Influence of Random Variable Dimension on the Fast Numerical Integration Method of Aero Engine Rotor Disk Failure Risk Analysis

2020 ◽  
Author(s):  
Liu Junbo ◽  
Ding Shuiting ◽  
Li Guo
Keyword(s):  
Numerical Integration ◽  
Random Variable ◽  
Turbine Rotor ◽  
Large Sample Size ◽  
Security Design ◽  
Time Cost ◽  
Variable Dimension ◽  
Rotor Disk ◽  
Multiple Variables ◽  
Selection Of

Abstract In the risk assessment of turbine rotor disks, the probability of failure of a certain disk type (after N flight cycles) is a vital criterion for estimating whether the disk is safe to use. Monte Carlo simulation (MCS) is often used to calculate the failure probability but is costly because it requires a large sample size. The numerical integration (NI) algorithm has been proven more efficient than MCS in conditions entailing three random variables. However, the previous studies on the NI method have not dealt with the influence of random variable dimension on calculation efficiency. Hence, this study aims to summarize the influence of variable dimensions on the time cost of a fastintegration algorithm. The time cost increases exponentially with the number of variables in the NI method. This conclusion provides a reference for the selection of probability algorithms involving multiple variables. The findings are expected to be of interest to the practice of efficient security design that considers multivariable conditions.

Numerical integration by systematic sampling

1950 ◽  
Vol 46 (1) ◽  
pp. 111-115 ◽  
Author(s):  
P. A. P. Moran
Keyword(s):  
Numerical Integration ◽  
Bounded Variation ◽  
Mathematical Problem ◽  
Random Variable ◽  
Mean Value ◽  
Lattice Points ◽  
Systematic Sampling ◽  
Image Position ◽  
Infinite Sum

Recent investigations by F. Yates (1) in agricultural statistics suggest a mathematical problem which may be formulated as follows. A function f(x) is known to be of bounded variation and Lebesgue integrable on the range −∞ < x < ∞, and its integral over this range is to be determined. In default of any knowledge of the position of the non-negligible values of the function the best that can be done is to calculate the infinite sumfor some suitable δ and an arbitrary origin t, where s ranges over all possible positive and negative integers including zero. S is evidently of period δ in t and ranges over all its values as t varies from 0 to δ. Previous writers (Aitken (2), p. 45, and Kendall (3)) have examined the resulting errors for fixed t. (They considered only symmetrical functions, and supposed one of the lattice points to be located at the centre.) Here we do not restrict ourselves to symmetrical functions and consider the likely departure of S(t) from J (the required integral) when t is a random variable uniformly distributed in (0, δ). It will be shown that S(t) is distributed about J as mean value, with a variance which will be evaluated as a function of δ, the scale of subdivision.

Assessing the Difficulty and Time Cost of De-identification in Clinical Narratives

2006 ◽  
Vol 45 (03) ◽  
pp. 246-252 ◽  
Author(s):  
W. F. Phillips ◽  
S. Phansalkar ◽  
S. A. Sims ◽  
J. F. Hurdle ◽  
D. A. Dorr
Keyword(s):  
Regular Expression ◽  
Free Text ◽  
Time Cost ◽  
Clinical Notes ◽  
The Us ◽  
Important Challenge ◽  
Automated Technique ◽  
Manual Review ◽  
Simple Search ◽  
Selection Of

Summary Objective: To characterize the difficulty confronting investigators in removing protected health information (PHI) from cross-discipline, free-text clinical notes, an important challenge to clinical informatics research as recalibrated by the introduction of the US Health Insurance Portability and Accountability Act (HIPAA) and similar regulations. Methods: Randomized selection of clinical narratives from complete admissions written by diverse providers, reviewed using a two-tiered rater system and simple automated regular expression tools. For manual review, two independent reviewers used simple search and replace algorithms and visual scanning to find PHI as defined by HIPAA, followed by an independent second review to detect any missed PHI. Simple automated review was also performed for the “easy” PHI that are number- or date-based. Results: From 262 notes, 2074 PHI, or 7.9 ± 6.1 per note, were found. The average recall (or sensitivity) was 95.9% while precision was 99.6% for single reviewers. Agreement between individual reviewers was strong (ICC = 0.99), although some asymmetry in errors was seen between reviewers (p = 0.001). The automated technique had better recall (98.5%) but worse precision (88.4%) for its subset of identifiers. Manually de-identifying a note took 87.3 ± 61 seconds on average. Conclusions: Manual de-identification of free-text notes is tedious and time-consuming, but even simple PHI is difficult to automatically identify with the exactitude required under HIPAA.

scholarly journals The use of modern plastics for the construction of high speed fluid-flow machinery

Mechanik ◽  
2018 ◽  
Vol 91 (7) ◽  
pp. 508-510
Author(s):  
Grzegorz Żywica ◽  
Tomasz Z. Kaczmarczyk ◽  
Eugeniusz Ihnatowicz
Keyword(s):  
Fluid Flow ◽  
High Speed ◽  
Material Selection ◽  
Metallic Alloys ◽  
Strength Analysis ◽  
Production Time ◽  
Rotor Disk ◽  
Selection Of

Discussed are issues related to the selection of plastics for manufacturing chosen components of high-speed fluid-flow machinery. In addition to discussing the criteria used for material selection, an exemplary strength analysis of a rotor disk made of plastic was presented. The work carried out was aimed at replacing commonly used metallic alloys with modern plastics, which in turn may shorten production time and reduce costs.

Testing and Acceptance of Semi-Machined Turbine Rotor Forging Elements

2021 ◽  
Author(s):  
Steve Ingistov ◽  
Douglas Nagy
Keyword(s):  
Elevated Temperatures ◽  
Turbine Rotor ◽  
Third Party ◽  
Test Material ◽  
Acceptance Testing ◽  
Critical Elements ◽  
Reverse Engineer ◽  
Compressive Stresses ◽  
High Integrity ◽  
Selection Of

Abstract Turbine wheels are critical elements and the integrity of their forgings is extremely important. The procurement of wheel forgings utilized oversized outside diameters in order to provide ample amount of material from which test material was cut out. Test specimens were produced in accordance with relevant ASTM standards. Test specimens were divided into three groups; tension, impact and hardness / metallography. Tension and impact tests at sub-zero, room and elevated temperatures were conducted in presence of owner’s inspectors at an independent certified laboratory. Once all specimens passed the tests, the semi-machined forgings were released to the machining facility. Machined forgings were then sent for over-speed tests at sub-zero and elevated temperatures. Over-speed testing under sub-zero temperature was the ultimate test of the forgings. Over-speed testing of the forgings under elevated temperatures served to minimize residual tensile stresses at the bore of the wheel and convert them to beneficial compressive stresses. The above described tests of turbine Elements forging are critical when the owner selects third party producers to reverse engineer and manufacture these elements. This paper details the selection of the tests, the execution of the owner’s acceptance testing program, especially the over-speed tests, and how this helps to ensure the high integrity of critical rotating elements for a mid-size heavy industrial frame gas turbine.

scholarly journals Selection of the rotor heat-up rate for supercritical parameter turbines

2013 ◽  
Vol 34 (3) ◽  
pp. 89-104
Author(s):  
Andrzej Rusin ◽  
Marian Lipka ◽  
Henryk Łukowicz
Keyword(s):  
Optimal Design ◽  
Turbine Rotor ◽  
Design Solution ◽  
Supercritical Steam Parameters ◽  
Start Up ◽  
Supercritical Parameter ◽  
Design Calculations ◽  
Steam Parameters ◽  
Start Ups ◽  
Selection Of

Abstract The paper presents the results of the numerical analyses for the steam turbine rotor, dedicated for the newly-designed 900 MW steam unit with supercritical steam parameters (650 °C, 30.0 MPa). Basing on the design calculations, an optimal design solution was determined. Review of the available literature on materials for turbine rotors with supercritical steam parameters was done. Then the start-ups of the turbine were simulated. Thermal and strength states were analyzed. As a result, an optimal start-up characteristic was obtained.

Probabilistic Analysis of Turbine Disc SCC Incubation and Propagation

2002 ◽  
Author(s):  
Tony C. T. Lam ◽  
Robert Dewey
Keyword(s):  
Growth Rate ◽  
Incubation Time ◽  
Chromium Content ◽  
Probabilistic Approach ◽  
Turbine Rotor ◽  
Time Data ◽  
Weld Repair ◽  
Low Pressure Turbine ◽  
Turbine Disc ◽  
Rotor Disk

Stress corrosion cracking (SCC) is a common problem found on aging low-pressure turbine (LP) rotors that operate in a wet/dry stream environment. While much has been published on the growth rate of SCC in turbine rotor-disk materials, incubation time is rarely addressed. Since no effective way has been demonstrated to prevent disk rim SCC from occurring other than to replace the damaged rim with a weld repair of higher chromium content, a better understanding of incubation time could provide operators with a means to treat SCC before cracks are large enough to start to grow. This paper discusses the critical mechanisms involved in the SCC incubation, process and describes a probabilistic approach to make meaningful assessments of incubation time. Data published for General Electric turbine rotors is used to test the model.

A Computer Analysis of Wind Turbine Blade Dynamic Loads

1986 ◽  
Vol 108 (1) ◽  
pp. 17-25 ◽  
Author(s):  
R. W. Thresher ◽  
A. D. Wright ◽  
E. L. Hershberg
Keyword(s):  
Wind Turbine ◽  
Equations Of Motion ◽  
Computer Code ◽  
Turbine Rotor ◽  
Flapping Motion ◽  
Turbine Rotor Blade ◽  
Loads Analysis ◽  
Rotor Disk ◽  
Equidistant Points ◽  
Blade Loads

The flapping motion of a single wind turbine rotor blade has been analyzed and equations describing the flapping motion have been developed. The analysis was constrained to allow only flapping motions for a cantilevered blade, and the equations of motion are linearized. A computer code, called FLAP (Force and Loads Analysis Program), to solve the equations of motion and compute the blade loads, has been completed and compared to measured loads for a 3-bladed downwind turbine with stiff blades. The results of the program are presented in tabulated form for equidistant points along the blade and equal azimuth angles around the rotor disk. The blade deflection, slope and velocity, flapwise shear and moment, edgewise shear and moment, blade tension, and blade torsion are given. The deterministic excitations considered in the analysis include wind shear, tower shadow, gravity, and a prescribed yaw motion.

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