scholarly journals A Christoffel function weighted least squares algorithm for collocation approximations

2016 ◽  
Vol 86 (306) ◽  
pp. 1913-1947 ◽  
Author(s):  
Akil Narayan ◽  
John D. Jakeman ◽  
Tao Zhou
Keyword(s):  
Least Squares ◽  
Weighted Least Squares ◽  
Christoffel Function ◽  
Least Squares Algorithm

An iterative re-weighted least-squares algorithm for the design of active absorbing wavemaker controller

2016 ◽  
Vol 28 (2) ◽  
pp. 206-218 ◽  
Author(s):  
Hong-qi Yang ◽  
Mu-guo Li ◽  
Shu-xue Liu ◽  
Fang-mei Chen
Keyword(s):  
Least Squares ◽  
Weighted Least Squares ◽  
Least Squares Algorithm

Interpretation of Weighted-Least-Squares Gas Path Analysis Results

2003 ◽  
Vol 125 (3) ◽  
pp. 624-633 ◽  
Author(s):  
D. L. Doel
Keyword(s):  
Path Analysis ◽  
Least Squares ◽  
Measurement Problem ◽  
Weighted Least Squares ◽  
Root Cause ◽  
Problem Situations ◽  
Fuel Flow ◽  
Least Squares Algorithm ◽  
Program Output ◽  
Sensor Errors

Gas turbine performance analysis programs convert raw measurements (thrust, fuel flow, gas path temperatures, and pressures) into engine and component figures of merit (e.g., specific fuel consumption, component efficiencies). The derived parameters allow a diagnostician to recognize a poorly performing engine and help to identify the root cause for the problem. These goals can be foiled by measurement problems or by analysis assumptions embedded in the programs. A gifted analyst learns to recognize measurement or assumption problems via characteristic “fingerprints” in the program output. The latest data analysis tools tackle the same issues using a weighted-least-squares algorithm which estimates sensor errors at the same time component health is being determined. The weighted-least-squares algorithm modifies the “fingerprint” of a measurement problem and also that of a problem-free solution. To develop intuition for these new programs, the analyst must understand how weighted-least-squares works and how normal and problem situations are reflected in the output. This paper describes the weighted-least-squares algorithm, as implemented in GE’s TEMPER program, with the goal of stimulating a new intuition for interpreting gas path analysis results.

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