Condition Monitoring in Marine Oil Separation Systems Using Wavelet Packet Transform and Genetic Technique

Abstract

Condition Monitoring is key to predictive maintenance and especially in the operational efficiency of the Marine Oil Separation System. These systems are crucial for environmental protection and compliance with international maritime regulations. Therefore, it is necessary to design a technique capable of analyzing the signals from sensors and estimating the remaining useful life in order to avoid breakage or unnecessary replacement. This work presents an intelligent method with signal processing based on Wavelet Packets Transform that provides energy data from vibration measurements as characteristic parameters. These values can be related to its RUL, and they are used as inputs for the training process. In particular, a Genetic Neuro-Fuzzy system is proposed as an intelligent classification technique. Once the training process is completed, it can be concluded that a good classifier has been built, since it relates the energy state of the oil separation system with its remaining useful life, and therefore, the necessary information for efficient predictive maintenance is achieved. Furthermore, a mechanism to obtain the final set of fuzzy rules has been developed, showing the correspondence between these fuzzy rules and the neural network structure.

1. Introduction

Centrifugal oil separation systems for ships are critical machines because of the possible environmental consequences of a malfunction. Energy efficiency and environmental emissions depend on the quality of the oil used for lubrication since their function is to clean lube oils. The weak point of these systems is their lack of accuracy for diagnosis. Usually, they only are monitored by a speed sensor, an imbalance sensor or an interlocking switch [1]; therefore, there is not enough monitoring to prevent serious and expensive failures. All this justifies a high maintenance effort.

The trend in recent years has been to employ predictive maintenance techniques based on condition monitoring, called Condition-Based Maintenance (CBM) [2]. CBM is nowadays applied in different sectors for its advantages (reducing downtime and costs by eliminating unnecessary tasks, enabling early failure detection, supporting better decision-making for staff, among others). In general, a CBM system involves three steps: data acquisition, data processing and decision-making processes. Among the different CBM approaches found in literature [2], the feature-based approach has been selected for this research as it involves the study of a complex system whose failure profiles require a non-stationary analysis technique of the system behavior to detect failures and to obtain their RUL.

In this sense, a good solution accepted in the literature is to acquire vibration signals and process them to obtain features of machine behavior applied to marine fuel oil separator systems and pipes. This type of signal has been used in works such as [3,4,5,6].

However, right now, the paradigm is maintenance 4.0, i.e., meeting the challenges of condition monitoring by adding artificial intelligence techniques and IoT (Internet of Things). In order to use artificial intelligence techniques to generate reliable models of machine behavior, it is necessary to provide the artificial intelligence with a multitude of signals at different conditions, and also to provide it with suitable patterns, so that it is able to learn and distinguish their differences at an affordable computational cost.

With the aim of minimizing the computational cost, while maintaining information about the defect, many previous works have studied different signal processing techniques based on the time or frequency domain [7,8,9]. One signal processing technique that has given very good results applied to condition monitoring has been the Wavelet Packet Transform (WPT), used for crack detection in rotating machines in [10], and diagnosis of motors [11], bearings [12], and gearboxes [13]. It has been also used for integral diagnosis of vertical Essential Service Water Pumps (SEC) in [14] under multi-fault conditions. The technique based on Wavelets (time-frequency domain) has proved to be a robust framework for non-stationary processes.

The WPT is an extension of the conventional Wavelet Transform that decomposes both low- and high-frequency components across multiple levels, continuing to a desired decomposition level. While the Wavelet Transform represents the correlation coefficients derived from comparing the studied signal to a reference signal, known as the wavelet mother, WPT offers a more comprehensive decomposition framework. A more detailed description can be found in [15]. Unlike the Wavelet Transform, which only captures the approximation and detail coefficients, WPT enables decomposition at each node of the decomposition tree, providing a more detailed representation of the signal’s frequency content. This feature reduces signal complexity by dividing the signal into frequency bands (or packets) and furnishing information in both the time and frequency domains [16]. However, the application of the WPT is not straightforward; it is necessary to decide the wavelet mother function used as a comparison reference, as well as the decomposition level. Both parameters will depend on the nature of the signals to analyze, as well as the type of defects to be diagnosed.

In this sense, the authors of the present work have developed a methodology to automate selection of key variables for the WPT, ensuring that the resulting patterns obtained are optimized for training and feeding into an intelligent classification system. This methodology was presented in [17] and has been previously applied to maritime oil separators signals in [18]. In this work, the optimal WPT structure identified in [13] serves as the foundation for implementing the current proposed technique.

Predictive maintenance needs to be supported, not only by a monitoring system, but also by an intelligent method that analyzes the signals. The Artificial Neural Network (ANN) and the evolutionary algorithm, as a genetic one, have been widely implemented for fault diagnosis [19,20,21,22]. The relevance acquired in the last decades is due to its magnificent adaptability, its excellent self-learning properties, its ability to uncover associations within complex datasets or its capability for obtaining associations between complex datasets. Most importantly, these techniques are able to manage large datasets, to detect intricate patterns and to build predictors or classifiers accurately [23,24]. There are several research studies that explore the combination of Wavelet Packet Transform (WPT) and Artificial Intelligence (AI) techniques, such as Artificial Neural Networks (ANNs) and Fuzzy Logic, for machine fault detection and diagnosis. In [7], WPT for signal processing and Convolutional Neural networks is applied to classify faults in bearings, and the study is validated in a rolling bearing testbench. In this case, no optimization study about the mother wavelet and decomposition level is performed. Furthermore, the study is applied to the isolated element and does not consider the dynamics of a machine as is the case in the present work, where also the selection of the mother wavelet and decomposition level has been carefully evaluated, optimizing the results.

The methodology is grounded in the analysis of vibration behavior, a critical factor for assessing the system’s operational status. To preprocess the vibration data, Wavelet Packet Transform (WPT) is employed to extract energy-related information from the measurements obtained from each separator. These extracted features are subsequently used as inputs for the training phase of the proposed classification technique, which was developed by the authors.

The present paper presents the development of a Genetic Neuro-Fuzzy classifier designed to estimate the Remaining Useful Life (RUL) of marine centrifugal separator systems. The study is based on the analysis of vibration behavior analysis as a critical factor for assessing the system’s operational status. Wavelet Packet Transform is applied to extract energy-related information from vibration measurements obtained from each separator. These extracted features are subsequently used as inputs for the training phase of the proposed classification technique, which was developed by the authors.

Once all training phases are concluded, a good classifier is achieved, since it is able to provide information about the internal state of the separators, in terms of the number of hours. It is noteworthy that the proposed algorithm exhibits several advantages over similar approaches found in the literature. On the one hand, it combines ANN, Fuzzy systems and Genetic algorithms; therefore, it is able to manage a large number of inputs, which expand the range of applications. On the other hand, the algorithm has been designed in order to provide the comprehensive set of Fuzzy rules that intervene in the resolution of the problem posed. With this proposal, it is possible to validate the obtaining rule process and to verify which rules are discarded during the training process and which ones are retained.

2. Materials and Methods

2.1. Experimental Measurements

This work has been focused on the particular model of centrifugal separator Alfa Laval SA 831 (Alfa Laval Tumba AB, SE-147 80, Tumba, Sweden) since the researchers had direct access to these onboard systems. The technical parameters of this oil centrifugal separator are shown in

Table 1. Marine oil separator Alfa Laval 831 (Alfa Laval Tumba AB, SE-147 80, Tumba, Sweden) characteristics.

Characteristics	Value
Electrical current frequency	data
Motor power (50 Hz)	data
Motor speed synchronous (50 Hz)	3000 rpm
Bowl speed, synchronous (50 Hz)	10,683 rpm
Maximum density of feed/sediment	1100/2659 kg/m3
Maximum density of operating liquid	1000 kg/m3
Feed temperature, min./max.	0 °C to 100 °C
Maximum viscosity of operating liquid	700 cSt at 50 °C

.

These separators show their internal problems through the vibrations, and when they are excessive, the centrifugal stops working, but that can mean that major damage has been produced. The vibrations in marine separator systems could come from a broken spring, a bent bowl spindle, damaged or worn out bearings, a damaged or broken belt transmission, etc. In order to guarantee a good function, the separator has alarms, such as error in the water pressure sensor, failure in the separator motor, error in the bowl speed sensor, high sludge tank level, heater failure, power failure or high vibrations [1]. In the case of a vibration alarm, it consists of a switch that interrupts the process when a certain level of vibration is exceeded. In this sense, the system works as a protector, and it does not provide vibration measurements. Therefore, it has been decided to monitor the signals by a vibration sensor.

Several actual measurements were carried out over four centrifugal separators onboard a Ro-Pax vessel. These measurements consisted in capturing vibrations signals on each oil separator several days in order to obtain data on different use states. Therefore, a triaxial accelerometer was fixed to all centrifugal separators, and vibrations were captured during 2 s with ten consecutive measurements in each centrifugal, using a sampling frequency of 2560 Hz. The sensor used was a Bruel & Kjaer 4504A model (Bruel &Kjaer, Naerum, Denmark) with three independent outputs corresponding to the measurement over the three Cartesian axes. This sensor was a piezoelectric accelerometer with a sensitivity of 10 mV/g, and it reached a range up to 9 KHz with a minimum of 1 Hz. The accelerometer operated on a constant current supply and provided output signals in the form of voltage modulation.

In order to process the recorded signals, the sensor is connected to the Bruel & Kjaer PHOTON+ analyzer with RT Pro Signal Analysis Software (BZ-8007, Version 6.34.9104) that allows real-time analyzing, recording and post-processing sound and vibration measurements. Finally, this small data acquisition hardware is linked to a laptop by real-time signal analysis software that shows the recorded vibration. The vibration recording data were taken as an acceleration variable (m/s²) by the RT Pro software, this one being the measurement for the study. Figure 1 shows the block diagram of the proposed system. It can be seen that once the vibrations have been captured, the Dynamic Signal Analyzer converts these analogue signals to digital, before being processed by the software in the laptop.

The assembly for measurement in the marine oil separators and the location of the vibration sensor in detail is shown in Figure 2. As can be seen in Figure 2b in more detail, the sensor placed in the lubricating oil centrifuge is connected to the dynamic signal analyzer that converts the analog signal to digital, and this is connected to a laptop to record and process the measurements made. Figure 2c shows the position of the piezoelectric accelerometer and its measurement axes.

In order to carry out this study, two system conditions were taken into consideration for vibration data acquisition. The first is measurements after an extensive maintenance task, which are called overhaul (the system is considered new). The second measurements were taken after a certain number of working hours (varying depending on the machine).

These measurements should be related to the internal state of use of the separator in the moment they were captured. This data is crucial for designing effective predictive maintenance. In this study, interest is focused on the RUL, and in these devices, it means the number of working hours.

Generally, the maintenance of oil separators follows a planned machine outage recommended by the manufacturers. This planning is based on the time of use or the operating hours. In this particular model, an overhaul is accomplished after 18 months or 12,000 working hours at the most. This kind of maintenance, without knowledge of current device conditions, could involve premature and unnecessary action or even it could be applied too late if a failure is being developed. For this reason, predictive maintenance based on condition monitoring could represent the solution for these complex systems. In fact, it reduces costs.

The next step is to extract relevant information about these vibration measurements in a pre-processing signals phase.

2.2. Signal Processing

The Wavelet Packet Transform consists of the decomposition of a signal into correlation coefficients when the signal is compared to a signal called wavelet basis. There are different families of wavelet basis, each with its own properties, but only the Daubechies (db), Symlets (sym) and Coiflets (coif) families can be used for the application of the Wavelet Packet Transform in a discrete form, as intended in this work. This transformation is performed by splitting the signal into two halves of equal frequency resolution using discrete filters related to the wavelet basis. This decomposition is carried out recursively until the desired decomposition level is reached, thus obtaining a number of packets equal to 2^k, where k is the desired decomposition level, according to Figure 3.

Each group of coefficients W(k,j) represents the group of coefficients of each signal in a packet where k is the decomposition level and j is the position of the packet within the decomposition level. Each correlation vector has the structure of Equation (1).

$$W\left(k,j\right)=\left\{w_i\left(k,j\right),\dots ,w_N\left(k,j\right)\right\}=\left\{w_i\left(k,j\right)\right\}$$

(1)

where i is the position of the coefficient within the correlation vector W(k,j). Using these coefficients, an energy value can be calculated for each frequency band or packet it refers to, using Equation (2).

$$E_{(k,j)}={\sum }_i{w_i(k,j)}^2$$

(2)

The Packet Wavelet Transform has been widely used in several fields as a signal processing tool with the aim of extracting defect indicator patterns. However, it has been proven in previous works that it is important to make a previous study of its variables, such as the level of decomposition and the wavelet basis, for each particular machine. This allows maximizing the differences between the extracted patterns for elements in the conditions to be distinguished or classified. In the previous work [18], it was observed that working with MOSS using the wavelet basis symlet of order 9, and with a decomposition level 6 (64 energy values for each signal), an increasing evolution of the energy levels in the harmonics of the rotational speed could be observed with use. Therefore, in this work these parameters have been used, which have proved their worth on the same machines. Figure 4 shows an example of the decomposition of a vibration signal into its 64 corresponding energy values.

2.3. Intelligent Technique

Once the characteristic parameters of the vibration signal have been extracted, they are used as inputs to the classifier. Owing to the fact that the vibrations were measured in the three Cartesian axes, a packet of 64 energy values is obtained for each axis. In this work, it has been decided that the set of inputs is composed of the concatenation of these three energy packets, and therefore the input vector is established by 192 values.

Then, to each set of inputs a set of outputs should be assigned. As the purpose of this work is to achieve a classifier that provides the RUL of the analyzed separator, the outputs have to indicate its state of use. The RUL of the analyzed separators is labeled using four levels of use according to its working hours after the last maintenance. Moreover, owing to the developed algorithm, which will be exposed next, the output system should be binary. In this way, the classifier has four outputs and only one is activated in order to indicate the corresponding label for a particular vibration signal.

Table 2. Output activation according to the label classification.

Label Classification	Number of Classifier Output
	1	2	3	4
New	1	0	0	0
Hardly used	0	1	0	0
Very used	0	0	1	0
Approaching preventive maintenance	0	0	0	1

shows the activated output depending on the label of classification. At this point, it is important to remark that the new label corresponds to separators with up to 3000 h of use, the hardly used label to separators with 3000 up to 6000 h, the very used label to ones with 6000 up to 9000 h and finally the label of approaching preventive maintenance to ones with 9000 up to 12,000 working hours after the last maintenance.

Then, with this input–output data set, the training process is carried out. Specifically, a three-layer Genetic Neuro-Fuzzy System [25,26,27] with the ANFIS structure [28,29] is developed.

The system inputs U_ij are the inputs to the first layer. As mentioned, each wavelet transform is composed from an energy packet of 64 values for each axis; therefore, the input vector is composed of an array of 192 values.

The outputs of each neuron X_ij depend on the center (µ_ij) and the width (ƞ_ij) of the membership function. Equation (3) represents this relationship, where N₁ is the number of inputs, and N₂ is the number of intermediate layer nodes.

$$X_{ij}=\exp \left({\displaystyle \frac{-{\left(U_{ij}-{\mu }_{ij}\right)}^2}{{\eta }_{ij}^2}}\right);\mathrm{i}=1,\dots ,N_1;j=1,\dots ,N_2$$

(3)

The outputs of the second layer I_i are related to the rules; that means that N₂ is also indicative of the rule numbers.

$${\mathsf{{\rm I}}}_j=\min \left|X_{1j},\dots ,{\mathrm{X}}_{N_{1}j}\right|;j=1,\dots ,N_2$$

(4)

Finally, the outputs of system Z_k, which corresponds to the third layer outputs, are calculated with the second layer outputs and the estimated output δ_jk of each node j.

$${\mathrm{Z}}_k={\displaystyle \frac{\sum _{j=1}^{N_2}{\delta }_{jk}{Y}_j}{\sum _{j=1}^{N_2}{Y}_j}};k=1,\dots ,N_3,$$

(5)

where N₃ is the number of system outputs. In this work it is 4, as can be seen in Table 2.

The first two phases of the learning algorithm are dedicated to obtaining the parameters of these equations. Particularly in the first phase, a two-dimensional self-organizing Kohonen map [30,31] allows for establishing values for µ_ij and δ_jk, whose vector is composed through the set of the input–output system:

$$\mathsf{{\rm T}}=(U_1\dots U_{N_1}{Y}_1\dots Y_{N_3})$$

(6)

The initial point is a 10 × 10 map, what means that there are 100 nodes and consequently also 100 rules, initially. Each node starts with an associated weight vector linked to a classification label. These vectors are updated during the unsupervised learning phase. Moreover, the values for µ_ij and δ_jk are assigned after the unsupervised learning phase is concluded. These obtained values will be adjusted to more convenient ones during the next phase.

The implementation of the Genetic Neuro-Fuzzy System occurs in the second phase of the proposed algorithm. In this development, the parameter set obtained in the previous phase are adjusted, and the number of nodes of the hidden layer is reduced, and therefore, the number of rules is also reduced. The Genetic algorithm [32] is inspired by the biological process of natural selection where a set of possible solutions, called individuals, is evolved in order to achieve better results. The basic information provided by each individual is known as chromosomes or genes, which can be altered. In this research, the individual corresponds to a vector, where its components are its genes. In this way, each possible solution is composed of a vector of dimension N₁ × N₂. The first N₂ elements are binary values, which are indicative of the associated rule activation. This means that if the element is activated, this rule is taken into account, but if it is 0, this rule is rejected. On the other hand, the rest of the components of the vector are linked to the width of the membership function. Therefore, those elements with a value of 0 are rules which will not be included in the final result. With this kind of algorithm, each vector becomes a candidate GNF system, and its non-null components are involved in the learning process. In this case, mutations and crossover operators have been used. In fact, the crossover operator has been applied in 60% of the iterations and therefore, the mutation operator has been applied in 40% of the iterations. On the other hand, the fitness function has been chosen as the mean square error for each individual. Note that each individual is a particular solution to the problem. Once the learning phase is concluded, an adjustment of the rule number and the width of membership function is achieved.

This proposed algorithm is applied with different initial configurations using the pre-processing data. As was indicated, a vector of 192 energy values is the input for the training, and the output is a vector of four components. This structure is shown in Figure 5. Once all phases are concluded, the output is a classifier that indicates the RUL of the separator. The identification of the label associated with the input signal depends on the corresponding activated output, as Table 2 shows.

3. Results

In this research, 72 vibration signals were measured over four oil separator systems in different states of use. As was explained in the previous section, these signals are pre-processed and finally each signal is converted in a vector of 192 components. The GNF is trained with 75% of the patterns, while the rest are reserved to check the generalization capability of the GNF system after training.

Figure 6 shows the evolution of the Genetic phase. On the one hand, it can be seen that, generally, the fitness value decreases while the iterations grow, and that means that the candidate solution as input provides a more adequate output after each generation, reaching a stable value after 85 generations. As was mentioned in the previous section, this function is the mean square error, and specifically the mean is 0.0202034 for training patterns and 0.036009 for the generalization ones. On the other hand, the average distance between individuals also decreases with the generations, and this involves the initial number of rules that can be reduced. This fact can be seen in Figure 7. As was indicated in the previous section, it started with an initial network of 100 nodes, that is, 100 rules, and Figure 7 shows how this number of rules has been reduced to 80. It is important to remark that Figure 7 is a graphical representation as the learning algorithm discards some rules and takes into consideration other ones. Those rules considered as the final results of the algorithm have been pointed out as nodes highlighted in red. Note that this graphical representation allows seeing the evolution of the learning process with respect to the method used by the algorithm for choosing the most adequate rules.

In this paper, it has been decided to show the results of the proposed algorithm through the confusion matrix [33,34]. This method visualizes the learning capability comparing the predicted classes with the actual ones. It consists of a matrix that shows the successes and the errors of the classifier. In this research, as there are four labels to predict, the confusion matrix has a dimension of 4 × 4, as shown in Figure 8 and Figure 9. The diagonal elements correspond to the true positives, that is, correct identifications of the classifier, and the rest of the elements are erroneous classifications. For example, Figure 8 corresponds to the confusion matrix built with the training patterns, and it shows that the classifier obtains 100% accuracy with labels 1, 3 and 4, whereas there were five erroneous classifications of label 2 as label 3 that reduce the accuracy of label 2 to 83.9%, and owing to the false positives, there is 66.7% false identification for label 3. Note that these results are correct in most of the cases. However, it can be seen that in some cases label 2 is confused as label 3. This wrong selection is reasonable given that both sets are near each other. That is, level 2 refers to “hardly used” whereas level 3 refers to “very used” and between both there is not a clear demarcation.

A similar reading can be made in Figure 9, but in this case, the confusion matrix has been generated with generalization patterns. This involves the classifier having to deal with unknown data, since energy packets had not been introduced for the training process. It could be checked that the classifier achieved a satisfactory level of generalization, and it can also be considered as a good classifier, since it has a 100% accuracy in labels 1, 3 and 4, and there are only 5 erroneous classifications of the 18. In general terms, the classifier has a 90.7% success rate.

From these confusion matrices, it is possible to obtain other quantitative results such as precision, recall and F1-score [35]. Precision represents the proportion of properly predicted patterns (true positives) to the total predicted positives (true positives and false positives). It is shown in Equation (7) where TP represents true positives, and FP represents false positives. Regarding Recall, it is the ratio of properly predicted patterns (true positives) to all patterns in actual classes. It is represented in Equation (8), where FN represents false negatives. Finally, the F1-score is the weighted average between Precision and Recall, and it is exposed in Equation (9).

$$\mathrm{P}\mathrm{r}\mathrm{e}\mathrm{c}\mathrm{i}\mathrm{s}\mathrm{i}\mathrm{o}\mathrm{n}={\displaystyle \frac{TP}{TP+FP}}$$

(7)

$$\mathrm{R}\mathrm{e}\mathrm{c}\mathrm{a}\mathrm{l}\mathrm{l}={\displaystyle \frac{TP}{TP+FN}}$$

(8)

$$\mathrm{F}1\mathrm{s}\mathrm{c}\mathrm{o}\mathrm{r}\mathrm{e}={\displaystyle \frac{2·\left(\mathrm{P}\mathrm{r}\mathrm{e}\mathrm{c}\mathrm{i}\mathrm{s}\mathrm{i}\mathrm{o}\mathrm{n}·\mathrm{R}\mathrm{e}\mathrm{c}\mathrm{a}\mathrm{l}\mathrm{l}\right)}{\mathrm{P}\mathrm{r}\mathrm{e}\mathrm{c}\mathrm{i}\mathrm{s}\mathrm{i}\mathrm{o}\mathrm{n}+\mathrm{R}\mathrm{e}\mathrm{c}\mathrm{a}\mathrm{l}\mathrm{l}}}$$

(9)

In the case of training patterns, it has been obtained that the precision is equal to 1 for classes 1, 3 and 4, and it is equal to 0.84 for class 2. The Recall value is 1 for classes 1, 2 and 4, and 0.67 for class 3. These results are that the F1-score is 1 for classes 1 and 4, 0.91 for class 2 and 0.80 for class 3.

The same calculations are done with the generalization patterns obtaining a Precision of 1 for classes 1, 3 and 4 and 0.78 for class 2. Regarding Recall, similar results are obtained, with 1 for classes 1, 2 and 4, and 0.6 for class 3. Finally, the F1-score is 1 for classes 1 and 4, 0.87 for class 2 and 0.75 for class 3.

High precision and high recall values have been achieved, since there are few false negatives and few false positives. Therefore, these elevated scores for both indicate that the classifier is returning accurate results (high precision), as well as returning a majority of all relevant results (high recall). Moreover, the F1-score that combines precision and recall metrics always returns values higher than 0.75; consequently, it is possible to affirm that the trained classifier has achieved an adequate level of learning.

Generally, the confusion matrix usually comes with the ROC curve (Receiver Operation Characteristic) [36]. It is a graphic that represents the true positive rate (TPR) and the false positive rate (FPR) at different classification thresholds. By lowering the classification threshold, more items are classified as positive, which increases both false positives and true positives. In order to know the measure of performance across all possible classification thresholds, the area under curve (AUC) is calculated. One way to interpret the AUC is as the probability that the model will rank a random positive example higher than a random negative example. This means that the closer to 1 is this value, the better the classifier will be. The worst result for a classifier is an AUC close to 0.5, because it means that the identification is random, and the probability of success is 50%.

According to the ROC curve definition, one for each classification label has been obtained, and owing to the effectiveness of the classifier it must be checked with a binary result. This resulting visualization coincides with that previously shown. In the case of label 1 (corresponding to a new oil label) and of label 4 (corresponding to an approaching preventive maintenance label), the classifier is able to identify 100% of patterns correctly, and the resulting AUC is 1. This could be seen in Figure 10 and Figure 11, respectively. Moreover, although the AUC value obtained for label 2 and 3 is lower, it is possible to affirm that the proposed GNF is a good classifier, since it is 0.97904 for the very used label (Figure 12) and 0.98992 for the hardly used label (Figure 13), whose values are considerably high.

Once several kinds of result representations have been exposed, it could be affirmed that the proposed algorithm has generated a satisfactory classifier. However, in this research, it has been decided to take a further step and try to know the functioning of this algorithm. Artificial Neural Networks usually have a hidden development, and they are called black boxes, but in this research, there is a step focused on the study of the rules.

Figure 14 is a representation of the influence of each rule for the identification of an input corresponding to a new oil separator. The influence is expressed by a percentage. As could be seen, the majority of rules have little influence in this identification since they have close to zero values; however, there are five nodes with higher values, of which three values stand out among the rest with 55.7%, 22.4% and 15.2%.

Figure 15 shows the influence of each node or rule for the identification of an oil separator labeled as very used. In this case, it could be observed that there is a rule with an influence majority with 98.6%. This means that the classification of this label is focused practically exclusively on this node.

Therefore, as has been shown in Figure 14 and Figure 15, the developed algorithm allows knowing the level of influence of weight that each rule exerts in the classification of the corresponding label of an oil separator. Based on this information, a set of Fuzzy rules could be generated. In paper [37], a description of this generation process of Fuzzy rules could be consulted in detail.

At this point, it is convenient to comment that other algorithms could be used, and many researchers have discussed the comparison of the application of several algorithms [38,39,40,41]. However, several points of view are kept about the interpretation of these comparisons by the different researchers. One of them is pointed out by [41], where it is mentioned that it does not make sense to demonstrate that one classifier is, on average, better than the others based on the no free lunch theorem [42]. On the other hand, several tables could be seen in [39], where different machine learning algorithms are trained for a particular set of data and different results are achieved according to different cases. In this paper, the proposed algorithms integrate a combination of traditional machine learning techniques, and similar satisfactory results are achieved as in [39]. In addition, it is important to remark that this paper has focused especially on the process of gaining insights into the model’s results analyzing certain features of the Fuzzy rules. Note that it is a key point in the implementation of a machine learning algorithm as is pointed out in [38].

4. Discussion

It has been demonstrated that the measured vibrations on a centrifugal marine oil separator include essential information for knowing their levels of use. The signal processing by Wavelet Packet Transform has allowed extracting the characteristic energy packets of each vibration, which are used as inputs in the training process. The proposed Genetic Neuro-Fuzzy algorithm has reached a satisfactory level of classification, since it is capable of identifying the remaining useful life of the corresponding oil separator with a high accuracy. Specifically, the results show AUC values above 0.97904.

Moreover, in this research a study of the Fuzzy rule behavior has been developed. This has allowed for determining which rules affect a particular solution as well as their degree of influence. At this point, it is necessary to mention that this is a first step to reach a better generalization level, since by analyzing the Fuzzy rules, a better understanding of the algorithm is obtained. Therefore, on a particular resolution, a manual adjustment of the provided rules could be done in order to achieve more adequate responses.

The proposed Genetic Neuro-Fuzzy algorithm is able to classify the RUL of a marine oil separator, indicating its state of use from a vibration measurement. This involves an important advantage in premature fault diagnosis, and it provides the necessary information to apply effective predictive maintenance. That is, it is possible to know the deterioration status of the equipment without having to stop. Therefore, it allows the machinery to work for longer, avoiding unnecessary outage, and even failure or breakage could be prevented if the system detects an anomalous behavior. In conclusion, with the proposed classifier, maintenance is more effective in terms of time and cost, since the lifetime of the separator could be extended or a replacement or a repair could be carried out before a serious failure occurs.

Finally, it is important to underline the generalizability of the proposed method to different marine oil separators since it could be considered for any model, although the development of the technique considers the model of the separator which has been accessed. That is, the parametrization and the values of the parameters depend on the particular case. This is due to the fact that the application of the algorithm acquires the particular characteristics of the specific model of the oil separator under study. This implies that the algorithms take a particular separator in order to obtain parameters, and this process is key to the success of applying this proposed methodology. However, the algorithm is adaptable, and its training process can learn from measurements obtained from another separator model, since the parameterization of the algorithm depends on the particular oil separator under study.