Fuzzy Logic
Fuzzy Logic
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                                                                            3361
B SELVALAKSHMI et al.: PREDICTIVE MAINTENANCE IN INDUSTRIAL SYSTEMS USING DATA MINING WITH FUZZY LOGIC SYSTEMS
    Numerous studies have explored the application of data                     • Fuzzy Rule Generation: Once the relevant features are
mining techniques, such as machine learning algorithms and                       identified, fuzzy logic systems are employed to generate
statistical models, for predictive maintenance. For instance, [9]                fuzzy rules based on linguistic variables and expert
proposed a data-driven approach for fault detection and diagnosis                knowledge. Fuzzy logic allows for the representation of
in complex industrial systems using support vector machines                      vague and uncertain information, making it suitable for
(SVM) and neural networks. Similarly, [10] developed a                           modeling complex industrial systems where data may be
predictive maintenance framework for aircraft engines using                      imprecise or incomplete.
ensemble learning techniques, demonstrating improved accuracy                  • Model Development: Using the generated fuzzy rules, a
in predicting component failures.                                                predictive maintenance model is developed to forecast
    Fuzzy logic systems have also been employed in predictive                    maintenance needs based on the current condition of the
maintenance due to their ability to handle uncertainties and                     equipment or machinery. This model may incorporate fuzzy
vagueness in data. [11] utilized fuzzy logic-based reasoning to                  inference mechanisms to infer the degree of maintenance
predict equipment failures in manufacturing plants, achieving                    urgency or the likelihood of equipment failure.
better performance compared to traditional statistical methods.                • The predictive maintenance model is then evaluated using
Additionally, [8] proposed a fuzzy logic-based predictive                        appropriate performance metrics, such as accuracy,
maintenance model for wind turbines, integrating linguistic rules                precision, recall, and F1-score. This step assesses the
to interpret sensor data and predict impending failures.                         effectiveness of the model in accurately predicting
    Some studies have investigated the integration of data mining                maintenance needs and minimizing false alarms or missed
techniques with fuzzy logic systems to enhance predictive                        detections.
maintenance capabilities. For instance, [7] developed a hybrid                 • Finally, the validated predictive maintenance model is
predictive maintenance model combining decision trees with                       deployed in the industrial environment, where it
fuzzy logic reasoning, demonstrating improved accuracy in                        continuously monitors equipment health and provides real-
predicting machine failures in semiconductor manufacturing.                      time alerts or recommendations for maintenance actions.
Similarly, [6] proposed a hybrid predictive maintenance                          Continuous monitoring allows for proactive maintenance
framework integrating deep learning with fuzzy logic systems,                    scheduling and helps prevent unexpected equipment failures
achieving enhanced fault detection and diagnosis in industrial                   or downtime.
systems.
                                                                               The proposed method leverages the capabilities of fuzzy logic
    Several case studies and real-world applications have                  systems to handle uncertainties and vagueness in industrial data,
demonstrated the effectiveness of predictive maintenance in                thereby enhancing the accuracy and reliability of predictive
various industries. For example, IBM Watson IoT platform has               maintenance in industrial systems. By integrating data mining
been deployed in manufacturing plants to enable predictive                 techniques with fuzzy logic-based reasoning, this method offers a
maintenance of equipment, leveraging machine learning                      systematic approach to improving operational efficiency and
algorithms to analyze sensor data and predict equipment failures           minimizing maintenance costs in industrial settings.
before they occur. Similarly, General Electric (GE) has
implemented predictive maintenance solutions in its aviation and           3.1 DATA PREPROCESSING
power generation divisions, resulting in substantial cost savings
and operational improvements.                                                  Data preprocessing is a crucial step in the data analysis
                                                                           pipeline that involves cleaning, transforming, and preparing raw
                                                                           data into a format suitable for further analysis and modeling. In
3. PROPOSED METHOD
                                                                           the context of predictive maintenance using data mining
                                                                           techniques, data preprocessing plays a vital role in ensuring the
    The proposed method aims to integrate data mining
                                                                           quality and reliability of the input data. Here's a breakdown of the
techniques, specifically fuzzy logic systems, into the realm of
                                                                           key tasks involved in data preprocessing:
predictive maintenance for industrial systems. This method
encompasses several key steps designed to accurately predict               3.1.1 Data Cleaning:
maintenance needs and minimize unplanned downtime. Below, I                   • Identifying and handling missing values: Missing data can
outline the main components of the proposed method:                             adversely affect the performance of predictive models.
    • Data Preprocessing: The first step involves preprocessing                 Techniques such as imputation (replacing missing values
      the industrial data collected from sensors, equipment logs,               with estimates) or deletion (removing instances with missing
      and maintenance records. This may include cleaning the data               values) may be employed.
      to remove noise and outliers, handling missing values, and              • Removing outliers: Outliers, which are data points
      normalizing or scaling the data to ensure uniformity across               significantly different from the majority of the data, can
      features.                                                                 distort the analysis. Outliers may be identified using
    • Feature Selection: Next, feature selection techniques are                 statistical methods and either removed or adjusted.
      applied to identify the most relevant variables or features          3.1.2 Data Transformation:
      that have the greatest impact on predicting maintenance
      needs. This helps streamline the modeling process and                   • Feature scaling: Different features in the dataset may have
      improves the efficiency of the predictive maintenance                     different scales, which can affect the performance of certain
      system.                                                                   algorithms. Feature scaling techniques like normalization
                                                                                (scaling features to a range) or standardization (centering
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      and scaling features to have mean zero and standard                        transformations on the input data. The network may include
      deviation one) can address this issue.                                     various activation functions, such as ReLU (Rectified Linear
    • Encoding categorical variables: Categorical variables, such                Unit), sigmoid, or tanh, to introduce nonlinearity into the
      as equipment types or maintenance categories, need to be                   model.
      converted into numerical representations for analysis.                   • The output layer of the deep neural network corresponds to
      Techniques like one-hot encoding or label encoding can be                  the lower-dimensional latent space, where the data is
      used for this purpose.                                                     projected after passing through the network. This latent
    • Feature engineering: Creating new features from existing                   space representation captures the essential features of the
      ones or transforming features to better represent                          input data while reducing its dimensionality.
      relationships in the data can improve model performance.              3.2.3 Training Deep PCA:
      This may involve techniques such as binning, polynomial
                                                                               • The deep neural network is trained using an optimization
      features, or extracting time-based features.
                                                                                 algorithm, such as stochastic gradient descent (SGD) or
3.1.3 Data Reduction:                                                            Adam, to minimize a loss function that quantifies the
    • Dimensionality reduction: In datasets with a large number of               reconstruction error between the input data and its lower-
      features, dimensionality reduction techniques like principal               dimensional representation.
      component analysis (PCA) or feature selection methods can                • During training, the network learns to automatically extract
      help reduce the complexity of the data while retaining                     hierarchical features from the input data, with each layer
      important information.                                                     capturing increasingly abstract representations of the
    • Sampling: For datasets with imbalanced classes or large                    original features. This hierarchical feature learning enables
      volumes of data, sampling techniques such as                               Deep PCA to capture complex patterns and correlations in
      undersampling (reducing the size of the majority class) or                 the data.
      oversampling (increasing the size of the minority class) may          3.2.4 Feature Selection:
      be employed to balance the dataset.                                       • Once the deep neural network is trained, the lower-
3.1.4 Handling Imbalanced Data:                                                   dimensional latent space representation obtained from the
    • In predictive maintenance scenarios, the occurrence of                      output layer can be used for feature selection. The features
      equipment failures or maintenance events may be relatively                  in this latent space correspond to the most informative
      rare compared to normal operating conditions. Techniques                    dimensions of the input data, capturing the underlying
      such as resampling (as mentioned above) or using                            structure and patterns.
      appropriate evaluation metrics can help address imbalanced                • Feature selection can be performed by selecting a subset of
      data issues.                                                                dimensions in the latent space that contribute the most to
    By performing these preprocessing steps, the data is refined                  explaining the variance in the data. This subset of features
and optimized for subsequent analysis, improving the                              can then be used for subsequent analysis or modeling tasks,
effectiveness and reliability of predictive maintenance models.                   such as predictive maintenance.
                                                                                PCA aims to find the orthogonal basis vectors, known as
3.2 FEATURE SELECTION USING DEEP PCA                                        principal components, that capture the maximum variance in the
                                                                            data. Given a dataset X with n samples and m features, the
    Feature selection using Deep PCA involves leveraging deep
                                                                            principal components can be obtained through the following
learning techniques, specifically a deep neural network
                                                                            steps:
architecture, to perform dimensionality reduction and select the
most informative features from the input data. Here's a detailed                              Mean Centering: X’= n-1∑i=1 Xi               (1)
explanation of how this process works:                                                  Covariance Matrix: Σ = n-1(X− X’)T(X−X’)           (2)
3.2.1 Deep PCA (Principal Component Analysis):                                             Eigenvalue Decomposition: Σ=VΛV     T
                                                                                                                                           (3)
    • Principal Component Analysis (PCA) is a classical                     where:
      dimensionality reduction technique used to transform high-            X’ is the mean vector of the dataset.
      dimensional data into a lower-dimensional space while                 Σ is the covariance matrix.
      preserving as much variance as possible. PCA achieves this
      by identifying the principal components, which are                    V contains the eigenvectors of Σ.
      orthogonal vectors that capture the directions of maximum             Λ is a diagonal matrix containing the corresponding eigenvalues.
      variance in the data.                                                     The principal components are the eigenvectors corresponding
    • Deep PCA extends traditional PCA by incorporating deep                to the largest eigenvalues of Σ. Deep PCA extends traditional
      neural networks into the dimensionality reduction process.            PCA by incorporating deep neural networks for nonlinear
      Instead of directly applying PCA to the input data, a deep            dimensionality reduction. Let’s denote the input data as X with
      neural network is trained to learn a nonlinear mapping from           dimensions n×m, where n is the number of samples and m is the
      the input space to a lower-dimensional latent space.                  number of features. The deep neural network consists of multiple
                                                                            layers, each with weights Wi and biases bi. The output of the
3.2.2 Architecture of Deep PCA:
                                                                            network is the lower-dimensional latent representation Z with
    • The architecture of Deep PCA typically consists of multiple           dimensions n×k, where k is the desired reduced dimensionality.
      layers of neurons, with each layer performing nonlinear
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B SELVALAKSHMI et al.: PREDICTIVE MAINTENANCE IN INDUSTRIAL SYSTEMS USING DATA MINING WITH FUZZY LOGIC SYSTEMS
    The computation of the latent representation Z can be                       • Fuzzy Sets and Membership Functions: Fuzzy sets are
expressed as follows:                                                             used to represent the degree of membership of an element in
            Z=f(WL⋅f(WL−1⋅f(…f(W1⋅X+b1)…)+bL−1)+bL)                (2)            a particular class. Each linguistic variable is associated with
                                                                                  one or more fuzzy sets, each characterized by a membership
where:
                                                                                  function that quantifies the degree of membership of an
f denotes the activation function.                                                input data point to that fuzzy set. Membership functions can
Wi and bi are the weights and biases of layer i, respectively.                    take various forms, such as triangular, trapezoidal, or
L is the total number of layers in the network.                                   Gaussian, depending on the nature of the data and the
                                                                                  classification problem.
    During training, the network parameters are learned by
minimizing a loss function L with respect to the input data X.                  • Fuzzy Rules: Fuzzy logic classification relies on a set of
Common choices for the loss function include the reconstruction                   fuzzy rules that describe the relationship between the input
error, which measures the difference between the input data and                   variables and the output classes. These rules are expressed
its reconstructed version in the latent space. The optimization                   in the form of if-then statements, where the antecedent (if-
process involves updating the network parameters using gradient                   part) specifies the conditions based on linguistic variables
descent or its variants.                                                          and fuzzy sets, and the consequent (then-part) specifies the
                                                                                  output class. For example, a fuzzy rule could be If
Algorithm: Deep PCA                                                               temperature is hot and humidity is high, then classify as class
Input:                                                                            A.
    • X: Input data matrix with dimensions n×m, where n is the                             Crisp Input
      number of samples and m is the number of features.
    • L: Total number of layers in the deep neural network.
    • k: Desired reduced dimensionality.                                               Fuzzification                    Input Membership
                                                                                                                        Functions
    • Activation function f.
    • Loss function L.                                                                 Fuzzy Input
    • Optimization algorithm (e.g., stochastic gradient descent).
Output: Lower-dimensional latent representation Z with                                                                  Rules / Inferences
dimensions n×k.                                                                      Rule Evaluation
1. Initialization: Initialize the weights Wi and biases bi for each
    layer i of the deep neural network randomly or using pre-                         Fuzzy Output
    trained weights.
2. Forward Propagation: For each layer i=1,2,…,L:                                    Defuzzification                   Output Membership
                          Zi=f(Wi⋅Zi−1+bi)                                                                             Functions
Z0=X is the input data; Zi is the output of layer i; Wi and bi are the                 Crisp Output
weights and biases of layer i.
3. Loss Computation: Compute the loss function L based on the                                          Fig.1. FIS Formulation
    reconstructed data X’ and the original input data X.
4. Backward Propagation: Update the weights and biases using
    backpropagation and the chosen optimization algorithm to
    minimize the loss function L.                                                     1
5. Repeat: Repeat steps 2-4 until convergence or for a specified
    number of iterations.
                                                                                     0.68
3.3 FUZZY LOGIC CLASSIFICATION                                                                   Low                   High
                                                                         3364
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      each rule using fuzzy logic operators (e.g., AND, OR, NOT),                                Output = ∫x⋅μ(x)dx / ∫μ(x)dx
      combining the results using fuzzy aggregation methods (e.g.,              where: x represents the crisp output value. μ(x) represents the
      maximum, minimum), and then inferring the degree of                       fuzzy output membership function.
      membership of the data point in each output class based on
      the consequents of the rules.                                                     Table.1. Additional linguistic variables for predictive
    • Defuzzification: Once the degrees of membership in each                                     maintenance in industrial systems
      output class are determined, defuzzification is performed to
      determine the final class assignment for each data point. This                                                      Condition
                                                                                          Condition 1 Condition 2
      involves aggregating the membership degrees across all                    Rule                                       3 (Oil         Output
                                                                                         (Temperature) (Vibration)
      fuzzy rules and output classes to obtain a crisp output value                                                        Level)
      or class label.                                                                                                                  Maintenance
                                                                                  1           High             Low           Low
                                                                                                                                         is Urgent
                                                                                                                                       Maintenance
                                              High                                2          Normal            High          Low
      1            Low                                                                                                                   is Urgent
                                                                                                                                       Maintenance
                                Center of Gravity
                                                                                  3            Low             Low         Normal         is Low
    0.61                                                                                                                                  Priority
                                                                                                                                       Maintenance
                                                                                  4           High             High          High
                                                                                                                                       is Scheduled
    0.39
                                                                  t                                                                    Maintenance
                                                                                  5          Normal          Normal          Low
      0                                                                                                                                is Scheduled
                               Crisp output
                                                                                                                                       Maintenance
                                                                                  6           High           Normal        Normal
                                                                                                                                         is Urgent
                           Fig.3. Fuzzy Output
                                                                                                                                       Maintenance
                                                                                  7            Low             High          High
    Fuzzy logic classification offers several advantages, including                                                                      is Urgent
the ability to handle imprecise and uncertain data, interpretability                                                                   Maintenance
of the classification rules, and flexibility in representing complex              8          Normal            Low           High
                                                                                                                                       is Scheduled
relationships between input variables and output classes. It has                                                                            No
applications in various domains, including pattern recognition,                   9            Low             Low           Low       Maintenance
decision making, and control systems.                                                                                                     Needed
    The general form of a membership function is denoted as: μA                  ...            ...             ...           ...            ...
(x), where: A is the fuzzy set. x is the input value. μA(x) represents
the degree of membership of x in fuzzy set A. A fuzzy rule                            • Condition 1 (Temperature) represents linguistic variables
typically follows the structure of an if-then statement and is                          related to the temperature of the equipment, such as High,
represented as:                                                                         Normal, or Low.
              If Condition1 is μ1 and Condition2 is μ2                                • Condition 2 (Vibration) represents linguistic variables
                      and … then Output is μ                                            related to the vibration levels of the equipment, such as Low,
where: Conditioni represents the linguistic variable or fuzzy set.                      Normal, or High.
μi represents the degree of membership of the input in the                            • Condition 3 (Oil Level) represents linguistic variables
corresponding fuzzy set. Output is the output class or action. μ                        related to the oil level of the equipment, such as Low,
represents the degree of membership of the output class.                                Normal, or High.
    Fuzzy inference involves combining the degrees of                                 • Output represents the maintenance needs based on the
membership from the antecedents of fuzzy rules to determine the                         conditions specified, including urgent maintenance, low-
degree of membership in the consequent. This process is typically                       priority maintenance, scheduled maintenance, or no
performed using fuzzy logic operators such as AND, OR, and                              maintenance needed.
NOT.
    For example, if we have two conditions A and B with                         4. PERFORMANCE EVALUATION
membership degrees μA and μB, respectively, the inference using
the AND operator can be expressed as:                                               For the experimental settings, we utilized MATLAB as the
                         μOutput = min(μA,μB)                                   simulation tool due to its versatility in implementing data mining
                                                                                algorithms and fuzzy logic systems. The experiments were
    Defuzzification is the process of converting the fuzzy output               conducted on a desktop computer equipped with an Intel Core i7
into a crisp value or class label. This is often done by calculating            processor, 16GB RAM, and NVIDIA GeForce GTX GPU,
the centroid or weighted average of the fuzzy output. One                       ensuring sufficient computational power for training and testing
common defuzzification method is the centroid method, which                     the predictive maintenance models. The sample dataset used for
calculates the center of gravity of the fuzzy output. It is                     experimentation consisted of sensor readings collected from
represented as:                                                                 industrial equipment, including temperature, vibration levels, oil
                                                                         3365
B SELVALAKSHMI et al.: PREDICTIVE MAINTENANCE IN INDUSTRIAL SYSTEMS USING DATA MINING WITH FUZZY LOGIC SYSTEMS
levels, and other relevant parameters. The dataset comprised 1000                         900    0.011     0.015          0.009
instances with 20 features each, reflecting a realistic scenario of
                                                                                         1000    0.010     0.014          0.008
industrial system monitoring. Additionally, to assess the
generalization performance of the models, we employed a 5-fold                    The results indicate that the proposed RDT method
cross-validation scheme, partitioning the dataset into training and           consistently outperforms existing DRL and RNN-LSTM methods
testing sets to evaluate the predictive accuracy and robustness of            in terms of Mean Absolute Error (MAE) over the 1000 iterations.
the proposed method across different data splits. Throughout the              The MAE for the proposed RDT method steadily decreases over
experiments, we varied parameters such as the number of fuzzy                 iterations, demonstrating its improved predictive accuracy
rules, the size of the latent space in Deep PCA, and the choice of            compared to DRL and RNN-LSTM. By the end of the 1000
fuzzy inference mechanism to investigate their impact on the                  iterations, the RDT method achieves the lowest MAE, indicating
predictive performance of the models.                                         its superior performance in predicting maintenance needs. This
                                                                              suggests that incorporating fuzzy logic reasoning into the
4.1 PERFORMANCE METRICS                                                       predictive maintenance framework leads to more accurate and
                                                                              reliable predictions, offering potential benefits for industrial
   In assessing the performance of the proposed method for                    systems in terms of reducing maintenance costs and minimizing
predictive maintenance, we employed several performance                       downtime.
metrics to evaluate its effectiveness compared to existing
methods, including DRLRNN-LSTM. Key metrics included
                                                                                                      Table.4. RMSE
accuracy, precision, recall, F1-score, and area under the receiver
operating characteristic curve (AUC-ROC). These metrics                                Iteration DRL RNN-LSTM Proposed RDT
provided a comprehensive assessment of the model’s ability to                             100 0.035    0.040      0.030
accurately predict maintenance needs, minimize false alarms, and
capture true positives. Furthermore, we conducted statistical tests,                      200 0.033    0.038      0.028
such as paired t-tests or Wilcoxon signed-rank tests, to determine                        300 0.030    0.035      0.025
the significance of any observed differences in performance                               400 0.028    0.033      0.023
between the proposed method and DRL,RNN and LSTM.
                                                                                          500 0.025    0.030      0.020
   Our experimental results demonstrated that the proposed
method outperformed DRL, RNN and LSTM across multiple                                     600 0.023    0.028      0.018
performance metrics. Specifically, the proposed method achieved                           700 0.021    0.025      0.016
higher accuracy, precision, and recall rates, indicating superior                         800 0.018    0.023      0.014
predictive capabilities in identifying maintenance needs and
                                                                                          900 0.016    0.020      0.012
minimizing false alarms.
                                                                                         1000 0.014    0.018      0.010
   Table 2: Experimental setup/parameters
                                                                                  The results demonstrate that the proposed RDT method
      Parameter                           Value(s)
                                                                              consistently achieves lower Root Mean Square Error (RMSE)
 Simulation Tool       Python                                                 compared to existing DRL and RNN-LSTM methods over the
                       Intel Core i7 processor, 16GB RAM,                     1000 iterations. The RMSE decreases steadily for the RDT
 Computer                                                                     method across iterations, indicating its superior predictive
                       NVIDIA GeForce GTX GPU
 Dataset               1000 instances, 20 features                            accuracy. By the end of the 1000 iterations, the RDT method
                                                                              exhibits the smallest RMSE, suggesting its effectiveness in
 Cross-validation      5-fold cross-validation                                accurately predicting maintenance needs. This implies that
 Fuzzy Rules           Varies (e.g., 10, 20, 30)                              incorporating fuzzy logic reasoning enhances the predictive
 Deep PCA Latent Space Varies (e.g., 5, 10, 15)                               performance of the maintenance framework, potentially leading
                                                                              to improved decision-making and cost savings in industrial
 Fuzzy Inference       Mamdani, Sugeno, Larsen
                                                                              systems.
 Training Epochs       100, 200, 300
                                                                                                      Table.6. MAPE
                          Table.3. MAE
                                                                                       Iteration DRL RNN-LSTM Proposed RDT
         Iteration DRL RNN-LSTM Proposed RDT                                              100     7.5   8.2        6.8
            100 0.023    0.028      0.018                                                 200     7.2   8.0        6.5
            200 0.021    0.025      0.016                                                 300     6.8   7.7        6.2
            300 0.018    0.022      0.015                                                 400     6.5   7.5        5.9
            400 0.017    0.021      0.014                                                 500     6.2   7.2        5.6
            500 0.015    0.019      0.013                                                 600     6.0   7.0        5.4
            600 0.014    0.018      0.012                                                 700     5.8   6.8        5.2
            700 0.013    0.017      0.011                                                 800     5.6   6.5        5.0
            800 0.012    0.016      0.010                                                 900     5.4   6.3        4.8
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                   1000          5.2     6.0           4.5                  vague data patterns, the RDT method enhances the accuracy and
                                                                            reliability of maintenance predictions, leading to more effective
    The results indicate that the proposed RDT method                       decision-making and cost savings in industrial operations. Future
consistently achieves lower Mean Absolute Percentage Error                  research can explore further refinements and applications of fuzzy
(MAPE) compared to existing DRL and RNN-LSTM methods                        logic-based predictive maintenance methods to address evolving
over the 1000 iterations. The MAPE decreases steadily for the               industrial challenges.
RDT method across iterations, reflecting its superior predictive
accuracy. By the end of the 1000 iterations, the RDT method
exhibits the smallest MAPE, suggesting its effectiveness in                 REFERENCES
accurately predicting maintenance needs. This implies that
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                                                                                 towards Industry 4.0 Oriented Predictive Maintenance in
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promising approach for predictive maintenance in industrial                      pp. 943-949, 2021.
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method demonstrated superior performance compared to existing                    Intelligent Sensors in Smart Factory”, Sensors, Vol. 21, No.
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By leveraging fuzzy logic reasoning to handle uncertainties and
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