Device Performance Degradation Evaluation Method and System Based on Sparse Degradation Modeling

Abstract

The present invention provides a method and system for evaluating the performance degradation of a device based on sparse degradation modeling, including: collecting time-domain vibration data of the device throughout its life cycle by collecting vibration signals at fixed time intervals; converting the vibration data sequence collected during the entire life cycle into the amplitude of the squared envelope spectrum; a health index for the entire life cycle based on the fusion of the amplitudes of the squared envelope spectrum; constructing a sparse degradation convex optimization model based on the matrix of the amplitudes of the squared envelope spectrum of the vibration data throughout the life cycle to automatically determine the weights of the amplitudes of the squared envelope spectrum; solving the weights of the amplitudes of the squared envelope spectrum according to the constructed sparse degradation convex optimization model; calculating HI according to the definition of the health index for the entire life cycle, and performing early fault detection and monotonic degradation evaluation on the entire life cycle of the device. The present invention constructs a full-life health index by adopting a method of fusing the amplitudes of the squared envelope spectrum, and solves the problems of early fault detection and monotonic degradation evaluation in the entire life cycle of the device.

Description

Technical Field

[0001] The present invention relates to the technical field of performance degradation assessment. Specifically, it relates to a method and system for equipment performance degradation assessment based on sparse degradation modeling, and particularly to a method for equipment performance degradation assessment based on the fusion of sparse degradation modeling and squared envelope spectrum. Background Art

[0002] Generally, the strategy for equipment service performance degradation assessment is to construct a full-life-cycle health index to monitor the early faults of the equipment and achieve monotonic degradation assessment. How to construct a suitable full-life-cycle health index to accurately evaluate the equipment degradation level has always been a research hotspot at home and abroad. However, due to the weak early fault characteristics and the existence of strong environmental noise, it is challenging to construct a health index with early fault degradation trend and monotonic degradation trend.

[0003] In the patent document with the publication number CN107356431A, a method for rolling bearing performance degradation assessment based on ADMM and sparse combined learning is disclosed. The method includes the following steps: (1) learning the normal mode of the rolling bearing, and establishing a knowledge base of the normal mode by using the learned knowledge; (2) establishing a quantization index solver based on each knowledge, and solving the quantization index Φ of the detected rolling bearing; (3) analyzing the quantization index Φ to realize the assessment of the rolling bearing performance degradation degree. However, the constructed health index is not interpretable and requires complex feature extraction and combined learning processes.

[0004] In the patent document with the publication number CN108398268A, a method for bearing performance degradation assessment based on stacked denoising autoencoders and self-organizing maps is disclosed, which is used in the field of bearing degradation assessment technology. The present invention solves the problems existing in the construction of traditional HI curves, such as the extraction of degradation features relying on a large amount of expert experience and supervised training, and the label selection relying on manual participation. Six denoising autoencoder mechanisms of the present invention construct a stacked denoising autoencoder to perform multi-layer feature extraction on the original vibration signal data. After the training set data is used to pre-train the network, the parameters are fine-tuned using the BP algorithm. The output 100-dimensional features are input into the SOM network to train the HI corresponding to each time point, and the HI curve of the training set is constructed; the test set data is input into the trained stacked denoising autoencoder and SOM network to obtain the HI at each time point, and the HI curve is constructed; the HI curves of the training set and the test set are respectively smoothed to obtain the smoothed HI curves. The present invention can be applied to the field of bearing performance degradation assessment. However, the constructed health index is not interpretable and requires sample label information.

[0005] Therefore, a new technical solution needs to be proposed to improve the above technical problems. Summary of the Invention

[0006] Aiming at the defects in the prior art, the purpose of the present invention is to provide a device performance degradation evaluation method and system based on sparse degradation modeling.

[0007] According to a device performance degradation evaluation method based on sparse degradation modeling provided by the present invention, the method includes the following steps:

[0008] Step S1: Collect the time-domain vibration data matrix X∈R of the entire life cycle of the device by collecting vibration signals at fixed time intervals, which is expressed as follows: N×A as follows:

[0009]

[0010] where N represents the number of sampling times during the entire life cycle of the device; A represents the number of samples per sampling; χ j,· ∈R 1 ×A represents the vibration sample sequence collected from the device for the j-th time, j = 1, 2…, N; x j,k represents the k-th sample point in the j-th sampling, k = 1, 2,…, A;

[0011] Step S2: Convert the N vibration data sequences into the squared envelope spectrum amplitude SES∈R based on the Hilbert transform and the fast Fourier transform, which is expressed as follows: N×A as follows:

[0012]

[0013] where ses j,k represents the squared envelope spectrum amplitude corresponding to the k-th sample point in the j-th sampling, which is obtained from x j,k obtained by the Hilbert transform and the fast Fourier transform;

[0014] Step S3: Define the health index HI∈R of the entire life cycle based on the fusion of the squared envelope spectrum amplitudes as follows: N×1 is defined as follows:

[0015]

[0016] where hi j , j = 1, 2…, N is the health index at the j-th sampling time point; w∈R A×1 =[w1, w2,…, w A ′ is the weight of the squared envelope spectrum amplitude; w k , k = 1, 2,…, A is the weight of the k-th squared envelope spectrum amplitude in each sampling;

[0017] Step S4: Based on the squared envelope spectrum amplitude matrix SES of the full life cycle vibration data, construct a sparse degradation convex optimization model to automatically determine the weight w of the squared envelope spectrum amplitude;

[0018] Step S5: Solve the weight w of the squared envelope spectrum amplitude according to the sparse degradation convex optimization model constructed in Step S4;

[0019] Step S6: Calculate HI according to the definition of the full life cycle health index in Step S3, and conduct early fault detection and monotonic degradation assessment for the full life cycle of the equipment.

[0020] Preferably, the said Step S2 includes the following steps:

[0021] Step S2.1: First, use the Hilbert transform operation to convert the vibration data sequence of N times into an analytic signal matrix E ∈ R N×A It is expressed as follows:

[0022]

[0023] where, |·| represents the complex modulus symbol; X ∈ R N×A represents the time-domain vibration data matrix of the full life cycle of the equipment; x j,· ∈ R 1×A , j = 1, 2…, N represents the j-th vibration sample sequence collected from the equipment; e j,k represents the analytic signal corresponding to the k-th sample point in the j-th sampling, which is obtained from x j,k by the Hilbert transform; hilbert(·) represents the Hilbert transform operation, and the specific operation formula is as follows:

[0024]

[0025] As can be seen from the above formula, the essence of the Hilbert transform operation is to convolve the original signal x(t) with 1 / πt;

[0026] Step S2.2: Calculate the squared envelope amplitude matrix SE ∈ R of the analytic signal E of the full life cycle vibration data of the equipment N×A as follows:

[0027]

[0028] where, se j,k represents the squared envelope amplitude corresponding to the k-th sample point in the j-th sampling, which is obtained by taking the amplitude square of e j,k ;

[0029] Step S2.3: Based on the fast Fourier transform, calculate the squared envelope spectrum amplitude matrix SES ∈ R of the full life cycle vibration data of the equipment N×AAs follows:

[0030]

[0031] Among them, ses j,k represents the square envelope spectrum amplitude corresponding to the k-th sample point in the j-th sampling, and is obtained by performing a fast Fourier transform on se j,k .

[0032] Preferably, the weight w constructed in step S4 is as follows:

[0033]

[0034] s.t. w'M'B = r

[0035] Mw ≥ 0, Dw ≥ 0, HI = SESw

[0036] j = 1, 2, …, N - 1, ε j ≥ 0

[0037] Among them, ε j = max(hi j - hi j+1 , 0) is a slack variable, representing the monotonicity of the health index difference sequence; c j is the weight of ε j and is set by an arithmetic progression or a geometric progression.

[0038] Preferably, the arithmetic progression calculation of c j is as follows:

[0039]

[0040] c j The geometric progression calculation of is as follows:

[0041] c j = c1·q j-1 , j = 1, …, N - 1

[0042] Among them, c1 is preset as a constant to determine the c j sequence; therefore, the objective term is used to represent the number of non-monotonic health index sequences; if a monotonically increasing health index sequence is expected, then the more zero elements ε j should contain, the better, that is, the sparser; r is the weight sum of the square envelope spectrum amplitude; λ is a hyperparameter; M ∈ R A×A is a diagonal matrix, and its diagonal elements are determined according to the trend of the square envelope spectrum amplitude; if the square envelope spectrum amplitude at a certain frequency has an increasing trend, the corresponding diagonal element of M is 1, otherwise it is -1; D ∈ R (N-1)×Adenotes the square envelope spectrum amplitude difference matrix, and the specific expression is as follows:

[0043]

[0044] The first constraint w'M'B = r represents the weighted sum of the square envelope spectrum amplitudes, and the specific expression is as follows:

[0045]

[0046] The second constraint Mw ≥ 0 restricts the sign of the weights of the square envelope spectrum amplitudes, and the specific expression is as follows:

[0047]

[0048] The third constraint Dw ≥ 0 restricts the consistency between the square envelope spectrum amplitude differences and the signs of the weights of the square envelope spectrum amplitudes, and the specific expression is as follows:

[0049]

[0050] The present invention also provides a device performance degradation evaluation system based on sparse degradation modeling. The system includes the following modules:

[0051] Module M1: Collect the time-domain vibration data matrix X ∈ R of the entire life cycle of the device by collecting vibration signals at fixed time intervals, which is expressed as follows: N×A , which is expressed as follows:

[0052]

[0053] where N represents the number of sampling times during the entire life cycle of the device; A represents the number of samples per sampling; x j,· ∈ R 1 ×A represents the vibration sample sequence collected from the device for the j-th time, j = 1, 2..., N; x j,k represents the k-th sample point in the j-th sampling, k = 1, 2,..., A;

[0054] Module M2: Convert the N vibration data sequences into square envelope spectrum amplitudes SES ∈ R based on the Hilbert transform and the fast Fourier transform, which is expressed as follows: N×A , which is expressed as follows:

[0055]

[0056] where ses j,k represents the square envelope spectrum amplitude corresponding to the k-th sample point in the j-th sampling, which is obtained from x j,k obtained based on the Hilbert transform and the fast Fourier transform;

[0057] Module M3: The full life cycle health index HI ∈ R based on the fusion of the squared envelope spectrum amplitude N×1 is defined as follows:

[0058]

[0059] where hi j , j = 1, 2…, N is the health index at the j-th sampling time point; w ∈ R A×1 = [w1, w2, …, w A ′ is the weight of the squared envelope spectrum amplitude; w k , k = 1, 2, …, A is the weight of the k-th squared envelope spectrum amplitude in each sampling;

[0060] Module M4: Based on the squared envelope spectrum amplitude matrix SES of the full life cycle vibration data, construct a sparse degradation convex optimization model to automatically determine the weight w of the squared envelope spectrum amplitude;

[0061] Module M5: Solve the weight w of the squared envelope spectrum amplitude according to the sparse degradation convex optimization model constructed by Module M4;

[0062] Module M6: Calculate HI according to the definition of the full life cycle health index of Module M3, and perform early fault detection and monotonic degradation assessment on the full life cycle of the equipment.

[0063] Preferably, the Module M2 includes the following modules:

[0064] Module M2.1: First, use the Hilbert transform operation to convert the vibration data sequence of N times into an analytic signal matrix E ∈ R N×A which is expressed as follows:

[0065]

[0066] where, |·| represents the complex modulus symbol; X ∈ R N×A represents the time-domain vibration data matrix of the full life cycle of the equipment; x j,· ∈ R 1×A , j = 1, 2…, N represents the vibration sample sequence collected from the equipment for the j-th time; e j,k represents the analytic signal corresponding to the k-th sample point in the j-th sampling, which is obtained from x j,k by the Hilbert transform; hilbert(·) represents the Hilbert transform operation, and the specific operation formula is as follows:

[0067]

[0068] As can be seen from the above formula, the essence of the Hilbert transform operation is to convolve the original signal x(t) with 1 / πt;

[0069] Module M2.2: Calculate the squared envelope amplitude matrix SE ∈ R of the analytic signal E of the vibration data over the entire life cycle of the computing device N×A as follows:

[0070]

[0071] where se j,k represents the squared envelope amplitude corresponding to the k-th sample point in the j-th sampling, which is obtained by taking the squared amplitude of e j,k ;

[0072] Module M2.3: Based on the fast Fourier transform, calculate the squared envelope spectrum amplitude matrix SES ∈ R of the vibration data over the entire life cycle of the computing device N×A as follows:

[0073]

[0074] where ses j,k represents the squared envelope spectrum amplitude corresponding to the k-th sample point in the j-th sampling, which is obtained by performing the fast Fourier transform on se j,k ;

[0075] Preferably, the weight w constructed in the module M4 is as follows:

[0076]

[0077] s.t. w'M'B = r

[0078] Mw ≥ 0, Dw ≥ 0, HI = SESw

[0079] j = 1, 2, …, N - 1, ε j ≥ 0

[0080] where ε j = max(hi j - hi j+1 , 0) is a slack variable representing the monotonicity of the health index difference sequence; c j is the weight of ε j and is set by an arithmetic progression or a geometric progression.

[0081] Preferably, the arithmetic progression calculation of the c j is as follows:

[0082]

[0083] c j The geometric progression calculation of c

[0084] c j = c1·q j-1, j = 1, …, N-1

[0085] Among them, c1 is preset as a constant to determine c j sequence; therefore, the target term is used to represent the number of non-monotonic health index sequences; if a monotonically increasing health index sequence is expected, then ε j should contain as many zero elements as possible, that is, the sparser the better; r is the weighted sum of the square envelope spectrum amplitudes; λ is a hyperparameter; M ∈ R A×A is a diagonal matrix, and its diagonal elements are determined according to the trend of the square envelope spectrum amplitude; if the square envelope spectrum amplitude at a certain frequency has an increasing trend, the corresponding diagonal element of M is 1, otherwise it is -1; D ∈ R (N-1)×A represents the square envelope spectrum amplitude difference matrix, and the specific expression is as follows:

[0086]

[0087] The first constraint w'M'B = r represents the weighted sum of the square envelope spectrum amplitudes, and the specific expression is as follows:

[0088]

[0089] The second constraint Mw ≥ 0 restricts the weight sign of the square envelope spectrum amplitude, and the specific expression is as follows:

[0090]

[0091] The third constraint Dw ≥ 0 restricts the consistency between the square envelope spectrum amplitude difference and the weight sign of the square envelope spectrum amplitude, and the specific expression is as follows:

[0092]

[0093] Compared with the prior art, the present invention has the following beneficial effects:

[0094] 1. The present invention constructs a full-life health index by adopting the method of square envelope spectrum amplitude fusion, and solves the problems of early fault detection and monotonic degradation evaluation in the whole life cycle of equipment;

[0095] 2. The present invention automatically determines the weights of the square envelope spectrum amplitudes through a sparse degradation convex optimization model, and solves the problems of manual feature extraction and feature screening;

[0096] 3. The health index constructed by the present invention has a clear mathematical definition and physical interpretability;

[0097] 4. The weights of the square envelope spectrum amplitudes optimized by the present invention can effectively extract sparse equipment fault characteristic frequencies for evaluating the performance degradation of equipment in the whole life cycle. Description of the Drawings

[0098] Other features, objects, and advantages of the present invention will become more apparent from the following detailed description of non - limiting embodiments read in conjunction with the accompanying drawings:

[0099] Figure 1 is a flowchart of the present invention;

[0100] Figure 2 is a schematic diagram of Example 1 of the weights of the full - life - cycle health index and the amplitude of its squared envelope spectrum of the present invention;

[0101] Figure 3 is a schematic diagram of Example 2 of the weights of the full - life - cycle health index and the amplitude of its squared envelope spectrum of the present invention. Detailed Description of the Invention

[0102] The present invention will be described in detail below in conjunction with specific embodiments. The following embodiments will help those skilled in the art to further understand the present invention, but do not limit the present invention in any form. It should be noted that for those of ordinary skill in the art, without departing from the concept of the present invention, several changes and improvements can still be made. These all fall within the protection scope of the present invention.

[0103] The present invention utilizes the sparse characteristics of fault - feature signals on the squared envelope spectrum to propose a method for evaluating equipment performance degradation based on sparse degradation modeling and squared envelope spectrum fusion. This method constructs a sparse degradation evaluation convex optimization model to automatically optimize and determine the weights of the squared envelope spectrum to construct a full - life - cycle health index. Based on the constructed full - life - cycle health index and the optimized envelope - spectrum weights, early fault detection of equipment and evaluation of monotonic degradation trends are realized.

[0104] A method for evaluating equipment performance degradation based on sparse degradation modeling includes the following steps:

[0105] Step S1: Assume that vibration signals are collected at fixed time intervals, and the time - domain vibration data of a device over its full life cycle is collected. The full - life - cycle vibration data matrix X ∈ R N×A is represented as follows:

[0106]

[0107] where N represents the number of sampling times during the full life cycle of the device; A represents the number of samples per sampling; x j,· ∈ R 1 ×A represents the vibration sample sequence collected from the device for the j - th time, j = 1, 2…, N; x j,k represents the k - th sample point in the j - th sampling, k = 1, 2,…, A.

[0108] Step S2: Convert the vibration data sequence of N times into the square envelope spectrum amplitude SES ∈ R based on Hilbert transform and fast Fourier transform N×A , which is expressed as follows:

[0109]

[0110] where ses j,k represents the square envelope spectrum amplitude corresponding to the k-th sample point in the j-th sampling, which is obtained from x j,k and is obtained based on Hilbert transform and fast Fourier transform.

[0111] The specific process is as follows:

[0112] Step S2.1: First, use the Hilbert transform operation to convert the vibration data sequence of N times into an analytic signal matrix E ∈ R N×A , which is expressed as follows:

[0113]

[0114] where |·| represents the complex modulus symbol; X ∈ R N×A represents the time-domain vibration data matrix of the entire life cycle of the device; x j,· ∈ R 1×A , j = 1, 2…, N represents the j-th vibration sample sequence collected from the device; e j,k represents the analytic signal corresponding to the k-th sample point in the j-th sampling, which is obtained from x j,k and is obtained based on Hilbert transform; hilbert(·) represents the Hilbert transform operation, and the specific operation formula is as follows:

[0115]

[0116] As can be seen from the above formula, the essence of the Hilbert transform operation is to convolve the original signal x(t) with 1 / πt.

[0117] Step S2.2: Calculate the square envelope amplitude matrix SE ∈ R of the analytic signal E of the vibration data of the entire life cycle of the device N×A as follows:

[0118]

[0119] where se j,k represents the square envelope amplitude corresponding to the k-th sample point in the j-th sampling, which is obtained by taking the square of the amplitude of e j,k ;

[0120] Step S2.3: Based on the fast Fourier transform, calculate the square envelope spectrum amplitude matrix SES of the vibration data over the entire life cycle of the device as follows:

[0121]

[0122] where ses j,k represents the square envelope spectrum amplitude corresponding to the k-th sample point in the j-th sampling, which is obtained from x j,k obtained based on the Hilbert transform and the fast Fourier transform. Since the square envelope spectrum amplitude of the vibration data sequence collected from the device each time is symmetric, generally only the first half of the square envelope spectrum amplitude is taken.

[0123] Step S3: The health index HI ∈ R over the entire life cycle based on the fusion of the square envelope spectrum amplitude is defined as follows: N×1 is defined as:

[0124]

[0125] where hi j , j = 1, 2…, N represents the health index at the j-th sampling time point; w ∈ R A×1 = [w1, w2, …, w A ′ represents the weight of the square envelope spectrum amplitude; w k , k = 1, 2, …, A represents the weight of the k-th square envelope spectrum amplitude in each sampling.

[0126] Step S4: Based on the square envelope spectrum amplitude matrix SES of the vibration data over the entire life cycle, a sparse degradation convex optimization model is constructed to automatically determine the weight w of the square envelope spectrum amplitude, which is constructed as follows:

[0127]

[0128] s.t. w'M'B = r

[0129] Mw ≥ 0, Dw ≥ 0, HI = SESw

[0130] j = 1, 2, …, N - 1, ε j ≥ 0

[0131] where ε j = max(hi j - hi j+1 , 0) is a slack variable, representing the monotonicity of the health index difference sequence; c j is the weight of ε j , which can be set by an arithmetic progression or a geometric progression;

[0132] c j The arithmetic progression of can be calculated as follows:

[0133]

[0134] c j The geometric progression of c can be calculated as follows:

[0135] c j = c1·q j-1 , j = 1, …, N - 1

[0136] where c1 is pre-set as a constant to determine c j sequence; thus, the target term can be used to represent the number of non-monotonic elements in the health index sequence; if a monotonically increasing health index sequence is desired, then the more zero elements ε j should contain, the better, that is, the sparser the better; thus, ||ε||1 is used to enhance its sparsity to improve the monotonicity of the health index sequence; ||w||1 is used to enhance the sparsity of the squared envelope spectrum amplitude weights; r is the weight sum of the squared envelope spectrum amplitudes, which can usually be set to 1 or other integers; λ is a hyperparameter used to adjust the monotonicity of the health index and the sparsity of the squared envelope spectrum amplitude weights; M ∈ R A×A is a diagonal matrix whose diagonal elements can be determined according to the trend of the squared envelope spectrum amplitudes; if the squared envelope spectrum amplitude at a certain frequency has an increasing trend, the corresponding diagonal element of M is 1, otherwise -1; D ∈ R (N-1)×A represents the squared envelope spectrum amplitude difference matrix, and its specific expression is as follows:

[0137]

[0138] The first constraint w'M'B = r represents the weight sum of the squared envelope spectrum amplitudes, and its specific expression is as follows:

[0139]

[0140] The second constraint Mw ≥ 0 restricts the sign of the squared envelope spectrum amplitude weights, and its specific expression is as follows:

[0141]

[0142] The third constraint Dw ≥ 0 restricts the consistency of the squared envelope spectrum amplitude difference and the sign of the squared envelope spectrum amplitude weights, and is used to further enhance the monotonic degradation trend of the health index. Its specific expression is as follows:

[0143]

[0144] Step S5: Solve for the weight w of the squared envelope spectrum amplitude according to the sparse degradation convex optimization model constructed in step S4.

[0145] Step S6: Calculate the HI according to the definition of the full life cycle health index in Step S3, which is used for early fault detection and monotonic degradation evaluation of the equipment throughout its life cycle.

[0146] The present invention also provides a device performance degradation evaluation system based on sparse degradation modeling, and the system includes the following modules:

[0147] Module M1: Assume that the vibration signals are collected at fixed time intervals, and the time-domain vibration data of a device throughout its life cycle is collected. The vibration data matrix X ∈ R of the device throughout its life cycle is N×A expressed as follows:

[0148]

[0149] where N represents the number of sampling times during the full life cycle of the device; A represents the number of samples in each sampling; x j,· ∈ R 1 ×A represents the vibration sample sequence collected from the device for the jth time, j = 1, 2…, N; x j,k represents the kth sample point in the jth sampling, k = 1, 2,…, A.

[0150] Module M2: Based on the Hilbert transform and the fast Fourier transform, the N-time vibration data sequence is transformed into the squared envelope spectrum amplitude SES ∈ R N×A , which is expressed as follows:

[0151]

[0152] where ses j,k represents the squared envelope spectrum amplitude corresponding to the kth sample point in the jth sampling, which is obtained from x j,k by the Hilbert transform and the fast Fourier transform.

[0153] The specific process is as follows:

[0154] Module M2.1: First, use the Hilbert transform operation to transform the N-time vibration data sequence into an analytic signal matrix E ∈ R N×A which is expressed as follows:

[0155]

[0156] where |·| represents the complex modulus symbol; X ∈ R N×A represents the time-domain vibration data matrix of the device throughout its life cycle; χ j,· ∈ R 1×A , j = 1, 2…, N represents the vibration sample sequence collected from the device for the jth time; e j,kdenotes the analytic signal corresponding to the k-th sample point in the j-th sampling, which is obtained from x j,k and is obtained by the Hilbert transform; hilbert(·) represents the Hilbert transform operation, and the specific operation formula is as follows:

[0157]

[0158] As can be seen from the above formula, the essence of the Hilbert transform operation is to convolve the original signal x(t) with 1 / πt.

[0159] Module M2.2: Calculate the squared envelope amplitude matrix SE ∈ R of the vibration data of the whole life cycle of the computing device N×A as follows:

[0160]

[0161] where, se j,k denotes the squared envelope amplitude corresponding to the k-th sample point in the j-th sampling, which is obtained by taking the squared amplitude of e j,k ;

[0162] Module M2.3: Based on the fast Fourier transform, calculate the squared envelope spectrum amplitude matrix SES of the vibration data of the whole life cycle of the computing device as follows:

[0163]

[0164] where, ses j,k denotes the squared envelope spectrum amplitude corresponding to the k-th sample point in the j-th sampling, which is obtained from x j,k and is obtained by the Hilbert transform and the fast Fourier transform. Since the squared envelope spectrum amplitude of the vibration data sequence collected from the device each time is symmetric, generally, the first half of the squared envelope spectrum amplitude is taken.

[0165] Module M3: The whole life cycle health index HI ∈ R based on the fusion of squared envelope spectrum amplitudes N×1 is defined as follows:

[0166]

[0167] where, hi j , j = 1, 2…, N represents the health index at the j-th sampling time point; w ∈ R A×1 = [w1, w2,…, w A ′ represents the weight of the squared envelope spectrum amplitude; w k , k = 1, 2,…, A represents the weight of the k-th squared envelope spectrum amplitude in each sampling.

[0168] Module M4: Based on the squared envelope spectrum amplitude matrix SES of the vibration data over the entire life cycle, a sparse degradation convex optimization model is constructed to automatically determine the weight w of the squared envelope spectrum amplitude, which is constructed as follows:

[0169]

[0170] s.t. w'M'B = r

[0171] Mw ≥ 0, Dw ≥ 0, HI = SESw

[0172] j = 1, 2, …, N - 1, ε j ≥ 0

[0173] where ε j = max(hi j - hi j+1 , 0) is a slack variable, representing the monotonicity of the health index difference sequence; c j is the weight of ε j and can be set by an arithmetic series or a geometric series;

[0174] c j 's arithmetic series can be calculated as follows:

[0175]

[0176] c j 's geometric series can be calculated as follows:

[0177] c j = c1·q j-1 , j = 1, …, N - 1

[0178] where c1 is preset as a constant to determine the c j sequence; therefore, the objective term can be used to represent the number of non - monotonic elements in the health index sequence; if a monotonically increasing health index sequence is expected, the more zero elements ε j should contain, the better, that is, the sparser the better; therefore, ||ε||1 is used to enhance its sparsity to improve the monotonicity of the health index sequence; ||w||1 is used to enhance the sparsity of the squared envelope spectrum amplitude weight; r is the sum of the squared envelope spectrum amplitude weights and can usually be set to 1 or other integers; λ is a hyperparameter used to adjust the monotonicity of the health index and the sparsity of the squared envelope spectrum amplitude weight; M ∈ R A×A is a diagonal matrix, and its diagonal elements can be determined according to the trend of the squared envelope spectrum amplitude; if the squared envelope spectrum amplitude at a certain frequency has an increasing trend, the corresponding diagonal element of M is 1, otherwise - 1; D ∈ R (N-1)×A represents the squared envelope spectrum amplitude difference matrix, and the specific expression is as follows:

[0179]

[0180] The first constraint w'M'B = r represents the weighted sum of the squared envelope spectrum amplitudes, and the specific expression is as follows:

[0181]

[0182] The second constraint Mw ≥ 0 restricts the sign of the weights of the squared envelope spectrum amplitudes, and the specific expression is as follows:

[0183]

[0184] The third constraint Dw ≥ 0 restricts the consistency between the difference of the squared envelope spectrum amplitudes and the sign of the weights of the squared envelope spectrum amplitudes, which is used to further enhance the monotonic degradation trend of the health index, and the specific expression is as follows:

[0185]

[0186] Module M5: Solve for the weights w of the squared envelope spectrum amplitudes according to the sparse degradation convex optimization model constructed by Module M4.

[0187] Module M6: Calculate HI according to the definition of the full life cycle health index of Module M3, which is used for early fault detection and monotonic degradation evaluation of the equipment during its full life cycle.

[0188] Those skilled in the art know that in addition to implementing the system and its various devices, modules, and units provided by the present invention in the form of pure computer-readable program code, the method steps can be logically programmed to enable the system and its various devices, modules, and units provided by the present invention to be implemented in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers, etc., to achieve the same functions. Therefore, the system and its various devices, modules, and units provided by the present invention can be regarded as a kind of hardware component, and the devices, modules, and units included therein for implementing various functions can also be regarded as the structures within the hardware component; the devices, modules, and units for implementing various functions can also be regarded as both software modules for implementing the method and the structures within the hardware component.

[0189] The specific embodiments of the present invention have been described above. It should be understood that the present invention is not limited to the above specific embodiments, and those skilled in the art can make various changes or modifications within the scope of the claims, which does not affect the essence of the present invention. Without conflict, the embodiments of the present application and the features in the embodiments can be combined arbitrarily with each other.

Claims

1. A device performance degradation evaluation method based on sparse degradation modeling, characterized in that The method includes the following steps: Step S1: Collect the time-domain vibration data matrix \(X\in R\) of the entire life cycle of the device by collecting vibration signals at fixed time intervals, which is expressed as follows: N×A as follows: Where, N represents the number of samplings during the whole life cycle of the device; A represents the number of samples for each sampling; x j,· ∈R 1×A represents the vibration sample sequence collected from the device for the j-th time, j = 1, 2, …, N; x j,k represents the k-th sample point in the j-th sampling, k = 1, 2, …, A; Step S2: Convert the N - time vibration data sequence into the square envelope spectrum amplitude SES ∈ R based on Hilbert transform and fast Fourier transform, which is expressed as follows: N×A , as follows: Among them, ses j,k represents the square envelope spectrum amplitude corresponding to the k-th sample point in the j-th sampling, which is obtained from x j,k based on the Hilbert transform and the fast Fourier transform; Step S3: The full life cycle health index HI ∈ R based on the fusion of the square envelope spectrum amplitudes is defined as follows: N×1 is defined as follows: where, hi j , j = 1, 2…, N is the health index at the j-th sampling time point; w ∈ R A×1 = [w1, w2, …, w A ′ is the weight of the square envelope spectrum amplitude; w k , k = 1, 2, …, A is the weight of the k-th square envelope spectrum amplitude in each sampling; Step S4: Based on the squared envelope spectrum amplitude matrix SES of the full life cycle vibration data, construct a sparse degradation convex optimization model to automatically determine the weight w of the squared envelope spectrum amplitude; Step S5: Solve the weight w of the squared envelope spectrum amplitude according to the sparse degradation convex optimization model constructed in step S4; Step S6: Calculate HI according to the definition of the full life cycle health index in step S3, and conduct early fault detection and monotonic degradation assessment for the full life cycle of the equipment; The weight w constructed in step S4 is as follows: s.t. w'M'B = r Mw ≥ 0, Dw ≥ 0, HI = SESw j = 1, 2, …, N - 1, ε j ≥ 0 where, ε j = max(hi j - hi j+1 , 0) is a slack variable representing the monotonicity of the health index difference sequence; c j is the weight of ε j , set by an arithmetic progression or a geometric progression; ||ε||1 is used to enhance its sparsity to improve the monotonicity of the health index sequence; ||w||1 is used to enhance the sparsity of the squared envelope spectrum amplitude weights; r is the sum of the squared envelope spectrum amplitude weights; λ is a hyperparameter; M ∈ R A×A is a diagonal matrix, the diagonal elements of which are determined according to the trend of the squared envelope spectrum amplitude; if the squared envelope spectrum amplitude at a certain frequency has an increasing trend, the corresponding diagonal element of M is 1, otherwise -1; D ∈ R (N -1)×A represents the squared envelope spectrum amplitude difference matrix, and the specific expression is as follows: The first constraint condition w'M'B = r represents the sum of the weights of the squared envelope spectrum amplitude, and the specific expression is as follows: The second constraint condition Mw ≥ 0 restricts the sign of the weight of the squared envelope spectrum amplitude, and the specific expression is as follows: The third constraint condition Dw ≥ 0 restricts the consistency between the difference of the squared envelope spectrum amplitude and the sign of the weight of the squared envelope spectrum amplitude, and the specific expression is as follows: The said c j is calculated as an arithmetic progression as follows: c j The geometric progression of is calculated as follows: c j = c1·q j-1 , j = 1, …, N - 1 Among them, c1 is preset as a constant to determine c j sequence; therefore, the target item is used to represent the number of non-monotonic elements in the health index sequence; if a monotonically increasing health index sequence is expected, then ε j should contain as many zero elements as possible, that is, the sparser the better.

2. The device performance degradation evaluation method based on sparse degradation modeling according to claim 1, characterized in that, Step S2 includes the following steps: Step S2.1: First, use the Hilbert transform operation to convert the vibration data sequence of N times into an analytic signal matrix E ∈ R N×A which is expressed as follows: where |·| represents the complex modulus symbol; X ∈ R N×A represents the time-domain vibration data matrix of the equipment's entire life cycle; x j,· ∈ R 1×A , j = 1, 2…, N represents the j-th vibration sample sequence collected from the equipment; e j,k represents the analytical signal corresponding to the k-th sample point in the j-th sampling; hilbert(·) represents the Hilbert transform operation, and the specific operation formula is as follows: As can be seen from the above formula, the essence of the Hilbert transform operation is to perform convolution between the original signal x(t) and 1 / πt; Step S2.2: Calculate the square envelope amplitude matrix SE ∈ R of the analytic signal E of the vibration data over the entire life cycle of the device N×A as follows: Among them, se j,k represents the squared envelope amplitude corresponding to the k-th sample point in the j-th sampling, which is obtained by taking the square of the amplitude of e j,k ; Step S2.3: Based on the fast Fourier transform, calculate the square envelope spectrum amplitude matrix SES ∈ R of the vibration data throughout the life cycle of the device N×A as follows: Among them, ses j,k represents the squared envelope spectrum amplitude corresponding to the k-th sample point in the j-th sampling, which is obtained by performing a fast Fourier transform on se j,k ​ 3. A device performance degradation evaluation system based on sparse degradation modeling, characterized in that, The system includes the following modules: Module M1: Collect the time-domain vibration data matrix X ∈ R of the entire life cycle of the device by collecting vibration signals at fixed time intervals, as follows: N×A It is expressed as follows: Among them, N represents the number of samplings during the entire life cycle of the device; A represents the number of samples in each sampling; x j,· ∈R 1×A represents the vibration sample sequence collected from the device for the j-th time, where j = 1, 2, …, N; x j,k represents the k-th sample point in the j-th sampling, where k = 1, 2, …, A; Module M2: Convert the N - time vibration data sequence into the square envelope spectrum amplitude SES ∈ R based on Hilbert transform and fast Fourier transform, expressed as follows: N×A , as follows: Among them, ses j,k represents the square envelope spectrum amplitude corresponding to the k-th sample point in the j-th sampling, which is obtained from x j,k based on Hilbert transform and fast Fourier transform; Module M3: The full life cycle health index HI ∈ R based on the fusion of the squared envelope spectrum amplitude N×1 Is defined as follows: where, hi j , j = 1, 2…, N is the health index at the j-th sampling time point; w ∈ R A×1 = [w1, w2, …, w A ′ is the weight of the squared envelope spectrum amplitude; w k , k = 1, 2, …, A is the weight of the k-th squared envelope spectrum amplitude in each sampling; Module M4: Based on the squared envelope spectrum amplitude matrix SES of the full life cycle vibration data, construct a sparse degradation convex optimization model to automatically determine the weight w of the squared envelope spectrum amplitude; Module M5: Solve the weight w of the squared envelope spectrum amplitude according to the sparse degradation convex optimization model constructed by Module M4; Module M6: Calculate HI according to the definition of the full life cycle health index of Module M3, and conduct early fault detection and monotonic degradation assessment for the full life cycle of the equipment; The weight w constructed in Module M4 is as follows: s.t. w'M'B = r Mw ≥ 0, Dw ≥ 0, HI = SESw j = 1, 2, …, N - 1, ε j ≥ 0 where, ε j = max(hi j - hi j+1 , 0) is a slack variable representing the monotonicity of the health index difference sequence; c j is the weight of ε j , set by an arithmetic progression or a geometric progression; ||ε||1 is used to enhance its sparsity to improve the monotonicity of the health index sequence; ||w||1 is used to enhance the sparsity of the squared envelope spectrum amplitude weights; r is the sum of the squared envelope spectrum amplitude weights; λ is a hyperparameter; M ∈ R A×A is a diagonal matrix whose diagonal elements are determined according to the trend of the squared envelope spectrum amplitude; if the squared envelope spectrum amplitude at a certain frequency has an increasing trend, the corresponding diagonal element of M is 1, otherwise -1; D ∈ R (N -1)×A represents the squared envelope spectrum amplitude difference matrix, and the specific expression is as follows: The first constraint condition w'M'B = r represents the sum of the weights of the squared envelope spectrum amplitude, and the specific expression is as follows: The second constraint condition Mw ≥ 0 restricts the sign of the weight of the squared envelope spectrum amplitude, and the specific expression is as follows: The third constraint condition Dw ≥ 0 restricts the consistency between the difference of the squared envelope spectrum amplitude and the sign of the weight of the squared envelope spectrum amplitude, and the specific expression is as follows: The said c j is calculated as an arithmetic progression as follows: c j The geometric series is calculated as follows: c j = c1·q j-1 , j = 1, …, N - 1 Among them, c1 is preset as a constant to determine c j sequence; thus, the target item is used to represent the number of non-monotonic elements in the health index sequence; if a monotonically increasing health index sequence is expected, then ε j should contain as many zero elements as possible, that is, the sparser the better.

4. The device performance degradation evaluation system based on sparse degradation modeling according to claim 3, characterized in that, Module M2 includes the following modules: Module M2.1: First, using the Hilbert transform operation, the vibration data sequence of N times is transformed into an analytic signal matrix E ∈ R N×A It is expressed as follows: where |·| represents the complex modulus symbol; X ∈ R N×A represents the time-domain vibration data matrix of the equipment's entire life cycle; x j,· ∈ R 1×A , j = 1, 2…, N represents the j-th vibration sample sequence collected from the equipment; e j,k represents the analytical signal corresponding to the k-th sample point in the j-th sampling; hilbert(·) represents the Hilbert transform operation, and the specific operation formula is as follows: As can be seen from the above formula, the essence of the Hilbert transform operation is to perform convolution between the original signal x(t) and 1 / πt; Module M2.2: Square envelope amplitude matrix SE ∈ R of the analytic signal E of the vibration data over the entire life cycle of the computing device N×A is as follows: Among them, se j,k represents the squared envelope amplitude corresponding to the k-th sample point in the j-th sampling, which is obtained by taking the square of the amplitude of e j,k ; Module M2.3: Based on the fast Fourier transform, calculate the squared envelope spectrum amplitude matrix SES ∈ R of the vibration data of the equipment throughout its life cycle N×A as follows: Among them, ses j,k represents the squared envelope spectrum amplitude corresponding to the k-th sample point in the j-th sampling, which is obtained by performing a fast Fourier transform on se j,k ​

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