1. Introduction
Nowadays, highreliable mechanical systems are expected [
1]. Condition monitoring is known as a fundamental program for maintaining and assuring the safety, permanence, and performance of a machine [
2,
3]. Lubricant in a machine acts almost the same as blood in a living organism [
4]. In other words, lubricants are responsible for many tasks like reducing friction and wear, transferring heat and energy, and reducing noise [
5]. However, the primary function of a lubricant is to reduce the tribological operation problems relevant to friction and wear [
6]. From maintenance point of view, oil analysis is an effective technique to evaluating the operational condition of mechanical systems [
7]. The evolution of maintenance strategies over time is presented in
Figure 1. Currently, there are several different methods for evaluating lubricating oil, which include [
8]:
Physical and chemical methods, such as chromatography.
Spectral analysis techniques, mainly infrared absorption spectroscopy (IAS) and Raman spectroscopy.
Electrical diagnosis methods, including return voltage measurement and frequencydomain spectroscopy.
The timeline for changing and testing lubricants is a controversial issue. Although the laboratory methods can report the exact results, however they cannot determine timely maintenance [
10,
11]. Having this, the electrical techniques are promising methods since they provide insitu measurement and allow easy to use and costeffective [
12,
13]. On the other hand, the soft computing methods have been employed to analyze without experts [
11,
14,
15].
Several research works on the issue of lubricant condition monitoring can be found in the literature, which are reviewed hereinafter, some of them have concentrated on modeling and using soft computing [
11,
16,
17,
18,
19]. Research was recently accomplished and applied a preliminary test on engine lubricant spectral analysis based on Knearest neighbor (KNN) and Radial Basis Function (RBF). By doing that, twelve indexes were reduced to seven indexes including iron, chromium, lead, copper, aluminum, nickel, and TDPQ. They reported that RBFANN modeling was able to provide detection for all three sizes of the training set with accuracy of approximately 99.85% [
11]. In another study, to identify and predict external wear failure the Recursive Feature Elimination (RFE) method was used to reduce the independent variables. They could achieve the accuracy of 94.20%. They also observed that iron, aluminum, and lead were more important in assessing wear condition [
18].
Dielectric or Impedance Spectroscopy (IS) is another way of measuring the electrical indexes of various materials (concrete, paper, liquids, biofuels, etc.) as an effective, economical, and nondestructive method [
20]. One research has assumed a method for locomotive system maintenance. Actually, this study has studied the relationship between dielectric properties and metallic and nonmetallic particles. Artificial neural networks have been employed to determine the relationship between the dielectric constant and oil impurities, and also the dielectric loss factor and oil impurities. In the modeling process, the oil impurities (chemical properties) have been considered inputs, and dielectric properties as outputs. The highest regression values (R) have been obtained for the dielectric constant (0.8513) and the dielectric loss factor (0.8015) at 7.4 GHz [
11].
In this study, the primary purpose was to compare soft computing models employed to predict the chemical properties (Fe, Pb, Cu, Cr, Al, Si, Zn) of lubricants through their electrical properties (ε′, ε″, tan δ). The dataset was obtained from two sources: data extruded from other papers and data experimented in this study. More detailed information was given in
Section 2. The result of this work will make to develop monitoring condition engine lubricant and promote online and portable methods for sensing and detecting faults in engine health. The research process and results are as follows.
2. Materials and Methods
2.1. Data Set
The required data set was supplied from two sources. Some of them (33 records) were extracted from previous research [
10] and the rest (16 records) were provided by an Iranian company (Tirage). These records are mainly the chemical properties (Fe, Pb, Cu, Cr, Al, Si, Zn) of the lubricants. While, their electrical factors (ε′, ε″, tan δ) were measured through this work. The procedure of data collection is depicted in
Figure 2. The additional information is provided in
Section 2.1.1 and
Section 2.1.2. To remove the effect of amplitude of changes in the values, normalization was accomplished in the range of 1 to 1 as follow [
21,
22]:
where,
$E=\left[{E}_{1},{E}_{2},\dots ,{E}_{n}\right]$ represents the principal value of the index vector.
E_{n} represents the normalized value of the index vector.
E_{max} and
E_{min} represent the maximum and minimum values of the index.
2.1.1. Extracted Datasets
As mentioned, the 33 records were extracted from a published work. These data included the chemical (Fe, Pb, Cu, Cr, Al, Si, Zn) and electrical properties (ε′, ε″, tan δ) of the secondhand lubricant [
10]. Also, the 16 records were provided by an Iranian local company called Tirage. The lubricant samples had been picked up from engines and were shared by Tirage, along with their chemical properties (
Table 1). Therefore, their electrical properties (ε′, ε″, tan δ) were measured in this work and reported in
Section 2.1.2.
2.1.2. Experimental Datasets
The 16 lubricant samples that had been extracted from engines were provided by Tirage Company (
Table 1). Their chemical properties including Fe, Pb, Cu, Cr, Al, Si, and Zn contents were provided by the company, however their electrical properties (e.g., ε′, ε″, tan δ) are not specified. Therefore, the electrical properties (ε′, ε″, tan δ) were measured through current research by a Vector Network Analyzer (VNA) (R&S ZVL 13, made in USA). This device can analyze microwave absorbing properties in the frequency range of 9 kHz–13.6 GHz with ±0.2 dB accuracy. The lubricant sample of 50 ml was poured into a beaker, and a coaxial dielectric probe was inserted inside the oil sample, as seen in
Figure 3. The measurements were performed at 2.4, 5.8, and 7.4 GHz frequencies in triplicate, under similar conditions for all samples. The results of measurements are reported in
Table 2.
2.2. Soft Computing Methods
2.2.1. Fundamentals and Theories
Soft computing models make the possibility of doing maintenance without experts. In this article, some models were designed to meet the objectives of performing maintenance and are explained below. MLP is the most commonly used type of neural network in most academic research [
23,
24]. In MLP, the summation functions (Eq. 24) is used to obtain the output of hidden neurons [
25].
where,
${z}_{j}$ is the input of the j
^{th} neuron in the hidden layer,
${b}_{j}$ is the bias of j
^{th} neuron in the hidden layer,
${W}_{ij}$ is the weight value between the i
^{th} input neuron and the j
^{th} neuron in the hidden layer,
$f\left({z}_{j}\right)$ is the activation function,
${y}_{j}$ is the outputs of j
^{th} neuron,
${p}_{k}$ is the output of the neurons in the k
^{th} output,
${W}_{jk}$ is the weight value between the neuron in the j
^{th} hidden layer and the neuron in the k
^{th} output layer, and
${n}_{1}$ is the number of neurons in the hidden layers. MLP commonly uses the backpropagation algorithm to find its parameters.
The Adaptive NeuroFuzzy Inference System (ANFIS) applies as a machine learning technique that integrates the adaptive neural network (ANN) rules and fuzzy logic (FL) theories inside an adaptive network framework to form a logical relationship between inputs and outputs [
26,
27]. ANFIS is a fivelayered structure consisting of the fuzzy layer, product layer, normalized layer, defuzzy layer, and the total output layer [
28].
RBF network acts as a feedforward neural network with one hidden layer of RBF units and a linear output layer [
29,
30]. The output is given as [
31]:
where,
${p}_{i}$ is the output,
${b}_{i}$ is the bias terms,
$N$ is the number of basic functions,
${W}_{ij}$ is the weight between hidden and output layers,
$E$ is the input data vector,
$\mu $ is the center of RBF unit, and
$\sigma $ represents the spread of the Gaussian basis function.
Support Vector Machine (SVM) was first developed by Vladimir Vapnik and further employed by others for various applications (e.g., [
32]). The SVM is based on statistical learning and the estimation function of y(i) was provided as [
33,
34,
35]:
where,
$\phi \left(E\right)$ defines a nonlinear mapping of E,
$W$ is a weight vector, and
$b$ represents the bias factor.
Gaussian Process Regression (GPR) is a nonparametric Bayesian approach to regression. This method has been employed in various scientific fields [
36]. GPR is providing a reliable response for the input data [
37]. In Gaussian process regression, it is supposed that the output can be calculated as [
38,
39]:
where,
${\sigma}_{noise}^{2}$ is the equal noise variance for
${E}_{i}$ of all samples.
The current study is focused on the soft computing approaches, however the theoretical principles of these methods are not addressed, as they can be found elsewhere in the literature. Comparing the performance of several different soft computing models as an intelligent way to improve the maintenance and monitoring of engine lubricantion conditions based on their electrical properties (ε′, ε″, tan δ).
2.2.2. Application
Considering the aforementioned section, the soft computing models were employed and their performance were comparatively evaluated to provide an innovative way for engine lubricant monitoring condition through their electrical properties (ε′, ε″, tan δ). In this regard, practical steps were performed to implement their algorithm (soft computing algorithms) in the MATLAB software. The inputs of models are the electrical properties (ε′, ε″, tan δ) of lubricants and the outputs of models are the chemical properties (Fe, Pb, Cu, Cr, Al, Si, Zn) of lubricants. The models were trained using 80% of the total data, while the rest is used for testing and validation. The optimizing indexes for the selected model were reported. The most common way to adjust model indexes is to experiment or trial and error [
23].
2.3. Performance Criteria
Performance criteria must be used to evaluate the predictive accuracy of models. It will help to improve and choose the optimal model. The Mean Absolute Percentage Error (MAPE) (Eq.8) and Root Means Square Error (RMSE) (Eq.10) were used as metrics in assessing and comparing [
40,
41,
42,
43,
44,
45].
where,
${y}_{ei}$ is the i
^{th} component of the desired (actual) output for the j
^{th} pattern, and
${y}_{pi}$ is the component of the predicted (fitted) output produced by the network for the i
^{th} pattern. The
$"n"$ is the number of lubricant samples.
3. Results and Discussion
3.1. Preliminary Statistical Analysis
Correlation is a statistical measure of how two or more variables change in connection with each other. On the other hand, it expresses the extent to which two variables are linearly related. Consequently, its results make it possible to select the best modeling method. In other words, some of the statistical models such as Multiple Linear Regression (MLR) are not appropriate when the correlation indicates a weak relation. In addition, it shows that it is a complex and nonlinear issue. The closer the correlation to one, the better relation between the two variables. Also, the sign of correlation indicates a direct or inverse relationship. In this study, the best correlation observed between Zn and tan δ, and with inverse relationship. However, the least correlation achieved between Fe and
ε′, and with inverse relationship. All correlations are illustrated in
Table 3.
3.2. Performance Evaluation of Models
Table 4 shows the statistical analysis of the models. Comparison and judgment are possible considering the values of RMSE and MAPE. The closer the RMSE and MAPE, to zero, the better model performance. It can be seen that the smallest value of MAPE and RMSE was obtained for all variables in RBF at 7.40 GHz. For instance, RMSE and MAPE were respectively equal to 0.4 and 0.7 for Si in RBF at 7.40 GHz
3.2.1. Adjusting RBF Parameters
As mentioned earlier, this work is aimed to compare soft computing models performance in predicting the chemical properties (Fe, Pb, Cu, Cr, Al, Si, Zn) of lubricants based on their electrical properties (ε′, ε″, tan δ). Considering the statistical results of the models, the RBF exhibited the best performance. So, in this section, RBF parameters are discussed to promote its performance.
Figure 4 shows the RBF efficiency (EF) in different hidden sizes for various chemical properties (Fe, Pb, Cu, Cr, Al, Si, Zn) at train and test steps. For example, if the hidden size is set to 12, the efficiency is the highest with no notable difference between the efficiency at train and test steps in “
Fe” prediction.
Figure 5 illustrates the RBF efficiency (EF) when employing different training algorithms for various chemical properties (Fe, Pb, Cu, Cr, Al, Si, Zn) at train and test steps. The "
Trainlm" provided approximately the best RBF efficiency to predict all chemical properties (Fe, Pb, Cu, Cr, Al, Si, Zn) at train and test steps.
Figure 6 plotted the coefficient of determination (R
^{2}) between the actual and predicted values of the spectral analysis indices of the lubricant. The coefficient is reported separately for the testing and training stages. It is seen that the slope of the regression line between the actual and predicted values in the RBF model is close to one and the intercept is very close to zero. Thus, the RBF model could predict the values of most spectral analysis indices of engine lubricant by a coefficient of 0.99.
3.2.2. Sensitivity Analysis
The ability of soft computing models to predict the chemical properties (Fe, Pb, Cu, Cr, Al, Si, Zn) of lubricants through electrical properties (ε′, ε″, tan δ) was investigated step by step as follow.
In
Section 3.2, the performance of the models was evaluated, and the appropriate model (RBF) was reported. In
Section 3.2.1, RBF parameters were set, and then sensitivity analysis was performed as an essential part to have a comprehensive study. In this section, the results of the sensitivity analysis are presented which are illustrated in
Figure 7. The sensitivity analysis prioritizes the model inputs. For instance, if ε′ is removed from inputs, the RMSE is greatly increased in all terms. Since decreasing RMSE indicates that the model is more suitable, this means that ε′ is detected as a more effective input. In general, removing any of the inputs cannot improve the RMSE, so it is not recommended to remove any of the inputs.
4. Conclusion
This study focused on comparing the performance of soft computing models to predict the chemical properties (Fe, Pb, Cu, Cr, Al, Si, Zn) of engine lubricants through their electrical properties (ε′, ε″, tan δ). This can help to promote predictive maintenance. It is also an efficient method to promote academic efforts in terms of saving time, energy, and financial costs. In this work, the data was gained from two sources, consisting of data extracted from a published work and the data experimented during the current research. Subsequently, the RMSE and MAPE of the model’s performance were obtained for several frequency points. The RBF was the best model in predicting chemical properties (Fe, Pb, Cu, Cr, Al, Si, Zn) via electrical properties (ε′, ε″, tan δ) at 7.4 GHz frequency. The RBF parameters were then adjusted and optimized. For instance, in the RBF implemented to predict Al, the best hidden size and train algorithmic were 15 and ‘trainlm’, respectively. Finally, sensitivity analysis was implemented to prioritize the RBF inputs for each chemical property (Fe, Pb, Cu, Cr, Al, Si, Zn). The results showed that removing any of the inputs worsened the RMSE. In other words, none of the electrical attributes (ε′, ε″, tan δ) are recommended to be removed. It is concluded that soft computing models can promote condition monitoring of the lubricants through electrical properties (ε′, ε″, tan δ).
Acknowledgments
We thank the Ferdowsi University of Mashhad, Iran for funding the research project and also Tirage Company for making its maintenance database available.
Conflicts of Interest
The authors declare that there is no conflict of interest.
Abbreviations
ANN 
Artificial neural network 
MLP 
Multilayer perceptron 
ANFIS 
Adaptive neurofuzzy inference system 
MLR 
Multiple Linear Regression 
FL 
Fuzzy logic 
RFE 
Recursive feature elimination 
GPR 
Gaussian process regression 
RBF 
Radial basic function 
IAS 
Infrared absorption spectroscopy 
RMSE 
Root means square error 
IS 
Impedance spectroscopy 
SVM 
Support vector machine 
KNN 
Knearest neighbor 
TDPQ 
Time depending on the particle quantifier 
MAPE 
Mean absolute percentage error 
VNA 
Vector Network Analyzer 
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