Estimators#

The estimators in Moirae determine the health and transient states for a storage system provided observations of it operating.

Estimators come in several categories:

  • Online Estimators which update parameter estimates after each new observation.

  • Offline Estimators which generate a single parameter estimate using all observations.

Offline Estimators#

Offline estimators determine the initial state and ASOH which minimize a loss function.

The OfflineEstimator defines the interface for all offline estimators. The Estimator finds the minimum of a Loss function by adjusting inferences for both the initial transient state of a system and any state-of-health parameters marked as updatable.

The Loss function translates the inputs from the estimator into the initial state (\(h_0\)) and ASOH parameters (\(\theta\)) then uses those parameters to simulate the evolution of the system according to a Model following the inputs (\(u\)) provided in operation Data. Loss functions typically compare the voltage observed in the data (\(y\)) to that predicted by the model (\(y^\prime\)) The objective returns a scalar fitness metric used by the Estimator to find best parameters.

Building an Estimator#

First construct an objective function for the optimizer, which requires

  1. The CellModel defining system physics

  2. A starting guess for the transient state

  3. A starting guess for the state of health

  4. The observation data as a BatteryDataset

loss = MeanSquaredLoss(
    cell_model=ecm,
    state=state,
    asoh=asoh,
    observations=dataset
)

Then provide the objective function to an OfflineEstimator class along with any options related to how that optimizer functions.

scipy = ScipyMinimizer(loss, method='Nedler-Mead')

Using an Estimator#

Begin the state estimation by calling the estimate method of the Estimator, which optimizes the transient state and ASOH parameters.

state_0, asoh, result = scipy.estimate()

The state_0 is an estimate for the starting transient state, asoh is an estimate for the state of health during the entire extent of the battery data, and result is a diagnostic measure specific to the Estimator.

Online Estimators#

Online estimators receive data from a battery dataset then pass inputs and outputs to Filters, which rely on Models to estimate state changes and measurements

The OnlineEstimator defines the interface for all online estimators. The Estimator operates using at least one Filter, which each rely on a Model to estimate how parameters evolve with time.

Building an Estimator#

The online estimator is composed of one or more filters which estimate the values of different parts of the battery state in tandem. The framework in which the filters interact is defined by the choice of OnlineEstimator, which includes the JointEstimator.

Build an estimator by first constructing a BaseCellWrapper that defines how to update or estimate the measurements of a system for each subset of variables being estimated. Each estimator how the they interact with the underlying CellModel and DegradationModel. Moirae provides a library of wrappers with a consistent interface so that all estimators can work with any Filter or Model. For example, the JointEstimator requires the JointCellModelWrapper.

cell_function = JointCellModelWrapper(
  cell_model=ecm,
  asoh=rint_asoh,
  transients=rint_transient,
  input_template=rint_inputs,
  asoh_inputs=('r0.base_values',),
)

Build the filters that will update the estimate of parameters next. Every type of filter requires the model wrapper and initial estimates for the values of parameters. The initial estimates for parameters and the inputs to the system are defined as probability distributions, which are created from NumPy arrays of parameters. The Unscented Kálmán Filter is a common choice:

ukf = UKF(
  model=cell_function,
  initial_hidden=MultivariateGaussian(
    mean=np.array([0., 0., 0.05]),  # Three parameters: SOC, hysteresis, R0
    covariance=np.diag([0.01, 0.01, 0.01])
  ),
  initial_controls=MultivariateGaussian(
    mean=np.array([0., 1., 25.]),  # Three inputs: Time, Current, Temperature
    covariance=np.diag([0.001, 0.001, 0.5])
  )
)

Assemble the filters together to form the estimator as the last step.

ukf_joint = JointEstimator(joint_filter=ukf)

Estimators provide class methods that assemble common patterns of wrapper and filters in a single step. Read the documentation on each filter type for further details.

Using an Estimator#

Use the estimator by calling the step function to update the estimated state provided a new observation of the outputs of the system.

The step function returns a probability distribution of the expected state and expected outputs.

# Generate inputs and expected outputs
next_inputs = ECMInput(time=1., current=1.)
expected_transients = ECMTransientVector.provide_template(has_C0=False, num_RC=0)
next_outputs = ecm.calculate_terminal_voltage(next_inputs, expected_transients, rint_asoh)

# Step the estimator
state_dist, output_dist = ukf_joint.step(
  next_inputs,
  next_outputs
)

All estimators provide access to the state through the estimator.state attribute, which can include elements from the transient and ASOH.

Retrieve the identities of each state variable using estimator.state_names or access the current estimates for the transient state and ASOH via the get_estimated_state method.

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