 株式会社インテック Anomaly detection device, anomaly detection method and anomaly detection program
CN110135492B (en) * 2019-05-13 2020-12-22 山东大学 Equipment fault diagnosis and abnormality detection method and system based on multiple Gaussian models
CN112326246A (en) * 2020-11-02 2021-02-05 北京航空航天大学 Bearing safety state online monitoring method based on periodic data and nuclear density estimation

Also Published As

Publication number Publication date
CN115758260A (en) 2023-03-07

Similar Documents

Publication Publication Date Title
CN108829933B (en) Method for predictive maintenance and health management of semiconductor manufacturing equipment
US20150219530A1 (en) Systems and methods for event detection and diagnosis
US8989888B2 (en) Automatic fault detection and classification in a plasma processing system and methods thereof
KR100306856B1 (en) Quality management system and recording medium
CN109524139A (en) A kind of real-time device performance monitoring method based on equipment working condition variation
CN112284440B (en) Sensor data deviation self-adaptive correction method
CN112629905A (en) Equipment anomaly detection method and system based on deep learning and computer medium
KR20210017651A (en) Method for Fault Detection and Fault Diagnosis in Semiconductor Manufacturing Process
TW202211341A (en) Predicting equipment fail mode from process trace
CN115758260B (en) Mechanical equipment state detection method based on Gaussian mixture model
CN109142979B (en) Method and device for detecting abnormal state of power distribution network
US7921350B2 (en) System and method for fault detection and localization in time series and spatial data
Jin et al. Changepoint-based anomaly detection for prognostic diagnosis in a core router system
CN114046993A (en) Slewing bearing state evaluation method based on multi-feature parameter fusion and FCM-HMM
CN116380496B (en) Automobile door fatigue endurance test method, system and medium
CN117435883A (en) Method and system for predicting equipment faults based on digital twinning
CN116400249A (en) Detection method and device for energy storage battery
US11339763B2 (en) Method for windmill farm monitoring
CN113919225B (en) Environmental test box reliability assessment method and system
CN113591376B (en) Platform door anomaly detection method and device based on curve association segmentation mechanism
KR20230102269A (en) Abnormal condition check method in wafer fabrication equipment and apparatus therefor
CN110210066B (en) Consistency test method for performance degradation data and fault data based on p value
CN111881502A (en) Bridge state discrimination method based on fuzzy clustering analysis
CN117469152B (en) Fluid pump abnormality detection method, fluid pump abnormality detection device, electronic device, and storage medium
US20220392187A1 (en) Image recognition system

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant