THERMAL-HYDRAULIC PROCESS SUPERVISION
AND MONITORING THROUGH A DATA-DRIVEN
DIGITAL TWIN

Osimone Imhogiemhe, Yoann Jus, Hubert Lejeune, Saïd Moussaoui

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Osimone Imhogiemhe, Yoann Jus, Hubert Lejeune, Saïd Moussaoui. THERMAL-HYDRAULIC PROCESS SUPERVISION AND MONITORING THROUGH A DATA-DRIVEN DIGITAL TWIN. International Design Engineering Technical Conferences & Computers and Information in Engineering Conference, American Society of Mechanical Engineers, Aug 2025, Anaheim (CA), United States. hal-05517371

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# THERMAL-HYDRAULIC PROCESS SUPERVISION AND MONITORING THROUGH A DATA-DRIVEN DIGITAL TWIN

Osimone Imhogiemhe¹,*, Yoann Jus², Hubert Lejeune², Saïd Moussaoui¹,

¹Nantes Université, Ecole Centrale Nantes, LS2N, CNRS UMR 6004, Nantes, 44300, France

²CETIM, Nantes, 44300, France

## ABSTRACT

Real-time supervision of industrial processes is of high importance in order to maximize operational efficiency and prevent system failures. The main purpose of this is to implement predictive maintenance techniques in order to ensure optimal cost, reduce unplanned downtime, and extend the life of the machinery. However, this maintenance and supervision of industrial processes remains a persistent barrier to the efficiency of industrial solutions. Current technological advancements, having provided useful simulation tools coupled with powerful machine learning and AI-based algorithms, have the potential to facilitate the development of data-driven and numerical tools for predictive maintenance and supervision. This paper outlines the implementation of a fault detection and diagnosis algorithm as the decision component of a digital twin. The proposed pipeline uses a three-step approach for fault detection, localization, and estimation using data-driven approaches for detection and estimation through machine learning algorithms and one-dimensional Computational Fluid Dynamics simulations. The proposed Fault Detection and Diagnosis Framework has been validated first through simulations in both the noiseless and noisy cases, and finally in the physical setup of the hydraulic system. The preliminary results indicate a high degree of accuracy in fault identification and good accuracy in fault estimation in a noisy physical environment.

**Keywords:** Digital Twin, Fault Detection, Fault Diagnosis, Thermal-Hydraulic, Predictive Maintenance, Machine Learning

## NOMENCLATURE

* x Scalar

* x Vector

* X Matrix

* ⊙ Hadamard or Element-wise product

## 1. INTRODUCTION

Thermal hydraulics is the branch of the study of the interaction between heat transfer (thermal) and fluid flow (hydraulic)

processes. Thermal hydraulic systems, built on these principles, involve the transfer of heat and fluid flow between components such as boilers, heat exchangers, pumps, and pipelines [1]. Key industries such as power generation, manufacturing, chemical processing, automobiles, and aerospace depend on these systems. There are a variety of problems faced in the use and implementation of these systems, including degradation, fouling, and corrosion, and they require effective maintenance policies to ensure the reliability and efficiency of the systems. Real-time monitoring is possible and is aided by the use of sensors to track the state of the physical system through its process parameters such as pressure, temperature, flows, vibration, etc. The integration of simulation tools allows for real-time modeling using all information acquired from the physical asset. Data and simulation tools are essential tools in the overall fault detection and diagnosis (FDD) process, but it is still necessary to choose appropriate FDD algorithms to preserve the reliability, safety, and efficiency of these systems [2].

Fault detection and diagnosis, a subdiscipline of control engineering, is a combination of procedures used for the tracking of a system in order to determine when faults have occurred, localize them and define the new status of the system (accommodation). Across industries, maintenance represents a substantial fraction of manufacturing costs, therefore, there is a lot of research investment on FDD to enhance cost efficiency [3]. The Fault Detection and Diagnosis process is a fundamental component in the maintenance and operation of thermal-hydraulic systems. It involves identifying faults and diagnosing their origins to facilitate timely corrective actions. FDD techniques include statistical, model-based, and data-driven approaches, with machine learning algorithms playing a crucial role in data-driven fault analysis [4]. Additionally, hybrid methods integrate multiple approaches to enhance diagnostic accuracy. Implementing effective FDD requires extensive high-quality data, substantial computational capacity, real-time processing capabilities, and in most cases advanced machine learning algorithms to ensure system reliability and efficiency.

The digital twin (DT) concept was proposed by Grieves in 2003 [5] and technology pioneered by NASA [6]. It has been tagged among the technologies of the future [7], has revolution-

<footnote>*Corresponding author: osimone.imhogiemhe@ls2n.fr</footnote>
ized many industries as a transformative innovation. It proffers
solution to many challenges faced across industries that cut across
different stages of the life-cycle of a product, system and in some
cases individuals. This technology is being implemented in in-
dustries such as medical, information technology, manufacturing,
aerospace, construction [8, 9], etc. It is mainly based on an adap-
tive virtual representation of the physical asset. However, the
precise definition and scope of DTs remain ambiguous, primar-
ily due to their broad applicability across different industrial use
cases. There have been calls for standardization efforts for inte-
gration across industries [10] and some of these include: ISO IEC
20924 IoT & DT vocabulary, IEC 63278-1, IEC 30141 [11]. DTs
have also been implemented for predictive maintenance [12, 13]
and fault detection and diagnosis [14–16] for different applica-
tions, some also in hydraulic systems but for different purposes
[17, 18].

Digital twin models are typically classified according to their approach to system modeling and numerical simulation methodology. These classifications include data-driven, physics-based, and hybrid models. The choice of model design is determined by the specific operational needs [19]. Data-driven models build predictive and descriptive frameworks using extensive datasets collected from sensors and other sources. In contrast, physics-based models employ physical principles to simulate system behaviour. Hybrid models offer a balanced approach, combining the adaptability of data-driven models with the accuracy of physics-based models.

The design of the fault detection and parameter estimation
system of the proposed digital twin is detailed in a preceding body
of work. This focused primarily on the use of simulation soft-
ware to validate the fault detection and diagnosis algorithm which
serves as the backbone of the physics-based digital twin. This
preliminary study carried out on an ideal system as a stepping
stone for further work. This paper delves into the implementation
of the fault detection algorithm of a thermal-hydraulic process
system in order to build the corresponding digital twin. It partic-
ularly intends to perform the parameter estimation using machine
learning algorithms trained with data generated by a numerical
simulation of the physical model of the system. It starts with the
testing of the methodology built in the previous work, its robust-
ness to noise and the first stage performance when implemented
on the test bench.

## 2. PROJECT ARCHITECTURE

Industry 4.0 is the fourth generation of the industrial revolution. It seeks to integrate digital technologies such as Internet of Things (IoT) sensors, big data analytics, cloud computing, and artificial intelligence to automate industrial processes [9]. Industry 4.0 aims to create intelligent, interconnected, and autonomous systems that improve efficiency, flexibility, and decision-making. In order to attain these goals, digital twins serve as a key enabler of Industry 4.0 by bridging the gap between the physical and digital domains.

### 2.1. Digital Twin

The Digital Twin is a virtual representation of a physical
object, system, or process that is continuously updated with real-

<figure><img src="image_2.png" /><figcaption>FIGURE 1: GENERAL VIEW OF THE PHYSICAL ASSET</figcaption></figure>

time data. Hence, the principal components of the digital twin
are the physical asset, virtual representation and the two-way
connectivity. The following definitions are also considered for
the proposed DT application:

* The DT is an organized set of models representing a real-world entity, in response to specific problems and uses.

* The DT is updated in relation to the real world, with a frequency and precision adapted to its issues and uses.

* The DT is equipped with advanced operating tools enabling it to understand, analyze, forecast, optimize operation and control of the real entity.

### 2.2. The Physical Process

The physical asset is a closed water hydraulic loop installed
with three user settings: the pump operational speed, the opening
of the control valve and the opening of a cooling on/off valve. The
loop is designed with a pressurized tank connected to the site's
compressed air circuit. In order to generate some defects, other
control devices are installed: heating collars, one manual valve
placed at pump suction (to generate cavitation) and one upstream
of the heat exchanger (to degrade its performance), an air pressure
regulator allows perturbation of the pressure level of the whole
loop. The physical system has an installed command control with
a Human-Machine Interface (HMI) as shown in Figure 1.

### 2.3. The Virtual Representation

The ideal virtual twin is not just a pictorial representation
but provides many useful tools that are of benefit. One of which
is to provide a dynamic and interactive model. Therefore, the
virtual twin needs to support multi-parameter simulations for
system analysis. Computational fluid dynamics (CFD) and other
advanced simulation tools are increasingly used to model and an-
alyze thermal-hydraulic systems. Generally, CFD computations
are varied on the level of complexity. There are 3-dimensional,
2-dimensional and 1-dimensional computations, these solve the
fundamental flow equations by resolving the flow in the 3, 2
<figure><img src="image_3.png" /><figcaption>FIGURE 2: THE 1D MODEL OF THE CLOSED HYDRAULIC LOOP ON SIMCENTER FLOMASTER SOFTWARE LOOP</figcaption></figure>

and 1 directions respectfully. Hence the 1D computations of the physical model use simplified equations related to the thermal-hydraulic process under the assumption that the characteristics of the fluid are homogeneous in all directions of the flow. This allows very rapid calculations to be made, which could then be integrated into a control system in real-time or near-real-time. Using commercial software suitable for fluid network modeling to produce this model rather than developing a specific tool for the loop was considered optimal with the choice being Simcenter Flomaster (version 2401)[20] for its ability to model complex fluid systems.

The aim is to find the best trade-off between complexity, calculation speed and accuracy. For this, the model is simplified, the piping elements, the heat exchangers and valves are represented by head loss components. Circuit pressure and flow are defined as the intersection of the pump curve (total head vs. flow) with the network curve (pressure drop vs. flow). There is less emphasis on details for this approach, hence, only the head loss information for the components are required, resulting in rapid pressure and flow calculations. The model constructed is shown in Figure 2. The circular FMU (Functional Mock-up Unit) points symbolise the sensors, while the square FMU points symbolise the control inputs.

## 2.4. Simulation Parameters

The physical asset has three actuators, but this is simplified to two with a fixed operating point of the temperature on the physical asset. The simplified simulation model is therefore a stationary incompressible isothermal 1D model, with only the control valve and the pump speed. The location of the static pressure taps in the physical loop are represented by the connection nodes between the different sections. This 1D model is made up of the following components: a) Pump, b) Regulation Valve, c) Tank, d) Piping Sections 1, 2 and 3.

There are three vectors that are used to define the state of

the system, the control vector, $u$, the component vector, $\theta$, and the process vector, $y$. The control vector is made up of the pump speed, $u_1$, with a maximum rated value of 1000rpm, and the valve opening expressed as a percentage, $u_2$ (%). The component vector is characterized by the parameters of the different components of the model, excluding the regulation valve. The simulation model replicates the physical asset with the nominal values of these parameters. The parameters and their nominal values are shown in Table 1.

The process vector describes the system through the measurements gotten of at five key nodes of the system. These five nodes enable system monitoring and are equipped with sensors for: a) Output pressure of pump "P1" (bar), b) Input pressure of pump "P2" (bar), c) Output pressure of heat exchanger "P3" (bar), d) Input pressure of the heat exchanger "P4" (bar), e) Hydraulic loop overall flow "FL" ($m^3/h$).

<table><caption>TABLE 1: NOMINAL VALUES OF THE COMPONENT VECTOR</caption><thead><tr><td>Description</td><td>Parameter</td><td>Value</td></tr></thead><tbody><tr><td>Head loss of piping section 1 "Loss1"</td><td>θ<sub>1</sub></td><td>2.4</td></tr><tr><td>Head loss of piping section 2 "Loss2"</td><td>θ<sub>2</sub></td><td>20.0</td></tr><tr><td>Head loss of piping section 1 "Loss3"</td><td>θ<sub>3</sub></td><td>1.4</td></tr><tr><td>Tank pressure "P_Tank" (bar)</td><td>θ<sub>4</sub></td><td>3.0</td></tr><tr><td>Pump rated flow "Debit"($m^3/h$)</td><td>θ<sub>6</sub></td><td>200</td></tr><tr><td>Pump rated head "HMT"(m)</td><td>θ<sub>5</sub></td><td>8.61</td></tr></tbody></table>

The proposed digital twin seeks to monitor the process, and implement an optimal fault detection and diagnosis algorithm to predict and correct faults. In that case, the algorithm is faced with some major problems. First, since the components influencing the process cannot be directly monitored, how can a fault be accurately detected through the measured process vector? Can the algorithm detect the specific component(s) in which the fault(s) occurred? Can the changed values be accurately estimated? Finally, what unbiased validation techniques can be used?

## 3. METHODOLOGY

Hydraulic systems can be grouped into these major parts: the actuators, the process, the control, and the sensors with each group having the potential of fault occurrences. This project focuses on component failures through a change in process conditions, ranging from be abrupt, gradual, and intermittent faults. In so doing, a database can be created for machine learning faster than creating one with the physical bench. The methodology focuses on the interface between and decision algorithm that connects the 1D model to the physical asset as seen in Figure 3. The Functional Mockup Interface (FMI) standard [21] was chosen. It is therefore possible to interact with the FMU model via the FMPyd python library developed by Dassault Systèmes. The
<figure><img src="image_4.png" /><figcaption>FIGURE 3: INTEGRATION OF THE 1D MODEL</figcaption></figure>

link with the test bench HMI is possible via the pyads python library (wrapper for TwinCAT ADS) [22]. The known vectors from the physical system are the control vector set by the operator, and the process vector measured by the sensors, and these are communicated through this link.

### 3.1. Fault detection

When both the 1D model and the system are operating with the same control vector, and the components are at the nominal operation points, the measured process vector should be equal or with negligible error due to noise and significant digits of the environment and sensors. This is the foundation of solving the detection problem. A comparative system is set up between the two models, periodically extracting the control vector, $u$, and process vector, $y_s$. It then runs the 1D simulation to get the nominal process vector, $y_m$, then compares this with the system process vector, $y_s$. This is demonstrated in Figure 4. This error vector, $\epsilon$, is expected to be less than a defined detection threshold vector, $\epsilon_d$, as given in Equation (1).

$$ \epsilon^k = |y_s^k - y_m^k| \\ \epsilon^k < \epsilon_d^k \qquad (1) $$

where

* $k$ is the index of the vector from 1 to 5 for the process vector.

* $\epsilon^k$ is the $k$th error value in the error vector.

* $y_s^k$ is the $k$th value of the measured system process vector.

* $y_m^k$ is the $k$th value of the simulated 1D model process vector.

* $\epsilon_d^k$ is the $k$th value of the set detection threshold.

This detection threshold vector, $\epsilon_d$, is tuned by empirical sensitivity analysis, testing for how much change in the component value causes significant drop or increase in the process vector, $y$. The test scenario also determines these values as compensation for noisy conditions increases this as opposed to the noise-free scenario. In the results section, the specific detection threshold will be stated for each scenario. At the moment where the calculated error vector is beyond the detection threshold vector at any of the values of the vector, the fault detection and diagnosis algorithm is initiated.

<figure><img src="image_5.png" /><figcaption>FIGURE 4: THE COMPARATIVE SYSTEM OF THE INTER-FACE</figcaption></figure>

### 3.2. Fault localization

In order to localize the specific component(s) that have experienced faults, a ML algorithm is utilized, creating a classification task. This is the data-driven aspect of the supervision and maintenance model. To solve this task we create a training database with the already designed 1D Simulation model. This database is created using samples of the control vector operation space, that is with different values of $u_1$ and $u_2$, ranging from the minimum value to the maximum value. The database used has 49 values of $u_1$ and 39 values of $u_2$, therefore 1911 operating points of the control vector $u$. At each of the operating points, one or more values of the component vector are increased or reduced from the nominal point and the measured process vector is recorded as well as the index, $n$, of the changed parameter(s). There are 25 changed values apart from the nominal values of the component vector in this database. In total, there are 286650 samples stored in the database and more points will be added as the algorithm is optimized. The aim of the ML algorithm is to learn a function, $\psi$, that maps each control vector combination and the measured process vector to the corresponding index. This function shown in Equation (2), allows any new values of $u$ and $y$ to predict the index, $n$. When the exact value of the operating points are not found in the database, there are two options to run the test. The first option is to use the nearest operating point's database, and the second option is to use the database of surrounding operating points. Prior testing shows better performance when using the surrounding operating points.

$$ \psi(U, Y) = n \qquad (2) $$

### 3.3. Fault estimation

As for estimation of the new value of the localized fault, another database is needed, but at the moment this database is only generated immediately after the localization step is completed. This is done in this way because the tested data points are not in the data points of the localization database, especially with the noisy state of the physical system. Each database is generated by the 1D model at the specific control vector values extracted from the real system and using 20 evenly spaced variations of the specific component value, in order to store the resulting process vector. This creates a regression task, which aims to fit the database created with the predicted component index, $n$, to a function, $g$, where $u$ and $y$ result in the changed component value
$\theta_n$. This function shown in Equation (3), allows the extracted values of $u$, $y$, and the predicted index, $n$, estimate the value of the particular component.

$$g(u, Y, n) = \theta_n \qquad (3)$$

For the purpose of validating the result, the component vector is updated and then the 1D model runs the simulation with this updated value and the control vector. The resulting process vector, $y_e$, has to be less than the set validation threshold, $\varepsilon_v$. This threshold is either equal to or less than the detection threshold. This is tuned empirically as each component has different sensitivities to the process vector.

$$\begin{aligned} \varepsilon^k &= |y_s^k - y_m^k| \\ \varepsilon^k &< \varepsilon_v^k \end{aligned} \qquad (4)$$

where

* $k$ is the index of the vector from 1 to 5 for the process vector.

* $\varepsilon^k$ is the k-th error value in the error vector.

* $y_s^k$ is the k-th value of the measured system process vector.

* $y_m^k$ is the k-th value of the simulated 1D model process vector.

* $\varepsilon_v^k$ is the k-th value of the set validation threshold.

There are a few errors that are possible and attempts are made to mitigate in the full application of the algorithm. If the detection threshold is not properly tuned, in the case where it is too high, several faults will not be detected (false negatives), but too low and noisy signals from the physical system will trigger the FDD algorithm (false positives). This also applies with the validation threshold. In the case where it is too low and there could be no converging, but too high and there will be several false positives. There is also dependency in the proposed algorithm so if there is a mistake in the localization this will lead to a wrong estimation. But even in the case of correct localization, it is also possible that the first estimated value is not within the set threshold. So as to circumvent these problems, the algorithm is allowed to loop in the same predicted component index, with an updated estimated value until each index can be tested as seen in Figure 5.

## 4. EXPERIMENTS AND RESULTS

There are three scenarios under which we test the algorithm including the physical system implementation. The intention is to mimic the physical system gradually so as to fine tune the algorithm. With that as the aim, the focus is only on the components for which faults can be really introduced on the physical set-up. These components are:

1. Head loss of piping section 2 "Loss2" ($\theta_2$)

2. Head loss of piping section 1 "Loss3" ($\theta_3$)

3. Tank pressure "P_Tank" (bar) ($\theta_4$)

<figure><img src="image_6.png" /><figcaption>FIGURE 5: THE FULL IMPLEMENTED ALGORITHM</figcaption></figure>

### 4.1. Noise-free Simulation

The aim of this test scenario is to validate as a first step the methodology. The 1D model is used in place of the real system. There are six control vector points that are tested each with five different values of the control vector. To set both the detection and validation threshold vectors, the resolution of the available sensors are considered. With installed pressure sensors of 0.01 bar, we consider changed values of the component that cause a significant change of 0.02 bar as faults. But since each component value affects the process vector in different ways we use the following threshold vectors:

$$\varepsilon_d = \begin{bmatrix} 0.02\text{bar} \\ 0.02\text{bar} \\ 0.02\text{bar} \\ 0.02\text{bar} \\ 1\text{m}^3/\text{h} \end{bmatrix}, \varepsilon_v = \begin{bmatrix} 0.01\text{bar} \\ 0.01\text{bar} \\ 0.01\text{bar} \\ 0.01\text{bar} \\ 1\text{m}^3/\text{h} \end{bmatrix} \qquad (5)$$

Table 2 illustrates the accuracy of the algorithm in the ideal case. The False Detection includes the situation where the system does not converge to any value. No Detection refers to scenarios where the FDD algorithm was not triggered.

<table><caption>TABLE 2: DETECTION RESULTS IN THE NOISE-FREE SCENARIO</caption><thead><tr><th>Component</th><th>True Detection</th><th>False Detection</th><th>No Detection</th></tr></thead><tbody><tr><td>θ<sub>2</sub></td><td>25</td><td>4</td><td>1</td></tr><tr><td>θ<sub>3</sub></td><td>24</td><td>1</td><td>5</td></tr><tr><td>θ<sub>4</sub></td><td>24</td><td>6</td><td>0</td></tr></tbody></table>

The detection accuracy in the noise-free scenario is about 81.1 %. As a result of the dependency of the algorithm, the
estimation error shown in Figure 6 is only for data points where the localization was accurate.

<figure><img src="image_7.png" /><figcaption>FIGURE 6: THE ESTIMATION ERROR OF THE SVR MODEL FOR THE NOISE-FREE TEST SCENARIO</figcaption></figure>

## 4.2. Noisy Simulation

In this scenario we add a random gaussian noise of 5% using the formula given in Equation (6). The aim is to test the robustness of the methodology and database to noise without changing the database. This is in order to validate its application to the physical system. The same combination of control vector and component vector tested in the ideal scenario are tested in this noisy scenario. The drop in accuracy of $\theta_2$ is expected due to its low impact on the measurements. This is why a large portion of it does not even trigger the alarm.

$$y = y_i + \eta \quad (6)$$

where

* $y$ is the measured noisy process vector used in the FDD algorithm.

* $y_i$ is the noise-free process vector from the 1D model.

* $\eta$ is a Gaussian noise with appropriate variance such that the noise level will be about 5%.

The standard deviation vector, $\sigma$, is calculated using the average of the process vector at the central point of the control vector of 500rpm and 50% valve opening. So as to compensate for the noise, the threshold vectors are updated to:

$$\varepsilon_d = \varepsilon_v = \begin{bmatrix} 0.1\text{bar} \\ 0.1\text{bar} \\ 0.1\text{bar} \\ 0.1\text{bar} \\ 3\text{m}^3/\text{h} \end{bmatrix} \quad (7)$$

The extreme estimation error of $\theta_2$ seen in Figure 7, is due to its insensitivity and inability to cause significant change in the process vector. One of the solutions considered is to have specific validation threshold vectors for each component.

<table><caption>TABLE 3: DETECTION RESULTS IN THE NOISY SCENARIO</caption><thead><tr><th>Component</th><th>True Detection</th><th>False Detection</th><th>No Detection</th></tr></thead><tbody><tr><td>θ<sub>2</sub></td><td>2</td><td>23</td><td>5</td></tr><tr><td>θ<sub>3</sub></td><td>19</td><td>3</td><td>8</td></tr><tr><td>θ<sub>4</sub></td><td>20</td><td>5</td><td>5</td></tr></tbody></table>

<figure><img src="image_8.png" /><figcaption>FIGURE 7: THE ESTIMATION ERROR OF THE SVR MODEL FOR THE NOISY TEST SCENARIO</figcaption></figure>

## 4.3. Physical Implementation

In the physical setup, the nominal of the system is dependent on the temperature, pump speed, and valve opening unlike the assumptions of the 1D model. Therefore, at present, the algorithm is only tested at a pump speed $u_1 = 800$ rpm and a valve opening $u_2 = 48\%$ at which the nominal values in Table 1 were calculated. The HMI of the Command Control is equipped with numerical calculations for a number of physical quantities which are evaluated from the various sensors using analytical formulations. These calculated values are used to compare the estimated values from the tests performed. However, it should be noted that these values are not very reliable at all temperature values nor control vector values. For example, low flow values in the heat exchanger section can give inconsistent results for pressure loss coefficients.

Figure 9 illustrates a section of the experimentation performed on the physical system. While Figure 8 presents the estimation error calculated in relation to the calculated component values extracted from the Command Control. $\theta_3$ and $\theta_4$ are easily detected as they both have visible effects on the current process vector while $\theta_2$ is very sensitive to noise.

# 5. DISCUSSION AND CONCLUSION

This paper has presented the implementation of a digital twin of a thermal-hydraulic process for predictive maintenance and supervision. Due to the mathematical complexities involved in such systems, a physics-based model using a 1D CFD of the physical system is implemented. The FMU module gives the possibility to create a database rapidly (on line) and also gives the certainty that the database is going to be on the same exact operating point. This model is then tested in the ideal and noisy scenarios to aid the physical implementation. There is dependency in the proposed
<figure><img src="image_9.png" /><figcaption>FIGURE 8: THE ESTIMATION ERROR OF THE SVR MODEL FOR THE PHYSICAL TEST SCENARIO</figcaption></figure>

algorithm, but the estimation model predicts within a maximum error range of ± 12% except in a few outlier cases. The precision of the sensors in the hydraulic loop is crucial to the accuracy. The model requires further tuning and optimization in the database, thresholds and both the detection and estimation models. Further work will involve creating a larger database with additive noise, testing for other fault sequencing.

REFERENCES

[1] Todreas, N.E. and Kazimi, M.S. *Nuclear Systems Volume 1: Thermal Hydraulic Fundamentals, Third Edition*. CRC Press (2021). URL https://books.google.fr/books?id=mwwLEAAAQBAJ.

[2] Leo H. Chiang, Richard D. Braatz, Evan L. Russell. *Fault Detection and Diagnosis in Industrial Systems*. Springer London (2012).

[3] Gareev, Albert, Protsenko, Vladimir, Stadnik, Dmitriy, Greshniakov, Pavel, Yuzifovich, Yuriy, Minaev, Evgeniy, Gimadiev, Asgat and Nikonorov, Artem. "Improved Fault Diagnosis in Hydraulic Systems with Gated Convolutional Autoencoder and Partially Simulated Data." *Sensors* Vol. 21 No. 13 (2021). DOI 10.3390/s21134410. URL https://www.mdpi.com/1424-8220/21/13/4410.

[4] Slimani, A., Ribot, P., Chanthery, E. and Rachedi, N. "Fusion of Model-based and Data-based Fault Diagnosis Approaches." *IFAC-PapersOnLine* Vol. 51 No. 24 (2018): pp. 1205-1211. DOI https://doi.org/10.1016/j.ifacol.2018.09.698. URL https://www.sciencedirect.com/science/article/pii/S2405896318324170. 10th IFAC Symposium on Fault Detection, Supervision and Safety for Technical Processes SAFEPROCESS 2018.

[5] Grieves, Michael and Vickers, John. *Digital Twin: Mitigating Unpredictable, Undesirable Emergent Behavior in Complex Systems*. Springer International Publishing, Cham (2017): pp. 85-113. DOI 10.1007/978-3-319-38756-7_4. URL https://doi.org/10.1007/978-3-319-38756-7_4.

[6] Grieves, Michael. "Digital Twin: Manufacturing Excellence through Virtual Factory Replication." *White Paper* (2014): pp. 1-7.

[7] VanDerHorn, Eric and Mahadevan, Sankaran. "Digital Twin: Generalization, characterization and implementation." *Decision Support Systems* Vol. 145 (2021): p. 113524. DOI https://doi.org/10.1016/j.dss.2021.113524. URL https://www.sciencedirect.com/science/article/pii/S0167923621000348.

[8] Tao, Fei, Zhang, He, Liu, Ang and Nee, A. Y. C. "Digital Twin in Industry: State-of-the-Art." *IEEE Transactions on Industrial Informatics* Vol. 15 No. 4 (2019): pp. 2405-2415. DOI 10.1109/TII.2018.2873186.

[9] Lo, C.K., Chen, C.H. and Zhong, Ray Y. "A review of digital twin in product design and development." *Advanced Engineering Informatics* Vol. 48 (2021): p. 101297. DOI https://doi.org/10.1016/j.aei.2021.101297. URL https://www.sciencedirect.com/science/article/pii/S1474034621000513.

[10] Sharma, Angira, Kosasih, Edward, Zhang, Jie, Brintrup, Alexandra and Calinescu, Anisoara. "Digital Twins: State of the art theory and practice, challenges, and open research questions." *Journal of Industrial Information Integration* Vol. 30 (2022): p. 100383. DOI https://doi.org/10.1016/j.jii.2022.100383. URL https://www.sciencedirect.com/science/article/pii/S2452414X22000516.

[11] Wang, K., Wang, Y., Li, Y., Fan, X., Xiao, S. and Hu, L. "A review of the technology standards for enabling digital twin [version 2; peer review: 2 approved]." *Digital Twin* Vol. 2 No. 4 (2022). DOI 10.12688/digitaltwin.17549.2.

[12] van Dinter, Raymon, Tekinerdogan, Bedir and Catal, Cagatay. "Predictive maintenance using digital twins: A systematic literature review." *Information and Software Technology* Vol. 151 (2022): p. 107008. DOI https://doi.org/10.1016/j.infsof.2022.107008. URL https://www.sciencedirect.com/science/article/pii/S0950584922001331.

[13] Aivaliotis, P., Georgoulias, K., Arkouli, Z. and Makris, S. "Methodology for enabling Digital Twin using advanced physics-based modelling in predictive maintenance." *Procedia CIRP* Vol. 81 (2019): pp. 417-422. DOI https://doi.org/10.1016/j.procir.2019.03.072. URL https://www.sciencedirect.com/science/article/pii/S2212827119303774. 52nd CIRP Conference on Manufacturing Systems (CMS), Ljubljana, Slovenia, June 12-14, 2019.

[14] Abdoune, Farah, Nouiri, Maroua, Cardin, Olivier and Castagna, Pierre. "An enhanced methodology of Fault Detection and Diagnosis based on Digital Twin." *IFAC-PapersOnLine* Vol. 55 No. 19 (2022): pp. 43-48. DOI https://doi.org/10.1016/j.ifacol.2022.09.181. URL https://www.sciencedirect.com/science/article/pii/S2405896322013945. 5th IFAC Workshop on Advanced Maintenance Engineering, Services and Technologies AMEST 2022.

[15] Xie, Xiang, Merino, Jorge, Moretti, Nicola, Pauwels, Pieter, Chang, Janet Yoon and Parlikad, Ajith. "Digital twin enabled fault detection and diagnosis process for building HVAC systems." *Automat-
<figure><img src="image_10.png" /><figcaption>FIGURE 9: THE SINGLE PERTURBATION SCENARIO TESTED ON THE PHYSICAL TEST SCENARIO</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>FIGURE 10: THE MEASURED AND ESTIMATED PROCESS VECTOR FOR THE SINGLE PERTURBATION SCENARIO TESTED ON THE PHYSICAL TEST SCENARIO</figcaption></figure>
tion in Construction Vol. 146 (2023): p. 104695.
DOI https://doi.org/10.1016/j.autcon.2022.104695.
URL https://www.sciencedirect.com/science/article/pii/
S0926580522005659.

[16] Nguyen, Tat Nghia, Ponciroli, Roberto, Bruck, Paul, Es-selman, Thomas, Rigatti, Joseph and Vilim, R. "A digital twin approach to system-level fault detection and diagnosis for improved equipment health monitoring." *Anals of Nuclear Energy* Vol. 170 (2022): p. 109002. DOI 10.1016/j.anucene.2022.109002.

[17] Gómez-Coronel, Leonardo, Santos-Ruiz, Ildeberto, Torres, Lizeth, López-Estrada, Francisco-Ronay, Gómez-Peñate, Samuel and Escobar-Gómez, Elías. "Digital Twin of a Hydraulic System with Leak Diagnosis Applications." *Proceedses* Vol. 11 No. 10 (2023). DOI 10.3390/pr11103009. URL https://www.mdpi.com/2227-9717/11/10/3009.

[18] Wang, Lintao, Liu, Yuchong, Yin, Hang and Sun, Wei. "Fault diagnosis and predictive maintenance for hydraulic system based on digital twin model." *AIP Advances* Vol. 12 (2022): p. 065213. DOI 10.1063/5.0098632. URL https://pubs.aip.org/aip/adv/article-pdf/doi/10.1063/5.0098632/16466602/065213_1_online.pdf, URL https://doi.org/10.1063/5.0098632.

[19] Erikstad, Stein. "Merging Physics, Big Data Analytics and Simulation for the Next-Generation Digital Twins." *Proceedings of the HIPER 2017, High-Performance Marine Vehicles, Zevenwacht, South Africa*: pp. 140-150. 2017.

[20] AG, Siemens. "Simcenter Flomaster." (2024). URL https://plm.sw.siemens.com/en-US/simcenter/systems-simulation/flomaster/.

[21] Blochwitz, Torsten, Otter, Martin, Arnold, Martin, Bausch, Constanze, Clauß, Christoph, Elmqvist, Hilding, Jung-hanns, Andreas, Mauss, Jakob, Monteiro, Manuel, Neid-hold, Thomas, Neumerkel, Dietmar, Olsson, Hans, Peetz, Jörg-Volker and Wolf, Susann. "The Functional Mockup Interface for Tool independent Exchange of Simulation Models." *Proceedings of the 8th International Modelica Conference*: pp. 105-114. 2011. DOI 10.3384/ecp11063105.

[22] Lehmann, Stefan. "Welcome to pyads's documentation!" (2015). URL https://pyads.readthedocs.io/en/latest/index.html.