ANFIS (Adaptive Neuro-Fuzzy Inference System)
ANFIS (Adaptive Neuro-Fuzzy Inference System) is a hybrid machine learning architecture that combines the learning capabilities of neural networks with the interpretability of fuzzy logic systems. It can learn from data like a neural network while expressing knowledge as human-readable "if-then" rules.
In additive manufacturing, ANFIS is particularly popular for predicting mechanical properties from process parameters because it provides both accurate predictions and insight into which parameters matter most.
Core Concept
ANFIS implements a Takagi-Sugeno fuzzy inference system using a neural network structure. The key idea is to represent fuzzy rules like:
IF temperature is high AND speed is low THEN strength = f(temperature, speed)
The membership functions ("high", "low") and rule outputs are learned from data rather than defined by experts.
Architecture (5 Layers)
Layer 1 Layer 2 Layer 3 Layer 4 Layer 5
(Fuzzify) (Rules) (Normalize) (Consequent) (Output)
x ──┬── μA1 ──┐
│ ├── w1 ──── w̄1 ──── w̄1·f1 ──┐
└── μA2 ──┘ │
├──── Σ ──── y
y ──┬── μB1 ──┐ │
│ ├── w2 ──── w̄2 ──── w̄2·f2 ──┘
└── μB2 ──┘
μ = membership degree, w = rule firing strength
w̄ = normalized strength, f = linear output function
| Layer | Function | Parameters |
|---|---|---|
| 1. Fuzzification | Compute membership degrees using Gaussian or bell-shaped functions | Premise parameters (center, width) |
| 2. Rule firing | Multiply membership degrees (AND operation) | None (fixed) |
| 3. Normalization | Normalize rule strengths (w̄ᵢ = wᵢ / Σw) | None (fixed) |
| 4. Consequent | Compute weighted rule outputs (w̄ᵢ × fᵢ) | Consequent parameters (linear coefficients) |
| 5. Summation | Sum all weighted outputs | None (fixed) |
Training
ANFIS uses a hybrid learning algorithm:
- Forward pass: Fix premise parameters, use least squares estimation (LSE) to optimize consequent parameters
- Backward pass: Fix consequent parameters, use gradient descent (backpropagation) to optimize premise parameters
This hybrid approach converges faster than pure backpropagation and avoids local minima better than pure LSE.
Applications in Additive Manufacturing
Saleh et al. (2023) used ANFIS to predict mechanical properties of TPMS lattice structures (Diamond, Gyroid, Primitive) made from carbon fiber-reinforced PLA. ANFIS achieved only 7.61% maximum deviation, compared to 21.11% for traditional mathematical models. [DOI]
Fouly et al. (2023) applied a 5-layer ANFIS to predict hardness, modulus, and strength of annealed PLA-date pit composites. Achieved remarkable accuracy: hardness error of 9.88×10⁻³%, modulus error of 0.18%. [DOI]
Common Use Cases
- Tensile strength prediction from print parameters (temperature, speed, infill)
- Surface roughness modeling as function of layer height and orientation
- Build time estimation from part geometry and settings
- Process parameter optimization using interpretable rules
Advantages & Limitations
Advantages
- Interpretability: Rules can be examined and understood by engineers
- Accuracy: Often outperforms pure neural networks on small datasets
- Fast training: Hybrid algorithm converges quickly
- Handles uncertainty: Fuzzy membership naturally represents imprecise inputs
Limitations
- Curse of dimensionality: Number of rules grows exponentially with inputs
- Limited to Sugeno-type: Less flexible than general fuzzy systems
- Requires feature engineering: Input selection is critical
- Not deep: Single hidden layer limits representation power
See Also
- Machine Learning — Overview of ML concepts
- CNN — Convolutional Neural Networks
- Predictive Modeling — ANFIS for property prediction
References
- Jang, J.S.R. (1993). ANFIS: Adaptive-network-based fuzzy inference system. IEEE Trans. Systems, Man, Cybernetics, 23(3), 665-685.
- Saleh, M., et al. (2023). Prediction of mechanical properties for CF/PLA lattice structures. Polymers, 15(7), 1720. DOI
- Fouly, A., et al. (2023). Mechanical properties of annealed 3D-printed PLA-date pits composite. Polymers. DOI