Estimation of the Mathematical Parameters of Double-Exponential Pulses Using the Nelder–Mead Algorithm

Magdowski, Mathias; Vick, Ralf

doi:10.1109/temc.2010.2052621

Cited by 20 publications

(6 citation statements)

References 3 publications

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“…Magdowski and Vick have studied this problem; they improved the method of how to directly find the t r -t FWHM from α and β. The equation fits well to all of our ranges [19]. Therefore in this paper, we will use the Magdowski method.…”

Section: The Emp Waveformmentioning

confidence: 90%

A PCB Noise Analysis Regarding Emp Penetration Using an Electromagnetic Topology Method

Han¹,

Bang²,

Huh³

et al. 2012

PIER

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Abstract-The usability of the EMT (Electromagnetic Topology) method is discussed and verified in this paper. The EMT results are compared to the results from a 3D fullwave electromagnetic solver. The electromagnetic wave shows a very fast rise time in the EMP (Electromagnetic Pulse) signal; the SUT (System Under Test) is a simple PCB strip line model. The resistances of the loads attached to each side of the strip line were 1 MΩ and 50 Ω. We then obtained the noise voltages occurring in each load when being penetrated by an EMP. We also discuss the frequency sweeps used to obtain the resonant frequencies of the model. The results agree well with those from the CST Microwave Studio. The EMT method would be more accurate if the dielectric tangent loss and copper loss are considered.

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Section: The Emp Waveformmentioning

confidence: 90%

A PCB Noise Analysis Regarding Emp Penetration Using an Electromagnetic Topology Method

Han¹,

Bang²,

Huh³

et al. 2012

PIER

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show abstract

“…Additionally the NM method thrives in more complex terrain of the objective function due to its capacity to rapidly adjust its shape, size and orientation based on local contours 79 . While it has faced some criticism from mathematicians due to its inability for convergence to be proven 80 , it has stood the test of time with engineers for its many examples of successful optimization, particularly in parameter estimation 81 , 82 .…”

Section: Methodsmentioning

confidence: 99%

Modelling the performance of an integrated fixed-film activated sludge (IFAS) system: a systematic approach to automated calibration

Pryce

Kapelan

Memon

2022

Sci Rep

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IFAS systems are inherently complex due to the hybrid use of both suspended and attached bacterial colonies for the purpose of pollutant degradation as part of wastewater treatment. This poses challenges when attempting to represent these systems mathematically due to the vast number of parameters involved. Besides becoming convoluted, large effort will be incurred during model calibration. This paper demonstrates a systematic approach to calibration of an IFAS process model that incorporates two sensitivity analyses to identify influential parameters and detect collinearity from a subset of 68 kinetic and stoichiometric parameters, and the use of the Nelder–Mead optimization algorithm to estimate the required values of these parameters. The model considers the removal of three critical pollutants including biochemical oxygen demand (BOD), total nitrogen (TN) and total suspended solids (TSS). Results from the sensitivity analyses identified four parameters that were the primary influence on the model. The model was found to be most sensitive to the two stoichiometric parameters including aerobic heterotrophic yield on soluble substrate whose total effects were responsible for 92.4% of the model’s BOD output sensitivity and 92.8% of the model’s TSS output sensitivity. The anoxic heterotrophic yield on soluble substrate was observed to be responsible for 54.3% of the model’s TN output sensitivity. To a lesser extent the two kinetic parameters, aerobic heterotrophic decay rate and reduction factor for denitrification on nitrite, were responsible for only 8.0% and 13.1% of the model’s BOD and TN output sensitivities respectively. Parameter estimation identified the need for only minor adjustments to default values in order to achieve sufficient accuracy of simulation with deviation from observed data to be only ± 3.6 mg/L, ± 1.3 mg/L, and ± 9.5 mg/L for BOD, TN and TSS respectively. Validation showed the model was limited in its capacity to predict system behaviour under extreme dissolved oxygen stress.

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“…However, the tumor-growth, metastasis, and detection models can be estimated separately, once multiple data points for tumor size and disease stage are available. Another method is to derive the least-squares function: , where is the simulated joint distribution of tumor size and stage and is the observed joint distribution, based on these parameters, and apply the Nelder-Mead method [18] , [19] , [20] to achieve the best fitted parameters in the model. We used the second approach because we did not have the multiple tumor-size measurements for individuals to estimate the models separately.…”

Section: Methodsmentioning

confidence: 99%

Modeling the Natural History and Detection of Lung Cancer Based on Smoking Behavior

et al. 2014

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In this study, we developed a method for modeling the progression and detection of lung cancer based on the smoking behavior at an individual level. The model allows obtaining the characteristics of lung cancer in a population at the time of diagnosis. Lung cancer data from Surveillance, Epidemiology and End Results (SEER) database collected between 2004 and 2008 were used to fit the lung cancer progression and detection model. The fitted model combined with a smoking based carcinogenesis model was used to predict the distribution of age, gender, tumor size, disease stage and smoking status at diagnosis and the results were validated against independent data from the SEER database collected from 1988 to 1999. The model accurately predicted the gender distribution and median age of LC patients of diagnosis, and reasonably predicted the joint tumor size and disease stage distribution.

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Estimation of the Mathematical Parameters of Double-Exponential Pulses Using the Nelder–Mead Algorithm

Cited by 20 publications

References 3 publications

A PCB Noise Analysis Regarding Emp Penetration Using an Electromagnetic Topology Method

A PCB Noise Analysis Regarding Emp Penetration Using an Electromagnetic Topology Method

Modelling the performance of an integrated fixed-film activated sludge (IFAS) system: a systematic approach to automated calibration

Modeling the Natural History and Detection of Lung Cancer Based on Smoking Behavior

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