Diego L. Guarin

Identification of a parametric, discrete-time model of ankle stiffness

Dynamic ankle joint stiffness defines the relationship between the position of the ankle and the torque acting about it and can be separated into intrinsic and reflex components. Under stationary conditions, intrinsic stiffness can described by a linear second order system while reflex stiffness is described by Hammerstein system whose input is delayed velocity. Given that reflex and intrinsic torque cannot be measured separately, there has been much interest in the development of system identification techniques to separate them analytically. To date, most methods have been nonparametric and as a result there is no direct link between the estimated parameters and those of the stiffness model. This paper presents a novel algorithm for identification of a discrete-time model of ankle stiffness. Through simulations we show that the algorithm gives unbiased results even in the presence of large, non-white noise. Application of the method to experimental data demonstrates that it produces results consistent with previous findings.

Time-varying identification of ankle dynamic joint stiffness during movement with constant muscle activation.

Dynamic joint stiffness defines the torque generated at the joint in response to position perturbations. Dynamic stiffness is modulated by the angular position and the muscle activation level, making it difficult to estimate during large movements and/or time-varying muscle contractions. This paper presents a new methodology for estimating dynamic joint stiffness during movement and muscle activation. For this, we formulate a novel, nonlinear, dynamic joint stiffness model and present a new algorithm to estimate its parameters. The algorithm assumes that the variability in the model parameters is a function of the mean joint position. Using this methodology we estimated the dynamic joint stiffness at the ankle throughout ramp and hold displacements during a constant muscle contraction. The estimated model accurately predicted the intrinsic and reflex torques produced at the ankle as a response to small position perturbations during large displacement with muscle activation. Preliminary results show that during muscle contraction, ankle intrinsic stiffness estimated during movement is significantly lower than that estimated during quasi-stationary experiments.

A NARMAX method for the identification of time-varying joint stiffness

Dynamic joint stiffness defines the dynamic relationship between the position of a joint and the torque acting about it and can be separated into intrinsic and reflex components. Under stationary conditions, these can be identified using a nonlinear parallel-cascade algorithm that models intrinsic stiffness and reflex stiffness as parallel pathways. Experimental results demonstrate that both intrinsic and reflex stiffness depend strongly on the operating point defined by mean joint position and the activation level. Consequently, both intrinsic and reflex stiffness will appear to be time-varying (TV) whenever the operating point changes, as during movement. This paper describes and validates a new method for identification of TV ankle stiffness. The method is based on the TV nonlinear autorregresive, moving average exogenous (NARMAX) model class. Simulation results demonstrated that the algorithm can accurately estimate the TV parameters of the ankle stiffness. We conclude that the algorithm is potentially a powerful new tool for the study of joint stiffness during TV conditions.

Pruebas de no linealidad: El método de los datos sustitutos.

In the following we present an introduction to the method of surrogate data, we start by mentioning the general proceeding of the M onte Carlo hypothesis test, then we introduce the method of surrogate data for non linearity test, proposing an hierarchy of null hypothesis and a battery of no n linear statistics that allow us to compare the behavior of a real time series again st a set of surrogates which were generated to fit the null hypothesis, we prese nt a discriminating criterion whereby we can accept o reject a null hypothesis. Finally we present an example of how the algorithm works using the Lorenz time se ries.

Identification of a Time-Varying, Box-Jenkins Model of Intrinsic Joint Compliance

The mechanical properties of a joint are determined by the combination of intrinsic and reflex mechanisms. However, in some situations the reflex contributions are small so that intrinsic mechanisms play the dominant role in the control of posture and movement. The intrinsic mechanisms, characterized by the joint compliance, can be described well by a second order, linear model for small perturbations around an operating point defined by mean position and torque. However, the compliance parameters depend strongly on the operating point. Thus, for functional activities, such as walking, where position and torque undergo large, rapid changes, the joint compliance will also present large, fast changes and so will appear to be Time-Varying (TV). Therefore, a TV system identification algorithm must be used to characterize these changes. This paper introduces a novel TV system identification algorithm that achieves this. The method extends an instrumental-variable based algorithm for the identification of linear, TV, parametric, Box-Jenkins models to use periodic data. Simulation studies demonstrate that the new algorithm accurately tracks the changes in intrinsic joint compliance expected during walking. Moreover, the method performs well with the complex noise encountered in practice. Consequently the new method should be a valuable tool for the study of joint mechanics during functional activities.

Multiple-Input/Single-Output identification of the dynamic relation between EMG and torque at the human ankle during isometric contractions

Generation of torque around a joint usually involves the activation of several agonist muscles and may also involve the co-activation of antagonist muscles. Therefore, a valid model for the dynamic relation between surface EMG (an indirect measured of the muscles neural input) and the torque should take the form of a Multiple-Input/Single-Output (MISO) system to account for the contributions of the different muscles. This paper presents a new method to accurately estimate the dynamic EMG/Torque relation when multiple muscles are active simultaneously. Using our method we found that flexor and extensor muscles at the ankle have different dynamic properties.

Complex networks: Application to pathology detection in voice signals

The method of complex networks has been proposed as a novel approach to analyze time series from a new perspective. However, only few studies have applied this methodology to certain types of pseudo-periodic signals. In this article, the network-based technique is applied on voice signals, a kind of pseudo-periodic signals which has not been analyzed using complex networks, to differentiate between a healthy subject and subjects with pathological disorders. The results obtained demonstrated that through a set of statistic computed from the complex networks is possible to differentiate between healthy and non-healthy subjects, contrary to what was observed using well known non-linear statistics, such as Lempel-Ziv complexity and sample entropy. We conclude that by seeing voice signals as complex networks new information can be extracted from the time series that may help in the diagnosis of pathologies.

Estimation of Time-Varying, Intrinsic and Reflex Dynamic Joint Stiffness during Movement. Application to the Ankle Joint

Dynamic joint stiffness determines the relation between joint position and torque, and plays a vital role in the control of posture and movement. Dynamic joint stiffness can be quantified during quasi-stationary conditions using disturbance experiments, where small position perturbations are applied to the joint and the torque response is recorded. Dynamic joint stiffness is composed of intrinsic and reflex mechanisms that act and change together, so that nonlinear, mathematical models and specialized system identification techniques are necessary to estimate their relative contributions to overall joint stiffness. Quasi-stationary experiments have demonstrated that dynamic joint stiffness is heavily modulated by joint position and voluntary torque. Consequently, during movement, when joint position and torque change rapidly, dynamic joint stiffness will be Time-Varying (TV). This paper introduces a new method to quantify the TV intrinsic and reflex components of dynamic joint stiffness during movement. The algorithm combines ensemble and deterministic approaches for estimation of TV systems; and uses a TV, parallel-cascade, nonlinear system identification technique to separate overall dynamic joint stiffness into intrinsic and reflex components from position and torque records. Simulation studies of a stiffness model, whose parameters varied with time as is expected during walking, demonstrated that the new algorithm accurately tracked the changes in dynamic joint stiffness using as little as 40 gait cycles. The method was also used to estimate the intrinsic and reflex dynamic ankle stiffness from an experiment with a healthy subject during which ankle movements were imposed while the subject maintained a constant muscle contraction. The method identified TV stiffness model parameters that predicted the measured torque very well, accounting for more than 95% of its variance. Moreover, both intrinsic and reflex dynamic stiffness were heavily modulated through the movement in a manner that could not be predicted from quasi-stationary experiments. The new method provides the tool needed to explore the role of dynamic stiffness in the control of movement.

Nonlinear statistics for bearing diagnosis

This document presents the preliminary results of an ongoing study related to the use of nonlinear statistics for bearing diagnosis. In this study, we propose a methodology based on the K-nearest neighbor algorithm to test the ability of a group of nonlinear statistic to differentiate between vibration signals obtained from rotatory machines with bearings in good and in bad condition. Results showed that statistics such as Lempel-Ziv complexity, Sample Entropy, and others derived from the recurrence plot, unlike the correlation dimension, are good at detecting a failure in a bearing. Additionally, we found that the Sample Entropy is exceptionally good at this task.

Pseudo-periodic surrogate data method on voice signals

In the following article, Pseudo-Periodic surrogate data method is described as a tool to detect the underlying dynamics existing in non-linear phenomena, in order to know beforehand the best approach when analyzing with these types of time series. This method is applied to voice signals, a non-linear phenomenon observed from the vocal tract, to try determine its underlying dynamic structure and therefore use the appropriate approach. Lempel-Ziv complexity, based on the counting of sequences, and Sample Entropy, based on the extent of the irregularity in a signal, are introduced as discriminating statistics for null hypothesis testing within the surrogate data method. In addition, a methodology is explained on how to apply this method to voice signals. Our results showed that Lempel-Ziv complexity rejects the proposed hypothesis while sample entropy gives results beyond expectation.