Autothermal Reformer Flowsheet Optimization with OMLT (TensorFlow Keras) Surrogate Object

Autothermal Reformer Flowsheet Optimization with OMLT (TensorFlow Keras) Surrogate Object#

Maintainer: Brandon Paul
Author: Brandon Paul
Updated: 2023-06-01

1. Introduction#

This example demonstrates autothermal reformer optimization leveraging the OMLT package utilizing TensorFlow Keras neural networks. In this notebook, sampled simulation data will be used to train and validate a surrogate model. IDAES surrogate plotting tools will be utilized to visualize the surrogates on training and validation data. Once validated, integration of the surrogate into an IDAES flowsheet will be demonstrated.

2. Problem Statement#

Within the context of a larger NGFC system, the autothermal reformer generates syngas from air, steam and natural gas for use in a solid-oxide fuel cell (SOFC).

2.1. Main Inputs:#

Bypass fraction (dimensionless) - split fraction of natural gas to bypass AR unit and feed directly to the power island
NG-Steam Ratio (dimensionless) - proportion of natural relative to steam fed into AR unit operation

2.2. Main Outputs:#

Steam flowrate (kg/s) - inlet steam fed to AR unit
Reformer duty (kW) - required energy input to AR unit
Composition (dimensionless) - outlet mole fractions of components (Ar, C2H6, C3H8, C4H10, CH4, CO, CO2, H2, H2O, N2, O2)

from IPython.display import Image
from pathlib import Path

def datafile_path(name):
    return Path("..") / name

Image(datafile_path("AR_PFD.png"))

3. Training and Validating Surrogates#

First, let’s import the required Python, Pyomo and IDAES modules:

# Import statements
import os
import numpy as np
import pandas as pd
import random as rn
import tensorflow as tf

# Import Pyomo libraries
from pyomo.environ import (
    ConcreteModel,
    SolverFactory,
    value,
    Var,
    Constraint,
    Set,
    Objective,
    maximize,
)
from pyomo.common.timing import TicTocTimer

# Import IDAES libraries
from idaes.core.surrogate.sampling.data_utils import split_training_validation
from idaes.core.surrogate.sampling.scaling import OffsetScaler
from idaes.core.surrogate.keras_surrogate import (
    KerasSurrogate,
    save_keras_json_hd5,
    load_keras_json_hd5,
)
from idaes.core.surrogate.plotting.sm_plotter import (
    surrogate_scatter2D,
    surrogate_parity,
    surrogate_residual,
)
from idaes.core.surrogate.surrogate_block import SurrogateBlock
from idaes.core import FlowsheetBlock

# fix environment variables to ensure consist neural network training
os.environ["PYTHONHASHSEED"] = "0"
os.environ["CUDA_VISIBLE_DEVICES"] = ""
np.random.seed(46)
rn.seed(1342)
tf.random.set_seed(62)

3.1 Importing Training and Validation Datasets#

In this section, we read the dataset from the CSV file located in this directory. 2800 data points were simulated from a rigorous IDAES NGFC flowsheet using a grid sampling method. For simplicity and to reduce training runtime, this example randomly selects 100 data points to use for training/validation. The data is separated using an 80/20 split into training and validation data using the IDAES split_training_validation() method.

# Import Auto-reformer training data
np.set_printoptions(precision=6, suppress=True)

csv_data = pd.read_csv(datafile_path("reformer-data.csv"))  # 2800 data points
data = csv_data.sample(n=100)  # randomly sample points for training/validation

input_data = data.iloc[:, :2]
output_data = data.iloc[:, 2:]

# Define labels, and split training and validation data
input_labels = input_data.columns
output_labels = output_data.columns

n_data = data[input_labels[0]].size
data_training, data_validation = split_training_validation(
    data, 0.8, seed=n_data
)  # seed=100

3.2 Training Surrogates with TensorFlow Keras#

TensorFlow Keras provides an interface to pass regression settings, build neural networks and train surrogate models. Keras enables the usage of two API formats: Sequential and Functional. While the Functional API offers more versatility, including multiple input and output layers in a single neural network, the Sequential API is more stable and user-friendly. Further, the Sequential API integrates cleanly with existing IDAES surrogate tools and will be utilized in this example.

In the code below, we build the neural network structure based on our training data structure and desired regression settings. Offline, neural network models were trained for the list of settings below, and the options bolded and italicized were determined to have the minimum mean squared error for the dataset:

Activation function: relu, sigmoid, tanh
Optimizer: Adam, RMSprop, SGD
Number of hidden layers: 1, 2, 4
Number of neurons per layer: 10, 20, 40

Typically, Sequential Keras models are built vertically; the dataset is scaled and normalized. The network is defined for the input layer, hidden layers, and output layer for the passed activation functions and network/layer sizes. Then, the model is compiled using the passed optimizer and trained using a desired number of epochs. Keras internally validates while training and updates each epoch’s model weight (coefficient) values.

Finally, after training the model, we save the results and model expressions to a folder that contains a serialized JSON file. Serializing the model in this fashion enables importing a previously trained set of surrogate models into external flowsheets. This feature will be used later.

# capture long output (not required to use surrogate API)
from io import StringIO
import sys

stream = StringIO()
oldstdout = sys.stdout
sys.stdout = stream

# selected settings for regression (best fit from options above)
activation, optimizer, n_hidden_layers, n_nodes_per_layer = "tanh", "Adam", 2, 40
loss, metrics = "mse", ["mae", "mse"]

# Create data objects for training using scalar normalization
n_inputs = len(input_labels)
n_outputs = len(output_labels)
x = input_data
y = output_data

input_scaler = None
output_scaler = None
input_scaler = OffsetScaler.create_normalizing_scaler(x)
output_scaler = OffsetScaler.create_normalizing_scaler(y)
x = input_scaler.scale(x)
y = output_scaler.scale(y)
x = x.to_numpy()
y = y.to_numpy()

# Create Keras Sequential object and build neural network
model = tf.keras.Sequential()
model.add(
    tf.keras.layers.Dense(
        units=n_nodes_per_layer, input_dim=n_inputs, activation=activation
    )
)
for i in range(1, n_hidden_layers):
    model.add(tf.keras.layers.Dense(units=n_nodes_per_layer, activation=activation))
model.add(tf.keras.layers.Dense(units=n_outputs))

# Train surrogate (calls optimizer on neural network and solves for weights)
model.compile(loss=loss, optimizer=optimizer, metrics=metrics)
mcp_save = tf.keras.callbacks.ModelCheckpoint(
    ".mdl_wts.keras", save_best_only=True, monitor="val_loss", mode="min"
)
history = model.fit(
    x=x, y=y, validation_split=0.2, verbose=1, epochs=1000, callbacks=[mcp_save]
)

# save model to JSON and create callable surrogate object
xmin, xmax = [0.1, 0.8], [0.8, 1.2]
input_bounds = {input_labels[i]: (xmin[i], xmax[i]) for i in range(len(input_labels))}

keras_surrogate = KerasSurrogate(
    model,
    input_labels=list(input_labels),
    output_labels=list(output_labels),
    input_bounds=input_bounds,
    input_scaler=input_scaler,
    output_scaler=output_scaler,
)
keras_surrogate.save_to_folder(
    keras_folder_name="keras_surrogate", keras_model_name="keras_model"
)

# revert back to normal output capture
sys.stdout = oldstdout

# display first 50 lines and last 50 lines of output
celloutput = stream.getvalue().split("\n")
for line in celloutput[:50]:
    print(line)
print(".")
print(".")
print(".")
for line in celloutput[-50:]:
    print(line)

3.3 Visualizing surrogates#

Now that the surrogate models have been trained, the models can be visualized through scatter, parity, and residual plots to confirm their validity in the chosen domain. The training data will be visualized first to confirm the surrogates fit the data. Then the validation data will be visualized to confirm the surrogates accurately predict new output values.

# visualize with IDAES surrogate plotting tools
surrogate_scatter2D(
    keras_surrogate, data_training, filename="keras_train_scatter2D.pdf"
)
surrogate_parity(keras_surrogate, data_training, filename="keras_train_parity.pdf")
surrogate_residual(keras_surrogate, data_training, filename="keras_train_residual.pdf")

3.4 Model Validation#

# visualize with IDAES surrogate plotting tools
surrogate_scatter2D(
    keras_surrogate, data_validation, filename="keras_val_scatter2D.pdf"
)
surrogate_parity(keras_surrogate, data_validation, filename="keras_val_parity.pdf")
surrogate_residual(keras_surrogate, data_validation, filename="keras_val_residual.pdf")

4. IDAES Flowsheet Integration#

4.1 Build and Run IDAES Flowsheet#

Next, we will build an IDAES flowsheet and import the surrogate model object. A single Keras neural network model accounts for all input and output variables, and the JSON model serialized earlier may be imported into a single SurrogateBlock() component.

# create the IDAES model and flowsheet
m = ConcreteModel()
m.fs = FlowsheetBlock(dynamic=False)

# create flowsheet input variables
m.fs.bypass_frac = Var(
    initialize=0.80, bounds=[0.1, 0.8], doc="natural gas bypass fraction"
)
m.fs.ng_steam_ratio = Var(
    initialize=0.80, bounds=[0.8, 1.2], doc="natural gas to steam ratio"
)

# create flowsheet output variables
m.fs.steam_flowrate = Var(initialize=0.2, doc="steam flowrate")
m.fs.reformer_duty = Var(initialize=10000, doc="reformer heat duty")
m.fs.AR = Var(initialize=0, doc="AR fraction")
m.fs.C2H6 = Var(initialize=0, doc="C2H6 fraction")
m.fs.C3H8 = Var(initialize=0, doc="C3H8 fraction")
m.fs.C4H10 = Var(initialize=0, doc="C4H10 fraction")
m.fs.CH4 = Var(initialize=0, doc="CH4 fraction")
m.fs.CO = Var(initialize=0, doc="CO fraction")
m.fs.CO2 = Var(initialize=0, doc="CO2 fraction")
m.fs.H2 = Var(initialize=0, doc="H2 fraction")
m.fs.H2O = Var(initialize=0, doc="H2O fraction")
m.fs.N2 = Var(initialize=0, doc="N2 fraction")
m.fs.O2 = Var(initialize=0, doc="O2 fraction")

# create input and output variable object lists for flowsheet
inputs = [m.fs.bypass_frac, m.fs.ng_steam_ratio]
outputs = [
    m.fs.steam_flowrate,
    m.fs.reformer_duty,
    m.fs.AR,
    m.fs.C2H6,
    m.fs.C4H10,
    m.fs.C3H8,
    m.fs.CH4,
    m.fs.CO,
    m.fs.CO2,
    m.fs.H2,
    m.fs.H2O,
    m.fs.N2,
    m.fs.O2,
]

# create the Pyomo/IDAES block that corresponds to the surrogate
# Keras
keras_surrogate = KerasSurrogate.load_from_folder(
    keras_folder_name="keras_surrogate", keras_model_name="keras_model"
)
m.fs.surrogate = SurrogateBlock()
m.fs.surrogate.build_model(
    keras_surrogate,
    formulation=KerasSurrogate.Formulation.FULL_SPACE,
    input_vars=inputs,
    output_vars=outputs,
)

# fix input values and solve flowsheet
m.fs.bypass_frac.fix(0.5)
m.fs.ng_steam_ratio.fix(1)

solver = SolverFactory("ipopt")
results = solver.solve(m, tee=True)

Let’s print some model results:

print("Steam flowrate = ", value(m.fs.steam_flowrate))
print("Reformer duty = ", value(m.fs.reformer_duty))
print("Mole Fraction Ar = ", value(m.fs.AR))
print("Mole Fraction C2H6 = ", value(m.fs.C2H6))
print("Mole Fraction C3H8 = ", value(m.fs.C3H8))
print("Mole Fraction C4H10 = ", value(m.fs.C4H10))
print("Mole Fraction CH4 = ", value(m.fs.CH4))
print("Mole Fraction CO = ", value(m.fs.CO))
print("Mole Fraction CO2 = ", value(m.fs.CO2))
print("Mole Fraction H2 = ", value(m.fs.H2))
print("Mole Fraction H2O = ", value(m.fs.H2O))
print("Mole Fraction N2 = ", value(m.fs.N2))
print("Mole Fraction O2 = ", value(m.fs.O2))

4.2 Optimizing the Autothermal Reformer#

Extending this example, we will unfix the input variables and optimize hydrogen production. We will restrict nitrogen below 34 mol% of the product stream and leave all other variables unfixed.

Above, variable values are called in reference to actual objects names; however, as shown below this may be done much more compactly by calling the list objects we created earlier.

# unfix input values and add the objective/constraint to the model
m.fs.bypass_frac.unfix()
m.fs.ng_steam_ratio.unfix()
m.fs.obj = Objective(expr=m.fs.H2, sense=maximize)
m.fs.con = Constraint(expr=m.fs.N2 <= 0.34)

# solve the model
tmr = TicTocTimer()
status = solver.solve(m, tee=True)
solve_time = tmr.toc("solve")

# print and check results
assert abs(value(m.fs.H2) - 0.33) <= 0.01
assert value(m.fs.N2 <= 0.4 + 1e-8)
print("Model status: ", status)
print("Solve time: ", solve_time)
for var in inputs:
    print(var.name, ": ", value(var))
for var in outputs:
    print(var.name, ": ", value(var))