A mechanical state monitoring method based on an interpretable sparse optimization unfolding network

Abstract

The application provides a mechanical state monitoring method based on an interpretable sparse optimization unfolding network, comprising the following steps: S100, performing mechanical state data monitoring test to obtain mechanical state signals; S200, constructing a sparse optimization model, and using sparse feature representation for the extracted mechanical state features; S300, using an alternating multiplier method to derive an iterative optimization solving algorithm of the sparse optimization model; S400, introducing learnable parameters to replace the parameters in the iterative optimization solving algorithm; S500, using an unfolding algorithm framework to construct an interpretable sparse optimization unfolding network; S600, using the interpretable sparse optimization unfolding network to identify the health state of a test machine; the application embeds a Q-adjusted wavelet transform into a sparse optimization model, and uses the multi-scale characteristics and wavelet dictionary structure for sparse feature representation, so that accurate capture of key state information can be realized in the feature extraction stage.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of mechanical state monitoring, and particularly relates to a mechanical state monitoring method based on an interpretable sparse optimization unfolding network. BACKGROUND

[0002] Mechanical equipment is an important part of modern industrial production, and plays an irreplaceable role in the fields of aerospace, transportation, wind power generation, etc. Among them, key mechanical components such as bearings and gears are long-term served in complex and harsh environments such as high load, strong interference and high speed, and are prone to performance degradation and even failure. Therefore, it is of great significance to carry out efficient and reliable state monitoring research on mechanical equipment to ensure stable operation and prolong service life.

[0003] The rise of deep learning technology provides a new idea and means for complex signal analysis and intelligent state monitoring. Deep learning has strong non-linear feature learning and representation ability, can automatically extract high-level features from raw signals, reduce the dependence on prior knowledge and artificial feature design, and thus significantly improve the accuracy and adaptability of state monitoring. At present, classical deep structures such as convolutional neural network, deep autoencoder, deep belief network and recurrent neural network have been widely used in state monitoring and fault identification of different mechanical systems.

[0004] However, the internal feature extraction and decision mechanism of the pure data-driven deep learning model lacks physical mechanism support and explicit inter-layer mapping relationship, and the model training process and state monitoring result are often difficult to be directly understood, so it is often regarded as a "black box" model. Therefore, how to improve the physical interpretability and decision transparency of the model has become an important research problem that needs to be solved in the field of intelligent state monitoring.

[0005] In existing prior interpretability research, wavelet analysis method as a signal processing tool with clear physical meaning is embedded into deep neural network as an interpretable function module to enhance the interpretability of the network. At the same time, researchers also incorporate physical prior knowledge from the loss function level to enhance the physical meaning of the learning features. In addition to embedding physical knowledge in network structure or loss function, algorithm structure equivalence is also an effective prior interpretability design concept. Compared with the embedding of interpretable function modules and the design of physical loss function, algorithm structure equivalence directly maps the solving process of traditional signal processing methods to the neural network architecture, thereby giving the network global interpretability and having greater potential. Among them, algorithm unfolding is a typical algorithm structure equivalence method, which unfolds the iterative optimization algorithm of sparse optimization model along the iteration direction into a corresponding network structure layer by layer, so that the operation of each layer of the network corresponds to the solving process of each step of the algorithm, thereby inheriting the physical prior knowledge and enhancing the global interpretability.

[0006] Overall, algorithm expansion methods, by transforming iterative optimization algorithms into deep networks and inheriting physical mechanisms and prior knowledge, can achieve global interpretability in intelligent state monitoring, demonstrating great application potential. However, most algorithm expansion methods rely on conventional basic sparse optimization models, making it difficult to deeply mine potential weak features in signals, which can easily lead to a decrease in state monitoring accuracy.

[0007] Therefore, a new solution is urgently needed to address the defects and shortcomings of the existing technologies. Summary of the Invention

[0008] To address the shortcomings and deficiencies in the existing technologies, this invention provides a mechanical condition monitoring method based on interpretable sparse optimized unfolded networks.

[0009] The specific solution provided by this invention is as follows:

[0010] A method for monitoring the mechanical condition based on interpretable sparse optimization unfolded networks, characterized by the following steps:

[0011] S100: Perform mechanical condition data monitoring tests to obtain mechanical condition signals;

[0012] S200: Construct a sparse optimization model and represent the extracted mechanical state features using sparse features;

[0013] S300: Derive the iterative optimization solution algorithm for sparse optimization models using the alternating multiplier method;

[0014] S400: Introduces learnable parameters to replace the parameters in the iterative optimization algorithm;

[0015] S500: Constructing interpretable sparse optimized unfolded networks using an unfolding algorithm framework;

[0016] S600: Utilize interpretable sparse optimization to deploy network identification and test the health status of machinery.

[0017] As a further preferred embodiment of the present invention, in step S200, the constructed sparse optimization model is expressed by the following formula:

[0018] ;

[0019] In the formula: express Norms are used to measure sparsity. express Norm, used to measure signal reconstruction error; This is a regularization parameter used to balance reconstruction accuracy and sparsity; denotes an inverse Q-wavelet transform operator, i.e. a sparse dictionary; denotes a set of sparse wavelet coefficients, which are obtained by transforming the wavelet coefficients into the time domain; denotes a test mechanical state signal.

[0020] As a further preferred embodiment of the present application, in the step S300, the iterative optimization solving algorithm of the derived sparse optimization model is:

[0021] ;

[0022] ;

[0023] ;

[0024] wherein: denotes the i-th iteration, and satisfies , K denotes the iteration number; A denotes an inverse Q-wavelet transform operator, and satisfies , is an identity matrix; is a penalty parameter; is an auxiliary variable, and denotes the extracted state feature vector; is an intermediate scaling variable; denotes a soft threshold operator.

[0025] As a further preferred embodiment of the present application, in the step S400, the iterative optimization solving algorithm after introducing the learnable parameters is:

[0026] ;

[0027] ;

[0028] ;

[0029] wherein: denotes a linear rectifier function; and t are learnable parameters introduced when replacing.

[0030] As a further preferred embodiment of the present application, in the step S500, the constructed interpretable sparse optimization unfolding network comprises a plurality of layers of calculation units, and each calculation unit corresponds to each iteration process in the iterative optimization solving algorithm.

[0031] As a further preferred embodiment of the present application, the extracted state feature vector is calculated by the following formula: ​

[0032] ;

[0033] wherein, are learnable weight coefficients, and satisfy ; denotes the jth layer; L denotes the decomposition number of the Q-tuned wavelet transform.

[0034] As a further preferred embodiment of the present application, the learnable weight coefficients can be adaptively updated.

[0035] As a further preferred embodiment of the present application, the learnable weight coefficients are adaptively updated, corresponding to increasing the learnable weight coefficients corresponding to the input feature vectors containing more state information and fault features; and corresponding to decreasing the learnable weight coefficients corresponding to the input feature vectors containing less state information and fault features.

[0036] As a further preferred embodiment of the present application, in the step S500, the constructed interpretable sparse optimization unfolding network at least includes an initial layer, an intermediate layer and a final layer, and a plurality of intermediate layers connected in sequence are located between the initial layer and the final layer and are respectively data-connected with the initial layer and the final layer.

[0037] As a further preferred embodiment of the present application, in the step S500, the constructed interpretable sparse optimization unfolding network further includes a diagnosis layer, which is data-connected with the final layer to realize classification and identification of the mechanical state according to the output data of the final layer.

[0038] Compared with the prior art, the present application can realize the following technical effects:

[0039] 1) The present application provides a mechanical state monitoring method based on an interpretable sparse optimization unfolding network. In the sparse optimization model construction stage, in order to extract accurate features from the original mechanical state signal, the Q-tuned wavelet transform is embedded in the sparse optimization model, and the multi-scale characteristics and wavelet dictionary structure are used for sparse feature representation, so that accurate capture of key state information can be realized in the feature extraction stage.

[0040] 2) The present application provides a mechanical state monitoring method based on an interpretable sparse optimization unfolding network. The alternating multiplier method is used to derive the iterative optimization solving algorithm of the sparse optimization model, learnable parameters are introduced to replace the difficult-to-set parameters, and the algorithm unfolding method is used to map the iterative solving process of the sparse optimization model into an interpretable sparse optimization unfolding network with explicit physical and mathematical semantics, so as to realize globally interpretable feature extraction.

[0041] 3) The application provides a mechanical state monitoring method based on an interpretable sparse optimization unfolding network, wherein corresponding learnable weight coefficients are assigned to the input feature vectors in the extracted mechanical state signals, and the learnable weight coefficients can be updated adaptively, so that the input feature vectors corresponding to the learnable weight coefficients that contain more state information and fault features are increased correspondingly, and the input feature vectors corresponding to the learnable weight coefficients that contain less state information and fault features are reduced correspondingly, so that the components containing more state information and significant fault features obtain higher weights, thereby highlighting the key diagnostic information in the feature fusion stage and improving the accuracy and robustness of the final fault recognition. BRIEF DESCRIPTION OF DRAWINGS

[0042] Figure 1 The step flow chart of the method provided by the application;

[0043] Figure 2 The structural diagram of the interpretable sparse optimization unfolding network constructed by the application;

[0044] Figure 3 The physical schematic diagram of the motor bearing test bed;

[0045] Figure 4 The physical schematic diagram of the wheelset bearing test bed;

[0046] Figure 5 The accuracy bar chart of different methods in the state monitoring task of the motor bearing data set;

[0047] Figure 6 The accuracy bar chart of different methods in the state monitoring task of the wheelset bearing data set. DETAILED DESCRIPTION

[0048] The technical solutions in the embodiments of the application will be clearly and completely described below with reference to the drawings in the embodiments of the application. Obviously, the described embodiments are only part of the embodiments of the application, rather than all the embodiments of the application. Based on the embodiments in the application, all other embodiments obtained by those skilled in the art without creative labor fall within the scope of the application.

[0049] In the description of the present application, it should be noted that the terms "upper", "lower", "inner", "outer", "front end", "rear end", "both ends", "one end", "the other end" and the like indicate the orientation or positional relationship shown in the drawings, and are only for the convenience of describing the present application and simplifying the description, and do not indicate or imply that the devices or elements referred to must have a particular orientation, be constructed and operated in a particular orientation, and therefore cannot be understood as limiting the present application. In addition, the terms "first", "second" are only for descriptive purposes and cannot be understood as indicating or implying relative importance.

[0050] In the description of the present application, it should be noted that unless otherwise explicitly specified and limited, the terms "mounting", "provided with", "connection" and the like should be broadly understood, for example, "connection" can be fixed connection, can also be detachable connection, or integral connection; can be mechanical connection, can also be electrical connection; can be directly connected, can also be indirectly connected through an intermediate medium, can be internal communication of two elements. For those skilled in the art, the specific meaning of the above terms in the present application can be understood according to the specific circumstances.

[0051] [First embodiment]

[0052] As Figure 1 shown is the first embodiment provided by the present application, which provides a mechanical state monitoring method based on an interpretable sparse optimization expansion network, comprising the following steps:

[0053] S100: performing mechanical state data monitoring test to obtain mechanical state signal;

[0054] S200: constructing a sparse optimization model, and using sparse feature representation to represent the extracted mechanical state features;

[0055] In step S200, the constructed sparse optimization model is represented by the following formula:

[0056] ;

[0057] In the formula: represents norm, used to measure sparsity; represents norm, used to measure signal reconstruction error; is a regularization parameter, used to balance reconstruction accuracy and sparsity; represents inverse Q wavelet transform operator, i.e. sparse dictionary; represents a set of sparse wavelet coefficients, which is converted to time domain by ; ; represents the mechanical state signal obtained by testing.

[0058] Because the Q-switched wavelet transform possesses significant multi-scale analysis capabilities, it can simultaneously acquire signal features at different decomposition levels. Based on this advantage, this embodiment selects the Q-switched wavelet transform as the sparse dictionary in the sparse optimization model, thereby achieving accurate capture of key state information during the feature extraction stage. This design not only preserves the structured information at different scales in the original signal but also enables the sparse optimization process to fully utilize the time-frequency localization characteristics of the Q-switched wavelet transform, effectively improving the extraction capability of early weak faults and hidden features in complex backgrounds.

[0059] S300: Derive the iterative optimization solution algorithm for sparse optimization models using the alternating multiplier method;

[0060] In step S300, the iterative optimization algorithm for solving the derived sparse optimization model is as follows:

[0061] ;

[0062] ;

[0063] ;

[0064] In the formula: Indicates the first The iteration, and satisfying K represents the number of iterations; A represents the inverse Q-wavelet transform operator, and satisfies , It is the identity matrix; For penalty parameters; These are auxiliary variables, representing the extracted state feature vectors; It is an intermediate scaling variable; This represents the soft threshold operator.

[0065] The derivation process of the iterative optimization solution algorithm for the above sparse optimization model is as follows:

[0066] Due to sparse optimization model The equivalent form can be expressed as: And satisfy ;

[0067] In the formula, ; ; ; ; This represents a constrained objective function; G and C both represent auxiliary matrices, which are identity matrices in this case.

[0068] The augmented Lagrange form of the above equivalent expression is now:

[0069] ;

[0070] In the formula, represents a target-free constraint function;

[0071] Solve it by using the alternating direction multiplier method, and the iterative update step is:

[0072] ;

[0073] ;

[0074] ;

[0075] Where and The analytical solutions of and are respectively:

[0076] ;

[0077] ;

[0078] At this time, the iterative optimization solving algorithm of the sparse optimization model derived in step S300 is obtained, that is:

[0079] ;

[0080] ;

[0081] ;

[0082] S400: Introduce learnable parameters to replace the parameters in the iterative optimization solving algorithm;

[0083] In step S400, the iterative optimization solving algorithm after introducing learnable parameters is:

[0084] ;

[0085] ;

[0086] ;

[0087] In the formula: represents a linear rectifier function; and t are learnable parameters introduced when replacing.

[0088] The process of introducing learnable parameters to replace the parameters in the iterative optimization solving algorithm is as follows:

[0089] In order to conveniently replace and with and The mapping into the form of deep neural network needs to be reformed. According to the knowledge of Q wavelet transform tight frame theory, . Therefore, The form after conversion can be rewritten as:

[0090] ;

[0091] At the same time, The threshold parameter in the calculation formula needs to be replaced with another learnable parameter t, and the soft threshold operator is converted into a linear rectifier function ReLU (Rectified Linear Unit) to impose non-negative constraints on the extracted features.

[0092] Therefore, The calculation formula of

[0093] ;

[0094] In addition, when updating the intermediate scaling variable , a learnable parameter is introduced, which is converted into a new form:

[0095] ;

[0096] S500: Use the expansion algorithm framework to build an interpretable sparse optimization expansion network, as shown in Figure 2 The built interpretable sparse optimization expansion network includes several layers of calculation units, and each calculation unit corresponds to each iteration process in the iterative optimization solving algorithm. The built interpretable sparse optimization expansion network not only inherits the physical meaning and convergence characteristics of the original optimization algorithm, but also makes the calculation of each layer have a clear mathematical explanation, thereby realizing global interpretability.

[0097] As shown in Figure 2 , in step S500, the built interpretable sparse optimization expansion network includes at least an initial layer, an intermediate layer and a final layer, and several sequentially connected intermediate layers are located between the initial layer and the final layer and are respectively data connected with the initial layer and the final layer; the output data of the initial layer is input into the intermediate layer as input data of the intermediate layer, and the output data of the intermediate layer is input into the final layer as input data of the final layer, and the data connection mode of the several sequentially connected intermediate layers is also the same. The built interpretable sparse optimization expansion network also includes a diagnostic layer, which is data connected with the final layer to realize classification and identification of the mechanical state according to the output data of the final layer.

[0098] On this basis, the extracted state feature vector is calculated by the following formula:

[0099] ;

[0100] wherein, are learnable weight coefficients, and satisfy ; denotes the j-th layer; L denotes the decomposition level of the Q-shift wavelet transform.

[0101] wherein the learnable weight coefficients can be adaptively updated; as a further preferred, the learnable weight coefficients are adaptively updated, corresponding to increasing the learnable weight coefficients corresponding to the input feature vectors containing more state information and fault features; and corresponding to decreasing the learnable weight coefficients corresponding to the input feature vectors containing less state information and fault features. By using the representation ability of deep learning, the constructed interpretable sparse optimization unfolding network can automatically adjust the parameters while retaining the theoretical interpretability, to adapt to the feature extraction task under different working conditions and complex noise environments, so that those components containing more state information and significant fault features obtain higher weights, thereby highlighting the key diagnostic information in the feature fusion stage and improving the accuracy and robustness of the final fault recognition.

[0102] S600: identifying the health state of the test machine using the interpretable sparse optimization unfolding network.

[0103] To verify the effectiveness of the interpretable sparse optimization unfolding network proposed in this embodiment in state monitoring, two bearing data sets of different sources, i.e., motor bearing data set and wheelset bearing data set, are selected for experimental evaluation. The basic information of the two data sets is as follows:

[0104] (1) Motor bearing data set: This public data set is collected from a bearing test rig, as shown in Figure 3 , which consists of a motor, an accelerometer, a faulty bearing, a dynamometer, and a load sensor, with a sampling frequency of 12 kHz. The data set contains three typical fault types: inner ring fault, rolling element fault, and outer ring fault, each with three different damage sizes (0.007 inches, 0.014 inches, and 0.021 inches). In addition to the healthy (no fault) state, a total of 10 working conditions are formed. In addition, the test rig applies four constant loads of 0 HP, 1 HP, 2 HP, and 3 HP when collecting signals. All raw data are preprocessed by standardization, and a sliding window of length 1024 is used for segmentation to obtain input samples for network training and testing.

[0105] (2) Wheelset bearing data set: This private data set is collected from a comprehensive wheelset transmission test rig, as shown in Figure 4As shown, the test bench includes a motor, a gear box, an accelerometer, a faulty bearing, a dynamometer, and a variable load nut, etc., in which the bearing model is NJ204ET NSK. The test bench applies different radial loads by adjusting the bearing end cover nut, and data collection is performed at a constant speed of 400 rpm. The data set contains two types of faults: inner ring faults and outer ring faults, with three damage sizes (0.2 mm, 0.4 mm, and 0.6 mm) for each type of fault. Adding the healthy (no fault) state, a total of 7 working conditions are formed. For each state, the test applies four constant loads of 0 kN, 0.8 kN, 1.6 kN, and 2.4 kN. The same as the motor data set processing method, each file is standardized and segmented by a sliding window with a length of 1024 to generate input samples.

[0106] To comprehensively evaluate the monitoring performance of the interpretable sparse optimization unfolding network state monitoring method provided in this embodiment, interpretable intelligent state monitoring experiments are performed on the motor bearing data set and the wheelset bearing data set. At the same time, in order to verify the advantages of the method, four representative state monitoring methods are selected as comparison:

[0107] ResNet: A classic deep convolutional neural network that alleviates the gradient vanishing and gradient explosion problems in the training process of deep networks by introducing residual connections, but lacks interpretability.

[0108] MorletResNet and LaplaceLeNet: A hybrid model of wavelet transform and deep learning that retains the feature extraction capability of deep networks while introducing local interpretability into the network using Morlet wavelets or Laplace wavelets.

[0109] ML-LISTA: An algorithm unfolding model based on the multi-layer iterative shrinkage threshold algorithm, which uses a double convolutional dictionary filter channel.

[0110] The accuracy results of the monitoring method provided in this embodiment in the monitoring task are shown in Tables 1 and 2, and are presented in the form of bar charts in Figure 5 and Figure 6 .

[0111] Table 1 Accuracy (%) of different methods in the state monitoring task of the motor bearing data set

[0112]

[0113] Table 2 Accuracy (%) of different methods in the state monitoring task of the wheelset bearing data set

[0114]

[0115] From Tables 1-2 andFigures 5-6 As can be seen from the above table:

[0116] For the state monitoring tasks on the motor bearing dataset, the mechanical state monitoring method of the interpretable sparse optimization unrolling network provided in the embodiment performs excellently, all being higher than or close to 95%, and the state monitoring accuracy is significantly superior to the other four comparison methods. Among the four comparison methods, the state monitoring ability of LaplaceLeNet is the strongest, and the accuracy of each state monitoring task is more than 90%. However, compared with the interpretable sparse optimization unrolling network, LaplaceLeNet still has a certain gap. The state monitoring performance of ResNet and MorletResNet is quite similar, and the state monitoring accuracy of each task is about 85%, but is not higher than 90%. The state monitoring performance of ML-LISTA is more excellent than ResNet and MorletResNet, and is more than or close to 90%, but still has a large gap with the state monitoring accuracy of the mechanical state monitoring method of the interpretable sparse optimization unrolling network provided in the embodiment.

[0117] For the state monitoring tasks on the wheel bearing dataset, the mechanical state monitoring method of the interpretable sparse optimization unrolling network provided in the embodiment still maintains a high accuracy, and only the accuracy of one state monitoring task is lower than 95%, and the highest accuracy is more than 97%. Among the four comparison methods, the state monitoring performance of LaplaceLeNet is the best, and the accuracy of each state monitoring task is higher than 90%, but the highest accuracy is lower than 93%, and still has a large gap with the mechanical state monitoring method of the interpretable sparse optimization unrolling network provided in the embodiment. The state monitoring performance of MorletResNet is the worst, and the highest accuracy is close to 90%, and the lowest accuracy is lower than 80%, which indicates that when facing a dataset with more complex data distribution, MorletRestNet cannot maintain stable state monitoring ability. The state monitoring ability of ResNet and ML-LISTA is quite similar, and the robustness is greatly improved compared with MorletResNet, but the average accuracy is still lower than the mechanical state monitoring method of the interpretable sparse optimization unrolling network provided in the embodiment.

[0118] Through the above experimental comparison of the two groups of datasets, the mechanical state monitoring method of the interpretable sparse optimization unrolling network provided in the embodiment has the highest accuracy in all state monitoring tasks, and performs stably on the two types of datasets, and has outstanding state monitoring performance and strong generalization ability.

[0119] It will be apparent to those skilled in the art that the application is not limited to the details of the above-exemplified embodiments and that the present application can be implemented in other particular forms without departing from the spirit or essential characteristics of the present application. The embodiments should therefore be considered in all respects as illustrative and not restrictive, the scope of the application being indicated by the appended claims rather than by the above description, and all changes which come within the meaning and range of equivalency of the claims are therefore intended to be embraced therein. No reference signs in the claims should be considered as limiting the scope of the claims with respect to the figures of the patent document.

Claims

1. A mechanical state monitoring method based on an interpretable sparse optimization unfolding network, characterized in that: The method comprises the following steps: S100: performing a mechanical state data monitoring test to obtain a mechanical state signal; S200: constructing a sparse optimization model, and representing the extracted mechanical state features by using sparse features; S300: deriving an iterative optimization solving algorithm of the sparse optimization model by using an alternating multiplier method; S400: introducing learnable parameters to replace parameters in the iterative optimization solving algorithm; S5 S500: constructing an interpretable sparse optimization expansion network by using an expansion algorithm framework; S600: identifying a health state of a test machine by using the interpretable sparse optimization expansion network; In the step S300, the derived iterative optimization solving algorithm of the sparse optimization model is: ； ； ； In the formula: represents the first iteration, and satisfies , K represents the number of iterations; A represents an inverse Q wavelet transform operator, and satisfies , is a unit matrix; is a penalty parameter; is an auxiliary variable, representing the extracted state feature vector; is an intermediate scaling variable; represents a soft threshold operator; The state feature vector extracted is calculated by the following equation : ； In the formula, are learnable weight coefficients, and satisfy ; represents the jth layer; L represents the decomposition number of the Q-adjusted wavelet transform. the learnable weight coefficients adaptively updateable the learnable weight coefficients During the adaptive update, the learnable weight coefficients corresponding to the input feature vectors containing more state information and fault features are increased, and the learnable weight coefficients corresponding to the input feature vectors containing less state information and fault features are decreased. In the step S500, the constructed interpretable sparse optimization expansion network comprises a plurality of layers of calculation units, and each calculation unit corresponds to each iteration process in the iterative optimization solving algorithm; In the step S500, the constructed interpretable sparse optimization expansion network at least comprises an initial layer, intermediate layers and a final layer, a plurality of sequentially connected intermediate layers are located between the initial layer and the final layer and are respectively connected with the initial layer and the final layer in data; In the step S500, the constructed interpretable sparse optimization expansion network further comprises a diagnosis layer, the diagnosis layer is connected with the final layer in data to realize classification identification of the mechanical state according to output data of the final layer.

2. The mechanical state monitoring method based on the interpretable sparse optimization unfolding network according to claim 1, characterized in that: In the step S200, the constructed sparse optimization model is represented by the following formula: ； In the formula: represents norm, used to measure sparsity; represents norm, used to measure signal reconstruction error; is a regularization parameter, used to balance reconstruction accuracy and sparsity; represents the inverse Q wavelet transform operator, that is, the sparse dictionary; represents a set of sparse wavelet coefficients, which are obtained by converting the wavelet coefficients into the time domain; represents the test obtained mechanical state signal.

3. The mechanical state monitoring method based on the interpretable sparse optimization unfolding network according to claim 1, characterized in that: In the step S400, the iterative optimization solving algorithm after the introduction of the learnable parameters is: ； ； ； where: represents a linear rectification function; and t are learnable parameters introduced at replacement time.

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