Evaluating Steel Performance Using Evolutionary Algorithms

Student: Yichun Li, Northwestern University

Principal Investigator: Mark Messner, Argonne National Laboratory

 

  1. Introduction

Grade-91 Steel was developed around 30 years ago. Now a new design of nuclear reactors has been proposed and under review. Water was originally used as a moderator and coolant in existing nuclear reactors. Now liquid sodium has been considered as the new coolant because designs have forgone water as a coolant. However, steam is still used to transform the energy from nuclear reactions to electricity. Therefore, the new design adds in an intermediate heat exchanger with both water and liquid flowing through to perform the heat exchange process. In turn, the materials used for building the heat exchanger has been Grade-91 steel. However, such steel has not been used in such structure in the nuclear reactor before, therefore it is important to understand and examine its properties, such as stress and strain, and performance, especially under the condition of high temperatures. The designed proposed life of the steel for the heat exchanger is 60 years. However, there has not been enough research on this topic. Therefore, this project is to fill in the gap, by looking at the experimental data of such steel under different physical parameters under stress and strain. There are two other materials, though having less data that are considered for the same project.

 

The original goal of this project was to utilize machine learning techniques to configure a model that will help us understand the performance (deformation under high temperatures) better.

  1. EA (Evolutionary Algorithms): ODE-based models
  2. RNN (Recurrent Neural Network): Use the synthetic model to train and run the model first before using the big dataset.

 

Due to time constraint, a completion of EA on a simulated dataset was achieved. The following is the general timeline:

Week 1-4: Building and debugging the EA algorithm using DEAP package;

Week 5-9: Testing the algorithm on simulated datasets and analyzing results;

Week 10: Final wrap-up.

 

  1. Setup
  2. Data Processing (scaffold.py)

The file includes functions to read and load entries from a dataset of 200 experiments, parsing them and putting them into an evaluative model to assess individuals.

The fitness of the evaluation(R) is a Euclidean norm summation over all experiments. For purpose of fitting into the DEAP package, the goal of the algorithm instance is to maximize fitness(F), where , where F will take values between 0 and 1 (inclusive).

Additionally, a penalty (R = 10000) is added when evaluating F, which despite its mathematical bound, could result in invalid values. In those cases, the fitness of that individual will be set to the penalty, which will result in the individual being eliminated for selection of the next generation.

  1. Algorithm Build(small.py)

DEAP package is a Python package built for Evolutionary Algorithms. small.py is the file that implements an instance of an Evolutionary Algorithm using DEAP. The structure of the instance is as follows:

  1. Registering the algorithm to maximize fitness, an individual and a population that is made up of certain numbers of individuals into the instance toolbox. An individual is a list of attribute values with a fitness class and a population is a list of those individuals. In an individual, the attributes in order represents, E(Poisson’s Ratio) ranging from 0 to 300,000; Sy(Yield Stress) ranging from 0 to 1000; H (kinematic hardening modulus) ranging from 0 to 120,000; K (isotropic hardening modulus) ranging from 0 to 120,000.
  2. Registering evolutionary methods into the instance toolbox, namely:
    • Mutation: functions that will mutate and generate a new offspring from an individual in the population.
    • Crossover(mate): functions that will mate and reproduce a new offspring from two individuals in the population.
    • Selection: functions that will select a pre-determined number of individuals from the offspring or both offspring and old individuals in the population.
  3. Setting up the selected algorithm with parameters as follows: number of experiments used to evaluate the individuals, number of individuals, maximum number of generations, number of individuals selected to be in the next generation as will as an statistics object that records mean, standard deviation, minimum and maximum for each generation.

 

  • Methodology

The core idea of this optimization using EA is to find the best feasible algorithm, the best method for mutation, crossover and selection, where probabilities for the methods need to be tested and adjusted.

For algorithms, the following have been tested:

  • OneMax (similar to eaSimple in DEAP): both mutation and crossover is performed in every individual, and replaces the entire population with resulting offspring.
  • Evolution Strategies (using eaMuCommaLambda algorithm): either mutation or crossover is performed on a select amount of individuals to produce a determined number of offspring. Then, the next generation is selected only among the offspring. For crossover and mutation, the strategy restrains the standard deviation of the offspring.
  • eaMuPlusLambda: either mutation or crossover is performed on a select number of individuals to produce a determined number of offspring. Then, the next generation is selected among both the offspring and the parents.

For crossover, the following functions have been tested:

  • cxTwoPoint: individuals swap two of their attribute values.
  • cxUniform: individuals conditionally swap every attribute depending on a probability value.
  • cxESBlend: individuals swap attribute both attribute and strategy values.
  • cxSimulatedBinaryBounded: the attribute values will be converted into binary sequences, which the function will crossover the sequences and generate an attribute value. A lower and upper bound for each attribute value (same bound as initial setup), as well as a crowding degree of how much the resulting value will resemble the parental value, need to be set.

For mutation, the following functions have been tested:

  • mutFlipBit: convert the attribute value into a binary sequence and perform NOT operation. An independent probability for each attribute to be flipped needs to be provided.
  • mutShuffleIndexes: shuffle the attribute values inside an individual. An independent probability for each attribute value to be exchanged to another attribute needs to be provided.
  • mutESLogNormal: mutate the evolution strategy according to an extended log normal rule. Then the individual attribute values is mutated according to the generated strategy as standard deviation.
  • mutPolynomialBounded: mutate the attribute values using polynomial mutation as implemented in NSGA-II algorithm in C by Deb.

For selection, the following functions have been tested:

  • selTournament: select k individuals from the population using k tournaments.
  • selRoulette: select k individuals from the population using k spins of a roulette.
  • selBest: select k best individuals from the population.
  • selWorst: select k worst individuals from the population.

In addition, the following parameters are tested:

  • MUTPB and CXPB: the probability of an individual going through mutation and that of crossover. The summation of both needs to be smaller than 1.
  • Indpb: the independent probabilities of each attribute to be changed in terms of crossover and/or mutation.

As the goal is to maximize fitness, the goal is to generate an individual with the fitness(F) value of 1, which is R value of 0.

 

  1. Results and analysis

Initial Fitness

Maximum fitness is the most important statistics in the fitting process. Initial mx fitness varies proportionately to the number of experiments, which will extend the number of generations needed to converge to F valuing 1.

Number of Experiments 5 50 100
Average Max Initial Fitness(F) 0.25 0.03 0.01

Because of that, the penalty in scaffold.py needs to be a very big number in order to exclude individuals with very “bad” fitness.

On an additional note, the fitting process did not exact follow a systematic fashion as the number of experiments as well as the number of individuals in the population affects the time for each trial to finish.

 

Premature Convergence

Premature convergence was a significant issue with a big part of the fitting process, which means that the population tends to get stuck on a local maxima for F, resulting in a very low and consistent standard deviation as well as max F around generation 15. Most of the crossover methods tend to decrease the diversity of the population, as follows:

Methods Influence on diversity
cxTwoPoint Same as mutShuffleIndexes
cxUniform Same as mutShuffleIndexes
cxESBlend Same as mutShuffleIndexes
cxSimulatedBinaryBounded Will maintain a good diversity.

 

mutFlipBit It can produce values that are potentially outliers. The issue is that it could generate invalid values.
mutShuffleIndexes Shuffling does not necessarily bring in new values into the attributes pool, which will make the algorithm hard to converge to a right F.
mutESLogNormal The range of values upon mutation depends on the strategy value.

 

Another factor playing into premature convergence is the values of CXPB, MUTPB and indpb, as mentioned towards the end of the previous section. From the trials, it was also very apparent that mutation performs better than crossover in terms of increasing or maintaining a healthy diversity in the population. However, a heavy tilt towards mutation could result in the algorithm having a hard time locking up the correct direction to increase the fitnesses of most individuals, which will result in outliers and some hopping around. Therefore, having roughly a 0.4:0.6 for the CXPB:MUTPB is good ratio.

 

In addition, indpb dictates how possible is each attribute value likely to crossover/mutate. In that case, the probability of a single attribute to be mutated is usually: indpb * CXPB or indpb*MUTPB. Maintaning a high indpb (0.9) will help crossover and mutation in maintaining diversity as well as evolving the population correctly and timely.

 

A third factor for premature convergence is the relationship between the number of experiments and the size of the population. With 5 experiments, population of size 50 is a good number that will allow evolution to happen. With 100 experiments, population of size 400 will do the same. The following table shows the best performance of population under 5 experiments versus 100 experiments using eaMuPlusLambda:

 

Number of Experiments Population Size Initial Max F Final Max F E Sy H K
5 50 0.2642 0.9739 199807.2398

 

299.9368

 

3172.1629 3856.7229
100 400 0.0172 0.9999 200000.0000 300.0000 2999.9999 4000.0000

 

It is apparent that with more experiments and a much bigger population size, the algorithm is able to fit the model really well.

 

Results of different algorithms

There was no recorded statistics for trials done with OneMax algorithm, however, based on recall, the algorithm did marginal improvement to the initial avg max F.

The following table is a comparison between the other two algorithms:

Algorithm Tested Initial Avg Max F Final Avg Max F Change
Evolution Strategies (eaMuCommaLambda) 0.1896 0.2769 66.06547%

 

eaMuPlusLambda 0.06702 0.7246 981.1407%

 

 

For both OneMax and Evolution Strategies, experiments were not able to run past 25 generations because of the value error triggered by individuals with very “bad” fitness. However, both algorithms encounter premature convergence. Regardless of the number of experiments used as well as the size of the population, eaMuPlusLambda performs better than the other two. The reason might be that the other two both have, to a certain degree, an exclusive selection rule. Both algorithms, upon selection, replace the old population exclusively with offspring. This could potentially be problematic for the following reasons:

  • The parents with “good” fitness in the old population are not allowed onto the next generation, which might slow down the evolution.
  • The selection measure would allow more offspring with “bad” fitness to be in the next generation, which might slow down the evolution.

See Appendix for graphs on individual trials.

 

  1. Conclusion and Future Development

In conclusion, the evolutionary algorithm could fit the parameters of stress and strain rather well in order to predict a set of physical parameters that will work under the given experimental data. The following key components are important to building the algorithm that work well:

  • A big population
  • A balanced crossover-to-mutation ratio that can maintain a good diversity in the population
  • A selection measure that will be comprehensive

Given time, Evolution Strategies could be further studied to fit the model well as it learns and modifies the evolution according to the distribution of the individuals. Furthermore, we could use optimization measure in scipy package to benchmark against the performance of EA. RNN could be developed and trained to fit the model as well. Also, trying to fit a more complex model with more attributes could be valuable.

 

 

 

 

Northwestern Undergraduates: Plan now for a Summer 2018 internship at Argonne National Laboratory through DOE’s Summer Undergrad Lab Inhip (SULI) programterns

In 2017, Northwestern undergraduate students worked on the projects you can read about on this blog at Argonne National Laboratory.  The U.S. Department of Energy’s (DOE) Summer Undergraduate Laboratory Internships (SULI) program is one route to working at Argonne (or another national lab) over the summer.   (Although other routes are possible to summer internships at the lab, this is the best one for undergraduates.) The deadline for summer 2018 will be in Dec/Jan so now is the time to start thinking about applying!  Watch this space for the deadline when it is announced.

Participation in the SULI Program is a great way to get a taste of research and life at the national laboratories.  You’ll meet national laboratory researchers and many other undergraduates carrying out research in many disciplines.   Please apply to the SULI program through this DOE website link:

https://science.energy.gov/wdts/suli/

Argonne PIs have provided descriptions below about projects that will likely be available in 2018.  Many other projects will also be available.  As you complete your SULI application, you’ll be asked about your research interests. Please feel free to mention the topics in one of the projects below if they meet your research interests.  Please let NAISE know if you’ve applied (naise_summer(at)northwestern.edu).

Some details: SULI students can live on-site at the lab.  You must be a U.S. Citizen or Lawful Permanent Resident at the time of application.

Biology

Fe and S cycles’ role in contaminant mobility

Research in the Biogeochemical Process Group at Argonne National Laboratory is investigating the interplay between the Fe and S cycles and their roles in controlling contaminant mobility, carbon and nutrient cycling, and greenhouse gas emissions. The project’s long-term vision is to integrate their findings into multiscale modeling approaches to understand and predict relevant environmental processes. The program integrates two unique strengths—(1) the Advanced Photon Source (APS) for synchrotron-based interrogation of systems, and (2) next-generation DNA sequencing and bioinformatics approaches for microbial community and metabolic pathway analysis—with biogeochemistry and microbial ecology.

Bioinformatics and Computational Biology

We apply a wide range of computational approaches within the DOE Systems Biology Knowledgebase (KBase) to answer questions about complex biological systems, including: (i) how microbes and plants degrade or produce specific metabolites; (ii) how microbes, plants, and fungi interact within an environment (e.g. human gut, soil, bioreactor) to display a specific phenotype; and (iii) how microbial genomes evolve in response to stress, stimuli, and selection. Students in the Henry lab will learn to apply tools like (meta)genome assembly, genome annotation, RNA-seq read alignment, contig binning, and metabolic modeling to answer these questions. Students with programming skills can also contribute to the KBase platform by integrating new apps, visualizations, and algorithms.

Materials

The goal of the project is to significantly improve the understanding and prediction of thermodynamic stability/metastability of “imperfect” (e.g., highly defective, non-stoichiometric, or doped) oxide material phases, via innovative theory (i.e., embedded uncertainty), advanced experiments at APS, and “intelligent” software (i.e., able to learn and quickly solve new problems). We envision building the knowledge and capabilities that will allow, over the next decade, the prediction of thermodynamic properties of imperfect materials, with impact on materials design, synthesis, and smart manufacturing. Furthermore, we expect this methodology to accelerate the development of the material genome and next generation computers. We focus on high-k dielectric materials for complementary metal-oxide-semiconductor (CMOS), which are of particular importance for creating Dynamic Memory Allocation (DRAM) devices. Many CMOS properties strongly depend on material defects such as vacancies, interstitials, defect clusters that occur during synthesis, and thermal treatment. Inclusion of other chemical elements (e.g., dopants) in CMOS can significantly change physical properties such as thermal conductivity, electrical conductivity, and magnetism. Our approach is original and is based on calculating the free energy of each phase as function of temperature and composition (oxygen and dopant content) using atomistic (quantum mechanical, ab-initio Molecular Dynamics), meso-scale (reactive force fields and kinetic Monte Carlo), and continuum (phase diagram calculation) methods. Uncertainty evaluation is embedded in this multi-scale methodology via Bayesian analysis. We validate the models and computer simulations using high-temperature experiments at APS. Furthermore, we develop a machine learning (ML) open code to perform supervised and unsupervised computations on Mira (Aurora when available) for calculations/simulations, and on Athena for big data analytics. The intelligent software assists the development of interatomic potentials and force fields, performs analysis of massive sets of CMOS phases and defect structures, evaluates uncertainty of phase diagrams, and guides the experimental characterization measurements.

Chemical/Environmental Engineering

Bio-manufacturing of Porous Carbon as Catalyst Supports from Organic Waste Streams

Porous carbon materials, like activated carbon (AC), have demonstrated unmatched efficiency in applications such as filtration, catalysis, and energy storage. The problem is that conventional AC is produced from supply limited coal or coconut shells using multistage manufacturing processes that are energy intensive, polluting, and result in sub-par performance. In fact, an estimated 4 million metric tones of AC will be produced in 2025, requiring the harvesting and shipping of significant feedstock from around the world. We have been developing a biomanufacturing process to produce high performance, low cost porous carbon materials from low or negative value waste streams. High performance biocarbon manufacturing process (Patent App. No. PCT/US 2017-043304) has been scaled up from bench- to pilot-scale. The performance, cost, and life-cycle impact of AC and its end-uses are primarily determined by how it is fabricated.

Arrested Methanogenesis for Volatile Fatty Acid Production

Huge quantities of high organic strength wastewater and organic solid waste are produced and disposed of in the US each year (EPA, 2016). We have been developing a new high rate arrested anaerobic digestion (AD) processes for transforming organic waste supplanting starch, sucrose or glucose currently used as feedstock into VFAs and alcohols. We will design and construct a high rate sequencing batch reactor (SBR) and fluidized anaerobic membrane bioreactor (FAnMBR) technologies to produce and separate VFAs and alcohols from the fermenters to facilitate high product yield, minimize the toxicity of VFAs, reduce mass transfer limitations and ensure the health, stability, and productivity of AD communities. This research will specifically determine the links between organic wastewater characteristics, microbe community structure and the design and operation of high rate arrested AD system at the bench-scale. Specific research targets include the isolation and integration of highly diverse microbial functionalities within high rate arrested AD fermenters for high strength organic wastewater treatment coupled to renewable chemical production.

Ecosystem, Environment, Water Resources

Ecosystem services of bioenergy

The Fairbury Project studies sustainable ways to produce bioenergy and evaluates the dual provision of biomass (as a commodity crop) and ecosystem services (environmental benefits) through the integration of short rotation shrub willow buffers into a Midwest row cropping system. The project started in 2009 on a 16 acre agricultural corn field in Fairbury, IL. The field site is close to the Indian Creek which sits at the headwaters of the Vermillion River, considered impaired by the Illinois EPA. The strategic placement of the willow buffers on the landscape was designed to improve land use efficiency by providing farmers and landowners with an alternative land management strategy. In this case, the placement of the willow buffers were to target areas on the field that would have the greatest impact on nutrient reduction while mitigating conflicts with grain production by targeting areas that are underproductive as well. In order to assess the success of the use of willow buffers in a traditional row-cropping system on biomass production and ecosystem service provision, many field and crop based parameters are continually or annually measured. These parameters include assessing crop impact on water quality (water collection, ion exchange resins), water quantity (soil moisture, transpiration and water table elevation), nutrient uptake and storage (vegetation collection), biomass production (vegetation collection and allometric measurements), soil health (chemical & physical parameters), greenhouse gas flux (gas sample collections), and habitat provision (soil microbiology and macroinvertebrates including pollinators).

Student involvement:
As part of The Fairbury Project, students will work alongside Argonne staff and fellow interns doing an array of tasks in the field, lab, and office. Students are expected to travel to the field once or more a week under various weather conditions for data and sample collection. In the lab students may be involved in sample processing and analysis including ion exchange resin extraction, water quality testing (UV spectroscopy), greenhouse gas analysis (gas chromatographer), aboveground vegetation processing, and root analysis. In the office, students will be tasked with processing and analyzing data using software including but not limited to excel, R, DNDC, and ArcGIS. Additional tasks may include literature reviews and method development. Students will work both collectively with their fellow interns and staff as well as independently on various assigned tasks.

Qualified candidates:
Candidates must meet the general requirements for SULI. Additional requirements include but are not limited to previous experience or general interests related to water, soil, greenhouse gases, biodiversity, bioenergy production, environmental engineering, environmental sciences, and agriculture. Candidates should have a flexible schedule over the 10 weeks of the internship and must be available for the full 10 weeks. Field days start at 6am, therefore qualified candidates are required to have some form of transportation to the lab on field days (transportation from the lab to the field site will be provided), if not living on site.

Water Resources- Fuel production

Water resource is a critical component in energy production. Water resource availability varies by region throughout the United States. Population growth, energy development, and increased production increase pressure on water demand. This project evaluates potential of using ground water resource and municipal wastewater for fuel production in the United States. It will examine various level of water quality and estimate the water available for use from both historical production and future production perspective. Factors affecting regional resource use, feedstock production, and technology deployment and their trade-offs will be analyzed.

Water Resources- Crop production

Agriculture crop production requires water. However, not all of the crop production requires irrigation and the irrigation needs for the same crop varies from region to region. This project will analyze the amount of fresh water used for irrigation by different crops and irrigation technology surveyed in last few years in the United States. Spatial and temporal analysis will be conducted to calculate amount of irrigation water applied to produce a unit of grains and other products. The dataset will be compared with historical irrigation data to identify potential issues related to production of food, fiber, and fuel.