1 / 21

Construction of a 21-Component Layered Mixture Experiment Design

PNNL-SA-37314 Construction of a 21-Component Layered Mixture Experiment Design Greg F. Piepel and Scott K. Cooley Pacific Northwest National Laboratory Bradley Jones, SAS Institute Inc. Fall Technical Conference Valley Forge, PA October 17-18, 2002 Introduction

jana
Download Presentation

Construction of a 21-Component Layered Mixture Experiment Design

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. PNNL-SA-37314 Construction of a21-Component Layered Mixture Experiment Design Greg F. Piepel and Scott K. Cooley Pacific Northwest National Laboratory Bradley Jones, SAS Institute Inc. Fall Technical Conference Valley Forge, PA October 17-18, 2002

  2. Introduction • We discuss the solution to a unique and challenging mixture experiment design problem involving: • 19 and 21 components for two different parts of the design • many constraints, single- and multi-component • augmentation of existing data • a layered design developed in stages • a no-candidate-point optimal design approach Greg Brad 2

  3. Mixture Experiment • End product is a mixture of q components, with proportions xi such that (1) • May have additional constraints (2) • Experimental region for: (1) a simplex, (2) generally an irregular polyhedron 3

  4. Tried (Tired?) But True Mixture Experiment Examples Pu Th U Sheepshead Croaker Mullet Etc. Si B Al Waste Glass Piepel Cornell Fish Patties 4

  5. Waste Glass Background • Hanford Site in WA state has 177 underground waste tanks • Wastes will be retrieved from the tanks, separated into high-level waste (HLW) and low-activity waste (LAW) fractions, and separately vitrified (i.e., made into waste glass) 5

  6. Experimental Design for GlassProperty-Composition Models • Need data to support fitting glass property-composition models (used for many things) • Use mixture experiment designs that cover the constrained experimental regions • Want design points on the boundary and interior of the glass experimental region • Boundary glass compositions less likely, but still need models able to predict • Interior compositions more likely, so must explore adequately to support models 6

  7. Layered Design • A layered design (LD) consists of points on: • an outer layer • one or more inner layers • one or more center points • May also contain replicates Outer Layer Center Point Inner Layer 7

  8. Spinel Liquidus TemperatureExperimental Design Problem • Liquidus temperature (TL) is the highest temperature at which crystalline phases exist in a glass melt • TL will limit the waste loading in nearly all Hanford HLW glasses • Spinel (Ni,Fe,Mn)(Cr,Fe)2O4 crystals of concern • Property-composition models are required to implement spinel TL constraints • Hence, data are required to develop models 8

  9. Overview of Experiment Design Approach for Spinel TL Problem • 144 existing glass compositions relevant to Hanford HLW were selected and augmented • A layered design approach for mixture experiments was used • Outer layer • Inner layer • Center point • Non-radioactive and radioactive glasses • 40 glasses not containing uranium (U3O8) and thorium (ThO2) • 5 glasses containing U3O8 and ThO2 9

  10. Step 1: Define the HLW Glass Composition Experimental Region • Glass scientists selected 21 HLW glass components to study their effects on spinel TL (see Table 1 in handout) • The 21 components included two radioactive components, U3O8 and ThO2 • A 22nd component “Others” (a mixture of the remaining minor waste components) was to be held constant at 0.015 for new design glasses • Hence 10

  11. Step 1: Define the ExperimentalRegion (cont.) • Single- and multi-component constraints on the proportions of the 21 glass components were specified to define outer and inner layers of the experimental region • Single-component constraints • 38 outer- and inner-layer, nonradioactive • 42 inner-layer, radioactive • 6 multi-component constraints • See Tables 1 and 2 at the end of the handout for the specific constraints 11

  12. Step 2: Screen the Existing Database • More than 200 existing glasses with spinel TL values from many other studies • Insufficient glasses inside the single- and multi-component constraints defining the outer layer in Step 1 • Expanded the outer-layer single-component constraints by 10% (see Table 3 in handout) • 144 glasses satisfied the revised constraints and were selected for design augmentation 12

  13. Step 3: Assess 144 ExistingData Points • Of the 144 existing glasses: • 14 contained U3O8 • None contained ThO2 • Compositions graphically assessed using dot plots and scatterplot matrix • Existing data spanned ranges of some components fairly well • For B2O3, Cr2O3, F, K2O, MnO, P2O5, SrO, TiO2, and ZnO there were limited data for larger values within component ranges • None of the 144 glasses contained Bi2O3 or ThO2 13

  14. Conversion to 19 Components for Nonradioactive Portion of Design • The 144 existing glass compositions were expressed as normalized mass fractions of the 19 components w/o U3O8 and ThO2 • The single-component constraints were adjusted by li = Li /0.985 and ui = Ui /0.985 • The multi-component constraints were adjusted as described in the paper 14

  15. Step 4: Augment 144 Existing Glasses with8 Outer-Layer Nonradioactive Glasses • Initially tried generating the outer-layer vertices with the goal of selecting a subset using traditional candidate-point optimal design • However, too many vertices to generate • Ideas for generating a “random” subset of vertices to select from were unsuccessful • JMP no-candidate-point D-optimal design capability was used (Brad will discuss later) • 8 outer-layer glasses were selected to augment the 144 existing glasses 15

  16. Step 5: Select 27 Inner-LayerNonradioactive Glasses • Again used JMP no-candidate D-optimal design capability to select 27 inner-layer nonradioactive glasses to augment • 144 existing glasses • 8 outer-layer glasses from Step 4 • Steps 4 and 5 performed several times • Compared compositions and predicted property values (from preliminary models) using dot plots and scatterplot matrices • Selected the set of 8 outer + 27 inner glasses judged best 16

  17. Step 6: Add Overall Centroid and Replicates to the Experimental Design • A center point for nonradioactive glasses was formed by averaging the 8 outer-layer and 27 inner-layer glasses • 4 replicates chosen • Center point • 3 existing nonradioactive glasses • Replicates chosen to “span” composition as well as property spaces 17

  18. Step 7: Select 5 NewRadioactive Glasses • Radioactive glasses selected within a 21-component (19 + U3O8 + ThO2) glass composition region defined by: • inner-layer single-component constraints • multi-component constraints • 5 radioactive glasses (containing U3O8 and ThO2) selected to augment • 144 existing glass • 8 + 27 + 5 = 40 new nonradioactive glasses using JMP no-candidate D-optimal design 18

  19. Step 8: Assess the Existing Glasses & New Experimental Design Glasses • Dot plots and scatterplot matrices used to assess 1-D and 2-D projective properties of the existing and new glasses, e.g. 19

  20. Summary Challenging problem to construct a constrained mixture experiment design for studying spinel TL in nuclear waste glass • Separate design portions for nonradioactive glasses (19 components) and radioactive glasses (21 components) • Existing data to select and augment • Layered design approach with separate outer- and inner-layer experimental regions • Had to use no-candidate optimal design capability of JMP because problem was too big to use traditional approach of selecting design from candidate points ( Brad) 20

  21. Electronic Copy of Paper • If interested in receiving a copy of the paper Piepel, G.F., S.K. Cooley, and B. Jones (2002), “Construction of a 21-Component Layered Mixture Experiment Design”, PNNL-SA-37340, Rev. 0, Pacific Northwest National Laboratory, Richland, WA. email to greg.piepel@pnl.gov to receive a PDF electronic copy by return email 21

More Related