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:174

Data class for the chamber parameters.

Signature

class ChamberParameters: ...

calculate_optimized_rates

Show source in chamber_rate_fitting.py:294

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).

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.

Signature

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

See also

• ChamberParameters

calculate_pmf_rates

Show source in chamber_rate_fitting.py:22

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.

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,
    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],
]: ...

coagulation_rates_cost_function

Show source in chamber_rate_fitting.py:122

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],
    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:185

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.

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],
) -> Tuple[NDArray[np.float64], List[Tuple[float, float]]]: ...

optimize_and_calculate_rates_looped

Show source in chamber_rate_fitting.py:363

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]],
) -> Tuple[Stream, Stream, Stream, Stream, Stream, Stream, Stream]: ...

See also

• ChamberParameters
• Stream

optimize_chamber_parameters

Show source in chamber_rate_fitting.py:232

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],
    chamber_parameters: ChamberParameters,
    fit_guess: NDArray[np.float64],
    fit_bounds: List[Tuple[float, float]],
    minimize_method: str = "L-BFGS-B",
) -> Tuple[float, float]: ...

See also

• ChamberParameters

optimize_parameters

Show source in chamber_rate_fitting.py:215

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]: ...