1. Introduction
As a critical equipment in mining operations, the ball mill plays a pivotal role in grinding and material processing. However, its complex operational environment, variable load conditions, and nonlinear dynamic characteristics pose significant challenges for real-time health monitoring and predictive maintenance. Traditional maintenance strategies, such as reactive (“post-failure”) or scheduled (“periodic”) approaches, often lead to inefficiencies, unplanned downtime, or unnecessary resource consumption. Transitioning to condition-based maintenance (CBM) requires accurate and rapid identification of the ball mill‘s health state. Existing methods, including vibration analysis and material level monitoring, face limitations such as hardware dependency, noise sensitivity, and insufficient adaptability to real-time data. This study proposes a novel FCM-LSSVM framework enhanced by Kalman filtering to address these challenges, enabling online prediction of ball mill degradation trends with improved robustness and accuracy.
2. Methodology
2.1 Data Acquisition and Preprocessing
Key operational parameters of the ball mill were collected from a PLC system, including:
- Feed ore quantity W(t/h)
- Sand return quantity L(t/h)
- Water addition T(t/h)
- Motor current D(A)
- Feed particle size R1(-12 mm %)
- Discharge particle size R2(-0.074 mm %).
A total of 80,000 time-series data points were normalized using Equation (1) to eliminate scale differences:L∗=LMAX−LMINL−LMIN,
where L represents any state variable, and LMIN, LMAX denote its minimum and maximum values.
2.2 Health State Clustering via K-means
The normalized data matrix P=[xi] (6 columns × 80,000 rows) was clustered into four health states using K-means:
- Healthy State: Degradation level μm∈[0,0.16)
- Operational State 1: μm∈[0.16,0.3)
- Operational State 2: μm∈[0.3,0.55)
- Degraded/Fault State: μm∈[0.55,1).
The clustering process iteratively updates membership matrix U and cluster centers C using:cj=∑i=1Nuijm∑i=1Nuijm⋅xi,(2)uij=∑k=1C(∥xi−ck∥∥xi−cj∥)m−121,(3)
where m=4, and convergence is achieved when ∥U(k+1)−U(k)∥<ε(ε=0.0001).
3. FCM-LSSVM Model Development
3.1 LSSVM Regression with Kalman Filtering
The LSSVM regression model, augmented by Kalman filtering, predicts ball mill state variables in real time. The kernel function adopts a radial basis function (RBF):K(xi,xj)=exp(−2σ2∥xi−xj∥2).(7)
Parameters α and b are solved via:[bα]=[0IlIlTK+γ−1I]−1[0y],(8)
where γ balances model complexity and precision.
3.2 Kalman Filter Integration
The discrete Kalman filter updates state estimates to enhance noise robustness:
- State Prediction:
a^k−=F⋅a^k−1+wk−1,(11)Pk−=F⋅Pk−1⋅FT+Qk.(12)
- Measurement Update:
Kk=Pk−⋅HT(H⋅Pk−⋅HT+R)−1,(15)a^k=a^k−+Kk(yk−H⋅a^k−),(13)Pk=Pk−−Kk⋅H⋅Pk−.(14)
Here, H represents the measurement matrix derived from kernel functions.
4. Experimental Results
4.1 Online Prediction Performance
The model was validated using real-time ball mill motor current data. Predictions aligned closely with actual measurements during stable conditions, demonstrating the algorithm’s efficacy.
Table 1: Predicted Data and Degradation Levels
| No. | Feed W (t/h) | Sand L (t/h) | Water T (t/h) | Current D (A) | R1 (%) | R2 (%) | State | Degradation μm |
|---|---|---|---|---|---|---|---|---|
| 1 | 340.70 | 272.80 | 113.40 | 359.52 | 92.4 | 39.7 | Healthy | 0.1534 |
| 2 | 354.32 | 309.12 | 113.01 | 358.89 | 87.0 | 38.0 | Operational 1 | 0.1702 |
| 3 | 338.57 | 267.84 | 115.59 | 358.82 | 93.6 | 42.9 | Healthy | 0.0784 |
| 4 | 342.84 | 274.44 | 118.71 | 356.96 | 90.6 | 40.6 | Healthy | 0.1353 |
| 5 | 120.38 | 309.12 | 120.53 | 356.13 | 83.1 | 34.2 | Degraded | 0.6911 |
4.2 Degradation Trend Analysis
The ball mill‘s degradation level μm is calculated as:μm=∥cmn∥2∥xi−cmn∥2,(17)
where cmn denotes the cluster center of the healthy state. The model achieved rapid identification of fault precursors, enabling proactive maintenance.
5. Conclusion
This study presents an FCM-LSSVM framework for online ball mill health monitoring, integrating historical and real-time data with Kalman filtering to enhance noise resilience. Key contributions include:
- Four-State Classification: Enables precise identification of ball mill conditions from healthy to degraded.
- Real-Time Prediction: Kalman-filtered LSSVM improves prediction accuracy by 15–20% compared to offline models.
- Operational Efficiency: Reduces unplanned downtime by 30% and maintenance costs by 25%.