Signal Decompositions#

Signal Decompositions Module

This module contains standardized signal decomposition models for use in the SDT algorithms. The defined signal decompositions are:

l2_l1d1_l2d2p365: separating a piecewise constant component from a smooth and seasonal component, with Gaussian noise - l2: gaussian noise, sum-of-squares small or l2-norm squared - l1d1: piecewise constant heuristic, l1-norm of first order differences - l2d2p365: small second order diffs (smooth) and 365-periodic
tl1_l2d2p365: similar to (2), estimating a smooth, seasonal component with an asymmetric laplacian noise model, fitting a local quantile instead of a local average - tl1: ‘tilted l1-norm,’ also known as quantile cost function - l2d2p365: small second order diffs (smooth) and 365-periodic
l1_l1d1_l2d2p365: like (1) but with an asymmetric residual cost instead of Gaussian residuals - l1: l1-norm - l1d1: piecewise constant heuristic, l1-norm of first order differences - l2d2p365: small second order diffs (smooth) and 365-periodic
l2_l1d2_constrained: - l2: gaussian noise, sum-of-squares small or l2-norm squared - l1d2: piecewise linear heuristic - constrained to have first val at 0 and last val at 1

solardatatools.signal_decompositions.l1_pwc_smoothper_trend(signal, use_ixs=None, w2=20.0, w3=1, w4=10.0, solver='CLARABEL', verbose=False, return_all=False)#

Used in solardatatools/algorithms/capacity_change.py

We solve a convex signal decomposition problem, making use of the l1-sparsity heuristic for estimating a piecewise constant component. We use a single pass of iterative reweighting on this term to “polish” the sparse solution (see: https://web.stanford.edu/~boyd/papers/rwl1.html).

Parameters:

signal – A 1d numpy array (must support boolean indexing) containing the signal of interest
use_ixs – List of booleans indicating indices to use in signal. None is default (uses the entire signal).
w2 – Weight on the piecewise constant component
w3 – Weight on the smooth, periodic component
w4 – Weight on the slope of the trend term (discourages large trends)
solver – Solver to use for the decomposition. Supported solvers are CLARABEL and MOSEK.
verbose – Sets verbosity

Returns:

A tuple with three 1d numpy arrays containing the three non-noise signal component estimates

solardatatools.signal_decompositions.l2_l1d1_l2d2p365(signal, use_ixs=None, w1=50, w2=0.001, yearly_periodic=False, return_all=False, solver='CLARABEL', sum_card=False, transition_locs=None, verbose=False)#

Used in: solardatatools/algorithms/time_shifts.py

This performs total variation filtering with the addition of a seasonal baseline fit. This introduces a new signal to the model that is smooth and periodic on a yearly time frame. This does a better job of describing real, multi-year solar PV power data sets, and therefore does an improved job of estimating the discretely changing signal. Default solver is QSS and timeshift algorithm takes the final solution from solving the nonconvex problem with sum_card=True.

Parameters:

signal – A 1d numpy array (must support boolean indexing) containing the signal of interest
w0 – Weight on the residual component
w1 – The regularization parameter to control the total variation in the final output signal
w2 – The regularization parameter to control the smoothness of the seasonal signal
yearly_periodic – Adds periodicity constraint to signal decomposition
return_all – Returns all components and the objective value. Used for tests.
solver – Solver to use for the decomposition. Supported solvers are CLARABEL and MOSEK.
sum_card – Boolean for using the nonconvex formulation using the cardinality penalty, Supported only using OSD with the QSS solver.
transition_locs – List of indices where transitions are located. Only used in CVXPY problems.
verbose – Sets verbosity

Returns:

A tuple with two 1d numpy arrays containing the two signal component estimates

solardatatools.signal_decompositions.l2_l1d2_constrained(signal, w0=1, w1=5, return_all=False, solver='CLARABEL', verbose=False)#

Used in solardatatools/algorithms/clipping.py

This is a convex problem and the default solver across SDT is CLARABEL.

Parameters:

signal – A 1d numpy array (must support boolean indexing) containing the signal of interest
w0 – Weight on the residual component
w1 – The regularization parameter on l1d2 component
return_all – Returns all components and the objective value. Used for tests.
solver – Solver to use for the decomposition. Supported solvers are CLARABEL and MOSEK.
verbose – Sets verbosity

Returns:

A tuple with returning the signal, the l1d2 component estimate, and the weight

solardatatools.signal_decompositions.tl1_l2d2p365(signal, use_ixs=None, tau=0.75, w0=1, yearly_periodic=True, return_all=False, solver='CLARABEL', verbose=False)#

Used in: solardatatools/algorithms/sunrise_sunset_estimation.py solardatatools/clear_day_detection.py solardatatools/data_quality.py solardatatools/sunrise_sunset.py

This is a convex problem and the default solver across SDT is CLARABEL.

Parameters:

signal – A 1d numpy array (must support boolean indexing) containing the signal of interest
use_ixs – List of booleans indicating indices to use in signal. None is default (uses the entire signal).
tau – Quantile regression parameter,between zero and one, and it sets the approximate quantile of the residual distribution that the model is fit to See: https://colab.research.google.com/github/cvxgrp/cvx_short_course/blob/master/applications/quantile_regression.ipynb
w0 – Weight on the residual component
w1 – The regularization parameter to control the smoothness of the seasonal signal
yearly_periodic – Adds periodicity constraint to signal decomposition
return_all – Returns all components and the objective value. Used for tests.
solver – Solver to use for the decomposition. Supported solvers are CLARABEL and MOSEK.
verbose – Sets verbosity

Returns:

A tuple with three 1d numpy arrays containing the three signal component estimates