Time-Series Forecasting

Autoregressive Integrated Moving Average (ARIMA) models form the classical statistical baseline. They model a univariate time series as a linear function of its own past values (autoregression) and past forecast errors (moving average), after differencing to achieve stationarity. SARIMA extends this by incorporating seasonal components, making it suitable for machinery exhibiting periodic load cycles. While interpretable, ARIMA struggles with non-linear degradation patterns common in complex mechanical systems.

A specialized Recurrent Neural Network (RNN) architecture engineered to solve the vanishing gradient problem. LSTMs utilize a cell state and three gating mechanisms—input, forget, and output gates—to selectively remember or discard information over long sequences. This makes them highly effective for Remaining Useful Life (RUL) estimation, where a subtle vibration pattern from 1,000 cycles ago may be the earliest precursor to a bearing failure today.

Originally dominant in NLP, Transformer architectures have been adapted for time series via self-attention mechanisms that weigh the importance of every historical data point simultaneously, rather than processing sequentially like LSTMs. Models like Informer and Autoformer introduce sparse attention and decomposition blocks to handle extremely long sequences efficiently. This parallel processing captures complex, non-linear cross-dependencies between multiple sensor channels without the bottleneck of recurrence.

Error-Trend-Seasonality (ETS) models generate forecasts as weighted averages of past observations, where weights decay exponentially over time. Unlike ARIMA's focus on autocorrelation, ETS explicitly decomposes the signal into level, trend, and seasonal components. It is computationally lightweight and highly effective for short-horizon forecasting of stable metrics like ambient temperature or pressure, but it lacks the capacity to incorporate exogenous variables such as load changes or maintenance events.

A non-parametric, Bayesian approach that provides not just a point forecast but a full predictive distribution with uncertainty bounds. A Gaussian Process (GP) is defined by a mean function and a covariance kernel (e.g., Radial Basis Function) that encodes assumptions about signal smoothness. In predictive maintenance, this quantified uncertainty is critical for risk-averse scheduling—a wide confidence interval on a RUL prediction signals the need for immediate inspection, even if the mean estimate is distant.

Developed by Meta, Prophet is a decomposable additive model with three core components: a piecewise linear or logistic growth trend, a Fourier series for seasonality, and a holiday effect term. It is exceptionally robust to missing data and outlier shifts, and its parameters are intuitively tunable by domain experts. While less accurate than deep learning for high-frequency vibration data, it excels at modeling daily or weekly operational cycles in industrial throughput forecasting.

A specialized recurrent neural network architecture engineered to learn long-term dependencies in sequential data. Unlike standard RNNs, LSTMs use a gating mechanism—input, forget, and output gates—to regulate information flow, preventing the vanishing gradient problem. This makes them exceptionally suited for time-series forecasting where degradation patterns span thousands of sensor readings. For example, an LSTM can track a bearing's gradual wear progression over months of vibration data, remembering early-stage frequency shifts that simpler models would discard.

A deep learning architecture that processes entire time-series sequences in parallel using self-attention mechanisms. Rather than analyzing data points sequentially like LSTMs, transformers compute relevance scores between all timestamps simultaneously, capturing complex, non-linear relationships across arbitrary time horizons. This parallelization enables faster training and superior performance on multivariate sensor streams. In predictive maintenance, a transformer can correlate a sudden temperature spike with a vibration anomaly that occurred hours earlier, identifying failure signatures invisible to sequential models.

An algorithm that decomposes a time-domain signal into its constituent frequency components, converting raw vibration waveforms into spectrograms. This transformation is critical for feature engineering in predictive maintenance, as specific mechanical faults—such as bearing inner race defects or shaft misalignment—produce characteristic frequency signatures. By applying FFT to accelerometer data, engineers extract the fundamental frequencies and harmonics that serve as direct inputs to forecasting models, dramatically improving prediction accuracy for rotating machinery.

The estimated operational time remaining before a component requires replacement or repair, expressed in hours, cycles, or distance. RUL is the primary regression target for time-series forecasting in predictive maintenance. Models ingest historical run-to-failure data to learn degradation trajectories and project future health states. Accurate RUL estimation enables just-in-time parts procurement and eliminates both premature replacements and catastrophic failures. For instance, a turbofan engine RUL model might predict 47 flight cycles remaining with a 95% confidence interval of ±3 cycles.

A phenomenon where the statistical relationship between sensor inputs and failure outputs changes over time, invalidating previously accurate forecasting models. Unlike simple sensor degradation, concept drift represents a fundamental shift in the underlying data distribution. Causes include equipment retrofits, new operating regimes, or changing raw material properties. Detecting concept drift requires continuous monitoring of prediction error distributions and triggers model retraining. A pump handling a new fluid viscosity, for example, will exhibit entirely different vibration-to-failure mappings than its original training data.

A composite metric that fuses multiple sensor readings—vibration, temperature, pressure, acoustic emissions—into a single normalized value representing overall asset degradation. Health indices simplify complex multivariate time-series into a monotonic curve that trends from 1.0 (healthy) to 0.0 (failed). This dimensionality reduction enables straightforward threshold-based alerting and provides a clear visual representation of degradation trajectories. Common fusion techniques include principal component analysis, Mahalanobis distance, and autoencoder reconstruction errors.