Validation of a Mathematical Model for Road Cycling Power

1998 ◽  
Vol 14 (3) ◽  
pp. 276-291 ◽  
Author(s):  
James C. Martin ◽  
Douglas L. Milliken ◽  
John E. Cobb ◽  
Kevin L. McFadden ◽  
Andrew R. Coggan
Keyword(s):  
Mathematical Model ◽  
Measurement System ◽  
Standard Error ◽  
Power Measurement ◽  
Model Parameters ◽  
Model Parameter ◽  
Road Cycling ◽  
Highly Correlated ◽  
Parameter Values ◽  
Measured Power

This investigation sought to determine if cycling power could be accurately modeled. A mathematical model of cycling power was derived, and values for each model parameter were determined. A bicycle-mounted power measurement system was validated by comparison with a laboratory ergometer. Power was measured during road cycling, and the measured values were compared with the values predicted by the model. The measured values for power were highly correlated (R2= .97) with, and were not different than, the modeled values. The standard error between the modeled and measured power (2.7 W) was very small. The model was also used to estimate the effects of changes in several model parameters on cycling velocity. Over the range of parameter values evaluated, velocity varied linearly (R2> .99). The results demonstrated that cycling power can be accurately predicted by a mathematical model.

scholarly journals Spatial and Temporal Transferability of a Distributed Energy-Balance Glacier Melt Model

2011 ◽  
Vol 24 (5) ◽  
pp. 1480-1498 ◽  
Author(s):  
Andrew H. MacDougall ◽  
Gwenn E. Flowers
Keyword(s):  
Energy Balance ◽  
Yukon Territory ◽  
Model Parameters ◽  
Distributed Energy ◽  
Meteorological Forcing ◽  
Model Parameter ◽  
Model Transferability ◽  
Space And Time ◽  
Surface Ablation ◽  
Parameter Values

Abstract Modeling melt from glaciers is crucial to assessing regional hydrology and eustatic sea level rise. The transferability of such models in space and time has been widely assumed but rarely tested. To investigate melt model transferability, a distributed energy-balance melt model (DEBM) is applied to two small glaciers of opposing aspects that are 10 km apart in the Donjek Range of the St. Elias Mountains, Yukon Territory, Canada. An analysis is conducted in four stages to assess the transferability of the DEBM in space and time: 1) locally derived model parameter values and meteorological forcing variables are used to assess model skill; 2) model parameter values are transferred between glacier sites and between years of study; 3) measured meteorological forcing variables are transferred between glaciers using locally derived parameter values; 4) both model parameter values and measured meteorological forcing variables are transferred from one glacier site to the other, treating the second glacier site as an extension of the first. The model parameters are transferable in time to within a <10% uncertainty in the calculated surface ablation over most or all of a melt season. Transferring model parameters or meteorological forcing variables in space creates large errors in modeled ablation. If select quantities (ice albedo, initial snow depth, and summer snowfall) are retained at their locally measured values, model transferability can be improved to achieve ≤15% uncertainty in the calculated surface ablation.

Model Parameter Identification and Simulation of Ship Power System Based on Recursive Least Squares Method

2012 ◽  
Vol 220-223 ◽  
pp. 482-486 ◽  
Author(s):  
Jin Hui Hu ◽  
Da Bin Hu ◽  
Jian Bo Xiao
Keyword(s):  
Mathematical Model ◽  
Power Systems ◽  
Parameter Identification ◽  
Least Squares ◽  
Least Squares Method ◽  
Recursive Least Squares ◽  
Design Parameters ◽  
Model Parameters ◽  
Model Parameter ◽  
Model Parameter Identification

According to the lack of the part of the equipment design parameters of a certain type of ship power systems, the algorithm of recursive least squares for model parameter identification is studied. The mathematical model of the propulsion motor is established. The model parameters are calculated and simulated based on parameter identification method of recursive least squares. The simulation results show that a more precise mathematical model can be simple and easily obtained by using of the method.

scholarly journals Mathematical Multiobjective Optimization for Metal Hip Arthroplasty with Medical Physics Applications

2021 ◽  
Keyword(s):  
Experimental Testing ◽  
Medical Physics ◽  
Optimization Methods ◽  
Model Parameters ◽  
Model Parameter ◽  
Erosion Prediction ◽  
Model Match ◽  
Acceptable Model ◽  
Parameter Values

Total hip metal arthroplasty (THA) model-parameters for a group of commonly used ones is optimized and numerically studied. Based on previous ceramic THA optimization software contributions, an improved multiobjective programming method/algorithm is implemented in wear modeling for THA. This computational nonlinear multifunctional optimization is performed with a number of THA metals with different hardnesses and erosion in vitro experimental rates. The new software was created/designed with two types of Sytems, Matlab and GNU Octave. Numerical results show be improved/acceptable for in vitro simulations. These findings are verified with 2D Graphical Optimization and 3D Interior Optimization methods, giving low residual-norms. The solutions for the model match mostly the literature in vitro standards for experimental simulations. Numerical figures for multifunctional optimization give acceptable model-parameter values with low residual-norms. Useful mathematical consequences/calculations are obtained for wear predictions, model advancements and simulation methodology. The wear magnitude for in vitro determinations with these model parameter data constitutes the advance of the method. In consequence, the erosion prediction for laboratory experimental testing in THA add up to the literature an efficacious usage-improvement. Results, additionally, are extrapolated to efficient Medical Physics applications and metal-THA Bioengineering designs.

Correlation Between In Silico Physicochemical Characteristics of Drugs and Their Mean Residence Time in Human and Dog

2012 ◽  
Vol 31 (1) ◽  
pp. 25-33 ◽  
Author(s):  
Tomasz Grabowski ◽  
Jerzy Jan Jaroszewski ◽  
Shayne Cox Gad ◽  
Marcin Feder
Keyword(s):  
Mathematical Model ◽  
Residence Time ◽  
Mean Residence Time ◽  
Physicochemical Parameters ◽  
Physicochemical Characteristics ◽  
Pharmacokinetic Data ◽  
Specific Drug ◽  
Highly Correlated ◽  
Parameter Values ◽  
The Relationship

The correlation between 52 physicochemical parameters and mean residence time (MRT) for 27 drugs used in human and dog were investigated. The physicochemical parameter values calculated provided a basis for deriving a series of arithmetic expressions, which were used to build a mathematical model describing the relationship between them and the MRT values. From the entire set of analyzed parameters, a subset of 14 was identified that contributed to the derivation of an arithmetic expression: [Formula: see text] the value of which is highly correlated with the MRT value in dogs ( P < .001) and allowed prediction of the MRT predicted (MRT(pred)). In humans, no correlation was found that allowed the calculation of MRT(pred). These results indicate that predicting the pharmacokinetics of any specific drug for humans based on pharmacokinetic data obtained in the dog should be undertaken with knowledge of the inherent limitations.

scholarly journals Mathematical Standard-Parameters Dual Optimization for Metal Hip Arthroplasty Wear Modelling with Medical Physics Applications

Standards ◽  
2021 ◽  
Vol 1 (1) ◽  
pp. 53-66
Author(s):  
Francisco Casesnoves
Keyword(s):  
Experimental Testing ◽  
Medical Physics ◽  
Model Parameters ◽  
Model Parameter ◽  
Erosion Prediction ◽  
Acceptable Model ◽  
Wear Modelling ◽  
In Vitro Simulation ◽  
Parameter Values

Total hip metal arthroplasty (THA) constitutes an important proportion of the standard clinical hip implant usage in Medical Physics and Biomedical Engineering. A computational nonlinear optimization is performed with two commonly metal materials in Metal-on-Metal (MoM) THA. Namely, Cast Co-Cr Alloy and Titanium. The principal result is the numerical determination of the K adimensional-constant parameter of the model. Results from a new more powerful algorithm than previous contributions, show significant improvements. Numerical standard figures for dual optimization give acceptable model-parameter values with low residuals. These results are demonstrated with 2D and 3D Graphical/Interior Optimization also. According to the findings/calculations, the standard optimized metal-model parameters are mathematically proven and verified. Mathematical consequences are obtained for model improvements and in vitro simulation methodology. The wear magnitude for in vitro determinations with these model parameter data constitute the innovation of the method. In consequence, the erosion prediction for laboratory experimental testing in THA adds valuable information to the literature. Applications lead to medical physics improvements for material/metal-THA designs.

scholarly journals Combining Physiology-Based Modeling and Evolutionary Algorithms for Personalized, Noninvasive Cardiovascular Assessment Based on Electrocardiography and Ballistocardiography

2022 ◽  
Vol 12 ◽  
Author(s):  
Nicholas Mattia Marazzi ◽  
Giovanna Guidoboni ◽  
Mohamed Zaid ◽  
Lorenzo Sala ◽  
Salman Ahmad ◽  
...  
Keyword(s):  
Blood Pressure ◽  
Mathematical Model ◽  
Blood Pressure Measurement ◽  
Model Parameters ◽  
Cardiovascular Monitoring ◽  
Cardiovascular Parameters ◽  
Physiological Variables ◽  
Novel Approach ◽  
Cardiovascular Assessment ◽  
Parameter Values

Purpose: This study proposes a novel approach to obtain personalized estimates of cardiovascular parameters by combining (i) electrocardiography and ballistocardiography for noninvasive cardiovascular monitoring, (ii) a physiology-based mathematical model for predicting personalized cardiovascular variables, and (iii) an evolutionary algorithm (EA) for searching optimal model parameters.Methods: Electrocardiogram (ECG), ballistocardiogram (BCG), and a total of six blood pressure measurements are recorded on three healthy subjects. The R peaks in the ECG are used to segment the BCG signal into single BCG curves for each heart beat. The time distance between R peaks is used as an input for a validated physiology-based mathematical model that predicts distributions of pressures and volumes in the cardiovascular system, along with the associated BCG curve. An EA is designed to search the generation of parameter values of the cardiovascular model that optimizes the match between model-predicted and experimentally-measured BCG curves. The physiological relevance of the optimal EA solution is evaluated a posteriori by comparing the model-predicted blood pressure with a cuff placed on the arm of the subjects to measure the blood pressure.Results: The proposed approach successfully captures amplitudes and timings of the most prominent peak and valley in the BCG curve, also known as the J peak and K valley. The values of cardiovascular parameters pertaining to ventricular function can be estimated by the EA in a consistent manner when the search is performed over five different BCG curves corresponding to five different heart-beats of the same subject. Notably, the blood pressure predicted by the physiology-based model with the personalized parameter values provided by the EA search exhibits a very good agreement with the cuff-based blood pressure measurement.Conclusion: The combination of EA with physiology-based modeling proved capable of providing personalized estimates of cardiovascular parameters and physiological variables of great interest, such as blood pressure. This novel approach opens the possibility for developing quantitative devices for noninvasive cardiovascular monitoring based on BCG sensing.

Use of Machine Learning algorithms in evaluating the WRF model parameter sensitivity for the simulation of tropical cyclones

2021 ◽  
Author(s):  
Baki Harish ◽  
Sandeep Chinta ◽  
Chakravarthy Balaji ◽  
Balaji Srinivasan
Keyword(s):  
Machine Learning ◽  
Sensitivity Analysis ◽  
Tropical Cyclones ◽  
Surrogate Model ◽  
Learning Algorithms ◽  
Wrf Model ◽  
Machine Learning Algorithms ◽  
Model Parameters ◽  
Model Parameter ◽  
Parameter Values

&lt;p&gt;The Indian subcontinent is prone to tropical cyclones that originate in the Indian Ocean and cause widespread destruction to life and property. Accurate prediction of cyclone track, landfall, wind, and precipitation are critical in minimizing damage. The Weather Research and Forecast (WRF) model is widely used to predict tropical cyclones. The accuracy of the model prediction depends on initial conditions, physics schemes, and model parameters. The parameter values are selected empirically by scheme developers using the trial and error method, implying that the parameter values are sensitive to climatological conditions and regions. The number of tunable parameters in the WRF model is about several hundred, and calibrating all of them is highly impossible since it requires thousands of simulations. Therefore, sensitivity analysis is critical to screen out the parameters that significantly impact the meteorological variables. The Sobol&amp;#8217; sensitivity analysis method is used to identify the sensitive WRF model parameters. As this method requires a considerable amount of samples to evaluate the sensitivity adequately, machine learning algorithms are used to construct surrogate models trained using a limited number of samples. They could help generate a vast number of required pseudo-samples. Five machine learning algorithms, namely, Gaussian Process Regression (GPR), Support Vector Machine, Regression Tree, Random Forest, and K-Nearest Neighbor, are considered in this study. Ten-fold cross-validation is used to evaluate the surrogate models constructed using the five algorithms and identify the robust surrogate model among them. The samples generated from this surrogate model are then used by the Sobol&amp;#8217; method to evaluate the WRF model parameter sensitivity.&lt;/p&gt;

scholarly journals Examining differences in streamflow estimation for gauged and ungauged catchments using evolutionary data assimilation

2013 ◽  
Vol 16 (2) ◽  
pp. 392-406 ◽  
Author(s):  
Gift Dumedah ◽  
Paulin Coulibaly
Keyword(s):  
Data Assimilation ◽  
Estimation Accuracy ◽  
Model Parameters ◽  
Ungauged Catchments ◽  
Model Parameter ◽  
Soil Moisture Accounting ◽  
Measurement Models ◽  
Daily Streamflow ◽  
Parameter Values ◽  
Ungauged Watersheds

Data assimilation has allowed hydrologists to account for imperfections in observations and uncertainties in model estimates. Typically, updated members are determined as a compromised merger between observations and model predictions. The merging procedure is conducted in decision space before model parameters are updated to reflect the assimilation. However, given the dynamics between states and model parameters, there is limited guarantee that when updated parameters are applied into measurement models, the resulting estimate will be the same as the updated estimate. To account for these challenges, this study uses evolutionary data assimilation (EDA) to estimate streamflow in gauged and ungauged watersheds. EDA assimilates daily streamflow into a Sacramento soil moisture accounting model to determine updated members for eight watersheds in southern Ontario, Canada. The updated members are combined to estimate streamflow in ungauged watersheds where the results show high estimation accuracy for gauged and ungauged watersheds. An evaluation of the commonalities in model parameter values across and between gauged and ungauged watersheds underscore the critical contributions of consistent model parameter values. The findings show a high degree of commonality in model parameter values such that members of a given gauged/ungauged watershed can be estimated using members from another watershed.

scholarly journals Identifying the connective strength between model parameters and performance criteria

2017 ◽  
Vol 21 (11) ◽  
pp. 5663-5679 ◽  
Author(s):  
Björn Guse ◽  
Matthias Pfannerstill ◽  
Abror Gafurov ◽  
Jens Kiesel ◽  
Christian Lehr ◽  
...  
Keyword(s):  
Performance Criterion ◽  
Performance Criteria ◽  
Joint Analysis ◽  
Model Parameters ◽  
Flow Conditions ◽  
Target Variable ◽  
Model Parameter ◽  
And Performance ◽  
Parameter Values ◽  
Three Components

Abstract. In hydrological models, parameters are used to represent the time-invariant characteristics of catchments and to capture different aspects of hydrological response. Hence, model parameters need to be identified based on their role in controlling the hydrological behaviour. For the identification of meaningful parameter values, multiple and complementary performance criteria are used that compare modelled and measured discharge time series. The reliability of the identification of hydrologically meaningful model parameter values depends on how distinctly a model parameter can be assigned to one of the performance criteria. To investigate this, we introduce the new concept of connective strength between model parameters and performance criteria. The connective strength assesses the intensity in the interrelationship between model parameters and performance criteria in a bijective way. In our analysis of connective strength, model simulations are carried out based on a latin hypercube sampling. Ten performance criteria including Nash–Sutcliffe efficiency (NSE), Kling–Gupta efficiency (KGE) and its three components (alpha, beta and r) as well as RSR (the ratio of the root mean square error to the standard deviation) for different segments of the flow duration curve (FDC) are calculated. With a joint analysis of two regression tree (RT) approaches, we derive how a model parameter is connected to different performance criteria. At first, RTs are constructed using each performance criterion as the target variable to detect the most relevant model parameters for each performance criterion. Secondly, RTs are constructed using each parameter as the target variable to detect which performance criteria are impacted by changes in the values of one distinct model parameter. Based on this, appropriate performance criteria are identified for each model parameter. In this study, a high bijective connective strength between model parameters and performance criteria is found for low- and mid-flow conditions. Moreover, the RT analyses emphasise the benefit of an individual analysis of the three components of KGE and of the FDC segments. Furthermore, the RT analyses highlight under which conditions these performance criteria provide insights into precise parameter identification. Our results show that separate performance criteria are required to identify dominant parameters on low- and mid-flow conditions, whilst the number of required performance criteria for high flows increases with increasing process complexity in the catchment. Overall, the analysis of the connective strength between model parameters and performance criteria using RTs contribute to a more realistic handling of parameters and performance criteria in hydrological modelling.

scholarly journals Forecasting the Bladder Tumor Size and Immune Response of a Patient Over the Time Using a Dynamic Mathematical Model

2018 ◽  
Author(s):  
Clara Burgos ◽  
Noemí García-Medina ◽  
David Martínez-Rodríguez ◽  
José-Luis Pontones ◽  
David Ramos ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Immune Response ◽  
Tumor Size ◽  
Model Calibration ◽  
Bladder Tumor ◽  
Tumor Evolution ◽  
Model Parameters ◽  
Single Patient ◽  
Dynamic Mathematical Model ◽  
Parameter Values

Bladder cancer is one of the most common malignant diseases in the urinary system and a highly aggressive neoplasm. The prognosis is not favourable usually and its evolution for particular patients is very difficult to find out. In this paper we propose a dynamic mathematical model that describes the bladder tumor growth and the immune response evolution. This model is customized for a single patient, determining appropriate model parameter values via model calibration. Due to the uncertainty of the tumor evolution, using the calibrated model parameters, we predict the tumor size and the immune response evolution over the next few months assuming three different scenarios: favourable, neutral and unfavourable. In the former, the cancer disappears; in the second a 5mm tumor is expected around the middle of August 2018; in the worst scenario, a 5mm tumor is expected around the end of May 2018. The patient has been cited around June 15th, 2018, to check the tumor size, if it exists.

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