Research on fault diagnosis method of the hydraulic system based on digital twin

As an advanced technology, digital-twin (DT) is an effective method to achieve information fusion and has been widely applied in fault diagnosis (FD). An integrated model, which consists of the DT model, consistency model, and FD network, is developed to detect faults in hydraulic systems (HS) by the dual effective information communication between the virtual model and real system. The consistency between the model and the real system can be guaranteed with the consistency model. A large number of labeled datasets generated by the DT model are used to train the FD network, which results in a significant reduction in the uncertainty of model parameters. A case study is done to investigate the performance of the DT method and the results show that the method can diagnose faults of HS effectively, efficiently, and accurately.


Introduction
The development of a DT virtual model is one of the key technologies for FD and life prediction of HS using the DT method.Many numerical models and methods [1] have been gradually applied to FD and the life management of HS.To improve the accuracy of HS prediction and diagnosis, various methods have been applied, such as expert systems [2] , optimization method of support vector machine [3] , wavelet packet transformation [4] , machine learning [5][6] , transfer learning [7] , and so on.However, neural networks still suffer from the problem of local minimization.The initialization of the network with different weights may lead to different results.Additionally, there is an issue of over-dependence on training samples.
DT technology is a good solution to address the aforementioned problems.Therefore, this work pioneers the framework of DT drive and develops a general method for the accurate diagnosis of HS.The proposed DT drive framework is capable of connecting virtual and physical models through virtual-real interactions.Genetic algorithms (GA) are also used to improve the efficiency of consistency maintenance.Furthermore, the FD accuracy of the network can be effectively enhanced by utilizing the PCA-BiLSTM network.As a result, the proposed DT drive framework will enhance the accuracy of HS FD.

DT-driven FD framework of HS
As shown in Figure 1, the DT-driven FD framework of HS consists of a physical entity, perception, To address the issue of model parameter uncertainty, a method for maintaining consistency between the DT model and the real object is proposed.The framework mainly consists of three parts: the real system, the DT model, and the dynamic system identification model.The framework of the HS consistency maintenance method is illustrated in Figure 1.

DT model theory
The hydraulic shift system operates according to the basic laws of fluid mechanics.The HS uses liquid as a working medium in series to form a functional circuit of basic hydraulic components to achieve shifting.The entire process follows the PASCAL principle of fluid mechanics, with the Bernoulli equation being an indispensable formula for analyzing the HS circuit.It is an expression of the law of conservation of energy in the HS.Formula 1 is shown as follows: Formula 1 can also be expressed as Formula Compared to the ideal formula, the formula expresses the energy loss during the flow of the liquid.This flow loss can be obtained by the Darcy-Weisbach formula:

DT consistency maintenance method
Determinism and virtual and real interaction of DT are achieved, and the concept of dynamic system identification is introduced.The objective is to minimize the steady-state error between the mathematical model of the HS and the real-world HS, meeting the specified requirements.This can be formulated as an optimization problem, where the objective function represents the minimum value to be found.The objective function can be expressed as follows: The dynamic error can be calculated by Formula 8: ( )/ In this way, the objective function can be designed so that the dynamic error of the system is less than 10%, that is: By transforming the consistency maintenance problem into a DT parameter optimization problem, we can obtain the dynamic response model of the system, which facilitates the deployment of subsequent control strategies.Additionally, it allows us to obtain parameters that are difficult to directly measure on the real test bench, enabling subsequent fault diagnosis and prediction.Furthermore, the bidirectional information exchange between the virtual model and the physical model distinguishes the DT driven framework from existing fault diagnosis and prediction methods for HS.
To compare the influence of different algorithms on the identification effect, the calculation formula for precision is introduced as follows: Because the HS model contains both linear and nonlinear components, the genetic algorithm is chosen in this study for parameter identification of the HS.This algorithm is selected due to its high computational accuracy, aiming to build a high-precision DT model.

FD network
Data-based diagnostics are effective when reliable labeled data is available throughout the entire lifecycle of the HS.However, HS typically operates under high-pressure and high-noise conditions, making it challenging to obtain sufficient labeled data.Testability analysis enhances the testability of the actual HS, and reliable labeled data is obtained based on the DT model.To enhance the FD accuracy of the hydraulic shift system, the HS network is studied.
The diagnosis framework mainly consists of two parts: the data layer and the network layer.The data layer supports the network layer, while the network layer performs the final FD application.Additionally, this framework is an integral part of the DT framework for HS.
T h e t r a i n i n g n e t w o r k u t i l i z e s a B i L S T M n e t w o r k .' B i ' i n B i L S T M n e t w o r k s t a n d s f o r b idirectional, which combines both forward and backward LSTM networks.The BiLSTM model effectively addresses the limitation of the LSTM model, which can only learn forward time sequence information and cannot utilize backward time sequence information.This improvement enhances the learning capability of the network model.The forward output of the hidden layer is represented by Formula 11, the backward output of the hidden layer is represented by Formula 12, and the concatenated output yt of the hidden layer is represented by Formula 13.

Consistency maintenance verification
Taking the hydraulic shift system as an example, AMESiM, SolidWorks, and ADAMS are used to build the fusion model.The fusion model is a co-simulation based on AMESim.The DT model is built in Simulink, and the parameters required for parameter identification are set as parameters in the model.This allows the GA algorithm to be implanted in the model and used.The collection of dynamic pressure data of the real system is completed by the test and control system of the hydraulic shift system.The system can automate the management of the test module and realize the basic function of information interaction between the hardware-in-the-loop simulation system and the actuator.
To further prove the effectiveness of the genetic algorithm in maintaining the consistency of the DT, two types of faults are selected for identification: filter clogging and insufficient pre-filled gas pressure in the accumulator, hydraulic pump leakage, and hydraulic cylinder leakage in the hydraulic shift system.The system identification results obtained by dynamic system identification with hydraulic cylinder displacement as the target are shown in Figure 2.  As shown in Figure 3, the comparative experiment demonstrates that the comprehensive accuracy rate based on experimental data can reach over 98% at its highest.The AMESim model exhibits the lowest diagnostic accuracy rate, and the diagnostic accuracy rate for different types of faults fluctuates significantly.In contrast, the algorithm trained using the data set generated after optimizing the consistency maintenance algorithm shows a significant improvement in accuracy.The comprehensive FD accuracy reaches over 96%, which proves that the virtual-real interaction feature plays a significant role in generating reliable data for FD.

Verification of network accuracy
In the comparative experiment, two types of BiLSTM neural networks (with or without PCA) were used for FD of HS.To study the difference between the BiLSTM network and the LSTM network, as well as the influence of PCA on the BiLSTM network, all other parameters of the network were kept unchanged.Only the use of PCA and the use of bidirectional LSTM structure were varied.The confusion matrix of the three different LSTM structures used for FD is shown in Figure 4. shows the confusion matrix of the three network structures.Among the three methods, the PCA-BiLSTM method achieves the highest accuracy, exceeding 98%.The LSTM method achieves an accuracy of 96.96875%, and the BiLSTM method achieves an observation accuracy of 97.75%.This indicates that most states can be correctly diagnosed and demonstrates the advantages of the BiLSTM network for multi-channel data in HS.

Conclusions
This paper addresses the challenges of consistency maintenance and FD in HS and analyzes the existing gaps in related fields.Based on the concept and method of DT, an FD framework for HS

Figure 1 .
Figure 1.HS consistency maintenance method framework.To address the issue of model parameter uncertainty, a method for maintaining consistency between the DT model and the real object is proposed.The framework mainly consists of three parts: the real system, the DT model, and the dynamic system identification model.The framework of the HS consistency maintenance method is illustrated in Figure1.

Figure 2 .
Figure 2. Dynamic identification results of hydraulic cylinder compound fault.To verify the validity of the DT model, the fault data set generated by the DT model is compared with the data obtained from the hydraulic shift test bench and the model without consistency maintenance.To ensure the reliability of the data, any data set that deviates from the simulation output curve is removed and re-simulated.The data set consists of 8-channel 201-point data.MATLAB script is used to accelerate the construction process of the database.Therefore, as shown in Figure3, six states of the database were selected for comparative experiments.

Figure 3 .
Figure 3.Comparison diagram of specific FD rate of three kinds of data.

Figure 4 .
Figure 4.shows the confusion matrix of the three network structures.Among the three methods, the PCA-BiLSTM method achieves the highest accuracy, exceeding 98%.The LSTM method achieves an accuracy of 96.96875%, and the BiLSTM method achieves an observation accuracy of 97.75%.This indicates that most states can be correctly diagnosed and demonstrates the advantages of the BiLSTM network for multi-channel data in HS.