scholarly journals Robust Adaptive Impedance Control With Application to a Transfemoral Prosthesis and Test Robot

2018 ◽  
Vol 140 (12) ◽  
Author(s):  
Vahid Azimi ◽  
Seyed Abolfazl Fakoorian ◽  
Thang Tien Nguyen ◽  
Dan Simon
Keyword(s):  
Boundary Layer ◽  
Degrees Of Freedom ◽  
Impedance Control ◽  
Lyapunov Stability Theory ◽  
Biomechanical Properties ◽  
Model Parameters ◽  
Parameter Uncertainties ◽  
Combined System ◽  
Control Effort ◽  
Barbalat’S Lemma

This paper presents, compares, and tests two robust model reference adaptive impedance controllers for a three degrees-of-freedom (3DOF) powered prosthesis/test robot. We first present a model for a combined system that includes a test robot and a transfemoral prosthetic leg. We design these two controllers, so the error trajectories of the system converge to a boundary layer and the controllers show robustness to ground reaction forces (GRFs) as nonparametric uncertainties and also handle model parameter uncertainties. We prove the stability of the closed-loop systems for both controllers for the prosthesis/test robot in the case of nonscalar boundary layer trajectories using Lyapunov stability theory and Barbalat's lemma. We design the controllers to imitate the biomechanical properties of able-bodied walking and to provide smooth gait. We finally present simulation results to confirm the efficacy of the controllers for both nominal and off-nominal system model parameters. We achieve good tracking of joint displacements and velocities, and reasonable control and GRF magnitudes for both controllers. We also compare performance of the controllers in terms of tracking, control effort, and parameter estimation for both nominal and off-nominal model parameters.

Stable Robust Adaptive Impedance Control of a Prosthetic Leg

2015 ◽  
Author(s):  
Vahid Azimi ◽  
Dan Simon ◽  
Hanz Richter
Keyword(s):  
Boundary Layer ◽  
Cost Function ◽  
Sliding Mode ◽  
Impedance Control ◽  
Reaction Force ◽  
Lyapunov Stability Theory ◽  
Design Parameters ◽  
System Parameters ◽  
Barbalat’S Lemma ◽  
Adaptation Law

We propose a nonlinear robust model reference adaptive impedance controller for an active prosthetic leg for transfemoral amputees. We use an adaptive control term to consider the uncertain parameters of the system, and a robust control term so the system trajectories converge to a sliding mode boundary layer and exhibit robustness to variations of ground reaction force (GRF). The boundary layer not only compromises between control chattering and tracking performance, but also bounds the parameter adaptation to prevent unfavorable parameter drift. We also prove the stability of the controller for the robotic system in the case of non-scalar boundary layer trajectories using Lyapunov stability theory and Barbalat’s lemma. The acceleration-free regressor form of the system removes the need to measure the joint accelerations, which would otherwise introduce noise in the system. We use particle swarm optimization (PSO) to optimize the design parameters of the controller and the adaptation law. The PSO cost function is comprised of control signal magnitudes and tracking errors. PSO achieves a 8% improvement in the objective function. Finally, we present simulation results to validate the effectiveness of the controller. We achieve good tracking of joint displacements and velocities for both nominal and perturbed values of the system parameters. Variations of ±30% on the system parameters result in an increase of the cost function by only 3%, which confirms the robustness of the controller.

scholarly journals Variation of Passive Biomechanical Properties of the Small Intestine along Its Length: Microstructure-Based Characterization

2021 ◽  
Vol 8 (3) ◽  
pp. 32
Author(s):  
Dimitrios P. Sokolis
Keyword(s):  
Small Intestine ◽  
Orientation Angle ◽  
Axial Direction ◽  
Material Model ◽  
Biomechanical Properties ◽  
Intestinal Wall ◽  
Model Parameters ◽  
Material Models ◽  
Hyper Elastic ◽  
Rat Tissue

Multiaxial testing of the small intestinal wall is critical for understanding its biomechanical properties and defining material models, but limited data and material models are available. The aim of the present study was to develop a microstructure-based material model for the small intestine and test whether there was a significant variation in the passive biomechanical properties along the length of the organ. Rat tissue was cut into eight segments that underwent inflation/extension testing, and their nonlinearly hyper-elastic and anisotropic response was characterized by a fiber-reinforced model. Extensive parametric analysis showed a non-significant contribution to the model of the isotropic matrix and circumferential-fiber family, leading also to severe over-parameterization. Such issues were not apparent with the reduced neo-Hookean and (axial and diagonal)-fiber family model, that provided equally accurate fitting results. Absence from the model of either the axial or diagonal-fiber families led to ill representations of the force- and pressure-diameter data, respectively. The primary direction of anisotropy, designated by the estimated orientation angle of diagonal-fiber families, was about 35° to the axial direction, corroborating prior microscopic observations of submucosal collagen-fiber orientation. The estimated model parameters varied across and within the duodenum, jejunum, and ileum, corroborating histologically assessed segmental differences in layer thicknesses.

scholarly journals Linking biogeochemistry to hydro-geometrical variability in tidal estuaries: a generic modeling approach

2015 ◽  
Vol 12 (7) ◽  
pp. 6351-6435
Author(s):  
C. Volta ◽  
G. G. Laruelle ◽  
S. Arndt ◽  
P. Regnier
Keyword(s):  
Sensitivity Analysis ◽  
World Ocean ◽  
Reaction Network ◽  
Co2 Exchange ◽  
Model Parameters ◽  
Parameter Uncertainties ◽  
Tidal Estuaries ◽  
Biogeochemical Indicators ◽  
C And N ◽  
Co2 Sink

Abstract. This study applies the Carbon-Generic Estuary Model (C-GEM) modeling platform to simulate the estuarine biogeochemical dynamics – in particular the air-water CO2 exchange – in three idealized end-member systems covering the main features of tidal alluvial estuaries. C-GEM uses a generic biogeochemical reaction network and a unique set of model parameters extracted from a comprehensive literature survey to perform steady-state simulations representing average conditions for temperate estuaries worldwide. Climate and boundary conditions are extracted from published global databases (e.g. World Ocean Atlas, GLORICH) and catchment model outputs (GlobalNEWS2). The whole-system biogeochemical indicators Net Ecosystem Metabolism (NEM), C and N filtering capacities (FCTC and FCTN, respectively) and CO2 gas exchanges (FCO2) are calculated across the three end-member systems and are related to their main hydrodynamic and transport characteristics. A sensitivity analysis, which propagates the parameter uncertainties, is also carried out, followed by projections of changes in the biogeochemical indicators for the year 2050. Results show that the average C filtering capacities for baseline conditions are 40, 30 and 22% for the marine, mixed and riverine estuary, respectively. This translates into a first-order, global CO2 outgassing flux for tidal estuaries between 0.04 and 0.07 Pg C yr−1. N filtering capacities, calculated in similar fashion, range from 22% for the marine estuary to 18 and 15% for the mixed and the riverine estuary, respectively. Sensitivity analysis performed by varying the rate constants for aerobic degradation, denitrification and nitrification over the range of values reported in the literature significantly widens these ranges for both C and N. Simulations for the year 2050 indicate that all end-member estuaries will remain net heterotrophic and while the riverine and mixed systems will only marginally be affected by river load changes and increase in atmospheric pCO2, the marine estuary is likely to become a significant CO2 sink in its downstream section. In the decades to come, such change of behavior might strengthen the overall CO2 sink of the estuary-coastal ocean continuum.

Nonintrusive Global Sensitivity Analysis for Linear Systems With Process Noise

2019 ◽  
Vol 14 (2) ◽  
Author(s):  
Souransu Nandi ◽  
Tarunraj Singh
Keyword(s):  
Sensitivity Analysis ◽  
Linear Systems ◽  
Global Sensitivity Analysis ◽  
Benchmark Problems ◽  
Model Parameters ◽  
Parameter Uncertainties ◽  
Sobol Indices ◽  
Global Sensitivity ◽  
Time Invariant ◽  
The Impact

The focus of this paper is on the global sensitivity analysis (GSA) of linear systems with time-invariant model parameter uncertainties and driven by stochastic inputs. The Sobol' indices of the evolving mean and variance estimates of states are used to assess the impact of the time-invariant uncertain model parameters and the statistics of the stochastic input on the uncertainty of the output. Numerical results on two benchmark problems help illustrate that it is conceivable that parameters, which are not so significant in contributing to the uncertainty of the mean, can be extremely significant in contributing to the uncertainty of the variances. The paper uses a polynomial chaos (PC) approach to synthesize a surrogate probabilistic model of the stochastic system after using Lagrange interpolation polynomials (LIPs) as PC bases. The Sobol' indices are then directly evaluated from the PC coefficients. Although this concept is not new, a novel interpretation of stochastic collocation-based PC and intrusive PC is presented where they are shown to represent identical probabilistic models when the system under consideration is linear. This result now permits treating linear models as black boxes to develop intrusive PC surrogates.

Robustness Analysis of a Simple and Augmented Proportional Plus Derivative Controller in Trajectory Following Robots Using the Floquet Theory

2018 ◽  
Vol 13 (7) ◽  
Author(s):  
B. Sandeep Reddy ◽  
Ashitava Ghosal
Keyword(s):  
Numerical Simulation ◽  
Degrees Of Freedom ◽  
Floquet Theory ◽  
Robustness Analysis ◽  
Periodic Trajectory ◽  
Model Parameters ◽  
Asymptotically Stable ◽  
Pd Controller ◽  
Simulation Results ◽  
Trajectory Following

This paper deals with the issue of robustness in control of robots using the proportional plus derivative (PD) controller and the augmented PD controller. In the literature, a variety of PD and model-based controllers for multilink serial manipulator have been claimed to be asymptotically stable for trajectory tracking, in the sense of Lyapunov, as long as the controller gains are positive. In this paper, we first establish that for simple PD controllers, the criteria of positive controller gains are insufficient to establish asymptotic stability, and second that for the augmented PD controller the criteria of positive controller gains are valid only when there is no uncertainty in the model parameters. We show both these results for a simple planar two-degrees-of-freedom (2DOFs) robot with two rotary (R) joints, following a desired periodic trajectory, using the Floquet theory. We provide numerical simulation results which conclusively demonstrate the same.

Numerical Towing Model for LNG Carrier Approach in Exposed Environment Calibrated With Full-Scale Measurements and Operability Criterion

2021 ◽  
Author(s):  
Erwan Auburtin ◽  
Quentin Delivré ◽  
Jason McConochie ◽  
Jim Brown ◽  
Yuriy Drobyshevski
Keyword(s):  
Numerical Model ◽  
Degrees Of Freedom ◽  
Line Tension ◽  
Full Scale ◽  
Model Parameters ◽  
Wave Loads ◽  
Simplified Approach ◽  
Large Matrix ◽  
Multi Body ◽  
The Impact

Abstract The Prelude Floating Liquefied Natural Gas (FLNG) platform is designed to offload liquefied natural and petroleum gas products to carrier vessels moored in a Side-by-Side (SBS) configuration. Prior to the mooring operation, the carrier vessel is escorted and held alongside the FLNG with the assistance of tugs connected to her bow and stern to ensure sufficient control over the vessel in this critical phase. In order to better understand the impact of environmental conditions, to determine the optimum length, strength, material and configuration of the towline stretcher, and to estimate the maximum operable environments, coupled multi-body simulations have been performed in time domain. The numerical model, which considered both the LNG carrier and the forward tug, was calibrated using full-scale measurements of tug motions and tow line tension recorded during a real approach and berthing manoeuvre at Prelude FLNG. The measured environment effects were generated numerically and the model parameters were adjusted to reproduce the recorded behavior as accurately as possible. Since actions of the tug master are difficult to model numerically and only the statistical environment parameters are known, a simplified approach has been adopted for modelling the tug propulsion and steering using a combination of static forces, stiffness and linear and quadratic damping for relevant horizontal degrees of freedom. The calibrated numerical model was first subjected to several sensitivity assessments of the modelling level (single- or multi-body, inclusion of second-order wave loads, inclusion of forward speed). Then sensitivity studies were performed to help address operational requirements related to the wave height and direction, and the stretcher length and strength. The conclusions have been taken into consideration for the selection of the tow line configurations for future operations. Finally, the calibrated coupled LNG carrier and tug model was used to derive Prelude-specific tug operability criteria that may be used for decision-making based on weather forecasts, prior to the SBS offloading operations. A large matrix of swell and wind driven waves was simulated over a range of wave heights, periods, directions and static towing forces to allow a criterion to be developed based on a stochastic extreme tow line tension. Such criterion considers relevant wave parameters while remaining simplified enough for easy use in operations. This paper describes the assumptions and process to numerically model the towing configuration and calibrate the different coefficients, discusses the results obtained for the various sensitivities, and explains the operability criteria. Important conclusions and lessons learnt are also shared.

scholarly journals Bayesian estimation of parameters in a regional hydrological model

2002 ◽  
Vol 6 (5) ◽  
pp. 883-898 ◽  
Author(s):  
K. Engeland ◽  
L. Gottschalk
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Hydrological Model ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Parameter Uncertainties ◽  
Daily Streamflow ◽  
Likelihood Model ◽  
Simulation Errors

Abstract. This study evaluates the applicability of the distributed, process-oriented Ecomag model for prediction of daily streamflow in ungauged basins. The Ecomag model is applied as a regional model to nine catchments in the NOPEX area, using Bayesian statistics to estimate the posterior distribution of the model parameters conditioned on the observed streamflow. The distribution is calculated by Markov Chain Monte Carlo (MCMC) analysis. The Bayesian method requires formulation of a likelihood function for the parameters and three alternative formulations are used. The first is a subjectively chosen objective function that describes the goodness of fit between the simulated and observed streamflow, as defined in the GLUE framework. The second and third formulations are more statistically correct likelihood models that describe the simulation errors. The full statistical likelihood model describes the simulation errors as an AR(1) process, whereas the simple model excludes the auto-regressive part. The statistical parameters depend on the catchments and the hydrological processes and the statistical and the hydrological parameters are estimated simultaneously. The results show that the simple likelihood model gives the most robust parameter estimates. The simulation error may be explained to a large extent by the catchment characteristics and climatic conditions, so it is possible to transfer knowledge about them to ungauged catchments. The statistical models for the simulation errors indicate that structural errors in the model are more important than parameter uncertainties. Keywords: regional hydrological model, model uncertainty, Bayesian analysis, Markov Chain Monte Carlo analysis

scholarly journals Nuclear data adjustment using Bayesian inference, diagnostics for model fit and influence of model parameters

2020 ◽  
Vol 239 ◽  
pp. 13003
Author(s):  
D. Kumar ◽  
S. B. Alam ◽  
H. Sjöstrand ◽  
J.M. Palau ◽  
C. De Saint Jean
Keyword(s):  
Bayesian Inference ◽  
Degrees Of Freedom ◽  
Nuclear Data ◽  
Information Criteria ◽  
Least Square ◽  
Model Fit ◽  
Adjustment Process ◽  
Model Parameters ◽  
Test Case ◽  
Bayesian Approximation

The mathematical models used for nuclear data evaluations contain a large number of theoretical parameters that are usually uncertain. These parameters can be calibrated (or improved) by the information collected from integral/differential experiments. The Bayesian inference technique is used to utilize measurements for data assimilation. The Bayesian approximation is based on the least-square or Monte-Carlo approaches. In this process, the model parameters are optimized. In the adjustment process, it is essential to include the analysis related to the influence of model parameters on the adjusted data. In this work, some statistical indicators such as the concept of Cook’s distance; Akaike, Bayesian and deviance information criteria; effective degrees of freedom are developed within the CONRAD platform. Further, these indicators are applied to a test case of 155Gd to evaluate and compare the influence of resonance parameters.

scholarly journals Generalized second-order slip for unsteady convective flow of a nanofluid: a utilization of Buongiorno’s two-component nonhomogeneous equilibrium model

2020 ◽  
Vol 9 (1) ◽  
pp. 156-168
Author(s):  
Seyed Mahdi Mousavi ◽  
Saeed Dinarvand ◽  
Mohammad Eftekhari Yazdi
Keyword(s):  
Boundary Layer ◽  
Equilibrium Model ◽  
Second Order ◽  
Model Parameters ◽  
Slip Parameter ◽  
Two Phase ◽  
Convective Boundary ◽  
First Order ◽  
Special Cases ◽  
Two Component

AbstractThe unsteady convective boundary layer flow of a nanofluid along a permeable shrinking/stretching plate under suction and second-order slip effects has been developed. Buongiorno’s two-component nonhomogeneous equilibrium model is implemented to take the effects of Brownian motion and thermophoresis into consideration. It can be emphasized that, our two-phase nanofluid model along with slip concentration at the wall shows better physical aspects relative to taking the constant volume concentration at the wall. The similarity transformation method (STM), allows us to reducing nonlinear governing PDEs to nonlinear dimensionless ODEs, before being solved numerically by employing the Keller-box method (KBM). The graphical results portray the effects of model parameters on boundary layer behavior. Moreover, results validation has been demonstrated as the skin friction and the reduced Nusselt number. We understand shrinking plate case is a key factor affecting non-uniqueness of the solutions and the range of the shrinking parameter for which the solution exists, increases with the first order slip parameter, the absolute value of the second order slip parameter as well as the transpiration rate parameter. Besides, the second-order slip at the interface decreases the rate of heat transfer in a nanofluid. Finally, the analysis for no-slip and first-order slip boundary conditions can also be retrieved as special cases of the present model.

Uncertainty Quantification of Viscoplastic Parameters for Grade 91 Steel Through Bayesian Analysis

2020 ◽  
Author(s):  
Aritra Chakraborty ◽  
M. C. Messner ◽  
T.-L. Sham
Keyword(s):  
Experimental Data ◽  
High Temperature ◽  
Initial Guess ◽  
Mcmc Methods ◽  
Model Parameters ◽  
Parameter Uncertainties ◽  
Experimental Conditions ◽  
Materials Used ◽  
Grade 91 ◽  
Effective Component

Abstract Calibrating inelastic models for high temperature materials used in advanced reactor heat exchangers is a critical aspect in accurately predicting their deformation behavior under different loading conditions, and thus determining the corresponding failure times. The experimental data against which these models are calibrated often contains a wide degree of variability caused by heat-to-heat material property variations and general experimental uncertainty. Most often, model calibration is done against mean of these experimental data without considering this variability. In this work we aim to capture the bounds of the viscoplastic parameter uncertainties that enclose this observed scatter in the experimental data using Bayesian Markov Chain Monte Carlo (MCMC) methods. Bayesian inference provides a probabilistic framework that allows to coherently quantify parameter uncertainties based on some prior parameter distributions and the available data. To perform the statistical Bayesian MCMC analysis, a pre-calibrated model, fitted against mean of the experimental data, is used as an initial guess for the prior distribution and bounds, while further sampling is done using Meteropolis–Hastings algorithm for four Markov chains in tandem, to finally obtain the posterior distribution of the model parameters. Since different inelastic parameters are sensitive to different tests, data from multiple experimental conditions (tensile, and creep) are combined to capture the bounds in all the parameters. The developed statistical model reasonably captures the scatter observed in the experimental data. Quantifying uncertainty in inelastic models will improve high temperature engineering design practice and lead to safer, more effective component designs.

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