Feature Engineering

Deriving aggregate metrics from raw waveform data to capture signal energy and distribution.

• Root Mean Square (RMS): Measures the effective power of a vibration signal; a rising RMS trend often indicates overall degradation.
• Crest Factor: The ratio of peak amplitude to RMS, highly sensitive to early-stage spalling in bearings.
• Kurtosis: Quantifies the 'tailedness' of the signal distribution; sharp spikes in kurtosis detect impulsive defects like gear tooth cracks.
• Skewness: Measures asymmetry in the signal distribution, useful for identifying friction changes in sliding components.

Converting time-series signals into the frequency spectrum to isolate fault-specific signatures that are invisible in the time domain.

• Fast Fourier Transform (FFT): The foundational algorithm for spectral analysis, mapping amplitude against frequency to identify bearing defect frequencies (BPFO, BPFI).
• Power Spectral Density (PSD): Shows how signal power distributes across frequencies, essential for tracking energy shifts from healthy to faulty states.
• Envelope Analysis: A high-resolution technique that demodulates low-frequency impact signals from high-frequency carrier waves, critical for early bearing fault detection.
• Cepstrum Analysis: The inverse FFT of a log spectrum, used to detect periodic structures like gear mesh harmonics and sideband families.

Capturing temporal dynamics by computing statistics over sliding windows of sensor data to expose degradation trajectories.

• Moving Average & Standard Deviation: Smooth short-term noise while revealing long-term drift in sensor baselines.
• Exponentially Weighted Moving Average (EWMA): Assigns greater weight to recent observations, making the feature more responsive to sudden degradation onset.
• Rate of Change (First Derivative): Directly models the velocity of degradation, a powerful predictor for Remaining Useful Life (RUL) estimation.
• Lag Features: Incorporating sensor values from previous time steps (t-1, t-10, t-100) to provide models with explicit temporal context.

Engineering composite features that fuse multiple sensor streams into physics-informed degradation metrics.

• Health Index Construction: A normalized, unitless value (0 to 1) combining vibration, temperature, and pressure data to represent overall asset condition.
• Sideband Energy Ratio: Quantifies the energy in modulation sidebands around gear mesh frequencies, a direct indicator of gear wear severity.
• FM0 and FM4 Metrics: Specialized gear fault indicators; FM0 detects major tooth breakage, while FM4 isolates damage limited to a single tooth.
• Temperature Efficiency Ratio: Compares actual thermal output against expected thermal output under given load conditions to detect cooling system degradation.

Eliminating redundant or irrelevant features to prevent overfitting and reduce computational overhead in real-time inference.

• Principal Component Analysis (PCA): Orthogonally transforms correlated sensor features into a smaller set of uncorrelated principal components that retain maximum variance.
• Mutual Information Scoring: Quantifies the non-linear dependency between each engineered feature and the failure target, ranking features by predictive power.
• SHAP Value Filtering: Uses game-theoretic explanations post-training to identify and retain only features with the highest marginal contribution to predictions.
• Variance Inflation Factor (VIF): Detects multicollinearity among features; features with high VIF are removed to stabilize regression-based RUL models.

Structuring operational data to correctly represent both failed and surviving assets without introducing survivorship bias.

• Run-to-Failure Labeling: Assigning a continuous RUL target to each time step in a training sequence, decreasing linearly or exponentially until the failure event.
• Piecewise Linear Degradation Assumption: Modeling health as constant until a degradation onset point, then linearly decaying—a common assumption for bearing life models.
• Survival Feature Encoding: Incorporating Kaplan-Meier survival probability estimates as features to inform models about the conditional probability of continued operation.
• Censored Data Weighting: Applying instance weighting during training to ensure surviving (censored) units contribute proportionally less to the loss function than failed units.

The process of deriving aggregate statistical attributes from temporal windows of sensor data to capture signal trends and patterns. Raw high-frequency vibration or temperature streams are often too noisy for direct modeling.

• Rolling Window Statistics: Calculating moving averages, standard deviations, and variances over fixed intervals to smooth noise.
• Spectral Features: Using Fast Fourier Transform (FFT) to extract dominant frequencies and energy bands from time-domain signals.
• Lag Features: Creating input variables that represent past values of the target sensor to capture temporal autocorrelation.

Engineering attributes that encode explicit physical knowledge of the machinery being monitored. These features translate raw physics into mathematical inputs that a model can directly correlate with failure modes.

• Crest Factor: The ratio of peak amplitude to RMS value, highly indicative of early-stage bearing spalling.
• Kurtosis: A statistical measure of the 'tailedness' of a vibration distribution; spikes often signal impulsive defects.
• Motor Current Signature Analysis (MCSA): Extracting sideband frequencies around the line frequency to detect broken rotor bars without invasive sensors.

The systematic process of identifying and retaining only the most predictive variables while discarding redundant or noisy ones. This prevents the curse of dimensionality and reduces model overfitting.

• SHAP Values: A game-theoretic method to quantify the marginal contribution of each feature to a specific failure prediction.
• Principal Component Analysis (PCA): An unsupervised linear transformation that projects high-dimensional sensor data onto a lower-dimensional space while preserving variance.
• Recursive Feature Elimination (RFE): A wrapper method that iteratively trains a model and prunes the weakest features to find the optimal minimal subset.

The fusion of multiple disparate sensor features into a single, normalized composite metric representing the overall degradation state of an asset. This simplifies Remaining Useful Life (RUL) regression into a univariate forecasting problem.

• Mahalanobis Distance: Measures the distance of a multi-dimensional feature vector from a healthy baseline cluster, accounting for feature covariance.
• Logistic Regression Fusion: Trains a simple model to map multiple features to a bounded [0,1] probability of failure, serving as a smooth degradation curve.
• Autoencoder Reconstruction Error: Uses the error from a neural network trained only on healthy data as a continuous health indicator; higher error implies greater deviation from nominal behavior.