1. Introduction
The stable operation of a ball mill is critical for optimizing mineral processing efficiency and reducing operational costs. Traditional maintenance strategies, such as reactive (“post-failure”) or periodic maintenance, often lead to resource wastage and unplanned downtime. With advancements in condition monitoring, predictive maintenance has emerged as a viable solution. However, existing methods struggle with rapid detection and accurate identification of ball mill health states due to nonlinear and time-varying operational characteristics. This study proposes a hybrid approach combining Kalman Filter (KF) and Least Squares Support Vector Machine (LSSVM)—enhanced by Fuzzy C-Means (FCM) clustering—to predict the degradation trends of ball mill systems in real time.
2. Methodology
2.1. Framework of the FCM-LSSVM Model
The proposed framework integrates historical and real-time data to train a predictive model. Key steps include:
- Data Acquisition: Collect operational parameters from the ball mill PLC system.
- Data Preprocessing: Normalize and structure the data into a feature matrix.
- Health State Clustering: Use K-means to classify ball mill states into four categories.
- Model Training: Apply KF-LSSVM for noise-robust time-series prediction.
2.2. Key Parameters and Normalization
Six operational parameters were selected for modeling:
- Ore feed rate W (t/h)W(t/h)
- Sand sink rate L (t/h)L(t/h)
- Water addition T (t/h)T(t/h)
- Motor current D (A)D(A)
- Feed particle size R1 (-12 mm %)R1(-12 mm %)
- Discharge particle size R2 (-0.074 mm %)R2(-0.074 mm %)
Normalization Formula:L′=L−LMINLMAX−LMINL′=LMAX−LMINL−LMIN
where LL is the raw parameter value, and LMINLMIN/LMAXLMAX are its minimum/maximum historical values.
Table 1: Parameter Ranges and Units
| Parameter | Range | Unit |
|---|---|---|
| Ore feed rate (WW) | 120–360 | t/h |
| Motor current (DD) | 350–360 | A |
| Feed size (R1R1) | 85–95 | % |
2.3. Health State Classification via K-means
The ball mill states are categorized into four clusters using K-means:
- Healthy State: Degradation degree μm∈[0,0.16]μm∈[0,0.16]
- State 1: μm∈[0.16,0.3]μm∈[0.16,0.3]
- State 2: μm∈[0.3,0.55]μm∈[0.3,0.55]
- Degraded State: μm∈[0.55,1]μm∈[0.55,1]
Cluster Center Update Formula:cj=∑i=1Nuijmxi∑i=1Nuijmcj=∑i=1Nuijm∑i=1Nuijmxi
where uijuij is the membership degree of data point xixi to cluster jj, and mm is the fuzziness exponent.
2.4. Kalman Filter-Enhanced LSSVM
The LSSVM regression model is improved using Kalman Filter for noise suppression. The radial basis function (RBF) kernel is employed:K(xi,xj)=exp(−∥xi−xj∥22σ2)K(xi,xj)=exp(−2σ2∥xi−xj∥2)
The state-space model for KF-LSSVM is defined as:{a(k)=a(k−1)+w(k−1)y(k)=H⋅a(k)+v(k){a(k)=a(k−1)+w(k−1)y(k)=H⋅a(k)+v(k)
where ww and vv represent process and measurement noise, respectively.
3. Experimental Results
3.1. Real-Time Prediction Performance
The model was tested using 80,000 historical data points. Table 2 summarizes the degradation degrees predicted for five operational instances.
Table 2: Predicted Degradation Degrees
| Instance | W (t/h)W(t/h) | L (t/h)L(t/h) | D (A)D(A) | μmμm | State |
|---|---|---|---|---|---|
| 1 | 340.70 | 272.80 | 359.52 | 0.12 | Healthy |
| 2 | 354.32 | 309.12 | 358.89 | 0.24 | State 1 |
| 3 | 338.57 | 267.84 | 358.82 | 0.48 | State 2 |
| 4 | 342.84 | 274.44 | 356.96 | 0.62 | Degraded |
3.2. Model Accuracy and Efficiency
The FCM-LSSVM achieved a prediction accuracy of 93.6% with a response time of <2 seconds per data point. KF effectively reduced noise interference, improving the signal-to-noise ratio by 40%.
4. Discussion
- Advantages of FCM-LSSVM:
- Combines historical and real-time data for adaptive learning.
- KF enhances robustness against sensor noise.
- Clustering simplifies state interpretation.
- Limitations:
- Requires high-quality historical data for initial training.
- Parameter tuning (e.g., σσ in RBF) impacts performance.
5. Conclusion
This study demonstrates that the FCM-LSSVM algorithm significantly improves the accuracy and efficiency of ball mill health state prediction. By integrating Kalman Filter and K-means clustering, the model achieves real-time degradation trend analysis, enabling proactive maintenance. Future work will focus on optimizing hyperparameters and extending the framework to other industrial machinery.