estim8Beta 0.0.3

Conduct parameter estimations for Dymola and FMU models

Project Description: Estim8

Estim8 is a tool for parameter estimation of differential-algebraic models (DAEs) using either model formulations in Dymola (installation required) or FMU models. It uses global meta-heuristic optimization to solve parameter estimation problems, and provides methods for uncertainty quantification.

Installation

The installation via pip install estim8Beta is problematic, since the required PyGMO package is not available here. If you still installed this package via PyPI make sure to add PyGMO to your environment, using:

$ conda config --add channels conda-forge $ conda config --set channel_priority strict $ conda install pygmo

Alternatively, estim8 can be installed via conda-forge directly:

conda install -c conda-forge estim8

Usage

The workflow of estim8 can be divided into 5 steps:

1. Initializing the model
2. Defining Estimation Prerequisites
3. Starting Estimation
4. Conducting Uncertainty Qunatification
5. Visualize Results

1. Initializing the Model

To initialize a model, use the class DymolaModel(), or FmuModel() depending on your model formulation, and initialize it:

MyModel = FmuModel('MyModel')
MyModel.initialize()

After the initialization all information on parameters and variables of the model are retrieved, and it can be simulated by the simulate() method:

Results, Parameters = MyModel.simulate(0,20,0.1, #(t0, t_end, stepsize)
									parameter={"par1":10},
									observe=["Trajectory1","Trajectory2"],
									tolerance=1e-4,
									)

Where the 3 positional arguments in the beginning form the timevector to simulate (similar to numpy.linspace()).

2. Defining Estimation Prerequisites

To conduct a parameter estimation, it is necessary to provide at least:

• A model as FmuModel or DymolaModel
• Experimental data to fit the parameters to (as pandas.DataFrame with time as index and columns as variable names. For Replicates: {'Rid1':pd.DataFrame, ..., 'RidN':pd.DataFrame} )
• Boundaries for the parameters to estimate
• A dictionary, mapping the names of the experimental data columns to the variables of the model (observation_mapping)

Optional the following settings can be made:

• Metric for the discrepancy ('SS': Sum of squares, 'WSS' Weighted sum of squares, 'negLL': negative Log-Likelihood)
• ParameterMapping and Replicate IDs if multiple replicates or experiments are included
• Custom time vector in case a finer discretization as 0.1 is required

Example Code:

# Data import
import pandas
MyData = pandas.read_excel('MyExpermentalData.xlsx', 
							index_col=0,
							header=[0,1], 
							sheet_name=None
							)

# Bound definition
bounds = {
		"par1" : [8,12],
		"par2" : [0.1,0.4],
		}

# Observation mapping
obs_map = {	
		"ExpDat1" : "Obs1",
		}

After specifying the prerequisites, the Estimator() can be instantiated:

MyEstimator = Estimator(MyModel, 
						data                = MyData,
						bounds              = bounds,
						observation_mapping = obs_map,
						)

3. Starting Estimation

For the estimation process there are 2 possibilities, which are estimate() and estimate_parallel(). Both return an optimal parameter vector according to the specified bounds, and an info struct:

# Single Core
optimum, info = MyEstimator.estimate(
					method   = 'local', 	# optimization method
					p0       = {'par1':10, 'par2':0.25},  # initial pnt
					max_iter = 20,          # maximum iterations 
					)

# Parallel 
optimum, info = MyEstimator.estimate_parallel(
					method   = 'de', 		# optimization method
					n_workers= 4,       	# number of parallel proc.
					max_iter = 20,
					) 

# Parallel (PyGMOs generalized island approach)
optimum, info = MyEstimator.estimate_parallel(
					method   = ['pg_de1220','pg_sga']*2,   # Islands 	
					n_workers= 4,       	# overwritten by no. islands
					max_iter = 20,
					) 

4. Uncertainty Qunatification

For UQ estim8 provides profile_likelihood()method, and classical Monte Carlo sampling method mc_sampling().

# MC sampling
MC_Samples = MyEstimator.mc_sampling(
				method         = ['pg_sea']*4,  # Optimization method
				n_samples      = 200, 			# No. samples
				evos2reset     = 50,  			# No. Iter until RAM reset
				# Terminate after:
				no_progress    = 10,   			#10 iters w.o. progress
				tot_iter       = 200,    		#More than 200 iters
				final_loss     = 500,    		#If loss of 500 is reached
				}

5. Visualize Results

For visualization of the results, the following automated plotting functions are available in the Visualization module:

Function	Arguments	Description
Visualization.plot_sim()	Results, observe=[]	Plots simulation trajectories generated by a Estim8Model
Visualization.plot_estimates()	optimum, MyEstimator, data=None, only_measured=False	Plots simulation trajectories of optimum in comparison to experimental data
Visualization.plot_correlations()	MC_Samples, thresholds=5, show_vals=False	Plotting the correlations for parameter results of a Monte Carlo Sampling as a heatmap
Visualization.plot_distribution()	MC_Samples, bins=5, est=MyEstimator	Creates a corner plot showing historgrams for parameter values on the diagonal, and scatter plots between parameter pairs on the LTM
Visualization.plot_many()	MC_Samples, MyEstimator, observe=[]	Plots all trajectories resulting from the MC samples together with the experimental data
Visualization.plot_bound_violation()	Optimum, bounds	Shows relative location of optimum within the bounds