# Monitoring Exhaust Valve Dead Time Behavior in Marine Dual-Fuel Engines Using Correlation-Based Clustering

Ayah Youssef, Hassan Dabaja, Hassan Noura, El Mostafa El Adel, Mustapha Ouladsine

► To cite this version:

Ayah Youssef, Hassan Dabaja, Hassan Noura, El Mostafa El Adel, Mustapha Ouladsine. Monitoring Exhaust Valve Dead Time Behavior in Marine Dual-Fuel Engines Using Correlation-Based Clustering. 6th International Conference on Control and Fault-Tolerant Systems (SysTol), Oct 2025, Ayia Napa, Cyprus. pp.145-150, 10.1109/SysTol66549.2025.11267289. hal-05313871

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Submitted on 14 Oct 2025

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<figure><img src="image_1.png" /></figure>
# Monitoring Exhaust Valve Dead Time Behavior in Marine Dual-Fuel Engines Using Correlation-Based Clustering*

Ayah Youssef, Hassan Dabaja, Hassan Noura, El Mostafa El Adel and Mustapha Ouladsine<fnref n="1" />

*Abstract*—Dual-fuel engines are well known for their low environmental impacts compared to other engines. However, continuous monitoring during propulsion is crucial to ensure safe navigation and reliability. Faults in the exhaust system can lead to severe consequences, including increased toxic emissions, power loss, and high vibrations. To identify abnormalities in exhaust valve closing dead time (EVCDT)—the duration between when the closing command is sent and the actual movement of the valve, this study applies a correlation-based clustering method using K-means on EVCDT data from 12 cylinders. The developed algorithm continuously monitors the EVCDT data, distinguishing between healthy and potentially faulty cylinders. The findings underscore the effectiveness of correlation clustering-based diagnostics for predictive maintenance, supporting sustainable marine operations and relations among cylinders EVCDTS.

## I. INTRODUCTION

Dual-fuel engines have become increasingly important in the maritime industry due to their operational flexibility, enhanced efficiency, and lower environmental impact compared to traditional diesel engines. These engines can run on both diesel fuel and liquefied natural gas (LNG), allowing vessels to choose their fuel based on availability, cost, and adherence to emissions regulations. Studies indicate that utilizing LNG in dual-fuel engines can significantly reduce carbon dioxide (CO₂) emissions and nearly eliminate sulfur oxides (SOₓ) and particulate matter [1], which are pollutants that contribute to air pollution and ocean acidification [2].

Ensuring stability and safety is crucial for reliable propulsion during long voyages. However, in addition to hardware faults, due to the exposure of the engine to factors such as vibration, high temperature, humidity and dust, sensor and electrical failure can occur, leading to false alarms [3]. These circumstances render key engine components particularly vulnerable to faults, which can escalate into serious failures and potentially result in dangerous situations, including collisions.

Marine dual-fuel engines consist of five main subsystems that are also present in diesel engines: fuel injection, air intake, exhaust, lubrication, and cooling systems [4]. In addition, the gas supply system, which is specific to dual-fuel engines, facilitates the integration of LNG, and a pilot fuel supply system supports combustion in gas mode

by supplying small fuel quantities. Each subsystem has a distinct function that contributes to the overall stability and performance of the engine.

Monitoring marine engines is essential for maintaining operational efficiency, optimizing fuel consumption, and reducing emissions, all of which are key to sustainable maritime operations. Early detection of faults in critical components like cylinders and exhaust valves improves safety, lowers maintenance costs and ensures reliable vessel performance [5]. Identifying faults in the exhaust system is particularly important, as issues there can hinder combustion efficiency, resulting in power loss, increased fuel consumption, and higher exhaust gas temperatures. These problems not only diminish engine efficiency but also elevate emissions of CO₂, SOₓ, and nitrogen oxides (NOₓ), which are subject to international environmental regulations [6]. Developing effective fault detection systems is vital for spotting issues before they develop into serious engine failures, thus reducing vessel downtime and related repair expenses [7].

Data-driven diagnostic techniques are increasingly used in marine engine diagnosis. Such techniques require no prior knowledge and rely on the availability of abundant measured data, unlike model-based and qualitative empirical knowledge-based techniques. Data-driven techniques could be supervised or unsupervised learning, based on the type of available data. Supervised learning is used when training data are labeled, which is not the case in unsupervised learning [4].

A variety of methodologies are used for detecting exhaust valve faults through data-driven techniques including Neural Networks (NN) [7], Principal Component Analysis paired with Support Vector Machines (PCA-SVM) and One-Dimensional Convolutional Neural Networks (1D-CNN) [8], transfer learning with Modified VGG16 [9], and PCA clustering with Back Propagation (BP) Neural Networks [10]. This paper applies an unsupervised correlation clustering-based approach that employs K-means to analyse real historical data from a dual-fuel engine, focusing on detecting abnormalities in the Exhaust Valve Closing Dead Time (EVCDT) by comparing the behavior between all cylinders' EVCDT. Section II offers an overview of the exhaust system and exhaust valve timing. In Sections III, the mathematical principle of K-means clustering is elaborated. Section IV describes the algorithm used for monitoring EVCDTs among cylinders. In Section V, the results of the abnormality detection methodology in EVCDT are shown and discussed. Finally, concluding remarks are given in Section VI.

<footnote>*This work is supported by BPIFrance, Banque Publique d'Investissement, France.</footnote>

<footnote n="1">¹Aix Marseille Univ., CNRS, LIS (UMR 7020), Avenue Escadrille Normandie-Niemen, F-13397 Marseille Cedex 20, France.
(ayah.youssef, hassan.dabaja, hassan.noura, el-mostafa.el-adel,mustapha.ouladsine)
@lis-lab.fr</footnote>
## II. EXHAUST SYSTEM

The exhaust system is considered as one of the main subsystems of the marine engine. The exhaust manifold receives the exhaust gases from the combustion chamber by means of an exhaust valve (EV), which forms the main component of the exhaust system. The opening and closing mechanism of the EV is controlled by a spring air and oil system for the opening and closing action of the valve. This action is based on the position of the crank angle, indicating the phase of the cycle (compression-expansion-exhaust-intake-ignition).

### A. Exhaust valve mechanism

The Engine Control System (ECS) is responsible for sending the “open” and “close” commands to the EV actuator, allowing the servo oil to flow to the exhaust valve actuator, pushing the piston upward to open the valve. However, for the EV to close, the actuator pushes the spring down to drain the servo oil and close the EV (Fig. 1).

<figure><img src="image_2.png" /><figcaption>Fig. 1. EV opening/closing operation</figcaption></figure>

### B. Exhaust valve timing

The term “dead time” refers to the valve’s duration to complete its movement (opening or closing) starting from the moment the ECS sends the signal to actual initiation of the action. EVCDT projects the time from when the ECS sends a command to the actuator allowing the start of the drain of servo oil and the start of EV closure. Fig. 2 defines the position of EVCDT within a complete Otto-cycle combustion process.

### C. Cylinders Valve Dead-Time Synchronization

Under ideal engine operation, where load is shared equally among cylinders, the engine runs on constant speed and mode, and combustion is perfect, then EVCDT between cylinders is identical. In reality, however, variations in combustion efficiency and quality, injection-timing delays, fuel injection quantity, and operating speed and mode let the values of EVCDTs vary differently from one cylinder to another. Still, under healthy conditions at a given mode and speed, the behavior (trend) remains aligned between cylinders.

<figure><img src="image_3.png" /><figcaption>Fig. 2. Otto-cycle combustion process</figcaption></figure>

### D. Faults on Exhaust Valve

The exhaust valve is prone to faults, such as leakage, wear, and timing failures, which can cause loss of power, as shown in Table I. Late or early opening or closing impacts the cylinder scavenging, as the cylinders are connected to turbochargers that power the compressor for air scavenging. Furthermore, timing issues affect the temperature of exhaust gases and exhaust gases may remain trapped in the cylinder in case of early closure, compromising the efficiency of the combustion process. Therefore, studying the timing of the exhaust valve closing is critical for engine performance and proper scavenging. This paper examines behavior abnormalities in the closing dead time of the cylinder’s exhaust valve.

<table><caption>TABLE I
EV FAULTS CAUSES AND EFFECTS</caption><thead><tr><th>Fault</th><th>Cause</th><th>Effect</th></tr></thead><tbody><tr><td>Valve Leakage [11]</td><td>Weak valve spring, Faulty adjustment of valve clearance, Cranks on valve surface, Lack of maintenance</td><td>Loss scavenging efficiency, Ineffective combustion, Loss power</td></tr><tr><td>Late/Early Valve Timing [12]</td><td>High Valve Clearance - Valve wear</td><td>Elevated exhaust temperature- Loss scavenging efficiency- Elevated Noise and vibration</td></tr></tbody></table>

## III. K-MEANS

K-means is an unsupervised clustering method. It is commonly used to partition samples into k clusters automatically. The purpose of the K-means clustering method is to assign all N samples into k clusters by minimizing the sum of point-to-centroid distances as follows:

$$J = \arg \min_{C} \sum_{i=1}^{k} \sum_{x \in C_i} \| \vec{x} - \vec{\mu}_i \| \quad (1)$$

where $C = \{C_1, C_2, ..., C_k\}$ indicates k clusters, $\vec{x}$ is an $N \times R$ feature matrix, R represents the dimensions of the
<table><caption>TABLE II
K-MEANS CLUSTERING ALGORITHM</caption><thead><tr><th>Step</th><th>Description</th></tr></thead><tbody><tr><td>1 - Initialization</td><td>Randomly choose k cluster centroids from the feature samples.</td></tr><tr><td>2 - Assignment</td><td>Assign each sample x<sub>p</sub> to the nearest cluster centroid by measuring the distance to each centroid, as follows:<br>C<sub>i</sub><sup>t</sup> = {x<sub>p</sub> : ||x<sub>p</sub> - μ<sub>i</sub><sup>t</sup>||<sup>2</sup> ≤ ||x<sub>p</sub> - μ<sub>j</sub><sup>t</sup>||<sup>2</sup>, ∀j, 1 ≤ j ≤ k}</td></tr><tr><td>3 - Update</td><td>Update each centroid by calculating the mean of all samples assigned to the cluster:<br>μ<sub>i</sub><sup>t+1</sup> = <sup>1</sup>&frasl;<sub>N<sub>i</sub><sup>t</sup></sub> &sum;<sub>x<sub>j</sub> &isin; C<sub>i</sub><sup>t</sup></sub> x<sub>j</sub>,<br>where N<sub>i</sub><sup>t</sup> is the number of samples in the i-th cluster at iteration t.</td></tr><tr><td>4 - Repeat</td><td>Repeat Steps 2 and 3 until the cluster centroids remain unchanged or the algorithm converges.</td></tr></tbody></table>

matrix, each row is a single observation or sample, and $\vec{\mu}_i$ indicates the cluster centroid of the i-th cluster. The detailed process of the K-means clustering method is shown in Table II.

## IV. METHODOLOGY

Referring to the fact that cylinders' valve timing EVCDT's are synchronized in behavior a correlation analysis clustering-based methodology is built to detect abnormalities in EVCDT; actual historical data were extracted, preprocessed, and prepared for the clustering operation to achieve detection. To achieve this, a correlation matrix is calculated on each time interval then clustering is applied on the 12 vectors obtained each vector representing

### A. Data extraction and preprocessing

The data used in this study is real historical data measured by sensors, representing the EVCDTs of a 12-cylinder dual-fuel engine. The EVCDT data (unit: msec) of each cylinder is derived from the ECS, with a data collection system frequency of 0.1 Hz=10 sec. Observing valve opening/closing cycles or crank angle requires a very high frequency. For instance, to achieve one-degree crank angle precision at 60 rpm, a frequency of at least 360 Hz is necessary. Since the available data is recorded every 10 seconds, it is not feasible to analyze the EVCDTs as a function of engine stroke (crank position). Given that the engine operates at a maximum speed of 80 rpm, approximately 13.33 cycles are completed every 10 seconds, resulting in up to 13 potentially missing data points. The data recorded, however, consistently reflects the EVCDT value of the most recent cycle at each 10 second interval. For the purpose of analysis and diagnosis, the assumption is that the behavior of the exhaust valve across all cylinders in 10-second intervals should be highly correlated. Therefore, the input to the algorithm is the correlation between the EVCDTs of all cylinders.

1) Data preprocessing: Fig. 3 represents the raw collected data for EVCDT of 12 cylinders. As shown, high spikes (elevated sensor readings) exist and inconsistencies in the time sampling ranges between 8 to 11 seconds. To address these issues, data is resampled to 10 sec intervals, and clipping is applied at 190 msec (see Fig.4).

<figure><img src="image_4.png" /><figcaption>Fig. 3. Raw EVCDT data of the 12 cylinders in function of time</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>Fig. 4. Cleaned EVCDT data of the 12 cylinders in function of time</figcaption></figure>

2) Correlation Matrix Calculation: Over a time interval $\Delta T$, a matrix is calculated representing the Pearson correlation between one data feature and another. The data used in this study consists of 12 feature vectors so a 12x12 correlation matrix is built for every $\Delta T$ as given:

$$C_{\Delta T} = \begin{bmatrix} c_{11} & c_{12} & c_{13} & \cdots & c_{1,12} \\ c_{21} & c_{22} & c_{23} & \cdots & c_{2,12} \\ c_{31} & c_{32} & c_{33} & \cdots & c_{3,12} \\ \vdots & \vdots & \vdots & \ddots & \vdots \\ c_{12,1} & c_{12,2} & c_{12,3} & \cdots & c_{12,12} \end{bmatrix} \quad (2)$$

where $-1 < c_{ij} < 1$ represents the pearson correlation between cylinders i and j. Note that $i = [1, 2, \cdots, 12]$ and $j = [1, 2, \cdots, 12]$. Each row represents the correlation between the corresponding cylinder and the other cylinders. A value near 1 indicates a strong correlation between the cylinders, while a value near -1 marks an inverse correlation. On the other hand, the value is close to 0 in the case of an imperfect correlation between the cylinders (see Table III). A cylinder's EVCDT misbehavior is defined with a negative or less than 0.3 correlation value with another cylinder.

<table><caption>TABLE III
CORRELATION COEFFICIENT INTERPRETATION [13]</caption><thead><tr><th>Absolute Magnitude of the Observed Correlation Coefficient</th><th>Interpretation</th></tr></thead><tbody><tr><td>0.00–0.10</td><td>Negligible correlation</td></tr><tr><td>0.10–0.39</td><td>Weak correlation</td></tr><tr><td>0.40–0.69</td><td>Moderate correlation</td></tr><tr><td>0.70–0.89</td><td>Strong correlation</td></tr><tr><td>0.90–1.00</td><td>Very strong correlation</td></tr></tbody></table>
<figure><img src="image_6.png" /><figcaption>Fig. 5. EVCDT Detection Methodology</figcaption></figure>

## B. Detection Methodology

To detect anomalies using the EVCDT correlation data a two-stage process is applied as shown in Fig 5: (1) K-means clustering cylinders with similar correlation profiles, and (2) a centroid-based rule distinguishes healthy from faulty patterns, reinforced by a persistence check across successive ΔT windows.

1) **Clustering**: K-means clustering is applied to the 12 vectors derived from the rows of the $C_{ΔT}$ matrix, where each row encodes the correlation of a specific cylinder’s EVCDT with all other cylinders. These vectors are grouped based on their Euclidean distances, allowing K-means to cluster similar behavioral patterns across the features. The clustering outcome depends heavily on the selection of the parameter k, which defines the number of clusters. Selecting an optimal k is crucial to ensure meaningful grouping and can be guided by evaluation techniques such as the elbow method or the silhouette score [14].

The silhouette score, in particular, evaluates clustering quality by comparing intra-cluster cohesion and inter-cluster separation. A higher silhouette score indicates well-separated and dense clusters. To identify the most suitable number of clusters, the silhouette score is computed for various values of k, and the optimal k corresponds to the highest score achieved. As illustrated in Fig. 6, the maximum silhouette score of s = 0.58 is obtained at k = 2, indicating that the data is best partitioned into two distinct clusters.

2) **Detection**: Each of the two clusters resulting from K-means is represented by a centroid vector, denoted as a $1 \times 12$ array. In this representation, each element $x_{j,i}$ reflects the behavior of cylinder j in cluster i. The centroids are expressed as:

<figure><img src="image_7.png" /><figcaption>Fig. 6. Silhouette score vs number of clusters</figcaption></figure>

$$X_i = [x_{1,i} \ x_{2,i} \ \dots \ x_{12,i}], \quad i = 0, 1 \quad (3)$$

Due to the limited nature of the EVCDT dataset—which lacks statistical descriptors such as mean, maximum, and minimum—it is challenging to define an exact threshold for identifying abnormal behavior. To address this, a worst-case scenario approach is adopted: if all elements in a centroid vector exceed 0.3, and most of them are below 0.1, the centroid is considered to represent a low correlation profile, which is interpreted as abnormal behavior. If this condition is met for any centroid, the associated cluster is classified as a Faulty Cluster. Otherwise, it is considered a Healthy Cluster.

The threshold condition is chosen based on the fact that EVCDTs must be synchronised in behavior (increase and decrease) and not in magnitude, based on the fact that this variation can naturally occur due to changes in engine speed, operational mode, cylinder load, or combustion conditions. Pearson correlation measures how similarly two signals behave. A negative or near-zero correlation means the cylinders behave differently or opposite to each other, indicating a potential issue. Therefore, an anomaly is identified when cylinders consistently act differently from each other, highlighting periods of poor synchronisation.

Following this reclassification, a cylinder is marked as faulty over a given timespan only if it appears in the Faulty Cluster for at least two consecutive ΔT intervals. Isolated occurrences are disregarded and considered to indicate a healthy state, thus improving the robustness of the fault detection process.

## V. RESULTS

To evaluate the proposed correlation-based clustering methodology for detecting abnormalities in EVCDT, a five-month data set collected from a 12-cylinder marine dual-fuel engine was analyzed and validated against reported faults. The detection algorithm was applied using a one-hour sliding time window (ΔT = 1 hour), enabling continuous monitoring of cylinder behavior over time.
<figure><img src="image_8.png" /><figcaption>Fig. 7. Misbehavior EVCDT anomalies detected over the 12 cylinders (0: Healthy, 1: Faulty, - - - -: Reported Fault Date)</figcaption></figure>

## A. Reported Faults

A technical defect report prepared by the maintenance technicians documented the faults observed during the study period, specifically related to EVCDT across different cylinders. This report indicates the dates on which the faults were identified but does not include precise timestamps for when the abnormalities first occurred or when they were resolved. Table IV summarizes the reported EVCDT faults, listing the affected cylinders and the corresponding dates on or before which the abnormalities were noted.

<table><caption>TABLE IV
REPORTED FAULTS DATE</caption><thead><tr><td>Date</td><td>Fault</td></tr></thead><tbody><tr><td>20-09-2021</td><td>Cylinder 1, 2, 5, 7 and 11 EVCDT abnormality</td></tr><tr><td>03-11-2021</td><td>Cylinder 8 EVCDT abnormality</td></tr><tr><td>04-11-2021</td><td>Cylinder 4 EVCDT abnormality</td></tr><tr><td>04-01-2022</td><td>Cylinder 4 and 10 EVCDT abnormality</td></tr><tr><td>16-01-2022</td><td>Cylinder 5 EVCDT abnormality</td></tr></tbody></table>

## B. Detection

After applying the algorithm explained in Section IV on 5 months of data (from September 1, 2021 to the end of January 2022), using a sliding window of $\Delta T = 1hr$, the results are compared to the reported faults listed in Table IV and analyzed, where Fig 7 shows on:

20-09-2021: Abnormalities on Cylinders 1, 5, and 11 were detected before the reported dates (09-09-2021 and 16-09-2021). For Cylinder 2, no faults were detected near this date, indicating a missed fault detection. For Cylinder 7, the abnormality was detected after the reported date (24-09-2021).

03-11-2021: the fault on Cylinder 8 was detected on 02-11-2021, one day before the reported date.

<figure><img src="image_9.png" /><figcaption>Fig. 8. EVCDT of cylinders 1,2 and 5 vs 3 and 6 on 2021-11-02</figcaption></figure>
04-11-2021: early detection on 29-10-2021 and 02-11-2021 for Cylinder 4.

04-01-2022: an abnormality in Cylinder 4 was detected before the reported date, while for Cylinder 10, the fault was detected after the occurrence on 08-01-2022.

16-01-2021: the fault was detected prior to the report on 11-12-01-2022.

**Unreported dates:** The method detects EVCDTS abnormalities by flagging distinct behavior among cylinder EVCDTs as anomalies. For instance, on 02-11-2021, anomalies are flagged on Cylinders 1, 2, and 5 without any issue related to dead time being reported for these cylinders on that date. Referring to Fig. 8, the behavior compared to that of cylinders 3 and 6 shows an inverse or distinct behavior, marking them as false positive anomalies. Same for dates, such as 11-12-2021 and 26-01-2022, indicating false positive EVCDT abnormalities.

## VI. CONCLUSION

This study presented a methodology for monitoring the behavior of EVCDT in a marine dual-fuel engines using a correlation-based clustering approach. By analyzing historical EVCDT data from 12 cylinders from a cargo vessel and applying K-means clustering on correlation matrices, the methodology successfully detected abnormal behaviors that could indicate potential faults. The proposed algorithm proved capable of early fault detection, identifying many abnormalities before the officially reported dates. Although a few false positives were observed, the overall approach demonstrates strong potential for enhancing monitoring methodologies and supporting sustainable maritime operations. However, more faulty data with further information on reported faults as the exact date of occurrence is required to ensure the performance of the methodology against diagnosing EVCDT faults. Future work will focus on integrating additional operational parameters to refine detection accuracy and further reduce false alarms that result from mode, speed, load or combustion efficiency.

## ACKNOWLEDGMENT

This work is done in the framework of a research and development project: "Transformation Numerique du Transport Maritime (TNTM)". This project is funded by BPIFrance, Banque Publique d'Investissement, France.

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