Mechanical state monitoring method based on interpretable sparse optimization expansion network

Abstract

The invention provides a mechanical state monitoring method based on an interpretable sparse optimization expansion network, and the method comprises the following steps: S100, carrying out the monitoring and testing of mechanical state data, so as to obtain a mechanical state signal; s200, constructing a sparse optimization model, and representing the extracted mechanical state features by adopting sparse features; s300, deducing an iterative optimization solution algorithm of the sparse optimization model by using an alternating multiplier method; s400, introducing learnable parameters to replace parameters in an iterative optimization solution algorithm; s500, constructing an interpretable sparse optimization expansion network by using an expansion algorithm framework; s600, using the interpretable sparse optimization expansion network to identify the health state of the test machine; according to the method, the Q-switched wavelet transform is embedded into the sparse optimization model, and sparse feature representation is carried out by using the multi-scale characteristic and the wavelet dictionary structure, so that the key state information can be accurately captured in the feature extraction stage.

Description

Technical Field

[0001] This invention relates to the technical field of mechanical condition monitoring, and specifically to a mechanical condition monitoring method based on an interpretable sparse optimization unfolded network. Background Technology

[0002] Mechanical equipment is a crucial component of modern industrial production, playing an irreplaceable role in fields such as aerospace, transportation, and wind power generation. Key mechanical components, such as bearings and gears, operate under complex and harsh environments involving high loads, strong interference, and high speeds for extended periods, making them highly susceptible to performance degradation and even failure. Therefore, conducting research on efficient and reliable condition monitoring for mechanical equipment is of great significance for ensuring stable equipment operation and extending its service life.

[0003] The rise of deep learning technology has provided new ideas and methods for complex signal analysis and intelligent condition monitoring. Deep learning possesses powerful nonlinear feature learning and representation capabilities, enabling it to automatically extract high-level features directly from raw signals, reducing reliance on prior knowledge and manual feature design, thereby significantly improving the accuracy and adaptability of condition monitoring. Currently, classic deep structures such as convolutional neural networks, deep autoencoders, deep belief networks, and recurrent neural networks are widely used in condition monitoring and fault identification of various mechanical systems.

[0004] However, the internal feature extraction and decision-making mechanisms of purely data-driven deep learning models lack physical support and clear inter-layer mapping relationships. The model training process and state monitoring results are often difficult to understand directly, and are therefore often regarded as "black box" models. Therefore, how to improve the physical interpretability and decision transparency of the model has become an important research problem that urgently needs to be solved in the field of intelligent state monitoring.

[0005] In existing research on pre-interpretability, wavelet analysis, as a signal processing tool with explicit physical meaning, is embedded as an interpretable functional module in deep neural networks to enhance network interpretability. Simultaneously, researchers have incorporated prior physical knowledge at the loss function level to enhance the physical meaning of learned features. Besides embedding physical knowledge into the network structure or loss function, algorithmic structural equivalence is also an effective design concept for pre-interpretability. In comparison, the embedding of interpretable functional modules and the design of physical loss functions typically only achieve local interpretability, while algorithmic structural equivalence directly maps the solution process of traditional signal processing methods to a neural network architecture, thereby endowing the network with global interpretability and possessing greater potential. Among these, algorithm expansion is a typical algorithmic structural equivalence method, expanding the iterative optimization algorithm of a sparse optimization model along the iteration direction into a layer-by-layer corresponding network structure, so that the operation of each layer of the network corresponds to each step of the algorithm's solution process, thus inheriting prior physical knowledge and enhancing 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: A method for monitoring the mechanical condition based on interpretable sparse optimization unfolded networks, characterized by the following steps: S100: Perform mechanical condition data monitoring tests to obtain mechanical condition signals; S200: Construct a sparse optimization model and represent the extracted mechanical state features using sparse features; S300: Derive the iterative optimization solution algorithm for sparse optimization models using the alternating multiplier method; S400: Introduces learnable parameters to replace the parameters in the iterative optimization algorithm; S500: Constructing interpretable sparse optimized unfolded networks using an unfolding algorithm framework; S600: Utilize interpretable sparse optimization to deploy network identification and test the health status of machinery.

[0010] As a further preferred embodiment of the present invention, in step S200, the constructed sparse optimization model is expressed by the following formula: ; 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; This represents the inverse Q-wavelet transform operator, i.e., the sparse dictionary; Represented as a set of sparse wavelet coefficients, using wavelet coefficients Convert to the time domain; This represents the mechanical state signal obtained from the test.

[0011] As a further preferred embodiment of the present invention, the iterative optimization solution algorithm for the derived sparse optimization model in step S300 is as follows: ; ; ; 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.

[0012] As a further preferred embodiment of the present invention, the iterative optimization solution algorithm after introducing learnable parameters in step S400 is as follows: ; ; ; In the formula: Represents a linear rectified function; t are learnable parameters introduced during replacement.

[0013] As a further preferred embodiment of the present invention, in step S500, the constructed interpretable sparse optimization unfolding network includes several layers of computing units, and each computing unit corresponds to each iteration process in the iterative optimization solution algorithm.

[0014] As a further preferred embodiment of the present invention, the extracted state feature vector is calculated using the following formula. : ; In the formula, The weights are learnable weights and satisfy the following conditions: ; L represents the j-th layer; L represents the decomposition layer number of the Q-switched wavelet transform.

[0015] As a further preferred embodiment of the present invention, the learnable weight coefficients It can update adaptively.

[0016] As a further preferred embodiment of the present invention, the learnable weight coefficients During adaptive updates, the learnable weight coefficients corresponding to input feature vectors containing more state information and fault features are increased; the learnable weight coefficients corresponding to input feature vectors containing less state information and fault features are decreased.

[0017] As a further preferred embodiment of the present invention, in step S500, the constructed interpretable sparse optimization unfolded network includes at least 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 connected to the data of the initial layer and the final layer.

[0018] As a further preferred embodiment of the present invention, in step S500, the constructed interpretable sparse optimized unfolded network further includes a diagnostic layer, which is data-connected to the final layer to achieve classification and identification of mechanical state based on the output data of the final layer.

[0019] Compared with existing technologies, the technical effects that this invention can achieve include: 1) This invention provides a mechanical state monitoring method based on an interpretable sparse optimization unfolded network. In the stage of constructing the sparse optimization model, in order to extract accurate features from the original mechanical state signal, the Q-switched wavelet transform is embedded in the sparse optimization model, and its multi-scale characteristics and wavelet dictionary structure are used to perform sparse feature representation, which enables the accurate capture of key state information in the feature extraction stage.

[0020] 2) This invention provides a mechanical state monitoring method based on an interpretable sparse optimization unfolded network. It uses the alternating multiplier method to derive the iterative optimization solution algorithm of the sparse optimization model, introduces learnable parameters to replace the difficult-to-set parameters, and adopts the algorithm unfolding method to map the iterative solution process of the sparse optimization model into an interpretable sparse optimization unfolded network with explicit physical and mathematical semantics, thereby realizing globally interpretable feature extraction.

[0021] 3) This invention provides a mechanical condition monitoring method based on an interpretable sparse optimization unfolded network. By assigning corresponding learnable weight coefficients to the input feature vectors in the extracted mechanical condition signals, and by enabling adaptive updates of the learnable weight coefficients, the method increases the learnable weight coefficients corresponding to input feature vectors containing more state information and fault features, and decreases the learnable weight coefficients corresponding to input feature vectors containing less state information and fault features. This allows components containing more state information and significant fault features to receive higher weights, thereby highlighting key diagnostic information in the feature fusion stage and improving the accuracy and robustness of the final fault identification. Attached Figure Description

[0022] Figure 1 The flowchart of the method provided by the present invention; Figure 2 A schematic diagram of the structure of the interpretable sparse optimized unfolded network constructed in this invention; Figure 3 This is a schematic diagram of the actual motor bearing test bench; Figure 4 This is a schematic diagram of a wheelset bearing test bench. Figure 5 A bar chart showing the accuracy of different methods in the condition monitoring task of motor bearing dataset; Figure 6 A bar chart showing the accuracy of different methods in the wheelset bearing dataset condition monitoring task. Detailed Implementation

[0023] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0024] In the description of this invention, it should be noted that the terms "upper," "lower," "inner," "outer," "front end," "rear end," "both ends," "one end," and "the other end," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are used only for the convenience of describing this invention and for 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, they should not be construed as limitations on this invention. Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0025] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installed," "equipped with," "connected," etc., should be interpreted broadly. For example, "connection" can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection or an indirect connection through an intermediate medium; it can be a connection within two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0026] [First Embodiment] like Figure 1 The first embodiment of the present invention is shown, which provides a mechanical condition monitoring method based on an interpretable sparse optimized unfolded network, including the following steps: S100: Perform mechanical condition data monitoring tests to obtain mechanical condition signals; S200: Construct a sparse optimization model and represent the extracted mechanical state features using sparse features; In step S200, the constructed sparse optimization model is represented by the following formula: ; 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; This represents the inverse Q-wavelet transform operator, i.e., the sparse dictionary; Represented as a set of sparse wavelet coefficients, using wavelet coefficients Convert to the time domain; This represents the mechanical state signal obtained from the test.

[0027] 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.

[0028] S300: Derive the iterative optimization solution algorithm for sparse optimization models using the alternating multiplier method; In step S300, the iterative optimization algorithm for solving the derived sparse optimization model is as follows: ; ; ; 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.

[0029] The derivation process of the iterative optimization solution algorithm for the above sparse optimization model is as follows: Due to sparse optimization model The equivalent form can be expressed as: And satisfy ; In the formula, ; ; ; ; This represents a constrained objective function; G and C both represent auxiliary matrices, which are identity matrices in this case. The augmented Lagrange form of the above equivalent expression is now: ; In the formula, This represents a function without objective constraints. The problem is solved using the alternating direction multiplier method, with the following iterative update steps: ; ; ; in and The analytical solutions are as follows: ; ; At this point, the iterative optimization algorithm for solving the sparse optimization model derived in step S300 is obtained, namely: ; ; ; S400: Introduces learnable parameters to replace the parameters in the iterative optimization algorithm; In step S400, the iterative optimization solution algorithm after introducing learnable parameters is as follows: ; ; ; In the formula: Represents a linear rectified function; t are learnable parameters introduced during replacement.

[0030] The process of introducing learnable parameters to replace the parameters in the iterative optimization algorithm is as follows: For convenience and The mapping to a deep neural network requires modification and design. Based on the tight-frame theory of Q-switched wavelet transform, it is known that... .therefore, The transformed form can be rewritten as: ; at the same time, Threshold parameter in the calculation formula It needs to be replaced with another learnable parameter t, and the soft thresholding operator is converted into a ReLU (Rectified Linear Unit) function to impose a non-negative constraint on the extracted features.

[0031] therefore, The calculation formula can be restated as: ; In addition, updating the intermediate scaling variable Introducing learnable parameters Transformed into a new form: ; S500: Construct interpretable sparse optimized unfolded networks using an unfolding algorithm framework, such as... Figure 2 As shown, the constructed interpretable sparse optimization unfolding network comprises several layers of computational units, each corresponding to a single iteration in the iterative optimization algorithm. The constructed interpretable sparse optimization unfolding network not only inherits the physical meaning and convergence characteristics of the original optimization algorithm but also provides a clear mathematical interpretation for the computation of each layer, thus achieving global interpretability.

[0032] like Figure 2 As shown, in step S500, the constructed interpretable sparse optimization unfolded network includes at least an initial layer, intermediate layers, and a final layer. Several sequentially connected intermediate layers are located between the initial and final layers and are respectively connected to the data of the initial and final layers. The output data of the initial layer is used as input data for the intermediate layers, and the output data of the intermediate layers is then used as input data for the final layer. The sequentially connected intermediate layers are connected in the same way. The constructed interpretable sparse optimization unfolded network also includes a diagnostic layer, which is connected to the final layer to classify and identify the mechanical state based on the output data of the final layer.

[0033] Based on this, the extracted state feature vector is calculated using the following formula. : ; In the formula, The weights are learnable weights and satisfy the following conditions: ; L represents the j-th layer; L represents the decomposition layer number of the Q-switched wavelet transform.

[0034] Learnable weight coefficients It can adaptively update; as a further preferred option, the weight coefficients can be learned. During adaptive updates, the learnable weight coefficients corresponding to input feature vectors containing more state information and fault features are increased; conversely, the learnable weight coefficients corresponding to input feature vectors containing less state information and fault features are decreased. Leveraging the representational capabilities of deep learning, the constructed interpretable sparse optimization unfolded network can automatically adjust parameters while preserving theoretical interpretability to adapt to feature extraction tasks under different operating conditions and complex noise environments. This allows components containing more state information and significant fault features to receive higher weights, thereby highlighting key diagnostic information during the feature fusion stage and improving the accuracy and robustness of the final fault identification.

[0035] S600: Utilize interpretable sparse optimization to deploy network identification and test the health status of machinery.

[0036] To verify the effectiveness of the interpretable sparse optimization unfolded network proposed in this embodiment for state monitoring, two bearing datasets from different sources—a motor bearing dataset and a wheelset bearing dataset—were selected for experimental evaluation. The basic information of the two datasets is as follows: (1) Motor bearing dataset: This publicly available dataset was collected from a bearing test bench, such as Figure 3 As shown, the test bench consists of a motor, accelerometer, faulty bearing, dynamometer, and load sensor, with a sampling frequency of 12 kHz. The dataset contains three typical fault types: inner race fault, rolling element fault, and outer race fault, with three different damage sizes (0.007 inches, 0.014 inches, and 0.021 inches) for each type of fault. Including the healthy (fault-free) state, a total of 10 operating conditions are formed. Furthermore, the test bench applies four constant loads of 0 HP, 1 HP, 2 HP, and 3 HP during signal acquisition. All raw data underwent normalization preprocessing and were segmented using a sliding window of length 1024 to obtain input samples for network training and testing.

[0037] (2) Wheelset bearing dataset: This private dataset was collected from a comprehensive wheelset transmission test bench, such as Figure 4As shown, the test bench includes a motor, gearbox, accelerometer, faulty bearing, dynamometer, and variable load nut, with the bearing model being NJ204ET NSK. The test bench applies different radial loads by adjusting the bearing end cap nut, and data is acquired at a constant speed of 400 rpm. The dataset contains two fault types: inner race fault and outer race fault, each with three damage dimensions (0.2 mm, 0.4 mm, and 0.6 mm). Including the healthy (fault-free) state, a total of seven operating conditions are formed. For each condition, four constant loads of 0 kN, 0.8 kN, 1.6 kN, and 2.4 kN are applied. Similar to the motor dataset processing method, each file is standardized and segmented using a sliding window of length 1024 to generate input samples.

[0038] To comprehensively evaluate the monitoring performance of the interpretable sparse optimized unfolded network state monitoring method provided in this embodiment, interpretable intelligent state monitoring experiments were conducted on motor bearing datasets and wheelset bearing datasets, respectively. Furthermore, to verify the advantages of this method, four representative state monitoring methods were selected for comparison: ResNet: A classic deep convolutional neural network that alleviates the vanishing and exploding gradient problems during deep network training by introducing residual connections, but lacks interpretability.

[0039] MorletResNet and LaplaceLeNet: Hybrid models of wavelet transform and deep learning, which retain the feature extraction capabilities of deep networks while introducing local interpretability of the network using Morlet wavelets or Laplace wavelets.

[0040] ML-LISTA: An algorithmic unfolding model based on a multi-layer iterative shrinkage threshold algorithm, employing a dual-convolution dictionary filter channel.

[0041] 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. Figure 5 and Figure 6 middle.

[0042] Table 1. Accuracy (%) of different methods in motor bearing dataset condition monitoring task

[0043] Table 2. Accuracy (%) of different methods in wheelset bearing dataset condition monitoring task

[0044] From Table 1-2 and Figure 5-6 It can be seen from this: For the condition monitoring task on the motor bearing dataset, the mechanical condition monitoring method using the interpretable sparse optimized unfolded network provided in this embodiment performs excellently, with accuracy rates all above or close to 95%, significantly outperforming the other four comparative methods. Among the four methods, LaplaceLeNet exhibits the strongest condition monitoring capability, achieving accuracy rates exceeding 90% for each condition monitoring task. However, LaplaceLeNet still lags behind the interpretable sparse optimized unfolded network. ResNet and MorletResNet perform similarly, with accuracy rates around 85% for each task, but none exceeding 90%. ML-LISTA outperforms ResNet and MorletResNet, achieving accuracy rates exceeding or close to 90%, but still significantly lower than the mechanical condition monitoring accuracy of the interpretable sparse optimized unfolded network method provided in this embodiment.

[0045] For the condition monitoring task on the wheelset bearing dataset, the mechanical condition monitoring method using the interpretable sparse optimization unfolded network provided in this embodiment still maintains a high accuracy rate, with only one condition monitoring task having an accuracy rate below 95%, and the highest accuracy rate reaching over 97%. Among the four comparison methods, LaplaceLeNet performs best in condition monitoring, with an accuracy rate above 90% for each condition monitoring task, but the highest accuracy rate is below 93%, which is still significantly lower than the mechanical condition monitoring method using the interpretable sparse optimization unfolded network provided in this embodiment. MorletResNet performs worst in condition monitoring, with the highest accuracy rate approaching 90% but the lowest accuracy rate below 80%, indicating that MorletResNet cannot maintain stable condition monitoring capabilities when facing datasets with more complex data distributions. ResNet and ML-LISTA have comparable condition monitoring capabilities, and their robustness is significantly improved compared to MorletResNet, but their average accuracy rate is still lower than the mechanical condition monitoring method using the interpretable sparse optimization unfolded network provided in this embodiment.

[0046] Through experimental comparison of the two datasets mentioned above, it can be seen that the mechanical state monitoring method with interpretable sparse optimized unfolded network provided in this embodiment has achieved the highest accuracy in all state monitoring tasks and has stable performance on both types of datasets, demonstrating outstanding state monitoring performance and strong generalization ability.

[0047] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the invention can be implemented in other specific forms without departing from its spirit or essential characteristics. Therefore, the embodiments should be considered in all respects as exemplary and non-limiting, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, all variations falling within the meaning and scope of equivalents of the claims are intended to be included within the present invention. No reference numerals in the claims should be construed as limiting the scope of the claims.

Claims

1. A mechanical condition monitoring method based on interpretable sparse optimization unfolded networks, characterized in that: Includes the following steps: S100: Perform mechanical condition data monitoring tests to obtain mechanical condition signals; S200: Construct a sparse optimization model and represent the extracted mechanical state features using sparse features; S300: Derive the iterative optimization solution algorithm for sparse optimization models using the alternating multiplier method; S400: Introduces learnable parameters to replace the parameters in the iterative optimization algorithm; S5 00: Construct interpretable sparse optimized unfolded networks using an unfolding algorithm framework; S600: Utilize interpretable sparse optimization to deploy network identification and test the health status of machinery.

2. The mechanical condition monitoring method based on an interpretable sparse optimized unfolded network according to claim 1, characterized in that: In step S200, the constructed sparse optimization model is represented by the following formula: ； 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; This represents the inverse Q-wavelet transform operator, i.e., the sparse dictionary; Represented as a set of sparse wavelet coefficients, using wavelet coefficients Convert to the time domain; This represents the mechanical state signal obtained from the test.

3. The mechanical condition monitoring method based on an interpretable sparse optimized unfolded network according to claim 2, characterized in that: In step S300, the iterative optimization solution algorithm for the derived sparse optimization model is as follows: ； ； ； 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.

4. The mechanical condition monitoring method based on an interpretable sparse optimized unfolded network according to claim 3, characterized in that: In step S400, the iterative optimization solution algorithm after introducing learnable parameters is as follows: ； ； ； In the formula: Represents a linear rectified function; t are learnable parameters introduced during replacement.

5. A mechanical condition monitoring method based on an interpretable sparse optimized unfolded network according to claim 3, characterized in that: In step S500, the constructed interpretable sparse optimization unfolding network includes several layers of computational units, and each computational unit corresponds to each iteration process in the iterative optimization solution algorithm.

6. The mechanical condition monitoring method based on an interpretable sparse optimized unfolded network according to claim 5, characterized in that: The extracted state feature vector is calculated using the following formula. : ； In the formula, The weights are learnable weights and satisfy the following conditions: ; L represents the j-th layer; L represents the decomposition layer number of the Q-switched wavelet transform.

7. A mechanical condition monitoring method based on an interpretable sparse optimized unfolded network according to claim 6, characterized in that: The learnable weight coefficients It can update adaptively.

8. A mechanical condition monitoring method based on an interpretable sparse optimized unfolded network according to claim 7, characterized in that: The learnable weight coefficients During adaptive updates, the learnable weight coefficients corresponding to input feature vectors containing more state information and fault features are increased; the learnable weight coefficients corresponding to input feature vectors containing less state information and fault features are decreased.

9. A mechanical condition monitoring method based on an interpretable sparse optimized unfolded network according to claim 5, characterized in that: In step S500, the constructed interpretable sparse optimization unfolded network includes at least an initial layer, an intermediate layer, and a final layer. Several intermediate layers connected in sequence are located between the initial layer and the final layer and are respectively connected to the data of the initial layer and the final layer.

10. A mechanical condition monitoring method based on an interpretable sparse optimized unfolded network according to claim 9, characterized in that: In step S500, the constructed interpretable sparse optimized unfolded network also includes a diagnostic layer, which is connected to the final layer data to achieve classification and identification of mechanical state based on the output data of the final layer.

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