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At least 55 records · Page 3

[ ] or SUCCESS is Not Enough: Current Technology and Future Directions in Proof Presentation

Automated theorem provers for first order logic are now around for several decades. Over the last few years, their deductive power to solve hard problems has increased tremendously. The annual CASC system competitions [Se97] give a clear picture of this situation. However, today's automated theorem provers are restricted "more by general usability than by raw deductive power." As a result of this, there are only very few serious applications of automated theorem provers. There are numerous features which a theorem prover lacks for real-world applicability. An automated theorem prover (as it is currently seen) is nothing more than a fast and elaborate search procedure. In that sense, an ATP can compared to a formulated race car, cool and fast, but virtually unusable for shopping groceries around the corner. Many important features are missing, or are optimized for speed rather than for applicability. [Schol] identifies important features which are needed for practical usability like detection of non-theorems, handling of modal/inductive proof tasks, control of the prover, and proof output. In this paper, we will focus solely on the last point, the presentation of the ATP's result to the user. In the rest of this paper, we will first discuss the general importance of providing feedback to the user, then we will describe the system ExplainIt!, a part of the deductive synthesis system AMPHION/NAV. In the conclusions we will relate proof presentation to other ways of post-processing a proof found by an ATP and stress their role in the future of automated deduction.

Schumann, Johann↗

Analysis and Test Correlation of Proof of Concept Box for Blended Wing Body-Low Speed Vehicle

The Low Speed Vehicle (LSV) is a 14.2% scale remotely piloted vehicle of the revolutionary Blended Wing Body concept. The design of the LSV includes an all composite airframe. Due to internal manufacturing capability restrictions, room temperature layups were necessary. An extensive materials testing and manufacturing process development effort was underwent to establish a process that would achieve the high modulus/low weight properties required to meet the design requirements. The analysis process involved a loads development effort that incorporated aero loads to determine internal forces that could be applied to a traditional FEM of the vehicle and to conduct detailed component analyses. A new tool, Hypersizer, was added to the design process to address various composite failure modes and to optimize the skin panel thickness of the upper and lower skins for the vehicle. The analysis required an iterative approach as material properties were continually changing. As a part of the material characterization effort, test articles, including a proof of concept wing box and a full-scale wing, were fabricated. The proof of concept box was fabricated based on very preliminary material studies and tested in bending, torsion, and shear. The box was then tested to failure under shear. The proof of concept box was also analyzed using Nastran and Hypersizer. The results of both analyses were scaled to determine the predicted failure load. The test results were compared to both the Nastran and Hypersizer analytical predictions. The actual failure occurred at 899 lbs. The failure was predicted at 1167 lbs based on the Nastran analysis. The Hypersizer analysis predicted a lower failure load of 960 lbs. The Nastran analysis alone was not sufficient to predict the failure load because it does not identify local composite failure modes. This analysis has traditionally been done using closed form solutions. Although Hypersizer is typically used as an optimizer for the design process, the failure prediction was used to help gain acceptance and confidence in this new tool. The correlated models and process were to be used to analyze the full BWB-LSV airframe design. The analysis and correlation with test results of the proof of concept box is presented here, including the comparison of the Nastran and Hypersizer results.

Spellman, Regina L.↗

CHP-PRA Proof-of-Concept [Simulation] Sensitivity Assessment

An effort is underway to establish a Crew Health and Performance system (CHP) tradespace tool using a Probabilistic Risk Assessment (PRA) modeling and simulation system. The goal of the CHP-PRA effort is to provide a means of quantifying the integrated influence of CHP functions and capabilities on risk outcome metrics associated with health, performance, and long-term health. These metrics can then be used to establish potential risk-based trades on CHP system designed functionality and capabilities. Previously, our team demonstrated a proof-of-concept PRA approach that estimated the integrated influence of exercise countermeasures on 8 human system risks (Figure 1a) with outcomes associated with health and medical risk metrics. We reported that the change in the integrated relative health risk was small (Figure 1b) and that the small change in overall risk resulted from compounding and competing contribution levels of the individual risks. This interesting observation illustrates the emergent complexity of even straightforward representations of the human health and performance risk space and the ability of PRA models to capture this balance of global risk concerns. A key question that is not addressed in the initial analysis is “even though the global risk is relatively nominal, do any of the local risks become unacceptable?” In essence, we seek to determine what relative change in the human system risks are contributing to the relatively muted sensitivity of the proof-of-concept model combined risk assessments. Evaluations at the component risk level should elucidate if any individual risk reaches a high level that is subsequentially balanced by reductions in other areas. To further understand the relative changes in the component risks in the proof-of-concept model, and to elucidate how future refinements can be targeted, a means of establishing the contributions of the robustness of the proof-of-concept approach will be demonstrated.

astronaut health↗

A general proof of the quantum null energy condition

We prove a conjectured lower bound on ⟨T_ _(x)⟩ $ψ$ in any state $ψ$ of a CFT on Minkowski space, dubbed the Quantum Null Energy Condition (QNEC). The bound is given by the second order shape deformation, in the null direction, of the geometric entanglement entropy of an entangling cut passing through $x$. Our proof involves a combination of the two independent methods that were used recently to prove the weaker Averaged Null Energy Condition (ANEC). In particular the properties of modular Hamiltonians under shape deformations for the state ψ play an important role, as do causality considerations. We study the two point function of a “probe” operator $\mathcal{O}$ in the state $ψ$ and use a lightcone limit to evaluate this correlator. Instead of causality in time we consider causality on modular time for the modular evolved probe operators, which we constrain using Tomita-Takesaki theory as well as certain generalizations pertaining to the theory of modular inclusions. The QNEC follows from very similar considerations to the derivation of the chaos bound and the causality sum rule. We use a kind of defect Operator Product Expansion to apply the replica trick to these modular flow computations, and the displacement operator plays an important role. We argue that the proof extends to more general relativistic QFT with an interacting UV fixed point and also prove a higher spin version of the QNEC. Our approach was inspired by the AdS/CFT proof of the QNEC which follows from properties of the Ryu-Takayanagi (RT) surface near the boundary of AdS, combined with the requirement of entanglement wedge nesting. Our methods were, as such, designed as a precise probe of the RT surface close to the boundary of a putative gravitational/stringy dual of any QFT with an interacting UV fixed point.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A New Proof That the Number of Linear Elastic Symmetries in Two Dimensions Is Four

In this work, we present an elementary and self-contained proof that there are exactly four symmetry classes of the elasticity tensor in two dimensions: oblique, rectangular, square, and isotropic. In two dimensions, orthogonal transformations are either reflections or rotations. The proof is based on identification of constraints imposed by reflections and rotations on the elasticity tensor, and it simply employs elementary tools from trigonometry, making the proof accessible to a broad audience. For completeness, we identify the sets of transformations (rotations and reflections) for each symmetry class and report the corresponding equations of motions in classical linear elasticity.

42 ENGINEERING↗

Introducing a risk aggregation rationale for mapping risks to aquifers from point- and diffuse-sources–proof-of-concept using contamination data from industrial lagoons

Highlights: • Aquifer risk mapping is introduced for contaminants acting as point/diffuse-sources. • Innovations are framed by risk cells based on Source-Pathway-Receptor-Source (SPRC). • Point-source (Risk Cell 1) and diffuse-source (Risk Cell 2) use sets of algorithms. • Algorithms include MODPATH, DRASTIC, GWPI and are integrated on a modular basis. • Risk Cells 1/2 are aggregated giving fit-for-purpose results as proof-of-concept. - Abstract: Proof-of-concept for a methodology is presented on mapping risks to aquifers impacted from point- and diffuse-sources, where mapping or indexing refers to relative but not absolute values. The methodology is generic but tested by investigating impacts of a risk exposure from industrial wastewater lagoons. The methodology is innovative for using the qualitative Source-Pathways-Receptors-Consequences (SPRC) framework to aggregate risks from both point-sources and diffuse-sources through breaking down a study area into SPRC risk cells. In this paper, two risk cells are required as: (i) Cell 1 is directly impacted from a point-source; and (ii) Cell 2 is impacted by diffuse-sources to slowly contaminate the aquifer by infiltration over a large area. Indexing both types of risk cells generically comprise three tiered processes: (i) binary indexing establishes if a grid cell is at a potential risk or not; (ii) graded indexing measures the strength of the risk pathways from source to receptors; and (iii) local indexing measures intrinsic potentials at the grid cell to propagate the risk. These three processes apply to both point- and diffuse-sources but with different mathematical formulations. The proof-of-concept for the methodology of risk aggregation using the SPRC framework is supported by results of a study area, in which a set of performance metrics are used by comparing with the measurements. The results are found to be fit-for-purpose for serving as proactive management tools and to provide a deeper insight into potential impacts of adverse effects.

54 ENVIRONMENTAL SCIENCES↗

Optimum structural design based on reliability and proof-load testing

Proof-load test eliminates structures with strength less than the proof load and improves the reliability value in analysis. It truncates the distribution function of strength at the proof load, thereby alleviating verification of a fitted distribution function at the lower tail portion where data are usually nonexistent.

Shinozuka, M.↗

Proof test criteria for thin-walled 2219 aluminum pressure vessels. Volume 1: Program summary and data analysis

This experimental program was undertaken to investigate the crack growth behavior of deep surface flaws in 2219 aluminum. The program included tests of uniaxially loaded surface flaw and center crack panels at temperatures ranging from 20K (-423 F) to ambient. The tests were conducted on both the base metal and as-welded weld metal material. The program was designed to provide data on the mechanisms of failure by ligament penetration, and the residual cyclic life, after proof-testing, of a vessel which has been subjected to incipient penetration by the proof test. The results were compared and analyzed with previously developed data to develop guidelines for the proof testing of thin walled 2219 pressure vessels.

Finger, R. W.↗

Definition of mutually optimum NDI and proof test criteria for 2219 aluminum pressure vessels. Volume 1: Methods

The requirements for proof testing and nondestructive inspection of aluminum pressure vessels were discussed. The following conclusions are (1) lack-of-fusion weld defects are sufficiently tight in the as-welded condition to be considered undetectable; (2) proof-level loads are required to fully open lack-of-fusion weld defects; (3) significant crack opening occurs at subproof levels so that an inspection enhancement loading treatment designed to avoid catastrophic failure is feasible; (4) currently used proof levels for 2219 pressure vessels are adequate for postproof inspection; (5) quantification of defect size and location using collimated ultrasonic pitch-catch techniques appears sufficiently feasible for tankage to warrant developmental work; (6) for short-time single-cycle pressure-vessel applications, postproof inspection is desirable; and (7) for long-term multiple-cycle pressure-vessel applications, postproof inspection is essential for life assurance.

Schwartzberg, F. R.↗

Summary of theoretical considerations and wind tunnel tests of an aerodynamic spoiler for stall proofing a general aviation airplane

An airplane stall proofing system utilizing a spoiler was investigated for application on a low wing airplane representative of typical general aviation aircraft. Tests of the full scale airplane were conducted in the NASA Langley 30 x 60 foot full scale wind tunnel. The test velocity was 86 feet per second, corresponding to a Reynolds number of 2.20 million. The stall proofing capability of the spoiler is shown and a theoretical approach to the design of the spoiler and analysis of the spoiler's contribution to the airplane's trim and longitudinal stability is verified. Controlled spoiler deployment in a narrow angle of attack range, 4 degrees, immediately preceding the stall angle will stall proof the airplane. The results also show some of the limitations of flight tests to determine spoiler deployment rate for good handling qualities.

Chevalier, H. L.↗

The Proof of the SIFT Implementation

The Software Implemented Fault Tolerance SIFT specifications consist primarily of constraints on the schedule table and descriptions of the changes each routine makes to the global variables. The proof proceeds by proving that each routine is consistent with its specification. Each of these proofs is separate from the others and the order of the proofs is unimportant. A routine is proved by generating a set of verification conditions from the PASCAL code and the SPECIAL specifications. Each verification condition is a set of assertions derived from a particular path in the routine. A verification condition (VC) is generated for each possible path through the routine.

Source record↗

A comparison of single-cycle versus multiple-cycle proof testing strategies

An evaluation of single-cycle and multiple-cycle proof testing (MCPT) strategies for SSME components is described. Data for initial sizes and shapes of actual SSME hardware defects are analyzed statistically. Closed-form estimates of the J-integral for surface flaws are derived with a modified reference stress method. The results of load- and displacement-controlled stable crack growth tests on thin IN-718 plates with deep surface flaws are summarized. A J-resistance curve for the surface-cracked configuration is developed and compared with data from thick compact tension specimens. The potential for further crack growth during large unload/reload cycles is discussed, highlighting conflicting data in the literature. A simple model for ductile crack growth during MCPT based on the J-resistance curve is used to study the potential effects of key variables. The projected changes in the crack size distribution during MCPT depend on the interactions between several key parameters, including the number of proof cycles, the nature of the resistance curve, the initial crack size distribution, the component boundary conditions (load vs. displacement control), and the magnitude of the applied load or displacement. The relative advantages of single-cycle and multiple-cycle proof testing appear to be specific, therefore, to individual component geometry, material, and loading.

Hudak, S. J., Jr.↗

The design and proof of correctness of a fault-tolerant circuit

The flowing achievements are presented in view graph form: (1) a formal statement of interactive consistency conditions in the Boyer-Moore logic; (2) a formal statement of the oral messages (OM) algorithm in the Boyer-Moore logic; (3) a mechanically checked proof that OM satisfies the interactive consistency conditions; (4) a mechanically checked proof of the optimality result--no algorithm can tolerate fewer faults than OM yet still achieve interactive consistency; (5) the use of OM in a functional specification for a fault-tolerant device; (6) a formal description of the design of the device; (7) a mechanically checked proof that the device design satisfies the specification; and (8) an implementation of the design in programmable logic arrays.

Bevier, William R.↗

Formal proof of the AVM-1 microprocessor using the concept of generic interpreters

A microprocessor designated AVM-1 was designed to demonstrate the use of generic interpreters in verifying hierarchically decomposed microprocessor specifications. This report is intended to document the high-order language (HOL) code verifying AVM-1. The organization of the proof is discussed and some technical details concerning the execution of the proof scripts in HOL are presented. The proof scripts used to verify AVM-1 are also presented.

Windley, P.↗

Putting time into proof outlines

A logic for reasoning about timing properties of concurrent programs is presented. The logic is based on Hoare-style proof outlines and can handle maximal parallelism as well as certain resource-constrained execution environments. The correctness proof for a mutual exclusion protocol that uses execution timings in a subtle way illustrates the logic in action. A soundness proof using structural operational semantics is outlined in the appendix.

Schneider, Fred B.↗

Design and Control of a Proof-of-Concept Active Jet Engine Intake Using Shape Memory Alloy Actuators

The design and control of a novel proof-of-concept active jet engine intake using Nickel-Titanium (Ni-Ti or Nitinol) shape memory alloy (SMA) wire actuators is used to demonstrate the potential of an adaptive intake to improve the fuel efficiency of a jet engine. The Nitinol SMA material is selected for this research due to the material's ability to generate large strains of up to 5 percent for repeated operations, a high power-to-weight ratio, electrical resistive actuation, and easy fabrication into a variety of shapes. The proof-of-concept engine intake employs an overlapping leaf design arranged in a concentric configuration. Each leaf is mounted on a supporting bar that rotates upon actuation by SMA wires electrical resistive heating. Feedback control is enabled through the use of a laser range sensor to detect the movement of a leaf and determine the radius of the intake area. Due to the hysteresis behavior inherent in SMAs, a nonlinear robust controller is used to direct the SMA wire actuation. The controller design utilizes the sliding-mode approach to compensate for the nonlinearities associated with the SMA actuator. Feedback control experiments conducted on a fabricated proof-of-concept model have demonstrated the capability to precisely control the intake area and achieve up to a 25 percent reduction in intake area. The experiments demonstrate the feasibility of engine intake area control using the proposed design.

Song, Gangbing↗

Batch Proving and Proof Scripting in PVS

The batch execution modes of PVS are powerful, but highly technical, features of the system that are mostly accessible to expert users. This paper presents a PVS tool, called ProofLite, that extends the theorem prover interface with a batch proving utility and a proof scripting notation. ProofLite enables a semi-literate proving style where specification and proof scripts reside in the same file. The goal of ProofLite is to provide batch proving and proof scripting capabilities to regular, non-expert, users of PVS.

Munoz, Cesar A.↗

Analysis of Potential for Titanium Liner Buckling after Proof in a Large Kevlar/Epoxy COPV

We analyze the potential for liner buckling in a 40-in Kevlar49/epoxy overwrapped spherical pressure vessel (COPV) due to long, local depressions or valleys in the titanium liner, which appeared after proof testing (autofrettage). We begin by presenting the geometric characteristics of approximately 20 mil (0.02 in.) deep depressions measured by laser profilometry in several vessels. While such depths were more typical, depths of more than 40 mils (0.02 in.) were seen near the equator in one particular vessel. Such depressions are largely the result of overlap of the edges of overwrap bands (with rectangular cross-section prepreg tows) from the first or second wrap patterns particularly where they start and end. We then discuss the physical mechanisms of formation of the depressions during the autofrettage process in terms of uneven void compaction in the overwrap around the tow overlap lines and the resulting 10-fold increase in through-thickness stiffness of the overwrap. We consider the effects of liner plastic yielding mechanisms in the liner on residual bending moments and interface pressures with the overwrap both at the peak proof pressure (approx.6500 psi) and when reducing the pressure to 0 psi. During depressurization the Bauschinger phenomenon becomes very important whereby extensive yielding in tension reduces the magnitude of the yield threshold in compression by 30 to 40%, compared to the virgin annealed state of the liner titanium. In the absence of a depression, the liner is elastically stable in compression even at liner overwrap interface pressures nominally 6 times the approx. 1000 psi interface pressure that exists at 0 psi. Using a model based on a plate-on-an-elastic-foundation, we develop an extensive analysis of the possible destabilizing effects of a frozen-in valley. The analysis treats the modifying effects of the residual bending moments and interface pressures remaining after the proof hold as well as the Bauschinger effect on the compressive yield threshold. The key result is that depression depths of up to 40 mils can be tolerated, but above 40 mils, the Bauschinger effect drives destabilization, and buckling becomes increasingly likely depending on the details of depression formation during autofrettage. It is almost certain that destabilization and buckling will occur for depression depths beyond 55 mils. The main equations and formulas for treating the various phases of depression development and potential buckling, are only briefly outlined in the paper, but are available from the authors.

Phoenix, S. Leigh↗