Chamber Rate Fitting¶

Particula-beta Index / Particula Beta / Data / Process / Chamber Rate Fitting

Auto-generated documentation for particula_beta.data.process.chamber_rate_fitting module.

ChamberParameters¶

Show source in chamber_rate_fitting.py:287

Data class for the chamber parameters.

Signature¶

class ChamberParameters: ...

calculate_optimized_rates¶

Show source in chamber_rate_fitting.py:428

Calculate the coagulation rates using the optimized parameters and return the rates and R2 score.

Arguments¶

radius_bins - Array of particle radii in meters.
concentration_pmf - 2D array of concentration PMF values.
wall_eddy_diffusivity - Optimized wall eddy diffusivity.
alpha_collision_efficiency - Optimized alpha collision efficiency.
chamber_params - ChamberParameters object containing chamber-related parameters.
time_derivative_concentration_pmf - Array of observed rate of change of the concentration PMF (optional).
w_correction - W correction of the particles (optional).

Returns¶

coagulation_loss - Loss rate due to coagulation.
coagulation_gain - Gain rate due to coagulation.
dilution_loss - Loss rate due to dilution.
wall_loss_rate - Loss rate due to wall deposition.
net_rate - Net rate considering all effects.
r2_value - R2 score between the net rate and the observed rate.
chi_squared - Chi-squared error between the net rate and the observed rate.

Signature¶

def calculate_optimized_rates(
    radius_bins: NDArray[np.float64],
    concentration_pmf: NDArray[np.float64],
    wall_eddy_diffusivity: float,
    alpha_collision_efficiency: float,
    w_correction: float,
    fractional_uncertainty: NDArray[np.float64],
    chamber_parameters: ChamberParameters,
    time_derivative_concentration_pmf: Optional[NDArray[np.float64]] = None,
) -> Tuple[float, float, float, float, float, float]: ...

calculate_pmf_rates¶

Show source in chamber_rate_fitting.py:120

Calculate the coagulation, dilution, and wall loss rates, and return the net rate.

Arguments¶

radius_bins - Array of particle radii.
concentration_pmf - Array of particle concentration probability mass function.
temperature - Temperature in Kelvin.
pressure - Pressure in Pascals.
particle_density - Density of the particles in kg/m^3.
alpha_collision_efficiency - Collision efficiency factor.
volume - Volume of the chamber in m^3.
input_flow_rate - Input flow rate in m^3/s.
wall_eddy_diffusivity - Eddy diffusivity for wall loss in m^2/s.
chamber_dimensions - Dimensions of the chamber (length, width, height) in meters.
w_correction - W correction of the particles (optional).

Returns¶

coagulation_loss - Loss rate due to coagulation.
coagulation_gain - Gain rate due to coagulation.
dilution_loss - Loss rate due to dilution.
wall_loss_rate - Loss rate due to wall deposition.
net_rate - Net rate considering all effects.

Signature¶

def calculate_pmf_rates(
    radius_bins: NDArray[np.float64],
    concentration_pmf: NDArray[np.float64],
    temperature: float = 293.15,
    pressure: float = 101325,
    particle_density: float = 1000,
    alpha_collision_efficiency: float = 1,
    w_correction: float = 1,
    volume: float = 1,
    input_flow_rate: float = 1.6e-07,
    wall_eddy_diffusivity: float = 0.1,
    chamber_dimensions: Tuple[float, float, float] = (1, 1, 1),
) -> Tuple[
    NDArray[np.float64],
    NDArray[np.float64],
    NDArray[np.float64],
    NDArray[np.float64],
    NDArray[np.float64],
]: ...

chi_squared_error¶

Show source in chamber_rate_fitting.py:20

Calculate the chi-squared error between the observed and predicted values, accounting for uncertainties.

Arguments¶

observed - Array of observed values.
predicted - Array of predicted values.
fractional_uncertainty - Array or float of fractional uncertainty (e.g., 0.2 for 20%).

Returns¶

chi_squared - Chi-squared error between the observed and predicted values.

Signature¶

def chi_squared_error(
    observed: np.ndarray, predicted: np.ndarray, fractional_uncertainty: np.ndarray
) -> float: ...

coagulation_rates_cost_function¶

Show source in chamber_rate_fitting.py:225

Cost function for the optimization of the eddy diffusivity and alpha collision efficiency.

Signature¶

def coagulation_rates_cost_function(
    parameters: NDArray[np.float64],
    radius_bins: NDArray[np.float64],
    concentration_pmf: NDArray[np.float64],
    time_derivative_concentration_pmf: NDArray[np.float64],
    fractional_uncertainty: NDArray[np.float64],
    temperature: float = 293.15,
    pressure: float = 101325,
    particle_density: float = 1000,
    volume: float = 1,
    input_flow_rate: float = 1.6e-07,
    chamber_dimensions: Tuple[float, float, float] = (1, 1, 1),
) -> float: ...

create_guess_and_bounds¶

Show source in chamber_rate_fitting.py:298

Create the initial guess array and bounds list for the optimization.

Arguments¶

guess_eddy_diffusivity - Initial guess for eddy diffusivity.
guess_alpha_collision_efficiency - Initial guess for alpha collision efficiency.
bounds_eddy_diffusivity - Bounds for eddy diffusivity.
bounds_alpha_collision_efficiency - Bounds for alpha collision efficiency.
guess_w_correction - Initial guess for the W correction, optional. Typical range between 1 and 3.
bounds_w_correction - Bounds for the W correction.

Returns¶

initial_guess - Numpy array of the initial guess values.
bounds - List of tuples representing the bounds for each parameter.

Signature¶

def create_guess_and_bounds(
    guess_eddy_diffusivity: float,
    guess_alpha_collision_efficiency: float,
    bounds_eddy_diffusivity: Tuple[float, float],
    bounds_alpha_collision_efficiency: Tuple[float, float],
    guess_w_correction: float,
    bounds_w_correction: Tuple[float, float],
) -> Tuple[NDArray[np.float64], List[Tuple[float, float]]]: ...

hessian_standard_error¶

Show source in chamber_rate_fitting.py:49

Calculate the standard error for the optimized parameters using Hessian estimation with regularization and fallback to diagonal approximation.

Arguments¶

objective_function - The objective function.
parameters - Array of optimized parameters.
epsilon - Step size for numerical differentiation.
regularization - Regularization term for Hessian inversion.

Returns¶

standard_errors - Standard errors of the optimized parameters.

Signature¶

def hessian_standard_error(
    objective_function: Callable,
    parameters: np.ndarray,
    epsilon: float = 0.0001,
    regularization: float = 1e-08,
) -> np.ndarray: ...

optimize_and_calculate_rates_looped¶

Show source in chamber_rate_fitting.py:513

Perform optimization and calculate rates for each time point in the stream.

Arguments¶

pmf_stream - Stream object containing the fitted PMF data.
pmf_derivative_stream - Stream object containing the derivative of the PMF data.
chamber_parameters - ChamberParameters object containing chamber-related parameters.
fit_guess - Initial guess for the optimization.
fit_bounds - Bounds for the optimization parameters.

Returns¶

result_stream - Stream containing the optimization results for each time point.
coagulation_loss_stream - Stream containing coagulation loss rates.
coagulation_gain_stream - Stream containing coagulation gain rates.
coagulation_net_stream - Stream containing net coagulation rates.
dilution_loss_stream - Stream containing dilution loss rates.
wall_loss_rate_stream - Stream containing wall loss rates.
total_rate_stream - Stream containing total rates.

Signature¶

def optimize_and_calculate_rates_looped(
    pmf_stream: Stream,
    pmf_derivative_stream: Stream,
    chamber_parameters: ChamberParameters,
    fit_guess: NDArray[np.float64],
    fit_bounds: List[Tuple[float, float]],
    fractional_uncertainty: NDArray[np.float64],
    epsilon_hessian_estimation: float = 0.0001,
) -> Tuple[Stream, Stream, Stream, Stream, Stream, Stream, Stream]: ...

optimize_chamber_parameters¶

Show source in chamber_rate_fitting.py:357

Optimize the eddy diffusivity and alpha collision efficiency parameters for a given particle size distribution and its time derivative.

Arguments¶

radius_bins - Array of particle size bins in meters.
concentration_pmf - Array of particle mass fractions (PMF) concentrations at each radius bin.
time_derivative_concentration_pmf - Array of time derivatives of the PMF concentrations, representing the rate of change in concentration over time.
chamber_params - ChamberParameters object containing the physical properties of the chamber, including temperature, pressure, particle density, volume, input flow rate, and chamber dimensions.
fit_guess - Initial guess for the optimization parameters (eddy diffusivity and alpha collision efficiency).
fit_bounds - List of tuples specifying the bounds for the optimization parameters (lower and upper bounds for each parameter).
minimize_method - Optimization method to be used. Default is "L-BFGS-B". The following methods from scipy.optimize.minimize accept bounds, "L-BFGS-B", "TNC", "SLSQP", "Powell", "trust-constr".

Returns¶

wall_eddy_diffusivity_optimized - Optimized value of the wall eddy diffusivity (in 1/s).
alpha_collision_efficiency_optimized - Optimized value of the alpha collision efficiency (dimensionless).

Signature¶

def optimize_chamber_parameters(
    radius_bins: NDArray[np.float64],
    concentration_pmf: NDArray[np.float64],
    time_derivative_concentration_pmf: NDArray[np.float64],
    fractional_uncertainty: NDArray[np.float64],
    chamber_parameters: ChamberParameters,
    fit_guess: NDArray[np.float64],
    fit_bounds: List[Tuple[float, float]],
    minimize_method: str = "L-BFGS-B",
    epsilon_hessian_estimation: float = 0.0001,
) -> Union[Tuple[float, float, float], Tuple[float, float, float]]: ...

optimize_parameters¶

Show source in chamber_rate_fitting.py:340

Get the optimized parameters using the given cost function.

Signature¶

def optimize_parameters(
    cost_function: ignore,
    initial_guess: NDArray[np.float64],
    bounds: List[Tuple[float, float]],
    method: str,
) -> Tuple[float, float, float]: ...

Chamber Rate Fitting¶

ChamberParameters¶

Signature¶

calculate_optimized_rates¶

Arguments¶

Returns¶

Signature¶

See also¶

calculate_pmf_rates¶

Arguments¶

Returns¶

Signature¶

chi_squared_error¶

Arguments¶

Returns¶

Signature¶

coagulation_rates_cost_function¶

Signature¶

create_guess_and_bounds¶

Arguments¶

Returns¶

Signature¶

hessian_standard_error¶

Arguments¶

Returns¶

Signature¶

optimize_and_calculate_rates_looped¶

Arguments¶

Returns¶

Signature¶

See also¶

optimize_chamber_parameters¶

Arguments¶

Returns¶

Signature¶

See also¶

optimize_parameters¶

Signature¶