CEEMDAN battery forecasting

The charge a full discharge delivers, one number per cycle. On battery B0005 it starts at 1.856 Ah and ends at 1.325 Ah.

One charge followed by one discharge. Cycles are numbered from 1; they are the x-axis of every chart and the rows of the design matrix. The Dataset page numbers the same discharges from 0, so its discharge 0 is cycle 1 here.

The downward drift of capacity with cycling. It is not monotonic: the curve recovers locally, which is why a smooth fit and a decomposition disagree about what is noise.

A capacity level treated as end of life. Two are used here, 1.4 Ah and 1.3 Ah, and a crossing counts only when it is sustained for five consecutive cycles, so a single dip does not declare failure.

The number of cycles until that sustained crossing. Here it is read off a forecast curve, so a model that never crosses has no RUL at all rather than a large error.

Complete Ensemble Empirical Mode Decomposition with Adaptive Noise. It splits a 1-D signal into additive, data-adaptive oscillations plus a residue by repeatedly sifting the signal with small noise realisations added (100 of them here, noise seed 100). It is not a fixed filter bank: the components are derived from this signal, so decomposing a longer signal gives different components.

One additive component, ordered fast to slow. Here there are 4: the first three are small oscillations and IMF 4 is the degradation trend.

What is left after every IMF is removed. On this run it is empty: all 118 stored values are approximately zero at floating-point precision, so it is carried through the arithmetic and contributes nothing.

The variance of one component as a fraction of the total across components. It answers “how much of the movement is this?”, which is a different question from importance.

Pearson r between a component and the training capacity curve. High r means the component follows the level of the curve, not merely part of its variance.

Using information that would not be available at prediction time. EMD-family methods compute every component from the whole signal, so decomposing the full curve and then scoring on its tail lets the tail influence its own features. This demo avoids it by decomposing the training cycles only.

The split rule used here: cycles 1–118 for everything that is fitted, cycles 119–168 excluded from fitting and from choosing settings.

The 118 × 5 table handed to the random forest: one row per training cycle, one column per component, target = measured capacity.

The share of split quality attributable to a column, averaged over the trees. Because the columns sum to the target, it measures how much each component contributes to reconstructing capacity.

Long short-term memory network: a neural network that reads a sequence step by step and keeps a memory of earlier steps. Here: LSTM(1,16) → LSTM(16,8) → Linear(8,1), with standardized inputs and a target that is either the next value (level) or the change from the last value (delta). The target and number of epochs are chosen on cycles 89–118 (see “How the current models were trained”).

The 16 consecutive values a model sees as input. It also sets how much history a rollout needs before it can start.

Scoring in which each prediction receives the true previous window. Errors cannot accumulate, so it measures the one-step fit and not forecasting.

Scoring in which each prediction is fed back as input. Errors compound, which is what a real forecast has to survive.

Repeat the last training measurement for every held-out cycle. It has no parameters, so it sets the minimum a learned model has to beat to show any skill.

Fit a straight line to the last 16 values, step one cycle forward, repeat. This extrapolates a local slope without training a neural model.

Mean squared error, its square root, and mean absolute error, all over the 50 held-out cycles. RMSE is in Ah, so it is directly comparable with the capacity axis.

Fraction of variance explained. Reported here only for the random forest on its training rows, where it is near 1 because the components add up to capacity.