Harry R. Millwater Jr.

Joint Appointment, Computational Mathematics

Physical and Computational Sciences Directorate

Biography

Harry Millwater’s technical interests and experience are concentrated in the field of computational structural mechanics and structural integrity with an emphasis on probabilistic methods and applications. He has over thirty years of experience in the application of probabilistic mechanics methods to aerospace components, aircraft structures, and gas turbine engine disks.

He has been a key contributor to three major risk assessment software development efforts serving as the primary system integrator of the Numerical Evaluation of Stochastic Structures Under Stress (NESSUS) probabilistic finite element program and the R&D 100 award-winning Design Assessment of Reliability With INspection (DARWIN) for gas turbine rotors, and as principal investigator for the Small Aircraft Risk Assessment Software (Smart|DT).

Millwater developed the hypercomplex finite element method, ZFEM, that uses hypercomplex algebra to compute arbitrary-order high-accuracy shape, material property, and loading sensitivities from linear and nonlinear transient solid mechanics problems. The ZFEM has been used successfully in the fields of thermoelasticity, linear and nonlinear fracture mechanics, transient heat transfer, wave propagation, and others.

Research Interest

Probabilistic methods for risk assessment of gas turbine rotors
Development of enhanced probabilistic life prediction methodologies for engine rotor life extension
Innovative methods for engine health monitoring

Education

PhD in Engineering Mechanics, University of Texas at Austin
MS in Engineering Mechanics, University of Texas at Austin
BS in Mechanical Engineering, Rice University

Affiliations and Professional Service

Tau Beta Pi
American Society of Mechanical Engineers (ASME)
American Institute of Aeronautics and Astronautics (AIAA)

Awards and Recognitions

Most Prolific Researcher of the Year — University of Texas at San Antonio (UTSA) mechanical engineering, 2019
Strongest graduate student supporter of the Year — UTSA mechanical engineering 2018 and 2019
Daniel Ocampo, UTSA College of Engineering competitive engineering MS Student Scholarships, Spring and Summer 2019
Daniel Ramirez-Tamayo, UTSA mechanical engineering competitive engineering PhD Student Scholarship, 2016 and 2017
Nathan Crosby (MS student) and Harry Millwater, “Developing a high performance surrogate model implementation for risk assessment of aircraft fleets,” American Institute of Aeronautics and Astronautics (AIAA) Region IV Student Conference, second place in Master’s competition, April, 2015
E.E. Iglesias (MS student), “Sensitivity analysis of turbine engine sustainment,” AIAA Abe Zarem Award, 2013
Juan Ocampo (PhD student), "Probabilistic risk assessment of aerospace structures," Pilatus Aircraft Ltd, Switzerland. Valero international research scholar, August 2013.
A. Baines and H.R. Millwater, “Two-dimensional weight function development using ZFEM,” AIAA Region IV Student Conference, first place Master’s competition, April 2013
E.E. Iglesias and H.R. Millwater, “Sensitivity analysis of turbine engine sustainment,” AIAA Regional Student Conference, third place Master’s competition, April 2013
UTSA Leadership program, 2012
Juan Ocampo (PhD student), June 2012. "Probabilistic risk assessment methodology and application to aerospace structures," Institute for Aerospace Research, National Research Council, Canada, Valero International Research Scholar, June 2012
Carolina Dubinsky (PhD student), “Optimal allocation of testing resources for statistical simulations,” NSF Sivirt Center Student Poster Competition, first place, 2012
Jose Garza (PhD student), “Probability of detection, applications in structural reliability,” NSF Sivirt Center Student Poster Competition, third place, 2012
Juan Ocampo (PhD student), "Implementation and validation of a method for computing stress intensity factors and beta factor of collinear interacting cracks," Institute for Aerospace Research, National Research Council, Canada, Valero International Research Scholar, June 2011
D. Sparkman, and H.R. Millwater, "FORM-based filtering of limit states," Aircraft airworthiness & sustainment conference, Austin, Texas, first place student competition, May 2010
C. Dubinsky and H.R. Millwater, "Allocation of testing resources in statistical simulations using particle swarm optimization," AIAA Region IV Student Conference 2010, Houston, Texas, first place Master’s competition, April 2010
L. Domyancic and H.R. Millwater, “Advances in bounding techniques for aircraft structures,” AIAA Region IV Student Conference 2010, Houston, Texas, second place Master’s competition, April 2010
C. Acosta, J. Ocampo and H.R. Millwater, “High performance computing implementation and evaluation on a structural risk assessment code,” AIAA Region IV Student Conference 2010, Houston, Texas, third place team competition, April 2010
C. Acosta and J. Ocampo, and H.R. Millwater, “High performance computing implementation on a risk assessment problem,” AIAA Region IV Student Conference Program 2009, first place team competition, April 2009
A. Voorhees, R. Bagley, H.R. Millwater, P. Golden, “Application of complex variable methods for fatigue sensitivity analysis,” AIAA Region IV Student Conference Program 2009, third place Master's competition, April 2009
Air Force summer faculty fellowship program, Wright-Patterson Air Force Base, Sponsor: Dr. James Larsen, Air Force Research Laboratory Fellow, Materials Directorate, 2005, 2006, 2007
Research and Development magazine R&D 100 award for “DARWIN – Design Assessment of Reliability With INspection," September 2000
NASA Award, Turning goals into reality objective award for exceptional progress toward NextGeneration design tools and experimental aircraft, May 2000
Southwest Research Institute’s annual meeting, presentation to the Board of Trustees, "Airliner reliability by design," February 2000
General Dynamics, Electric Boat Division Honors Program, "Boundary element technology in engineering," 1987

Publications

2021

J.D. Navarro*, H.R. Millwater, A. Montoya, and D. Restrepo. "Arbitrary-order sensitivity analysis in phononic metamaterials using the multicomplex Taylor series expansion method coupled with Bloch’s theorem." Journal of Applied Mechanics 89, no. 2 (2021): 021007, https://doi.org/ 10.1115/1.4052830
Aguirre-Mesa*, M.J. Garcia-Ruiz, M. Aristizabal, D. Wagner, D. Ramirez-Tamayo*, A. Montoya, and H. Millwater, “A block forward substitution method for solving the hypercomplex finite element system of equations,” Computer Methods in Applied Mechanics and Engineering, Volume 387, 2021, 114195, ISSN 0045-7825, https://doi.org/10.1016/j.cma.2021.114195.
D. Ramirez-Tamayo*, A. Soulami, V. Gupta, D. Restrepo, A. Montoya, H.R. Millwater, “A Complex-variable Cohesive Finite Element Subroutine to Enable Efficient Determination of Interfacial Cohesive Material Parameters” Engineering Fracture Mechanics 247 (2021) 107638 https://doi.org/10.1016/j.engfracmech.2021.107638 4. M.R. Balcer*, H.R. Millwater, and J.A. Favorite, “Multidual Sensitivity Method in Ray-Tracing Transport Simulations,” Nuclear Science and Engineering, July 1, 2021. https://doi.org/10.1080/00295639.2021.1883949

2020

D. Ramirez-Tamayo*, M. Balcer*, A. Montoya, and H.R. Millwater, Mixed-mode stress intensity factors computation in functionally graded materials using a hypercomplex-variable finite element formulation. Int J Fract (2020) 226:219-232. https://doi.org/10.1007/s10704-020- 00489-5

2019

A.M. Aguirre-Mesa*, M.J. Garcia, and H.R. Millwater, “MultiZ: A library for computation of high order derivatives using multicomplex or multidual numbers,” ACM Trans. Math. Softw. 46, 3, Article 23 (July 2020), 30 pages, https://doi.org/10.1145/3378538 7. H.R. Millwater, J.D. Ocampo, N. Crosby*, “Probabilistic Methods for Risk Assessment of Airframe Digital Twin Structures,” Engineering Fracture Mechanics, 221 (2019) 106674 https://doi.org/10.1016/j.engfracmech.2019.106674
A.M. Aguirre-Mesa*, D. Ramirez-Tamayo*, M.J. Garcia, A. Montoya, and H.R. Millwater , “A Stiffness Derivative Local Hypercomplex-Variable Finite Element Method for Computing of the Energy Release Rate,” Engineering Fracture Mechanics, 218 (2019) 106581 https://doi.org/10.1016/j.engfracmech.2019.106581
C. Hegde, H.R. Millwater, M. Pyrcz, H. Daigle, and K. Gray, “Rate of penetration (ROP) optimization in drilling with vibration control”, Journal of Natural Gas Science and Engineering, 67 (2019): 71-81, https://doi.org/10.1016/j.jngse.2019.04.017
M. Aristizabal, D. Ramirez-Tamayo*, M. Garcia, A. Aguirre-Mesa*, A. Montoya, H.R. Millwater, “Quaternion and octonion-based finite element analysis methods for computing multiple first order derivative,” J. Comput. Phys., 397 (2019) https://doi.org/10.1016/j.jcp.2019.07.030
D. Wagner*, M. Garcia, A. Montoya, H.R. Millwater, “A Finite Element-based Adaptive Energy Response Function Method for 2D Curvilinear Progressive Fracture,” Int. J Fatigue 127 (2019) 229-245 https://doi.org/10.1016/j.ijfatigue.2019.05.036
R. Fielder*, H.R. Millwater, A. Montoya, P. Golden, “Efficient Estimate of Residual Stress Variance Using Complex Variable Finite Element Methods,” International Journal of Pressure Vessels and Piping, 173 (2019) 101-113 https://doi.org/10.1016/j.ijpvp.2019.05.004
C. Hegde, M. Pyrcz, H.R. Millwater, H. Daigle, and K. Gray, “Classification of drilling stick slip severity using machine learning”, J. Petrol. Science and Engineering, 179 (2019) 1023-1036 https://doi.org/10.1016/j.petrol.2019.05.021

2018

A. Montoya, D. Ramirez Tamayo*, H.R. Millwater, and M. Kirby*, “A Complex-Variable Virtual Crack Extension Finite Element Method for Elastic-Plastic Fracture Mechanics, Engineering Fracture Mechanics”, 202 (2018) 242-258 https://doi.org/10.1016/j.engfracmech.2018.09.023
D. Ramirez Tamayo*, A. Montoya, H.R. Millwater, “Application of the Complex-variable Finite Element Method to Mixed Mode Fracture and Interface Cracks”, AIAA Journal, V 56, No. 11 (2018), https://arc.aiaa.org/doi/abs/10.2514/1.J057231
D. Ramirez Tamayo*, A. Montoya, H.R. Millwater, “A Virtual Crack Extension Method for Thermoelastic Fracture Using a Complex-Variable Finite Element Method”, Engineering Fracture Mechanics 192 (2018) 328-342, https://doi.org/10.1016/j.engfracmech.2017.12.013

2017

C. Hegde, H. Daigle, H.R. Millwater, K. Gray, “Analysis of Rate of Penetration (ROP) Prediction in Drilling using Physics-based and Data-driven Models,” Journal of Petroleum Science and Engineering 159 (2017) 295–306, https://doi.org/10.1016/j.petrol.2017.09.020
R. Fielder*, A. Montoya, H.R. Millwater and P. Golden, “Residual Stress Sensitivity Analysis using a Complex Variable Finite Element Method,” International Journal of Mechanical Sciences 133 (2017) 112–120, http://dx.doi.org/10.1016/j.ijmecsci.2017.08.035
J.F. Monsalvo, M.J. Garcia, H.R. Millwater, Y. Feng, “Sensitivity Analysis for Radiofrequency Induced Thermal Therapies using the Complex Finite Element Method”, Finite Elements in Analysis and Design 135 (2017) 11–21, http://dx.doi.org/10.1016/j.finel.2017.07.001
A. Montoya and H.R. Millwater, “Sensitivity Analysis in Thermoelastic Problems using the Complex Finite Element Method,” J. of Thermal Stresses, 40:3 (2017) 302- 321http://dx.doi.org/10.1080/01495739.2016.1264871

2016

H.R. Millwater, D. Wagner*, A. Baines*, and A. Montoya, “A Virtual Crack Extension Method to Compute Energy Release Rates using a Complex Variable Finite Element Method,” Engineering Fracture Mechanics 162 (2016) 95–111, http://dx.doi.org/10.1016/j.engfracmech.2016.04.002
J. Garza* and H.R. Millwater, “Probabilistic Sensitivity Analysis of the Probability-of-Failure to Probability of Detection Curve Regions,” Int. J. of Pressure Vessels and Piping, 141 (2016) 26- 39, http://dx.doi.org/10.1016/j.ijpvp.2016.03.012
J. Garza* and H.R. Millwater, “Higher-Order Probabilistic Sensitivity Calculations Using the Multicomplex Score Function Method,” Probabilistic Engineering Mechanics, 45 (2016) 1-12, http://dx.doi.org/10.1016/j.probengmech.2015.12.001
S. Shirinkam, A. Aleaddini, and H.R. Millwater, “On the Application of Multicomplex Algebras in Numerical Integration”, Appl. Math. Inf. Sci. 10, N0. 1, 1-9 (2016), http://dx.doi.org/10.18576/amis/100101

2015

A. Gomez-Farias*, A. Montoya, H.R. Millwater, “Complex Finite Element Sensitivity Method for Creep Analysis,” International Journal of Pressure Vessels and Piping (2015), V 132-133, 27- 42, http://dx.doi.org/10.1016/j.ijpvp.2015.05.006
A. Kibria*, K.K. Castillo-Villar, and H.R. Millwater, (2015), “Minimizing the Discrepancy between Simulated and Historical Failures in Turbine Engines: A Simulated Annealing-based Optimization Method,” Mathematical Problems in Engineering, Special Issue on Mathematical Applications to Reliability and Maintenance Problems in Engineering Systems, V 2015, pp 11, Article ID 813565, http://dx.doi.org/10.1155/2015/813565
J. Garza* and H. Millwater, "Multicomplex Newmark-Beta Time Integration Method for Sensitivity Analysis in Structural Dynamics", AIAA Journal, Vol. 53, No. 5 (2015), pp. 1188- 1198, doi: http://arc.aiaa.org/doi/abs/10.2514/1.J053282l
C. Quintana*, H. R. Millwater, G. Singh, P. Golden, “Optimal Allocation of Testing Resources for Statistical Simulation,” Engineering Optimization, (2015), Vol. 47, No. 7, 979-993, http://dx.doi.org/10.1080/0305215X.2014.933824

2014

A. Montoya, R. Fielder*, A. Gomez-Farias*, H. Millwater, “Finite Element Sensitivity for Plasticity using Complex Variable Methods,” J. Eng. Mech. 141 2 (2014), DOI:10.1061/(ASCE)EM.1943-7889.0000837, 04014118.
H.R. Millwater and S. Shirinkam, “Multicomplex Taylor Series Expansion for Computing High Order Derivatives”, International Journal of Applied Mathematics, Vol. 27, No 4 (2014), DOI: http://dx.doi.org/10.12732/ijam.v27i4.2
T. Rahman*, H.R. Millwater, and H. Shipley, “Modeling and Sensitivity Analysis on the Transport of Aluminum Oxide Nanoparticles in Saturated Sand: Effects of Ionic Strength, Flow Rate, and Nanoparticle Concentration,” Science of the Total Environment 499, 2014, 402-412, DOI: 10.1016/j.scitotenv.2014.08.073
M.D. Brothers*, J.T. Foster, H.R. Millwater, “A comparison of different methods for calculating tangent-stiffness matrices in a massively parallel computational peridynamics code,” Comput. Methods Appl. Mech. Engrg. 279 (2014) 247–267, doi: 10.1016/j.cma.2014.06.034

2013

H.R. Millwater, D. Wagner*, A. Baines*, K. Lovelady*, “Improved WCTSE Method for the Generation of 2D Weight Functions through Implementation into a Commercial Finite Element Code,” Engng Fract Mech, 109 (2013) 302-309, http://dx.doi.org/10.1016/j.engfracmech.2013.07.012
D.S. Sparkman* and H.R. Millwater, S. Ghosh, “Probabilistic Sensitivity Analysis of DwellFatigue Crack Initiation Life for a 2-grain Microstructural Model,” Fatigue and Fracture of Engineering Materials and Structures, (2013) 36, 994-1008, https://doi.org/10.1111/ffe.12052

2012

G. Singh, M. Cortina*, H.R. Millwater, and A. Clauer. "Probabilistic Sensitivity Analysis of a Laser Peening Fatigue Life Enhancement Process," International Journal of Structural Integrity 3, no. 3 (2012): 210-235, https://doi.org/10.1108/17579861211264352
G. Singh, J. Ocampo*, H.R. Millwater, A. Clauer, (2012),"Simulation-Based Crack Growth Mitigation Through Optimum Laser Peened Residual Stress,” Int. J. Structural Integrity, Vol. 3 Iss: 3 pp. 236 – 259, https://dx.doi.org /10.1108/17579861211264361
D. Wagner*, and H.R. Millwater, “2D Weight Function Development using a Complex Taylor Series Expansion Method,” Engng Fract Mech 86 (2012), 23-37, 210- doi:10.1016/j.engfracmech.2012.02.006
L. Domyancic*, H.R. Millwater, “Advances in Bounding Techniques for Aircraft Structures,” AIAA Journal, 50, 6, (2012), 1307-1313, doi: 10.2514/1.J051403
A. Voorhees*, H.R. Millwater, R. Bagley, P. Golden, “Fatigue Sensitivity Analysis Using Complex Variable Methods,” Int J Fatigue 40 (2012) 61-73, doi:10.1016/ j.ijfatigue.2012.01.016
J. Garza*, H.R. Millwater, “Sensitivity of Probability-of-Failure Estimates with respect to Probability of Detection Curve Parameters,” International Journal of Pressure Vessels and Piping 92 (2012) 84-95, doi:10.1016/j.ijpvp.2011.11.009

2011

J.D. Ocampo*, H.R. Millwater, G. Singh, H. Smith, F. Abali, M. Nuss, M. Reyer, M. Shiao, “Development of a Probabilistic Linear Damage Methodology for Small Aircraft,” AIAA J. Aircraft. 48, 6 (2011), 2090-2106 doi: 10.2514/1.56674
A. Voorhees*, H.R. Millwater, R.L. Bagley, “Complex Variable Methods for Shape Sensitivity of Finite Element Models,” Finite Elem. Anal. Des., 47 (2011) 1146–1156, doi:10.1016/j.finel.2011.05.003
H.R. Millwater, G. Singh, M. Cortina*, “Development of a Localized Probabilistic Sensitivity Method to Determine Random Variable Regional Importance,” Reliability Engineering & System Safety. (2011) 10.1016/j.ress.2011.04.003
H.R. Millwater and Y. Feng, “Probabilistic Sensitivity Analysis with respect to Bounds of Truncated Random Variables,” ASME J. Mech. Des. 133, 061001 (2011), DOI:10.1115/1.4003819
H.R. Millwater, A. Bates*, E. Vazquez*, “Probabilistic Sensitivity Methods for Correlated Normal Variables,” Int. J. of Reliability and Safety, 5, No. 1, pp. 1-20 (2011), https://doi.org/10.1504/IJRS.2011.037344

2010

X.N. Dong, Q. Luo, D.M. Sparkman*, H.R. Millwater, and X. Wang, “Random Field Assessment of Nanoscopic Inhomogeneity of Bone,” Bone 47 (2010) 1080–1084, https://doi.org/10.1016/j.bone.2010.08.021
H.R. Millwater, “A Simple and Accurate Method for Computing Stress Intensity Factors of Collinear Interacting Cracks,” Aerospace Science and Technology 14 (2010) 542–550, doi:10.1016/j.ast.2010.04.003 (2010)
P. Golden, H.R. Millwater, X. Yang*, “Probabilistic Fretting Fatigue Life Prediction of Ti-6Al4V,” Int. J. Fatigue 32 (2010) 1937–1947, https://doi.org/10.1016/j.ijfatigue.2010.06.007
F.N. Momin*, H.R. Millwater, R.W. Osborn*, M.P. Enright, “A Non-Intrusive Method to Add Finite Element-Based Random Variables to a Probabilistic Design Code,” Finite Elements in Analysis and Design 46 (2010) 280–287
H.R. Millwater and D. Wieland, “Probabilistic Sensitivity-based Ranking of Damage Tolerance Analysis Elements,” AIAA J. Aircraft, (2010) V47 1 161-71

2009

S. Jha, H.R. Millwater, and J. Larsen, “Probabilistic Sensitivity Analysis in Life-Prediction of an α+β Titanium Alloy,” Fatigue and Fracture of Engineering Materials and Structures, 32(6), 493 – 504, doi:10.1111/j.1460-2695.2009.01352.x, (2009)
H.R. Millwater, “Universal Properties of Kernel Functions for Probabilistic Sensitivity Analysis,” Probabilistic Engineering Mechanics 24 (2009) 89–99

2008

X.N. Dong, T. Guda*, H.R. Millwater, X. Wang, “Probabilistic Failure Analysis of Bone Using a Finite Element Model of Mineral-Collagen Composites,” Journal of Biomechanics (2008), doi:10.1016/j.jbiomech.2008.10.022
B.D. Shook*, H.R. Millwater, M.P. Enright, S.J. Hudak, Jr., W.L. Francis, “Simulation of Recurring Automated Inspections on Probability-of-Fracture Estimates,” Structural Health Monitoring, 2008 7: 293-307
T. Guda*, T. Ross*, H.R. Millwater, L. Lang, “Probabilistic Analysis of Preload in the Abutment Screw of a Dental Implant Complex” The Journal of Prosthetic Dentistry, V100 3 pp 183-193, 2008

2007

H.R. Millwater, J. Larsen, R. John, “Effects of Residual Stresses on Probabilistic Lifing of Engine Disk Materials,” Materials Science and Engineering, Materials Science and Engineering: A, Volumes 468-470, 15 November 2007, Pages 129-136, doi:10.1016/j.msea.2006.10.169
H.R. Millwater, M.P. Enright, and S.H.K. Fitch, “A Convergent Zone-Refinement Method for Risk Assessment of Gas Turbine Disks Subject to Low-Frequency Metallurgical Defects,” Journal of Engineering for Gas Turbines and Power, 2007, Volume 129, Issue 3, pp. 827-835

2006

H.R. Millwater and R. W. Osborn*, “Probabilistic Sensitivities for Fatigue Analysis of Turbine Engine Disks,” International Journal of Rotating Machinery, vol. 2006, Article ID 28487, 12 pages, 2006. doi:10.1155/IJRM/2006/28487
M.P. Enright, H.R. Millwater, and L. Huyse, “Adaptive Optimal Sampling Methodology for Reliability Prediction of Series Systems,” AIAA J. Vol. 33, No. 3, March, 2006
M.P. Enright, S.J. Hudak, R.C. McClung, and H.R. Millwater, “Application of Probabilistic Fracture Mechanics to Prognosis of Aircraft Engine Components,” AIAA J. Vol. 44, No. 2, February, 2006

2004

G.R. Leverant, H.R. Millwater, R.C. McClung, M.P. Enright, “A New Tool for Design and Certification of Aircraft Turbine Rotors,” Journal of Engineering for Gas Turbines and Power, Vol. 126, No. 1, pp. 155-159, 2004

2002

Y.-T. Wu, M. P. Enright, H.R. Millwater, “Probabilistic Methods for Design Assessment of Reliability with Inspection”, AIAA Journal, V40, No. 5, pp 937-946, 2002
S. R. Runnels, R. A. Page, M.P. Enright, H.R. Millwater, “Advanced Experimental and Computational Tools for Robust Evaluation of On-Chip Interconnect Reliability,” IEEE Transactions on Semiconductor Manufacturing, Vol. 15, No. 3, Aug. 2002

Before 2000

G.G. Chell, C.J. Kuhlman, H.R. Millwater, and D.S. Riha, "Application of Reference Stress and Probabilistic Methodologies to Assessing Creep Crack Growth," ASTM Special Technical Publication, v 1297, 1997, p 54-73
A.J. Smalley, R.M. Baldwin, D.A. Mauney, and H.R. Millwater, "Towards Risk Based Criteria for Rotor Vibration," IMechE, No. C500/081/96, pp. 517-527, 1996.
H.R. Millwater, Y.-T. Wu, J. W. Cardinal, and G. G. Chell, "Application of Advanced Probabilistic Fracture Mechanics to Life Evaluation of Turbine Rotor Blade Attachments," Journal of Engineering for Gas Turbines and Power, Vol. 118, No. 2, pp. 394-398, April 1996.
D.S. Riha, H.R. Millwater, and B.H. Thacker, “Probabilistic Structural Analysis using a General Purpose Finite Element Program,” Finite Elements in Analysis and Design, Vol. 11, No. 3, Jul, 1992, p 201-211
C.T. Dyka, A.M. Remondi, and H.R. Millwater, "3D Boundary Elements and the Integration of Strong Singularities," Computers & Structures, Vol. 39, No. 5, pp. 513-524, 1991.
Y.-T. Wu, H.R. Millwater, T.A. Cruse, "Advanced Probabilistic Structural Analysis Method for Implicit Performance Functions,” AIAA Journal, Vol. 28, No. 9, pp. 1663-1669, September 1990.
C.T. Dyka and H.R. Millwater, "Formulation and Integration of Continuous and Discontinuous Quadratic Boundary Elements for Two Dimensional Potential and Elastostatics," Computers & Structures, Vol. 31, No. 4, pp. 495-504, 1989.
M. Stern, A. Bedford, and H.R. Millwater, "Wave Reflection from a Sediment Layer with Depth-dependent Properties," J. Acoust. Soc. Am., Vol. 77, No. 5, pp. 1781-1788, May 1985.

Book Chapters

H.R. Millwater, P. Wirsching - “Analysis Methods for Probabilistic Life Assessment”, American Society of Metals Failure Analysis Handbook, V 11, 2003, pp. 250-268
S. J. Hudak, Jr., B. R. Lanning, G. M. Light, J. M. Major, J. A. Moryl, M. P. Enright, R. C. McClung, and H.R. Millwater, in: J.M. Larsen, L. Christodoulou, J.R. Calcaterrra, M.L. Dent, M.M. Derriso, W.J. Hardman, J.W. Jones, S.M. Russ, (Eds.) Materials Damage Prognosis, “The Influence of Uncertainty in Usage and Fatigue Damage Sensing on Turbine Engine Prognosis,” The Minerals, Metals, & Materials Society, 2005, 157-166.
R.C. McClung, M.P. Enright, H.R. Millwater, G.R. Leverant, S.J. Hudak, Jr., (2004) “A Software Framework for Probabilistic Fatigue Life Assessment of Gas Turbine Engine Rotors,” STP 1450, Probabilistic Aspects of Life Prediction, ASTM

Peer-reviewed Conference Papers

J. Ocampo, H. Millwater, N. Crosby, B. Gamble, C. Hurst, M. Nuss, M. Reyer, and S. Mottaghi, “An Ultrafast Crack Growth Lifing Model to Support Digital Twin, Virtual Testing, and J. Probabilistic Damage Tolerance Applications,” Int. Conf. Aeronautical Fatigue (ICAF), Poland, Krakow 2-7 June 2019
D. Ramirez Tomayo*, A. Montoya, and H. Millwater, “A New Complex-variable Thermal Fracture Finite Element Method for Evaluating the Structural Integrity of Aircraft Structures,” AIAA SciTech Conference, Kissimmee, FL, Jan 8-12, 2018, AIAA-0649, https://doi.org/10.2514/6.2018-0649
J. Ocampo, H. Millwater, N. Crosby, B. Gamble, C. Hurst, M. Nuss, M. Reyer, S. Mottaghi, “Probabilistic Damage Tolerance for Aircraft Fleets Using the FAA-Sponsored SMART|DT Software,” Int. Conf. on Aeronautical Fatigue, Nagoya Japan, June 7-9, 2017
N. Crosby*, H. Millwater, J. Ocampo, E. Anagnostou, S. Engel, J. Madsen, K. Engel, “Probabilistic Damage Tolerance for Aviation Fleets Using a Kriging Surrogate Model,” AIAA SciTech Conference, Ft. Worth, TX, Jan 9-13, 2017
E. Anagnostou, S. Engel, J. Madsen, K. Engel, J. Nardiello, D. Hoitsma, H. Millwater, J. Ocampo, C. Quintana, and N. Crosby*, “Developing the Airframe Digital Twin Prognostic & Probabilistic Individual Aircraft Tracking Paradigm,” Aircraft Airworthiness & Sustainment, Grapevine, TX, March 21-24, 2016
D.M. Sparkman, J.E. Garza*, H.R. Millwater, and B.P. Smarslok, “Sampling-based PostProcessing Method for Global Sensitivity Analysis,” AIAA SciTech, 4-8 January 2016, San Diego, California, USA, 18th AIAA Non-Deterministic Approaches Conference
J. Ocampo and H.R. Millwater, “Probabilistic Damage Tolerance Analysis for Aircraft Fleets” Australian Aircraft Airworthiness & Sustainment Conference. Brisbane, Australia, July 2015.
H.R. Millwater, D. Wagner, “A New Progressive Curvilinear Strain Energy-based Crack Growth Modeling Algorithm using Multicomplex Variable Finite Elements,” Advanced Materials Research Vols. 891-892 (2014) pp 1015-1020 Online available at www.scientific.net © (2014) Trans Tech Publications, Switzerland doi:10.4028/www.scientific.net/AMR.891-892.1015
H.R. Millwater, J.D. Ocampo, T. Castaldo, “Probabilistic Damage Tolerance Analysis for General Aviation,” Advanced Materials Research Vols. 891-892 (2014) pp 1191-1196 Online available at www.scientific.net © (2014) Trans Tech Publications, Switzerland doi:10.4028/www.scientific.net/AMR.891-892.1191
C. Quintana, H.R. Millwater, and R.C. Penmetsa, “Integration of System Reliability Analysis and FMECA to Efficiently Identify Structural Hot Spots,” AIAA SciTech Conference, National Harbor, MD, Jan. 2014
H.R. Millwater, D. Wagner, J.E Garza, A. Baines, K. Lovelady, “Application of the Complex Variable Finite Element Method, ZFEM, to Structural Mechanics Sensitivity Analysis, 15th Nondeterministic Approaches Conference, April 8-12, 2013, Boston, MA
J.E. Garza, H.R. Millwater, “Sensitivity Analysis in Structural Dynamics using the ZFEM Complex Variable Finite Element Method,” 15th Nondeterministic Approaches Conference, April 8-12, 2013, Boston, MA
J.D. Ocampo, H.R. Millwater, “Probabilistic Damage Tolerance for Small Airplanes Using a Linear-Elastic Crack Growth Fracture Mechanics Surrogate Model,” 15th Nondeterministic Approaches Conference, April 8-12, 2013, Boston, MA
C. Quintana, H.R. Millwater, “Investigating the Feasibility of Interpolating Scatter in Material Property Data,” 15th Nondeterministic Approaches Conference, April 8-12, 2013, Boston, MA
C. Dubinsky, H.R. Millwater, G. Singh, and P. Golden, “Experimental Resource Allocation for Statistical Simulation of Fretting Fatigue,” 14th AIAA Nondeterministic Approaches Conference, 23 - 26 April 2012, Honolulu, Hawaii
L.C. Domyancic and H.R. Millwater, “Sensitivity Analysis for Risk Assessment of an Aircraft,” 14th AIAA Nondeterministic Approaches Conference, 23 - 26 April 2012, Honolulu, Hawaii
D.M. Sparkman, H.R. Millwater, P.Golden, R. John, “Probabilistic Framework for Prediction of Material Property Distributions from Small Microstructural Models,” 14th AIAA Nondeterministic Approaches Conference, 23 - 26 April 2012, Honolulu, Hawaii
M. Cortina, J. Ocampo, and H.R. Millwater, “Sensitivity analysis for General Aviation Risk Assessment,” 14th AIAA Nondeterministic Approaches Conference, 23 - 26 April 2012, Honolulu, Hawaii
G. Singh, J. Ocampo, and H.R. Millwater, “Extreme Value Modeling and Parametric Investigations of Gust and Maneuver Loads for General Aviation,” 23 - 26 April 2012, Honolulu, Hawaii
D. Wagner, A. Baines, T. Ross, C. Dubinsky and H.R. Millwater, “User-defined Elements with Complex Nodal Coordinates, Aircraft Airworthiness & Sustainment Conference, Baltimore, MD, April 2-6, 2012
J. Ocampo, H.R. Millwater, “Probabilistic Damage Tolerance Analysis for Small Airplanes,” Aircraft Airworthiness & Sustainment Conference, Baltimore, MD, April 2-6, 2012 22. J. Garza and H.R. Millwater, “Sensitivity of the Probability of Failure to POD Curve Regions”, Aircraft Airworthiness & Sustainment Conf., San Diego, CA, April 2011
H.R. Millwater, D. Sparkman L. Smith, L. Domyancic, and D. Wieland, “System Reliabilitybased Filtering Methods for Determining Critical Locations of Aircraft structures,” Aircraft Airworthiness & Sustainment Conf., San Diego, CA, April 2011
J.D. Ocampo and H.R. Millwater, “SMART|LD (Small Aircraft Risk Technology –Linear Damage) Technology and Case Studies Applications,” Aircraft Airworthiness & Sustainment Conf., San Diego, CA, April 2011
D. Wagner and H.R. Millwater, “2D Weight Function Development using a Complex Taylor Series Expansion Method”, Aircraft Airworthiness & Sustainment Conf., San Diego, CA, April 2011
Y.-T. Wu, H. Millwater, and F. Abali, “Significance of Including Missed-Detections in Structural Reliability Updating,” 52nd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference - 13th AIAA Nondeterministic Approaches Conference, April 4-7, 2011, Denver, CO
G. Singh, M. Cortina, and H. Millwater, “Sensitivity Analysis of Laser Peening, a Fatigue Life Enhancement Process,” 13th AIAA Nondeterministic Approaches Conference, April 4-7, 2011, Denver, CO
G. Singh, H. Millwater, Extreme Value Modeling of Gust and Maneuver Loads for General Aviation, 13th AIAA Nondeterministic Approaches Conference, April 4-7, 2011, Denver, CO
L. Domyancic, H.R. Millwater, “Advances in Bounding Techniques for Aircraft Structures,” 13th AIAA Nondeterministic Approaches Conference, April 4-7, 2011, Denver, CO, AIAA2011-1760
D. Sparkman, and H. Millwater, "FORM-Based Filtering of Limit States," Aircraft Airworthiness & Sustainment Conference, Austin, TX, May 10-13, 2010. First Place Student Competition.
J. Garza and H. Millwater, Sensitivity of Probability-of-Failure Estimates with respect to Probability of Detection Curve Parameters,” Aircraft Airworthiness & Sustainment Conference, Austin, TX, May 10-13, 2010
E. Vazquez, H. Millwater, Y.-T. Wu, and M. Shiao, Bayesian Updating with MCMC for Computational Efficiency,” Aircraft Airworthiness & Sustainment Conference, Austin, TX, May 10-13, 2010
J. Ocampo and H. Millwater, “Development of Probabilistic Stress Life Curves and Probabilistic Miner’s Damage Distribution Using Fatigue Testing Results,” Aircraft Airworthiness & Sustainment Conference, Austin, TX, May 10-13, 2010.
D. Sparkman, L. Domyancic, and H. Millwater, "FORM-Based Filtering of Limit States for Gaussian Random Fields," 12th AIAA Nondeterministic Approaches Conference, April 12-15, 2010, Orlando, FL 35. L. Smith, H. Millwater, "Series System Error-Based Identification of Critical Locations Using Sampling," 12th AIAA Nondeterministic Approaches Conference, April 12-15, 2010, Orlando, FL
E. Vazquez and H. Millwater, “Sensitivity Analysis of Markov Chain Monte Carlo,” 51st AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference. 12 - 15 April 2010, Orlando, Florida. AIAA 2010-2683
J. Ocampo, H. Millwater, H. Smith, E. Meyer, M. Nuss, M. Reyer, F. Abali and M. Shiao, “Probabilistic Risk Assessment for Small Airplanes,” 51st AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference. 12 - 15 April 2010, Orlando, Florida. AIAA 2010-2680
C. Dubinksy, G. Singh and H. Millwater, “Optimal Allocation of Testing Resources for Statistical Simulations, 51st AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference. 12 - 15 April 2010, Orlando, Florida. AIAA 2010-2845
G. Singh, J. Ocampo, C. Acosta and H. Millwater, “Distributed Computing for Probabilistic Structural Integrity Analysis of Aircraft Structures,” 51st AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference. 12 - 15 April 2010, Orlando, Florida. AIAA 2010-2848
Y.-T. Wu, J. Zhao, M. Shiao, H.R. Millwater, “Efficient Methods For Probabilistic Damage Tolerance Inspection Optimization,” 51st AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference. 12 - 15 April 2010, Orlando, Florida
Y.-T. Wu, M. Shiao, H.R. Millwater, “A Bayesian-Updating Computational Method for Probabilistic Damage Tolerance Analysis,” 51st AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference. 12 - 15 April 2010, Orlando, Florida
C. Dubinsky and H. Millwater, Allocation of Testing Resources in Statistical Simulations Using Particle Swarm Optimization. 2010 AIAA Region IV Student Conference 2-3 April 2010, Houston, Texas, 1st place Master’s competition.
L. Domyancic and H. Millwater, “Advances in Bounding Techniques for Aircraft Structures,” 2010 AIAA Region IV Student Conference 2-3 April 2010, Houston, Texas, 2nd place Master’s competition.
C. Acosta, J. Ocampo and H. Millwater, “High Performance Computing Implementation and Evaluation on a Structural Risk Assessment Code,” 2010 AIAA Region IV Student Conference 2- 3 April 2010, Houston, Texas, 3rd place team competition.
J. Garza and H.R. Millwater, A “Method for Estimating Sensitivities of the Probability-ofFailure with respect to Probability of Detection Curve Parameters,” 2010 AIAA Region IV Student Conference 2-3 April 2010, Houston, Texas
L. Domyancic, D. Sparkman, and H.R. Millwater, L. Smith and D. Wieland, “A Fast First-Order Method for Filtering Limit States,” 50th AIAA AIAA Nondeterministic Approaches Conference, May 4-7, 2009, Palm Springs, CA, AIAA 2009-2260
P. Golden, H.R. Millwater, and X. Yang, “Probabilistic Sensitivity Analysis of Fretting Fatigue,” 50th AIAA AIAA Nondeterministic Approaches Conference, May 4-7, 2009, Palm Springs, CA, AIAA 2009-2304
A. Voorhees, R. Bagley, H.R. Millwater, P. Golden, “Application of Complex Variable Methods for Fatigue Sensitivity Analysis,” 50th AIAA Nondeterministic Approaches Conference, May 4- 7, 2009, Palm Springs, CA
C. Acosta and J. Ocampo, and H.R. Millwater, “High Performance Computing Implementation on a Risk Assessment Problem,” 2009 AIAA Region IV Student Conference Program, April 17- 18, 2009, First Place Team Competition
D. Sparkman and L. Domyancic, and H.R. Millwater, Critical Failure Location Identification in an Exhaust Manifold,” 2009 AIAA Region IV Student Conference Program, April 17-18, 2009
A. Voorhees, R. Bagley, H.R. Millwater, P. Golden, “Application of Complex Variable Methods for Fatigue Sensitivity Analysis,” 2009 AIAA Region IV Student Conference Program, April 17- 18, 2009, Third Place Masters Competition
H.R. Millwater, R. John, J. Larsen, D. Buchanan, “Probabilistic Modeling of Residual Stress Data in IN100, AIAA Nondeterministic Approaches Conference, April 7-10, Schaumberg, IL, 2008
J.P. Moody, H.R. Millwater and M.P. Enright, “Adaptive Risk Refinement Methodology for Gas Turbine Engine Rotor Disks,” AIAA Nondeterministic Approaches Conference, April 7-10, Schaumberg, IL, 2008, AIAA-2008-2224
L. Smith, H.R. Millwater, K. Griffin, and D. Wieland, “Conditional Filtering for Simplification of Aircraft Structural System Reliability Calculation,” AIAA Nondeterministic Approaches Conference, April 7-10, Schaumberg, IL, 2008
J.P Moody, H.R. Millwater, and M.P. Enright, “Automatic Risk Assessment Methodology for Gas Turbine Engines Employing Adaptive Recursive Triangulation,” IGTI2006-90780, ASME IGTI conference, Montreal, Canada, May 2007, GT2007-27576
M.P. Enright, H.R. Millwater, J. Moody, “Efficient Integration of Sampling-Based Spatial Conditional Failure Joint Probability Densities,” 10th AIAA Nondeterministic Approaches Conference, Honolulu, HI, April 2007
M.P. Enright, R.C. McClung, S.J. Hudak, H.R. Millwater, “Application of Nonparametric Methods to Rainflow Stress Density Estimation of Gas Turbine Engine Usage,” IGTI2006-90780, IGTI conference, Barcelona, Spain, May 2006
H. Smith, H.R. Millwater, J.A. Wollschlager, R. Holzwarth, “An Approach to Validation Utilizing a Probabilistic Methodology as Applied to Composite Structural Design,” 9th AIAA Nondeterministic Approaches Conference, Newport, RI, May 2006
Y.H. Han, H.R. Millwater, J. Portillo, E. John, “Towards Hardware Implementation of a Probabilistic Fatigue Algorithm for Engine Health Monitoring,” 9th AIAA Nondeterministic Approaches Conference, Newport, RI, May 2006
B. Shook, H.R. Millwater, S. Hudak, M.P. Enright, and W.L. Francis, “Impact of Multiple OnBoard Inspections on Cumulative Probability of Detection,” IGTI conference, Reno, NV, June 2005, GT2005-68585
R.W. Osborn, and H.R. Millwater, “Application of Probabilistic Sensitivities to Probabilistic Fatigue Analysis of Gas Turbine Engine Disks,” 46th AIAA Structures, Dynamics and Materials Conference, Austin, TX, April 18-21, 2005
F. Momin, H.R. Millwater, R.W. Osborn, and M.P. Enright, “Application of the Generalized Conditional Expectation Method for Enhancing a Probabilistic Design Fatigue Code,” 46th AIAA Structures, Dynamics and Materials Conference, Austin, TX, April 18-21, 2005
B. Shook, H.R. Millwater, S. Hudak, M.P. Enright, and W.L. Francis, “Comparison of Continual On-Board Inspections to a Single Mid-Life Inspection for Gas Turbine Engine Disks,” 46th AIAA Structures, Dynamics and Materials Conference, Austin, TX, April 18-21, 2005
F. Momin, H.R. Millwater, R.W. Osborn, and M.P. Enright, (2004) "Application of a Conditional Expectation Response Surface Approach to Probabilistic Fatigue," ASCE 9th Joint Specialty Conference on Probabilistic Mechanics and Structural Reliability, Santa Fe, NM, June, 2004
H.R. Millwater, B. Shook, S. Guduru, and G. Constantinides (2004). “Application of Parallel Processing Methods to Probabilistic Fracture Mechanics Analysis of Gas Turbine Disks,” Proceedings, 45th Structures, Structural Dynamics, and Materials Conference, Palm Springs, CA, April 19-22, 2004, AIAA-2004-1745
M.P. Enright, H.R. Millwater, L. Huyse, (2004). “Adaptive Optimal Sampling Methodology for Reliability Prediction of Series Systems,” Proceedings, 45th Structures, Structural Dynamics, and Materials Conference, Palm Springs, CA, April 19-22, 2004, AIAA-2004-1829
S. Hudak, M.P. Enright, R.C. McClung, H.R. Millwater, and W. Francis, “A Probabilistic Damage-based Approach to Structural Health Management,” Proceedings, 45th Structures, Structural Dynamics, and Materials Conference, Palm Springs, CA, April 19-22, 2004, AIAA2004-1953
M.P. Enright, L. Huyse, R.C. McClung, and H.R. Millwater, “Probabilistic Methodology For Life Prediction of Aircraft Turbine Rotors,” 9th ASCE Aerospace Division International Conference on Engineering, Construction and Operations in Challenging Environments (Earth and Space 2004, League City/Houston, TX, U.S.A. during March 7-10, 2004
M.P. Enright, Y.-D. Lee, R.C. McClung, L. Huyse, G.R. Leverant, H.R. Millwater, S.H.K. Fitch, “Probabilistic Surface Damage Tolerance Assessment of Aircraft Turbine Rotors,” ASME International Gas Turbine Conference (IGTI), June 16-19, 2003, Atlanta, GA, ASME Paper no. GT2003-38731
Wieland, H.R. Millwater, “Probabilistic Sensitivity Analysis of Aircraft Damage Tolerance Estimates,” AIAA Structures, Structural Dynamics, and Materials Conference, AIAA Paper No. 2003-1836, Norfolk, VA, April 7-10, 2003
H.R. Millwater, S.H.K. Fitch, M.P. Enright, L. Huyse, “Application of an XML-based Database for Probabilistic Analysis,” 44th AIAA Structures, Structural Dynamics, and Materials Conference, Non-Deterministic Approaches Forum, AIAA Paper No. 2003-1837, Norfolk, VA, April 7-10, 2003
M. P. Enright, S. J. Hudak, R. C. McClung, and H.R. Millwater, "Probabilistic-Based System for Prognosis of Fatigue in Aircraft Engine Components," 44th AIAA Structures, Structural Dynamics, and Materials Conference, Non-Deterministic Approaches Forum, AIAA Paper No. 2003-8014, Norfolk, VA, April 7-10, 2003
H.R. Millwater, M. Enright, “A Convergent Probabilistic Technique for Risk Assessment of Gas Turbine Disks Subject to Metallurgical Defects,” AIAA Structures, Structural Dynamics, and Materials Conference, AIAA Paper No. 2002-1382, Denver, CO, April 22-25, 2002
M.P. Enright, H.R. Millwater, “Optimal Sampling Techniques for Zone-Based Probabilistic Fatigue Life Prediction,” AIAA Structures, Structural Dynamics, and Materials Conference, AIAA Paper No. 2002-1383, Denver, CO, April 22-25, 2002
G.R. Leverant, R.C. McClung, H.R. Millwater, M.P. Enright, “A New Tool for Design and Certification of Aircraft Turbine Rotors,” IGTI Conference, June, 2002, Amsterdam, Netherlands, Paper no. 2002-GT-30303
H.R. Millwater, M.P. Enright, R.C. McClung, and G.R. Leverant, “A Probabilistically-based Damage Tolerance Analysis Computer Program for Engine Rotor Integrity,” Proceedings of the 12th AeroMat Conference and Exhibition (AeroMat 2001), Paper TES-4.6, Long Beach, CA, June 2001
H.R. Millwater, M.P. Enright, R.C. McClung, and G.R. Leverant, “A Probabilistically-based Damage Tolerance Analysis Computer Program for Engine Rotor Integrity,” Forum 57, American Helicopter Society, Special Session on Engine Life Management: Addressing Fleet Risk with Innovative Approaches, Washington, DC, May 2001
B.H. Thacker, D.S. Riha, H.R. Millwater, and M.P. Enright, “Errors and Uncertainties in Probabilistic Engineering Analysis,” Proceedings of the 42nd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Non-Deterministic Approaches Forum, Seattle, WA, April 16-19, AIAA Paper 2001-1239.
H.R. Millwater, S. Fitch, Y.-T. Wu, D. Riha, M. Enright, G. Leverant, C. McClung, C. Kuhlman, G. Chell, Y.-D. Lee, “A Probabilistically-based Damage Tolerance Analysis Computer Program for Hard Alpha Anomalies in Titanium Rotors,” ASME International Gas Turbine Conference (IGTI), ASME Paper No. 2000-GT-0421, Munich, Germany, May 8-11, 2000
H.R. Millwater, K. Griffin, D. Wieland, A. West, H. Smith, M. Holly, R Holzwarth, “Probabilistic Analysis of an Advanced Fighter/Attack Composite Wing Structure,” Structures, Structural Dynamics, and Materials Conference, AIAA Paper No. 2000-1567, Atlanta, GA, April 3-6, 2000
D.S. Riha, B.H. Thacker, H.R. Millwater, Y.-T. Wu, and M.P. Enright, "Probabilistic Engineering Analysis Using the NESSUS Software," 41st Structural Dynamics and Materials Conference, Paper 2000-1512, Atlanta, Georgia, April 2000.
R. C. McClung, H.R. Millwater, and G. G. Chell, "Probabilistic Analysis of Multiple-Cycle Proof Testing", 1998 ASME/JSME Pressure Vessels & Piping Conference, San Diego, CA., July 26-30, 1998
H.R. Millwater, J. Wu, H. Burnside, and M. Mear, "Investigation of Probabilistic Methods for Mult-Site Damage," The First Joint DoD/FAA/NASA Conference on Aging Aircraft, The David Eccles Conference Center, Ogden, Utah, July 8-10, 1997
H.R. Millwater, J. Wu, H. Burnside, and M. Mear, "A Risk Assessment Method for Multi-Site Damage," ICAF'97 (International Committee on Aeronautical Fatigue), Edinburgh, Scotland, June 16-20, 1997.
G.R. Leverant, D.L. Littlefield, R.C. McClung, H.R. Millwater, and Y.-T. Wu, "A Probabilistic Approach to Aircraft Turbine Rotor Material Design," IGTI 97, Orlando, FL, June 2-5, 1997.
H.R. Millwater, G. G. Chell, and D.S. Riha, "A Probabilistic Creep Fatigue Computer Program for Structural Integrity Analysis," 41st International Gas Turbine Conference (IGTI), ASME Paper No. 96-GT-265, Birmingham, UK, June 10-13, 1996.
R. C. McClung, H.R. Millwater, and G.G. Chell, "A Probabilistic Fracture Mechanics Analysis of Multiple-Cycle Proof Testing," FATIGUE '96: The Sixth International Fatigue Congress, Berlin, FRG, May 6-10, 1996.
G. G. Chell, H.R. Millwater, D.A. Mauney, and S.J. Hudak, Jr., "Combining Probabilistic Failure Assessment and Decision Analysis for the Safe and Economic Management of Flawed Petrochemical Components," 1995 ASME Pressure Vessel and Piping Conference, AMD-Vol. 207, July 1995.
G.G. Chell, C.J. Kuhlman, H.R. Millwater, and D.S. Riha, "Application of Reference Stress and Probabilistic Methodologies to Assessing Creep Crack Growth," 27th National Symposium on Fatigue and Fracture Mechanics, Williamsburg, VA, June 26-29, 1995.
H.R. Millwater, Y.-T. Wu, J. W. Cardinal, and G. G. Chell, "Application of Advanced Probabilistic Fracture Mechanics to Life Evaluation of Turbine Rotor Blade Attachments," 40th International Gas Turbine Conference (IGTI), ASME Paper No. 95-GT-214, Houston, TX, June 5-8, 1995.
H.R. Millwater, Y.-T. Wu, and J.W. Cardinal, "Probabilistic Structural Analysis of Fatigue and Fracture," AIAA/ASME/ASCE/AHS/ASC 35th Structures, Structural Dynamics, and Materials Conference, AIAA Paper No. 94-1507, Hilton Head, SC, April 18-20, 1994.
H.R. Millwater and Y.-T. Wu, "Computational Structural Reliability Analysis of a Turbine Blade," 38th International Gas Turbine Conference (IGTI), ASME Paper No. 93-GT-237, Cincinnati, OH, May 24-27, 1993.
H.R. Millwater, and Y.-T. Wu, "Global/Local Methods for Probabilistic Structural Analysis," AIAA/ASME/ASCE/AHS/ASC 34th SDM - Structures, Structural Dynamics, and Materials Conference, AIAA Paper No. 93-1378, La Jolla, CA, April 19-21, 1993.
A.J. Smalley, H.R. Millwater, Y.-T. Wu, and B. F. Evans, "Probabilistic Rotor Dynamic Analysis Using the Fast Probability Integral," Fifth International Conference on Vibrations in Rotating Machinery, Paper No. C/044, pp. 485-491, University of Bath, England, September 7-10, 1992.
H.R. Millwater and Y.-T. Wu, "Structural Reliability Assessment Capability in NESSUS," AIAA/SAE/ASME/ASEE 28th Joint Propulsion Conference and Exhibit, AIAA Paper No. 92-3417, Nashville, TN, July 6-8, 1992.
H.R. Millwater, A. J. Smalley, Y.-T. Wu, T. Y. Torng, and B. F. Evans, "Computational Techniques for Probabilistic Analysis of Turbomachinery," International Gas Turbine and Aeroengine Congress and Exposition, ASME Paper No. 92-GT-167, Cologne, Germany, June 1-4, 1992.
H.R. Millwater and Y.-T. Wu, "Structural Reliability Assessment Capability in NESSUS," 1992 Conference on Advanced Earth-To-Orbit Propulsion Technology, NASA Marshall Space Flight Center, Huntsville, AL, May 19-21, 1992
T.Y. Torng, Y.-T. Wu, and H.R. Millwater, "Structural System Reliability Calculation Using a Probabilistic Fault Tree Analysis Method," 33rd SDM, Structures, Structural Dynamics, and Materials Conference, pp. 603-613, Dallas, Texas, April 13-15, 1992.
H.R. Millwater, T. Torng, B. Thacker, D. Riha, and C.-P. Leung, "Recent Developments of the NESSUS Probabilistic Structural Analysis Computer Program," 33rd SDM, Structures, Structural Dynamics, and Materials Conference, Paper No. AIAA-92-2411, Dallas, Texas, April 13-15, 1992.
H.R. Millwater, S.V. Harren, and B.H. Thacker, "A Probabilistic Methodology for Random Stress-Strain Curves," ASME 9th Biennial Conference on Reliability Stress Analysis and Failure Prevention, ASME Paper DE-Vol. 30, Book No. G00640 - 1991, pp. 37-41, Miami, FL, September 22-25, 1991.
Y.-T. Wu, T.Y. Torng, H.R. Millwater, A.F. Fossum, and M.H. Rheinfurth, "Probabilistic Methods for Rotordynamics Analyses," by, SAE Conference, SAE Paper No. 911110, Dayton, OH, April 22-26, 1991.
B.H. Thacker, H.R. Millwater, and S.V. Harren, "Computational Methods for Structural Load and Resistance Modeling," 32nd SDM Conference, Baltimore, MD, April 7-10, 1991.
H.R. Millwater, S.V. Harren, "Probabilistic Analysis of Structures Involving Random Stress-Strain Behavior," by, B.H. Thacker, presented at the 32nd SDM Conference, Baltimore, MD, April 7-10, 1991.
H.R. Millwater, "Probabilistic Fracture Mechanics Analysis Using the Boundary Element Method," First International Symposium on Uncertainty Modeling & Analysis (ISUMA), University of Maryland, MD, December 1990.
T.A. Cruse, A.F. Fossum, H.R. Millwater, "Probabilistic Design Methods for Advanced Flight Vehicles and Propulsion," Symposium on Computational Technology for Flight Vehicles and Propulsion, Washington, DC, November 5-7, 1990.
S.V. Harren, H.R. Millwater, and B.H. Thacker, "Structural Reliability and Resistance Modeling with the NESSUS Software System," AIAA/SAE/ASME/ASEE 26th Joint Propulsion Conference and Exhibit, Orlando, FL, July 17-18, 1990.
H.R. Millwater, Y.-T. Wu, and A.F. Fossum, "Probabilistic Analysis of a Materially Nonlinear Structure," AIAA/ASME/AHS/ASC 31st SDM Conference, Long Beach, CA, April 2-4, 1990.
B.H. Thacker, R.C. McClung, and H.R. Millwater, "Application of the Probabilistic Approximate Analysis Method to a Turbopump Blade Analysis," AIAA/ASME/AHS/ASC 31st SDM Conference, Long Beach, CA, April 2-4, 1990.
T.A. Cruse, H.R. Millwater, and S.V. Harren, "Application of Probabilistic Structural Modeling to Elastoplastic and Transient Analyses," 3rd IFIP Working Conference on Structural Reliability and Optimization of Structural Systems, Berkeley, CA, March 26-28, 1990.
C.T. Dyka, A.M. Remondi, and H.R. Millwater, "Integration of 3D Boundary Elements for Static Elasticity," International Symposium on Boundary Element Methods: Advances in Solid and Fluid Mechanics, United Technologies Research Center, East Hartford, CT, October 2-4, 1989.
T.A. Cruse, C.C. Chamis, and H.R. Millwater, "An Overview of the NASA (LeRC) - SwRI Probabilistic Structural Analysis (PSAM) Program," ICOSSAR '89/5th Int'l Conf., San Francisco, CA, August 7-11, 1989.
H.R. Millwater, Y. -T. Wu, J. B. Dias, R. C. McClung, S. T. Raveendra, and B. H. Thacker "The NESSUS Software System for Probabilistic Structural Analysis," ICOSSAR '89/5th Int'l Conf., San Francisco, CA, August 7-11, 1989.
R.C. McClung, H.R. Millwater, Y.-T. Wu, BH Thacker, "An Approximate Methods Approach to Probabilistic Structural Analysis," 30th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, Mobile, Alabama, April 3-5, 1989
R.C. McClung, H.R. Millwater, et al., "An Approximate Methods Approach to Probabilistic Structural Analysis," Structural Integrity and Durability of Reusable Space Propulsion Systems Conference, NASA-Lewis Research Center, Cleveland, OH, April 18-19, 1989.
H.R. Millwater and Y.-T. Wu, "Structural Reliability Analysis Using a Probabilistic Finite Element Program," AIAA/ASME/ASCE/AHS/ASC 30th Structures, Structural Dynamics and Materials Conference, Mobile, AL, April 3-5, 1989.
Y.-T. Wu, H.R. Millwater, and T.A. Cruse, "An Advanced Probabilistic Structural Analysis Method for Implicit Performance Functions," AIAA/ASME/ASCE/AHS/ASC 30th Structures, Structural Dynamics and Materials Conference, Mobile, AL, April 3-5, 1989.
H.R. Millwater, K. Palmer, and P. Fink, "NESSUS/EXPERT--An Expert System for Probabilistic Structural Analysis Methods," AIAA/ASME/ASCE/AHS 29th Structures, Structural Dynamics and Materials Conference, Williamsburg, VA, April 18-20, 1988.

Presentations (not peer-reviewed)

J. Ocampo, D. Posso, and H.R. Millwater, “Risk Based Optimized Inspections for Aircraft Fleets” Aircraft Airworthiness & Safety Conference, August, 2020.
N. Crosby, H. Millwater, “Adaptive Importance Sampling for Probabilistic Damage Tolerance Analysis,” Aircraft Airworthiness & Safety Conference, August, 2020
J. Ocampo, D. Posso, and H.R. Millwater, “Risk Based Optimized Inspections for Aircraft Fleets” 19th International Workshop on the Holistic Structural Integrity Process (HOLSIP), Salt Lake City, UT, February 2020.
H.R. Millwater, M. Balcer*, D. Ramirez*, and A. Montoya, “UQ Modeling of Structures and Materials Using the Hypercomplex Differentiation Method,” MS&T Conference, Sept. 29-Oct. 3, 2019, Portland OR
N. Crosby*, H.R. Millwater, J.D. Ocampo, B. Gamble, C. Hurst, M. Nuss, “Large Scale Cluster Computing for Comprehensive Risk Assessment,” Aircraft Airworthiness & Sustainment, April 22-26, 2019, Washington, DC
J.D. Ocampo, H.R. Millwater, N. Crosby, B. Gamble, C. Hurst, M. Reyer, S. Mottaghi, M. Nuss, “An Ultrafast Crack Growth Lifing Model for Efficient Prognosis, International Conference on Fatigue Damage of Structural Materials XII. Hyannis, MA, 16-21, Sept. 2018
H. Millwater, David Wagner, Daniel Ramirez-Tamayo, Andres Aguirre, Arturo Montoya, Manuel Garcia, Brendy Rincon-Troconis, “Two and Three Dimensional Progressive Fracture under Thermal Loading: Computational Modelling and Experimental Validation, International Conference on Fatigue Damage of Structural Materials XII. Hyannis, MA, 16-21, Sept. 2018
D. Ramirez Tamayo, A. Montoya, H.R. Millwater, D. Wagner, ”A Multicomplex Finite Element Approach for Thermoelastic Curvilinear Progressive Fracture”, 2018 conference of Engineering Mechanics Institute, Boston, MA, May 29-June 1, 2018
M. Aristizabal, M. Garcia, and H. Millwater, “General Purpose Finite Element Library for Computation of High-Order Multivariable Sensitivities,” 13th World Congress of Computational Mechanics, New York, NY July 2018
A. Aguirre, D. Ramirez-Tamayo, M. Garcia, and H. Millwater, “Computation of the Energy Release Rate using a Complex Stiffness Derivative Approach,” 13th World Congress of Computational Mechanics, New York, NY July 2018
D. Ramirez-Tamayo, A. Montoya, H. Millwater, and D. Wagner, “A Multicomplex Finite Element Approach for Thermoelastic Curvilinear Progressive Fracture,” 13th World Congress of Computational Mechanics, New York, NY July 2018
A. Montoya, H. Millwater, R. Fielder, & P. Golden, “A Complex Variable Finite Element Based Approach for Rapid Estimates of Residual Stress Variance,” 13th World Congress of Computational Mechanics, New York, NY July 2018
M. Garcia, M. Aristizabal, A. Aguirre, H. Millwater, and A. Montoya, “An Overview of Hypercomplex Algebras for Sensitivity Analysis in the Finite Element Method,” 13th World Congress of Computational Mechanics, New York, NY July 2018
H. Millwater, J. Ocampo, and N. Crosby, “An Ultrafast Crack Growth Lifing Algorithm for Probabilistic Damage Tolerance Analysis, Aircraft Airworthiness & Sustainment Conference, Jacksonville, FL, April 2018
J. Ocampo, H. Millwater, and N. Crosby “An Ultrafast Crack Growth Lifing Algorithm for Probabilistic Damage Tolerance Analysis”, 17th International Workshop on the Holistic Structural Integrity Process (HOLSIP), Salt Lake City, UT, February 2018.
J. Ocampo, A Horwath, S. Carlson, L. Smith, H. Millwater, N. Crosby “Incorporating Residual Stresses into Probabilistic Damage Tolerance Analysis – Case Study”, Engineered Residual Stress Implementation Workshop 2017, Salt Lake City, UT, September 2017.
J. Ocampo and H. Millwater, “Incorporating Residual Stresses into Probabilistic Damage Tolerance Analysis”, Aircraft Airworthiness & Sustainment Conf., Phoenix, AZ, May 2017.
J. Ocampo and H. Millwater “Incorporating Residual Stresses into Probabilistic Damage Tolerance Analysis – First Approach and Open Discussion”, 16th International Workshop on the Holistic Structural Integrity Process (HOLSIP), Salt Lake City, UT, February 2017.
J. Ocampo and H. Millwater “HOLSIP-Based Extensions to the SMART-DT Software”, 15th International Workshop on the Holistic Structural Integrity Process (HOLSIP), Salt Lake City, UT, February 2016.
H. Millwater, R. Fielder, F. Garcia, and C. Labowsky, Probabilistic and Sensitivity Method Development and Application in Life Prediction of metallic Materials and Structures,” AFRL Minority Leaders Research Collaboration Program Review, Dayton, OH, Sept 20-22, 2016
A. Aguirre, M. Garcia, M. Aristizabal, and H. Millwater, “MCX: A Multicomplex Finite Element Library for High Order Derivatives," World Congress on Computational Mechanics, July 2016, Seoul, Korea
H.R. Millwater, “Overview of the ZFEM Multicomplex Finite Element Method”, Parameterized Reduced Order Modeling Workshop Organized by Sandia National Laboratories in Albuquerque, New Mexico, June 1-2, 2016
M. Garcia, D. Wagner, H.R. Millwater, “Two Dimensional Curvilinear Progressive Fracture using a Multicomplex Finite Element Method,” Parameterized Reduced Order Modeling Workshop Organized by Sandia National Laboratories in Albuquerque, New Mexico, June 1-2, 2016
A. Aguirre, M. Garcia, H.R. Millwater, “Multi-Complex and Multi-Dual Numbers,” Parameterized Reduced Order Modeling Workshop Organized by Sandia National Laboratories in Albuquerque, New Mexico, June 1-2, 2016
H.R. Millwater, J. Ocampo, N. Crosby, B. Gamble, C. Hurst, M. Nuss, “Probabilistic Damage Tolerance using the FAA-Sponsored SMART|DT Software,” Air Force Structural Integrity Program, Dec. 1-3, 2015 San Antonio, TX
J. Ocampo and H.R. Millwater, “Risk Calculations Using the FAA SMART Probabilistic Damage Tolerance Software and AFGROW” AFGROW Users Workshop. Layton, UT, September 2015.
J. Ocampo and H.R. Millwater, “Latest Developments in Probabilistic Fatigue and Damage Tolerance Analysis”, 14th International Workshop on the Holistic Structural Integrity Process, (HOLSIP), Salt Lake City, UT, February 2015.
H.R. Millwater, and J. D. Ocampo, “An Overview of the SMART Damage Tolerance Software for Aircraft Risk Assessment,” Aircraft Airworthiness & Sustainment Conference, Baltimore, MD, March 30-Apr 2, 2015
J. Ocampo and H.R. Millwater “Multiple Repair Scenarios in Aricraft Fleets Using the Weighted Branch Integration (WBI) Method,” Aircraft Airworthiness & Sustainment Conference, Baltimore, MD, March 30-Apr 2, 2015
J. Ocampo and H.R. Millwater “Probabilistic Fatigue and Damage Tolerance Analysis for General Aviation”, 13th International Workshop on the Holistic Structural Integrity Process (HOLSIP), Salt Lake City, UT, February 2014.
A. Baines and H.R. Millwater, “Two-Dimensional Weight Function Development Using ZFEM, AIAA Region IV Student Conference, April, 2013
A. Baines and H. Millwater, “Two-Dimensional Weight Function Development Using ZFEM, AIAA Regional Student Conference, April 2013
E.E. Iglesias and H.R. Millwater, “Sensitivity Analysis of Turbine Engine Sustainment,” AIAA Regional Student Conference, April 2013
H.R. Millwater, D. Wagner, J. Garza, A. Baines, K. Lovelady, C. Quintana, T. Ross, “Complex Variable Finite Element Methods for Fracture Mechanics Analysis,” NavAir/DSTO Fatigue Technology Symposium, Melbourne, Australia, March 2013
H.R. Millwater, D. Wagner, J. Garza, A. Baines, K. Lovelady, “A New Finite Element Method based on Complex Variable Mathematics,” San Antonio Scientific Visualization Symposium, San Antonio, TX, Nov. 12-13, 2012
H.R. Millwater, “Probabilistic Sensitivity Analysis for General Aviation Risk Assessment”, Aircraft Airworthiness & Sustainment Conference, Baltimore, MD, Apr. 2-6, 2012
H.R. Millwater, NAVAIR Fatigue/Fracture Mechanics Workshop, UC-Irvine, November 17, 2011
J.D. Ocampo and H.R. Millwater, Probabilistic Stress Life Curves and Probabilistic Miner’s Damage Distribution Development Using Testing Data and Simulation Analysis, ASTM student competition, San Antonio, Texas November 17, 2010
H.R. Millwater, G. Singh, M. Cortina, Localized Probabilistic Sensitivity Method to Determine Random Variable Regional Importance, Sensitivity of Model Output conference, July 19-22. 2010, Milam, IT, and Engineering Mechanics Institute, Los Angeles, CA, August 8-11, 2010
H.R. Millwater, J. Ocampo, G. Singh, H. Smith, E. Meyer, F. Abali, M. Shiao, M. Nuss, M. Reyer, Probabilistic Structural Risk Assessment and Risk Management for Small Airplanes,” Aircraft Airworthiness & Sustainment Conference, Austin, TX, May 10-13, 2010.
H.R. Millwater, R. Bagley, A. Bates, A. Voorhees, J. Garza, and P. Golden “New Sensitivity Methods for Life Prediction Estimates,” Propulsion, Safety, Affordability, and Readiness, Myrtle Beach, SC, March 2009
H.R. Millwater, R. Bagley, A. Bates, A. Voorhees, J. Garza, and P. Golden “New Sensitivity Methods for Life Prediction Estimates,” Propulsion, Safety, Affordability, and Readiness, Myrtle Beach, SC, March 2008
H.R. Millwater, A. Bates, E. Vazquez, J. Larsen, S. Jha “Enhanced Probabilistic Sensitivity Methods For Life Prediction Estimates,” Propulsion, Safety, Affordability, and Readiness, San Diego, CA, March 2007
H.R. Millwater, “Probabilistic Sensitivities for Fatigue Analysis of Gas Turbine Engine Disks,” Propulsion, Safety, Affordability, and Readiness, Jacksonville, Fl, March 2006
M.P. Enright, L. Huyse, Y.-D. Lee, G. Chell, C. McClung, G. Leverant, H.R. Millwater, S.H.K. Fitch, “Summary of DARWINTM Capabilities for Surface Damage Tolerance Assessment and Related Enhancements,” 6th Annual FAA/Air Force/NASA/Navy Workshop on the Application of Probabilistic Methods to Gas Turbine Engines, March 18-20, Solomon’s Island, Maryland, 2003
L. Huyse, M.P. Enright, H.R. Millwater, and S.H.K. Fitch, “Recent Probabilistic Computational Efficiency Enhancements in DARWINTM,” 6th Annual FAA/Air Force/NASA/Navy Workshop on the Application of Probabilistic Methods to Gas Turbine Engines, March 18-20, Solomon’s Island, Maryland, 2003
D. Wieland, H.R. Millwater, A. Nagar, “Impact of Parameter Variation on Damage Tolerance Analysis Estimates,” USAF ASIP Conference, Williamsburg, VA, December 2002
H.R. Millwater, “An Extreme Value Approach to Probabilistic Evaluation of Multi-Site Damage,” ASTM Symposium on Probabilistic Aspects of Life Prediction, Miami FL, November 6-7, 2002
S. J. Hudak, Jr, M. P. Enright, H.R. Millwater, and R. C. McClung, “Enhanced Prognosis through Probabilistic Damage Assessment,” DARPA Prognostics Workshop, December 12-13, 2001, Arlington, Virginia
R.C. McClung, M.P. Enright, H.R. Millwater, G.R. Leverant, and S.J. Hudak, Jr., “A Software Framework for Probabilistic Fatigue Life Assessment,” ASTM Symposium on Probabilistic Aspects of Life Prediction, Miami FL, November 6-7, 2002
H.R. Millwater and T.A. Cruse, "Probabilistic Structural Analysis Methods for Select Space Propulsion System Components," Structural Integrity and Durability of Reusable Space Propulsion Systems Conference, NASA-Lewis Research Center, Cleveland, OH, April 18-19, 1989.
H.R. Millwater, B. Thacker, and Y.-T. Wu, "Structural Reliability Methods Code - Development Status," Structural Durability Conference, NASA-Lewis Research Center, May 14-15, 1991.

Reports

E.H. Glaessgen, L.E. Levine, P.W. Witherell, M.A. Donmez, M. Gorelik, N.A. Ashmore, R.R. Barto, C.C. Battaile, H.R. Millwater, G.J. Nanni, A.D. Rollett, E.J. Schwalbach, V. Venkatesh, “NASA / NIST / FAA Technical Interchange Meeting on Computational Materials Approaches for Qualification by Analysis for Aerospace Applications,” NASA/TM–20210015175 DOT/FAA/TC-20/38
R.C. McClung, M.P. Enright, Y.-D. Lee, W. Liang, J.P. Moody, S.H.K. Fitch, H.R. Millwater, J.P. Dubke, R.J. Maffeo, M.E. McClure, A.D. Peralta, “Probabilistic Design for Rotor Integrity,” Federal Aviation Administration DOT/FAA/TC-18/6, Oct. 2018
J. Ocampo, H.R. Millwater, G. Singh, H. Smith, E. Meyer, “Probabilistic Structural Risk Assessment and Risk Management for Small Airplanes,” Federal Aviation Administration DOT/FAA/AR-11/14, Nov. 2017
H.R. Millwater and J. Ocampo, “Probabilistic Damage Tolerance-Based Maintenance Planning for Small Airplanes,” Federal Aviation Administration DOT/FAA/TC-16/33, Oct. 2017
Y.-T. Wu and H.R. Millwater, “Analysis Methods for the Management of Structural Damage with Structural Health Monitoring”, Federal Aviation Administration DOT/FAA/TC-15/60, Oct. 2017
H.R. Millwater, D. Wagner, M. Garcia, A New Progressive Crack Growth Modeling Algorithm using Complex Variable Finite Elements, ONR final report. September 2016
M.R.W. Brake, B.I. Epureanu, and H.R. Millwater, Proceedings of the 2016 Parameterized Reduced Order Modeling Workshop, Sandia Report, SAND2016-9621, September, 2016
S.J. Hudak, Jr., M.P. Enright, R.C. McClung, L.J. Huyse, H.R. Millwater, T. Conquest, A. Del Amo, and S. Fitch, “Enhanced Life Prediction Technology for Engine Rotor Life Extension (ERLE),” AFRL-RX-WP-TR-2008-4287, Sept. 2008
D. Wieland, H.R. Millwater, “Impact of Parameter Variation on Damage Tolerance Analysis Estimates,” Final Report, AFRL-VA-TR-2002-3089, November 2002
S.J. Hudak, Jr., M.P. Enright, R.C. McClung, H.R. Millwater, and A. Sarlashkar, “Enhanced Prognosis through probabilistic Damage Assessment,” Final Report for ARFL DARPA, Air Force Materiel Command, Wright-Patterson AFB, OH, June 2002