Development of an Operational Digital Twin of a Locomotive Braking System Solenoid Valve for Fault Classification

In recent years, a growing role in digital technologies has been filled by model-based digital twinning. A digital twin produces a mapping of a physical structure, operating in the digital domain. Combined with sensor technology and analytics, a digital twin can provide enhanced monitoring, diagnostic, and optimization capabilities. This research harnesses the significant capabilities of digital twining for the unmitigated challenge of fault type classification of a locomotive braking system solenoid valve. We develop a digital twin of the solenoid valve and suggest a method for fault type classification based on the digital twin. The diagnostic ability of the approach is demonstrated on a large experimental dataset.  


INTRODUCTION
Solenoid valves are widely used in industry because of their simple operating mechanism (Fan et al., 2019;J. Y. Oh et al., 2012;Yoon et al., 2013).However, malfunctioning valves can cause serious injury and/or financial damage.Predictive maintenance strategies have been developed to mitigate unexpected failures (Escobar et al., 2011;Kwon et al., 2016;H. Oh et al., 2015;Park et al., 2016;Wang et al., 2018).Existing failure detection methods often use vibration signals.For example, Tsai et al (Tsai & Tseng, 2010) develop a dynamic model-based method for detecting damage to valve stems and valve seats for electronic diesel injection systems, while Guo et al (H. Guo et al., 2017) propose a datadriven method for detecting magnet wear in brake systems.Although vibration signal-based methods have high detection sensitivity, they require the installation of invasive sensors in the target valves, which can be a practical burden.Noninvasive current signal based fault detection methods are advantageous in this regard (B.Orner et al., n.d.;W. Guo et al., 2018).However, these models have not produced robust fault type classification algorithms due to significant differences between simulated data and real data measured under actual operating conditions.To address this problem, this study proposes a digital twin approach (DT) for classifying faults that occur in a solenoid valve of a locomotive braking system.Digital twins are virtual representations of physical systems.They are used to monitor systems, predict their behavior and optimize their performance (Chen et al., 2001;El Mejdoubi et al., 2016).Here, the proposed DT is based on a physical model of the brake system solenoid valve and is optimized using a machine learning approach.A learning model is trained to diagnose faults in the real twin (RT, i.e., the physical structure) based on the residual signal between the real life measured data of the RT and the estimated data of the DT.Implementing DTs is challenging because it is difficult to ensure that the DT accurately represents the system (Seo et al., n.d.).One a is to use machine learning algorithms to improve the accuracy of mathematical models using sensor data (Tsai & Tseng, 2010), which can compensate for the differences between simulation and reality and provide DT improvements.
DTs are becoming increasingly popular in various industries such as manufacturing, transportation, energy, and healthcare (Angadi et al., 2009;Trappey et al., 2015) because they provide accurate and reliable predictions of a system's behavior and state, allowing for longer time intervals between maintenance routines (Kawashima et al., 2004).DTs can be particularly useful for optimizing the performance of complex systems such as those found in manufacturing and transportation (Kawashima et al., 2004;Luomala & Hakala, 2015).
The contribution of this study is twofold: (i) to develop a DT of a solenoid valve for locomotive braking systems and (ii) to

THEORETICAL BACKGROUND
In the following sections, the solenoid valve of the locomotive braking system and the new DT of a locomotive solenoid valve are introduced.In Section 2.1 the solenoid and its role in the braking system are explained.The development of the physical model underlying the behavior of the DT and the relationship between the measured data of the RT and the internal latent physical variables of the DT are described by the equations presented in Section 2.2.

Solenoid Valve in the Braking System
The locomotive of type JTBW42 and other train locomotives have a solenoid valve that plays a critical role in ensuring rail vehicle safety.This valve is an essential part of the braking system.When the pressure in the system drops below a certain threshold, it triggers the solenoid valve to apply the brakes as soon as a brake signal is received.The structure of the braking system is shown in Fig. 1.The position of the solenoid valve between the relay valve and the pressure control valve is crucial for reliable emergency braking.Fig. 3 depicts a cylindrical ferromagnetic steel shell with a movable cylindrical steel piston inserted inside it.The piston is connected to a spring.A coil connected to a DC power source is positioned inside the casing.The coil, when excited, transforms electrical energy into magnetic field energy.This electromagnetic force moves the piston in the positive coordinate direction and reduces the reluctance of the magnetic circuit, which increases the inductance.Once the piston reaches an operating point where the electromagnetic force equals the spring force, the system is in equilibrium.If an external mechanical force,   , is applied suddenly and the piston moves, the inductance decreases, and the mechanical energy of the spring transfers the magnetic energy of the applied coupling.When the electromagnetic force equals the restraining force, a new operating point is reached.Once the mechanical force   drops to zero, the system returns to the starting point, and the mechanical energy of the spring transfers to the coupling field.However, part of the energy is dissipated during transients and due to friction losses in the circuit.
Using Kirchhoff's Voltage Law (2 nd low) and assuming magnetically linear system, the solenoid valve electrical subsystem is described as follows: where  is the resistance,  is the current,  is the voltage,  is the piston displacement,  is the flux linkage,  is the inductance and  is time.
Using Newton's second law the solenoid valve mechanical subsystem is described as follows: where  is the spring constant,  is the initial piston displacement,  is the damping coefficient,  is the piston displacement,  is a force acting on the piston,  is the electromagnetic force and  is mechanical parts mass.
Knowing the reluctance of the system, the Inductance could be derived: where  is the reluctance of the system,  is the piston diameter,  is the cylindrical steel shell geometrical size (see Fig. 3),  is the gap between the piston and the cylindrical steel shell and  is the windings around the coil.
Knowing that the magnetic system is linear and that the current was kept constant during the change of the working point, the electromagnetic force can be derived as follows: Two parameters were routinely measured on the tested locomotives.They are presented in Fig. 4: the solenoid valve current, marked by  , the solenoid valve displacement, marked by  and the solenoid valve voltage  .In the current study, the internal latent physical variables (,  and ) are estimated by solving a least squares problem, where the variables minimize the constraints presented in Eq. 5.This is achieved in Eq. 6, also known as a least squares estimation:

THE PROPOSED ALGORITHM
The proposed algorithm is integrated in the locomotive DT.It consists of five steps, illustrated in Fig. 5.
1.For each RT in the training set, an individualized DT is generated by estimating the internal variables ( ,  and  ).These variables are estimated by the least squares method presented in Eq. 5, as explained in Section 2.2.
2. Based on the internal estimated parameters, the DT calculates the residuals between the measured and estimated signals.transparency in the diagnostic process, which will promote the applicability of our approach in safety-critical train operations and maintenance activities.

DEMONSTRATION ON AN EXPERIMENTAL DATASET
In this section, the new algorithm described in Section 3 is tested and compared with other algorithms: A regular machine-learning algorithm consists of Steps 3, 4, and 5 of the new algorithm described in Section 3.This algorithm extracts the features directly from the measured signals, i.e.,  and  , and a model of deep neural network is trained on these extracted features, as described in Step 4 in Section 3.This algorithm does not use the DT.
The comparison process between the new algorithm and the regular machine-learning algorithm demonstrates the contribution of the DT concept.Unlike traditional fault detection methods, the method described is based on a physically derived solenoid valve model of the braking system, making it applicable to a wide range of operating points and easily transferable to other solenoid valves.In addition, the symptoms are easy to interpret and understand.This model-based approach DT has a broader impact than traditional engineering design, as it can improve train operations and maintenance activities by diagnosing and correcting maintenance faults.Ultimately, the greatest benefit of such DT is its impact on customer experience and operating costs.The paper shows how performance-based engineering, where real-time performance provides the input to an adaptive system packaged in a digital layer -the DTcan create significant value.
Professor Jacob Bortman is Senior Research Fellow at the, Ben-Gurion University of the Negev.As the former Head of the Materiel Command of the Israel Air Force, Prof. Bortman was responsible for all R&D of the Israel Air Force, including the development of unmanned vehicles (UAVs), engines, and satellites.In recent years, the PHM laboratory of Prof. Jacob Bortman performed numerous researches on prognostics of rotating machines parts (bearings, gears, shaft, cardan joints etc.) which were published in state of the art journals.In these studies, the laboratory conducted in researches combining dedicated experimental systems and physics-based models.The experimental systems were designed, built and assembled by the laboratory technician and the models were developed by previous Ph.D. students.The unique test rigs and models in the laboratory allow a thorough understanding of the various parameters which affect the measured and simulated data.
Professor Ron S. Kenett is Senior Research Fellow at the Samuel Neaman Institute, Technion, Haifa, Israel Chairman of the KPA Group, Israel, Chairman of the Data Science Society at AEAI and Research Professor at the University of Turin, Italy.He is an applied statistician combining expertise in academic, consulting and business domains.Ron is member of the Public Advisory Council for Statistics Israel, member of the of the executive academic council, Wingate academic college for sports education, member of the INFORMS QSR advisory board, member of the advisory board of DSRC, the University of Haifa Data Science Research Center and member of the board of directors in several start-up companies.He is Past President of the Israel Statistical Association (ISA) and of the European Network for Business and Industrial Statistics (ENBIS), authored and co-authored over 250 papers and 16 books on topics such as data science, industrial statistics, biostatistics, healthcare, customer surveys, multivariate quality control, risk management, system and software testing, and information quality.

First
Author et al.This is an open-access article distributed under the terms of the Creative Commons Attribution 3.0 United States License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
develop a robust diagnosis of various faults in a solenoid valve for locomotive braking systems by estimating the internal latent physical variables within a DT and training a learning model on the residuals.The study is divided into five sections.Section 2 provides a theoretical background and introduces the new DT, Section 3 presents the new algorithm based on DT, and Section 4 demonstrates the algorithm using experimental data.The study is summarized in Section 5.

Figure 1 .
Figure 1.Structure of the braking system in trains According to the statistics of the Israeli Railway maintenance department, the probability of solenoid valve failure on JTBW42 locomotives increases sharply when mileage exceeds 800,000 km.Many situations are responsible for solenoid valve failure, e.g.situations where the solenoid valve cannot be completely sealed due to corrosion inside the valves, loss of power or mechanical wear [1, 2].As shown in Fig.2, the solenoid valve controls the operation of a moving iron core in a solenoid coil to open or close the exhaust valve by turning the solenoid coil on or off.Of

Figure 2 .
Figure 2. Structure of the solenoid valve 2.2.DT of a Locomotive Solenoid Valve in the Braking System

Figure 3 .
Figure 3. Schematic description of the solenoid structure

3.
From each residual, five features are extracted: mean, variance, maximal value, kurtosis, and absolute sum. 4. A model of Deep Neural Network (DNN) is trained on the extracted features where, at first, the training set is divided into 80% training and 20% validation, and the number of trees is set to have maximal accuracy on the validation set. 5.The trained model is used to predict the classes of the test set.

Figure 5 .
Figure 5.The new suggested algorithm.We analyze the computational, time, and resource demands, especially with respect to large data sets, to provide a comprehensive understanding of the practical implementation of the algorithm.To improve the interpretability of the model, we also explore various methods such as layer-wise propagation of relevance, attention mechanisms, and sensitivity analysis.These additions aim to shed light on the decision-making process of the deep neural network ensemble and provide meaningful These two algorithms, i.e., the regular machine-learning algorithm, and the new suggested algorithm, were tested on an experimental dataset consisting of a 5,500 RT training set and a 250 RT test set.An example of the two measurements of an RT in the training set is depicted in Fig.4.Overall, five classes were tested, one healthy and four types of faults: damage coil, voltage sensor bias, current sensor bias, and damage spring Fig.6.The fault types were divided uniformly across different classes.

Figure 6 .Figure 7 .
Figure 6.Illustration of the damaged spring signal.The results of the two tested algorithms are presented in Fig.7on 250 test examples, 50 from each condition.As can be seen in Fig.7(a -c), the new algorithm achieved a significant improvement from accuracy of 68% to 87.1%.The error is reduced by more than a factor of 2. This result demonstrates the ability of the DT to improve diagnosis by incorporating physical knowledge of the system.