Gear health index construction method based on lognormal-normal mixed model

Abstract

The present application relates to a kind of gear health index construction methods based on lognormal-normal mixed model, belong to gear health state evaluation technical field.The method includes: S1: the vibration signal in the full life cycle of gear under specific working condition is collected, and it is carried out noise reduction processing, obtain the full life cycle data after processing;S2: the full life cycle data is carried out exponential transformation;S3: construct lognormal-normal mixed model LNMM;S4: the first N health data of full life cycle data and the data after exponential transformation are input into LNMM, utilize EM algorithm iterative training, obtain the benchmark distribution after estimation;S5: entire full life cycle data and the data after exponential transformation are input into LNMM, utilize EM algorithm iterative training, obtain the distribution of entire life cycle data;S6: the benchmark distribution and the distribution of entire life cycle data are used to calculate distribution coincidence degree value, to construct the health index of gear.

Description

Technical Field

[0001] This invention belongs to the field of gear health status assessment technology, and relates to a method for constructing gear health indicators based on a log-normal-normal hybrid model. Background Technology

[0002] As one of the most commonly used key transmission components in rotating machinery, the health of gears directly affects the operating condition of the equipment. Today, my country's manufacturing industry is booming, and the industrial sector places extreme demands on rotating machinery, such as high loads and high speeds. Complex and harsh working conditions can easily cause gear performance degradation or failures such as pitting, scuffing, wear, and tooth breakage. This can lead to downtime, component damage, and in severe cases, even major casualties. It is clear that the health of gears restricts the reliability, safety, and efficiency of the entire rotating machinery. Therefore, accurately obtaining the health status of gears can effectively ensure the safe and reliable operation of rotating machinery, thereby improving production efficiency and preventing catastrophic accidents.

[0003] The health status of gears can be reflected by constructing health indicators. Current methods for constructing health indicators can be done unsupervised by considering differences in data distribution. Gaussian mixture models are used to estimate the distribution of gear data, and then distance metrics are used to measure the differences between distributions, thereby constructing the gear health indicators. However, Gaussian mixture models can only estimate the distribution from a single data domain, and the distribution characteristics in a single data domain cannot fully reflect the health status and degradation trend of gears. Therefore, it is necessary to extract additional degradation features from other data domains to fully and effectively characterize the health status of gears. Thus, it is particularly important to research a health indicator construction method that can simultaneously mine distribution characteristics from different data domains. Summary of the Invention

[0004] In view of this, the purpose of this invention is to provide a method for constructing gear health indicators based on a log-normal-normal hybrid model, thereby improving the applicability of constructing gear health indicators.

[0005] To achieve the above objectives, the present invention provides the following technical solution:

[0006] A method for constructing gear health indicators based on a log-normal-normal mixture model includes the following steps:

[0007] S1: Vibration signals of the gear throughout its entire life cycle under specific operating conditions are collected using an installed accelerometer. Noise reduction methods are then used to process the collected vibration signals, resulting in the processed full life cycle data X = (x1, x2, ..., x...). M ) T, where x i =(x1,x2,…,x m ), where m is the data length of a single sample, and M is the total number of samples throughout the entire lifecycle;

[0008] S2: Perform an exponential transformation on the denoised full lifecycle data to obtain the exponentially transformed data as X′=(x′1,x′2,…,x′). M ) T , x′ i =(x′1,x′2,…,x′) m );

[0009] S3: Construct a lognormal-normal mixture model (LNMM);

[0010] S4: Convert the noise-reduced full lifecycle data X = (x1, x2, ..., x...) M ) T The data after exponential transformation are X′=(x′1,x′2,…,x′) M ) T The first N health data are input into the constructed LNMM, and the expectation-maximization algorithm (EM) is used for iterative training. After multiple iterations of training, the EM algorithm converges and the estimated baseline distribution P0 is obtained.

[0011] S5: Input the entire lifecycle data and the data after exponential transformation into the constructed LNMM, and perform iterative training using the EM algorithm; after multiple iterative updates and training, the EM algorithm converges, obtaining the distribution P = (P1, P2, ..., P...) of the entire lifecycle data. M );

[0012] S6: Using the baseline distribution P0 and the distribution of the entire lifecycle data P = (P1, P2, ..., P...) M To calculate the distribution overlap value H i The calculation formula is as follows:

[0013] H i =1-S i i = 1, 2, ..., M

[0014] Among them, S i Let the baseline distribution P0 and the distribution P be... i The area of ​​the overlapping region between them;

[0015] S7: Use the distribution overlap ratio value calculated in step S6 to construct the gear health index. The constructed health index is H = (H1, H2, ..., H...). M ).

[0016] Furthermore, in step S3, the probability density function P(x,x′|θ) of the constructed LNMM is defined as follows:

[0017]

[0018] Where x represents the original data, i.e., the full lifecycle data after noise reduction; x′ represents the data after exponential transformation; K and L represent the number of normal and log-normal distributions, respectively; α k and α l All are positive weight coefficients, and satisfy the following conditions:

[0019] Let be the normal density function, defined as follows:

[0020]

[0021] in, θ k Let μ represent the parameter set of the k-th normal distribution sub-model. k This represents the mean of the k-th normally distributed sub-model. This represents the variance of the k-th normally distributed sub-model.

[0022] φ(x′|θ l Let be the log-normal density function, defined as follows:

[0023]

[0024] in, θ l Let μ represent the parameter set of the l-th log-normal distribution sub-model. l Let represent the mean of the l-th log-normal distribution sub-model. Let represent the variance of the l-th log-normal distribution sub-model.

[0025] Furthermore, in step S4 or S5, the parameter estimation of LNMM is implemented using the EM algorithm. Specifically, the steps for iterative training using the EM algorithm are as follows:

[0026] 1) Start iterating with the initial values ​​of the given parameters;

[0027] 2) Step E: Based on the current model parameters, calculate the normal distribution sub-model k for each pair of original data x. j responsiveness The log-normal distribution sub-model l is used to compare the data x′ after exponential transformation. j responsiveness The calculation formula is:

[0028]

[0029]

[0030] 3) M-step: Calculate the model parameters for the new iteration. The calculation formula is:

[0031]

[0032]

[0033]

[0034]

[0035]

[0036]

[0037] 4) Repeat steps 2) and 3) until the expectation-maximization algorithm converges.

[0038] The beneficial effects of this invention are that it is superior to other unsupervised health indicator construction methods and is more suitable for the health indicator construction task of gears.

[0039] Other advantages, objectives, and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination, or may be learned from practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description

[0040] To make the objectives, technical solutions, and advantages of the present invention clearer, the preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings, wherein:

[0041] Figure 1 This is a flowchart of the gear health index construction method based on the log-normal-normal mixture model of the present invention;

[0042] Figure 2 This is a schematic diagram of a gear contact fatigue testing bench;

[0043] Figure 3 The gear index is constructed using the method of the present invention. Detailed Implementation

[0044] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Unless otherwise specified, the following embodiments and features can be combined with each other.

[0045] The accompanying drawings are for illustrative purposes only and are schematic diagrams, not actual pictures. They should not be construed as limiting the invention. To better illustrate the embodiments of the invention, some parts in the drawings may be omitted, enlarged, or reduced, and do not represent the actual product dimensions. It is understandable to those skilled in the art that some well-known structures and their descriptions may be omitted in the drawings.

[0046] In the accompanying drawings of the embodiments of the present invention, the same or similar reference numerals correspond to the same or similar components. In the description of the present invention, it should be understood that if terms such as "upper," "lower," "left," "right," "front," and "rear" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, they are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, the terms used to describe positional relationships in the drawings are only for illustrative purposes and should not be construed as limiting the present invention. For those skilled in the art, the specific meaning of the above terms can be understood according to the specific circumstances.

[0047] Please see Figures 1-3 This invention provides a method for constructing gear health indicators based on a log-normal-normal mixed model, such as... Figure 1 As shown, the specific steps are as follows:

[0048] Step 1: Use the installed accelerometer to collect vibration signals of the gear throughout its entire life cycle under specific operating conditions. The collected vibration signals are then processed using noise reduction methods. The processed life cycle data is X = (x1, x2, ..., x...). M ) T , where x i =(x1,x2,…,x m M represents the total number of samples throughout the entire lifecycle, and m represents the data length of a single sample.

[0049] Step 2: Perform an exponential transformation on the obtained full lifecycle data to obtain the exponentially transformed data as X′=(x1′,x′2,…,x′) M ) T , x′i =(x′1,x′2,…,x′) m ).

[0050] Step 3: Construct a Lognormal-Normal mixture model (LNMM) with K normal distribution components and L lognormal distribution components.

[0051] Building LNMM:

[0052] Gaussian mixture models can estimate the data distribution in a single data domain from the perspective of a normal distribution. However, the distribution characteristics in a single data domain cannot fully represent the health status and degradation process of mechanical equipment. Therefore, it is crucial to explore a new mixture model to extract more degradation characteristics from two data domains. In this invention, a log-normal-normal mixture model is designed to estimate the data distribution from two data domains, including the original data and the data after exponential transformation. The probability density function of this mixture model is defined as follows:

[0053]

[0054] Where x represents the original data, i.e., the full lifecycle data after noise reduction; x′ represents the data after exponential transformation; K and L represent the number of normal and log-normal distributions, respectively; and α is a positive weighting coefficient that satisfies...

[0055] Let be the normal density function, defined as follows:

[0056]

[0057] Let log-normal density function be defined as follows:

[0058]

[0059] Step 4: Convert the denoised original data X = (x1, x2, ..., x...) M ) T The data after exponential transformation are X′=(x′1,x′2,…,x′) M ) T The first N health data points are input into the constructed LNMM, and the EM algorithm is used for iterative training. After multiple iterations and updates, the EM algorithm converges, and the estimated baseline distribution P0 is obtained.

[0060] Parameter estimation of the log-normal-normal mixture model is achieved using the expectation-maximization (EM) algorithm. The steps of the EM algorithm for parameter estimation of the log-normal-normal mixture model are as follows:

[0061] 1) Start iterating with the initial values ​​of the given parameters;

[0062] 2) Step E: Based on the current model parameters, calculate the normal distribution sub-model k for each pair of original data x. j The responsiveness and log-normal distribution model l for the exponentially transformed data x′ j Response rate:

[0063]

[0064]

[0065] 3) M-step: Calculate the model parameters for the new iteration. The calculation formula is:

[0066]

[0067]

[0068]

[0069]

[0070]

[0071]

[0072] 4) Repeat steps 2) and 3) until the expectation-maximization algorithm converges.

[0073] Step 5: Input both the original data and the data after exponential transformation into the constructed LNMM, and perform iterative training using the EM algorithm. After multiple iterative training updates, the EM algorithm converges, obtaining the distribution P = (P1, P2, ..., P...) of the entire lifecycle data. M ).

[0074] Step 6: Utilize the baseline distribution P0 and the distribution of the entire lifecycle data P = (P1, P2, ..., P...) M To calculate the distribution overlap value H i The calculation formula is as follows:

[0075] H i =1-S i i = 1, 2, ..., M

[0076] Among them, S i Let the baseline distribution P0 and the distribution P be... iThe area of ​​the overlapping region between them.

[0077] Step 7: Use the calculated distribution overlap values ​​to construct a health index for the gears. The constructed health index is H = (H1, H2, ..., H...). M ).

[0078] The effectiveness of the method will be demonstrated through specific experiments below.

[0079] The gear life-cycle vibration signal data used in this experiment came from the cylindrical gear contact fatigue testing rig at the Gear Design Centre of Newcastle University, UK. The structural diagram of this testing rig is shown below. Figure 2 As shown. The gear contact fatigue testing bench mainly includes an electrical control system, a gear transmission platform, a cooling system, and an operating system control console. The two pairs of gears in the test bench are located in two separate gearboxes, each with independent hydraulic lines to cool the gears and bearings within the gearboxes. This allows for full utilization of both gearboxes; however, the center distance of the test bench cannot be changed; it is a fixed value of 160mm. The sampling rate of the gear vibration signal is 25kHz, the sampling time is 0.2s, and the sampling interval is 1min.

[0080] The above is a proposed method for constructing gear health indicators based on a log-normal-normal hybrid model. The following is a demonstration of the effectiveness of the method through specific experiments.

[0081] The gear life-cycle vibration signal data used in this experiment came from the cylindrical gear contact fatigue testing rig at the Gear Design Centre of Newcastle University, UK. The structural diagram of this testing rig is shown below. Figure 2 As shown. The gear contact fatigue testing bench mainly includes an electrical control system, a gear transmission platform, a cooling system, and an operating system control console. The two pairs of gears in the test bench are located in two separate gearboxes, each with independent hydraulic lines to cool the gears and bearings within the gearboxes. This allows for full utilization of both gearboxes; however, the center distance of the test bench cannot be changed; it is a fixed value of 160mm. The sampling rate of the gear vibration signal is 25kHz, the sampling time is 0.2s, and the sampling interval is 1min.

[0082] Comparative experiment:

[0083] To fully demonstrate the superiority of the method of this invention, it is compared with other unsupervised health indicator construction methods, focusing on monotonicity (Mon), correlation (Cor), robustness (Rob), and comprehensive evaluation index (CI). To calculate these evaluation indicators, the health indicator (HI) needs to be decomposed into trend and random terms:

[0084] H(t m )=H T (tm )+H R (t m )

[0085] Wherein, H(t) m ) indicates that at t m Health indicator values ​​at any given time, H T (t m H is its trend term. R (t m The random term is represented by (). Based on the obtained trend term and random term, the formulas for calculating monotonicity, correlation, robustness, and the comprehensive index are as follows:

[0086] 1) Monotonicity:

[0087]

[0088] 2) Correlation:

[0089]

[0090] 3) Robustness:

[0091]

[0092] Among them, dH T For H T The derivative of , where M is the number of health indicators. The parameter λ is a relaxation factor that controls robustness.

[0093] 4) Comprehensive evaluation indicators:

[0094] CI = θ1*Mon + θ2*Cor + θ3*Rob

[0095] Where, θ i Represent a positive number that satisfies Here, θ1, θ2, and θ3 are set to 0.4, 0.3, and 0.3, respectively.

[0096] Here, the first set of gear data is selected for comparative analysis. The comparison results are shown in Table 1. It can be seen from Table 1 that the health index construction method based on the log-normal-normal hybrid model proposed in this invention is superior to other unsupervised health index construction methods. The proposed method is more suitable for the health index construction task of gears.

[0097] Table 1 Evaluation results of different health indicator construction methods

[0098]

[0099] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for constructing gear health indicators based on a log-normal-normal mixed model, characterized in that, The method specifically includes the following steps: S1: Vibration signals of the gear throughout its entire life cycle under specific operating conditions are collected using an installed accelerometer. Noise reduction methods are then used to process the collected vibration signals, resulting in processed full life cycle data. ,in, , m The data length of a single sample. M The number of samples throughout the entire lifecycle; S2: Perform an exponential transformation on the denoised full lifecycle data to obtain the exponentially transformed data. , ; S3: Construct a log-normal-normal mixture model (LNMM); The probability density function of the constructed LNMM The definition is as follows: in, This refers to the original data, i.e., the full lifecycle data after noise reduction; The data is after exponential transformation. and These represent the number of normal distributions and the number of log-normal distributions, respectively. and All are positive weight coefficients, and satisfy the following conditions: ; Let be the normal density function, defined as follows: in, , Indicates the first k The parameter set of a normal distribution sub-model. Indicates the first k The mean of a normally distributed sub-model. Indicates the first k The variance of a normally distributed sub-model; Let log-normal density function be defined as follows: in, , Indicates the first l The parameter set of a log-normal distribution sub-model. Indicates the first l The mean of a log-normal distribution sub-model, Indicates the first l The variance of the log-normal distribution sub-model; S4: The full lifecycle data after noise reduction and data after exponential transformation The former N Health data are input into the constructed LNMM, and the expectation-maximization algorithm is used for iterative training. After multiple iterations and updates, the algorithm converges, and the estimated baseline distribution is obtained. ; S5: Input the entire lifecycle data and the data after exponential transformation into the constructed LNMM, and perform iterative training using the expectation-maximization algorithm; after multiple iterations and updates, the algorithm converges, and the distribution of the entire lifecycle data is obtained. ; S6: Utilizing the baseline distribution Distribution of data throughout the entire lifecycle To calculate the distribution overlap value The calculation formula is as follows: in, As a baseline distribution and distribution The area of ​​the overlapping region between them; S7: Use the distribution overlap value calculated in step S6 to construct a health index for the gears. The constructed health index is... .

2. The method for constructing gear health indicators according to claim 1, characterized in that, In step S4 or S5, the parameter estimation of LNMM is achieved using the expectation-maximization algorithm. Specifically, the steps for iterative training using the expectation-maximization algorithm are as follows: 1) Start iterating with the initial values ​​of the given parameters; 2) E-step: Based on the current model parameters, calculate the normal distribution sub-model respectively. For raw data responsiveness And log-normal distribution sub-model For the data after exponential transformation responsiveness The calculation formula is: 3) M-step: Calculate the model parameters for the new iteration. The calculation formula is: 4) Repeat steps 2) and 3) until the expectation-maximization algorithm converges.

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