Data Reconciliation and Parameter Estimation

This workflow generally describes features of the IDAES framework that are useful for data reconciliation and parameter estimation. Many of these features can be used for any task where plant data is to be used in conjunction with a process model. It is assumed that the user is familiar with the IDAES modeling platform and Pyomo. See the General Workflow for more information on how to set up a model.

This provides general information about IDAES functionality laid out in terms of typical use cases. See Tutorials and Examples, for specific complete examples of data reconciliation and parameter estimation examples. Relevant tutorials can be found in tutorials/advanced/data_recon_and_parameter_estimation.

Data Management

IDAES has functions to read and mange process data process data. Data management functions are contained in the idaes.dmf.model_data module.

Reading Data

A set of process data can be stored in two files, a data file and a metadata file. The data file is a CSV file where the first column contains a data point index, usually a timestamp. The first row contains a header with the measurement tag names. The rest of the files contains measurement data. The data file format is shown in the table below.

index tag (optional)	tag 1	tag 2	…
index 1	data(1,1)	data(1,2)	…
index 2	data(2,1)	data(2,2)	…
…	…	…	…

Metadata is provided for each tag in a separate CSV file. The metadata file has no header row, and aside from the tag name, any column my be blank. In the metadata csv file, the first column is the measurement tag name, the second column is a string that maps the tag to a specific model quantity, the third column is a description of the tag, and the fourth column is a for units of measure. Any columns past the fourth column are ignored and can be used to store any additional information.

tag 1	model reference string 1	description 1	units of measure 1
tag 2	model reference string 2	description 2	units of measure 1
…	…	…	…

The unit strings should be interpretable by pint, with the additional unit strings given in Unit String Information. The model reference string is the a string to reverence a model quantity. In the reference string the top-level model is always represented by m. For example, the reference string for a heater block outlet temperature could be m.flowsheet.heater.control_volume.properties_out[:].temperature. This reference will be indexed by time.

Reading data can be done with the idaes.dmf.model_data.read_data() function.

idaes.dmf.model_data.read_data(csv_file, csv_file_metadata, model=None, rename_mapper=None, unit_system=None, ambient_pressure=1.0, ambient_pressure_unit='atm')

Read CSV data into a Pandas DataFrame.

The data should be in a form where the first row contains column headings where each column is labeled with a data tag, and the first column contains data point labels or time stamps. The metadata should be in a csv file where the first column is the tag name, the second column is the model reference ( which can be empty), the third column is the tag description, and the fourth column is the unit of measure string. Any additional information can be added to columns after the fourth column and will be ignored. The units of measure should be something that is recognized by pint, or in the aliases defined in this file. Any tags not listed in the metadata will be dropped.

The function returns two items a pandas.DataFrame containing process data, and a dictionary with tag metadata. The metadata dictionary keys are tag name, and the values are dictionaries with the keys: “reference_string”, “description”, “units”, and “reference”.

Parameters:

• csv_file (str) – Path of file to read
• csv_file_metadata (str) – Path of csv file to read column metadata from
• model (pyomo.environ.ConcreteModel) – Optional model to map tags to
• rename_mapper (Callable) – Optional function to rename tags
• unit_system (str) – Optional system of units to atempt convert to
• ambient_pressure (float, numpy.array, pandas.series, str) – Optional pressure to use to convert gauge pressure to absolute. If a string is supplied, the corresponding data tag is assumed to be ambient pressure.
• ambient_pressure_unit (str) – Optional ambient pressure unit, should be a unit recognized by pint.

Returns:

(pandas.DataFrame, dict)

Binning Data

Process data can be divided into bins based on some criteria. This allows for estimating measurement uncertainty when no better information is available, and provides a way to look at how different process measurements vary for operating conditions that should be similar in some way. As an example, power plant data could be binned by power output, and assuming that operating procedures are standard, it could be assumed that measurements in each bin should be about the same. The variance of a measurement in a bin could be used a an approximation of uncertainty. Binning the data by load and time could show how process measurements change over time and be useful for things like fault detection and equipment degradation.

Adding bin information to a data frame is done with the idaes.dmf.model_data.bin_data() function.

idaes.dmf.model_data.bin_data(df, bin_by, bin_no, bin_nom, bin_size, min_value=None, max_value=None)

Sort data into bins by a column value. If the min or max are given and the value in bin_by for a row is out of the range [min, max], the row is dropped from the data frame.

Parameters:

• df (pandas.DataFrame) – Data frame to add bin information to
• bin_by (str) – A column for values to bin by
• bin_no (str) – A new column for bin number
• bin_nom (str) – A new column for the mid-point value of bin_by
• bin_size (float) – size of a bin
• min_value (in {float, None}) – Smallest value to keep or None for no lower
• max_value (in (float, None}) – Largest value to keep or None for no upper

Returns:

returns the data frame, and a dictionary with the number of rows

in each bin.

Return type:

(dict)

The idaes.dmf.model_data.bin_stdev() function can be used to calculate the standard deviation for each measurement in each bin.

idaes.dmf.model_data.bin_stdev(df, bin_no)

Calculate the standard deviation for each column in each bin.

Parameters:

• df (pandas.DataFrame) – pandas data frame that is a bin number column
• bin_no (str) – Column to group by, usually contains bin number

Returns:

key is the bin number and the value is a pandas.Serries with column

standard deviations

Return type:

dict

The function idaes.dmf.model_data.data_plot_book() creates a multipage PDF containing box plots for all the measurements based on the bins.

idaes.dmf.model_data.data_plot_book(df, bin_nom, file='data_plot_book.pdf', tmp_dir='tmp_plots', xlabel=None, metadata=None, cols=None, skip_cols=[])

Make box and whisker plots from process data based on bins from the bin_data() function.

Parameters:

• df – data frame
• bin_nom – bin mid-point value column
• file – path for generated pdf
• tmp_dir – a directory to store temporary plots in
• xlabel – Label for x axis
• metadata – tag meta data dictionary

Returns:

None

To compare reconciled data to original measurements the idaes.dmf.data_rec_plot_book() is used. For each bin there are two box plots one for the original data and one for reconciled data.

idaes.dmf.model_data.data_rec_plot_book(df_data, df_rec, bin_nom, file='data_rec_plot_book.pdf', tmp_dir='tmp_plots', xlabel=None, metadata=None, cols=None, skip_cols=[])

Make box and whisker plots from process data compared to data rec results based on bins from the bin_data() function. The df_data and df_rec data frames should have the same index set and the df_data data frame contains the bin data. This will plot the intersection of columns containg numerical data.

Parameters:

• df_data – data frame with original data
• df_rec – data frame with reconciled data
• bin_nom – bin mid-point value column
• file – path for generated pdf
• tmp_dir – a directory to store temporary plots in
• xlabel – Label for x axis
• metadata – tag meta data dictionary
• cols – List of columns to plot, if None plot all
• skip_cols – List of columns not to plot, this overrides cols

Returns:

None

Tagging the Model

Mapping process data to a model is typically done by creating model tag dictionaries. Where the dictionary key is a measurement tag and the value is a reference to a model variable, expression, or parameter. The tags may be process measurement tags, or any other convenient string. IDAES has some utilities to help facilitate tagging of models.

If model reference strings where provided in the tag metadata file, the tag metadata from the idaes.dmf.model_data.read_data() will contain model references. These references can be accessed in the metadata dictionary as metadata[tag]["reference"].

The reference strings are optional in the tag metadata file and can be added after reading the data. To add a reference string to the metadata, you can update the metadata dictionary like metadata[tag]["reference_string"] = reference_string. If you update the reference string, the idaes.dmf.model_data.upadate_metadata_model_references()`` function can be used to update the references in the tag metadata.

idaes.dmf.model_data.upadate_metadata_model_references(model, metadata)

Create model references from refernce strings in the metadata. This updates the ‘reference’ field in the metadata.

Parameters:

• model (pyomo.environ.Block) – Pyomo model
• metadata (dict) – Tag metadata dictionary

Returns:

None

An easy way to create a new tag dictionary from tag metadata is to use dictionary comprehension like so: data_tags = {k:v["reference"][0] for k, v in metadata.items() if v["reference"] is not None}

Often data reconciliation is performed using process data as the first step of parameter estimation or model validation. Data reconciliation can often fill in information for many unmeasured quantities. Most of this data can be associated with process streams. To make managing proliferation of data tags easier, it is often desirable to create a new set of tags based on stream (Arc) names that can be automatically obtained from the model.

The first step to creating a new set of tags based on streams is to get a dictionary of streams and their associated state blocks, with can be done with the idaes.core.util.tables.arcs_to_stream_dict() function.

idaes.core.util.tables.arcs_to_stream_dict(blk, additional=None, descend_into=True, sort=False)

Creates a stream dictionary from the Arcs in a model, using the Arc names as keys. This can be used to automate the creation of the streams dictionary needed for the create_stream_table_dataframe() and stream_states_dict() functions.

Parameters:

• blk (pyomo.environ._BlockData) – Pyomo model to search for Arcs
• additional (dict) – Additional states to add to the stream dictionary, which aren’t represented by arcs in blk, for example feed or product streams without Arcs attached or states internal to a unit model.
• descend_into (bool) – If True, search subblocks for Arcs as well. The default is True.
• sort (bool) – If True sort keys and return an OrderedDict

Returns:

Dictionary with Arc names as keys and the Arcs as values.

The stream dictionary can be converted to a corresponding dictionary of state at a specific time with the idaes.core.util.tables.stream_states_dict() function.

idaes.core.util.tables.stream_states_dict(streams, time_point=0)

Method to create a dictionary of state block representing stream states. This takes a dict with stream name keys and stream values.

Parameters:

• streams – dict with name keys and stream values. Names will be used as display names for stream table, and streams may be Arcs, Ports or StateBlocks.
• time_point – point in the time domain at which to generate stream table (default = 0)

Returns:

A pandas DataFrame containing the stream table data.

With the dictionary of states, a tag dictionary can be created automatically with the idaes.core.util.tables.stream_states_dict() function.

idaes.core.util.tables.stream_states_dict(streams, time_point=0)

Method to create a dictionary of state block representing stream states. This takes a dict with stream name keys and stream values.

Parameters:

• streams – dict with name keys and stream values. Names will be used as display names for stream table, and streams may be Arcs, Ports or StateBlocks.
• time_point – point in the time domain at which to generate stream table (default = 0)

Returns:

A pandas DataFrame containing the stream table data.

Objective Function

For either parameter estimation or data reconciliation the objective function is often written in the form:

\[\min \sum_i \frac{(x_{\text{data},i} - x_{\text{model},i})^2}{\sigma_i^2}\]

To add the data to be used in the objective standard practice has been to add a mutable parameter for data and standard deviation indexed by measurement tags. The parameter values can be set from the measurement data frame to a specific index.

The following code snippet exemplifies the use of data parameters in a model.

# df is from reading process data into a pandas.DataFrame. bin_stdev comes
# from binning the data and calculating the standard deviations, as described
# in the Data Management section.

# Add data parameters
m.data = pyo.Param(data_tags, mutable=True)
m.data_stdev = pyo.Param(data_tags, mutable=True)

# A function to set the data parameters from measurement data
def set_data(m, df, data_tags, index=None):
  m.bin_no = df.iloc[index]["bin_no"]
  for t in data_tags:
      m.data[t] = df.iloc[index][t]
      m.data_stdev[t] = bin_stdev[m.bin_no][t]

# Expressions for error in the objective function
@m.Expression(data_tags)
def err(m, i):
    return (m.data[i] - data_tags[i])/m.data_stdev[i]

Parameter Estimation

For parameter estimation and data reconciliation, it is recommended to use Paramest. If more control is needed a user can also set up their own parameter estimation problem, by combining multiple process models into a larger parameter estimation model.

APPENDIX: Unit String Information

This section provides additional detail about units strings that can be used to read data with the read_data() function.

Temperature Differences

The unit conversion for temperatures with offsets (C and F) are deferent depending on whether a measurement is temperature or temperature difference. It is important to ensure the temperature units are correctly specified before reading data. The units “delta_degC and delta_degF” are defined to handle temperature differences.

Units Not Converted

The following units are not affected by unit conversion.

• percent
• ppm
• ppb
• pH
• VAR
• MVAR
• H2O
• percent open
• percent closed

Gauge Pressure

The table below shows a list of unit string that are taken to be gauge pressure when data is read. Gauge pressures are converted to absolute pressure in the unit conversion process.

Gauge Pressure Unit	Absolute Pressure Unit
psig	psi
in water gauge	in water
in hg gauge	in hg

Additional Unit Definitions

Some units are common enough in process data that the read_data() function will recognize them and convert them to standard Pint unit strings. Unit strings are case sensitive to handle things like milli (m) and mega (M) prefixes.

The table below shows the additional units.

Unit String	Pint Unit String
Pressure
PSI	psi
PSIA	psi
psia	psi
PSIG	psig
INWC	in water
IN WC	in water
IN/WC	in water
” H2O	in water
INHG	in hg
IN HG	in hg
IN/HG	in hg
HGA	in hg
IN HGA	in hg
Fraction
PCT	percent
pct	percent
PERCT	percent
PERCT.	percent
PCNT	percent
PPM	ppm
PPB	ppb
% OPEN	percent open
% CLSD	percent closed
% CLOSED	percent closed
Length
IN	in
INS	in
INCHES	in
Inches	in
FT	ft
FEET	ft
FOOT	ft
Feet	ft
MILS	minch
Speed
MPH	mile/hr
IPS	in/s
Volume
KGAL	kgal
Vol Flow
GPM	gal/min
gpm	gal/min
CFM	ft^3/min
KCFM	ft^3/mmin
SCFM	ft^3/min
KSCFM	ft^3/mmin
Angle
DEG	deg
Angular Speed
RPM	rpm
Frequency
HZ	hz
Temperature
DEG F	degF
Deg F	degF
deg F	degF
DEG C	degC
Deg C	degC
deg C	degC
DEGF	degF
DegF	degF
DEGC	degC
DegC	degC
Temperature Difference
DELTA DEG F	delta_degF
DETLA Deg F	delta_degF
DETLA deg F	delta_degF
DETLA DEG C	delta_degC
DETLA Deg C	delta_degC
DELTA deg C	delta_degC
DELTA DEGF	delta_degF
DELTA DegF	delta_degF
DELTA degF	delta_degF
DELTA DEGC	delta_degC
DELTA DegC	delta_degC
DELTA degC	delta_degC
Delta DEG F	delta_degF
Delta Deg F	delta_degF
Delta deg F	delta_degF
Delta DEG C	delta_degC
Delta Deg C	delta_degC
Delta deg C	delta_degC
Delta DEGF	delta_degF
Delta DegF	delta_degF
Delta degF	delta_degF
Delta DEGC	delta_degC
Delta DegC	delta_degC
Delta degC	delta_degC
delta DEG F	delta_degF
delta Deg F	delta_degF
delta deg F	delta_degF
delta DEG C	delta_degC
delta Deg C	delta_degC
delta deg C	delta_degC
delta DEGF	delta_degF
delta DegF	delta_degF
delta degF	delta_degF
delta DEGC	delta_degC
delta DegC	delta_degC
delta degC	delta_degC
Energy
MBTU	kbtu
Mass
MLB	klb
K LB	klb
K LBS	klb
lb.	lb
Mass flow
TPH	ton/hr
tph	ton/hr
KLB/HR	klb/hr
KPPH	klb/hr
Current
AMP	amp
AMPS	amp
Amps	amp
Amp	amp
AMP AC	amp
pH
PH	pH
VARS (volt-amp reactive)
VARS	VAR
MVARS	MVAR