Online identification and nonlinear control of the electrically stimulated quadriceps muscle

A new approach for estimating nonlinear models of the electrically stimulated quadriceps muscle group under nonisometric conditions is investigated. The model can be used for designing controlled neuro-prostheses. In order to identify the muscle dynamics (stimulation pulsewidth-active knee moment relation) from discrete-time angle measurements only, a hybrid model structure is postulated for the shank-quadriceps dynamics. The model consists of a relatively well known time-invariant passive component and an uncertain time-variant active component. Rigid body dynamics, described by the Equation of Motion (EoM), and passive joint properties form the time-invariant part. The actuator, i.e. the electrically stimulated muscle group, represents the uncertain time-varying section. A recursive algorithm is outlined for identifying online the stimulated quadriceps muscle group. The algorithm requires EoM and passive joint characteristics to be known a priori. The muscle dynamics represent the product of a continuous-time nonlinear activation dynamics and a nonlinear static contraction function described by a Normalised Radial Basis Function (NRBF) network which has knee-joint angle and angular velocity as input arguments. An Extended Kalman Filter (EKF) approach is chosen to estimate muscle dynamics parameters and to obtain full state estimates of the shank-quadriceps dynamics simultaneously. The latter is important for implementing state feedback controllers. A nonlinear state feedback controller using the backstepping method is explicitly designed whereas the model was identified a priori using the developed identification procedure

Estimation Of Hybrid Models For Real-time Crash Risk Assessment On Freeways

Relevance of reactive traffic management strategies such as freeway incident detection has been diminishing with advancements in mobile phone usage and video surveillance technology. On the other hand, capacity to collect, store, and analyze traffic data from underground loop detectors has witnessed enormous growth in the recent past. These two facts together provide us with motivation as well as the means to shift the focus of freeway traffic management toward proactive strategies that would involve anticipating incidents such as crashes. The primary element of proactive traffic management strategy would be model(s) that can separate \u27crash prone\u27 conditions from \u27normal\u27 traffic conditions in real-time. The aim in this research is to establish relationship(s) between historical crashes of specific types and corresponding loop detector data, which may be used as the basis for classifying real-time traffic conditions into \u27normal\u27 or \u27crash prone\u27 in the future. In this regard traffic data in this study were also collected for cases which did not lead to crashes (non-crash cases) so that the problem may be set up as a binary classification. A thorough review of the literature suggested that existing real-time crash \u27prediction\u27 models (classification or otherwise) are generic in nature, i.e., a single model has been used to identify all crashes (such as rear-end, sideswipe, or angle), even though traffic conditions preceding crashes are known to differ by type of crash. Moreover, a generic model would yield no information about the collision most likely to occur. To be able to analyze different groups of crashes independently, a large database of crashes reported during the 5-year period from 1999 through 2003 on Interstate-4 corridor in Orlando were collected. The 36.25-mile instrumented corridor is equipped with 69 dual loop detector stations in each direction (eastbound and westbound) located approximately every ½ mile. These stations report speed, volume, and occupancy data every 30-seconds from the three through lanes of the corridor. Geometric design parameters for the freeway were also collected and collated with historical crash and corresponding loop detector data. The first group of crashes to be analyzed were the rear-end crashes, which account to about 51% of the total crashes. Based on preliminary explorations of average traffic speeds; rear-end crashes were grouped into two mutually exclusive groups. First, those occurring under extended congestion (referred to as regime 1 traffic conditions) and the other which occurred with relatively free-flow conditions (referred to as regime 2 traffic conditions) prevailing 5-10 minutes before the crash. Simple rules to separate these two groups of rear-end crashes were formulated based on the classification tree methodology. It was found that the first group of rear-end crashes can be attributed to parameters measurable through loop detectors such as the coefficient of variation in speed and average occupancy at stations in the vicinity of crash location. For the second group of rear-end crashes (referred to as regime 2) traffic parameters such as average speed and occupancy at stations downstream of the crash location were significant along with off-line factors such as the time of day and presence of an on-ramp in the downstream direction. It was found that regime 1 traffic conditions make up only about 6% of the traffic conditions on the freeway. Almost half of rear-end crashes occurred under regime 1 traffic regime even with such little exposure. This observation led to the conclusion that freeway locations operating under regime 1 traffic may be flagged for (rear-end) crashes without any further investigation. MLP (multilayer perceptron) and NRBF (normalized radial basis function) neural network architecture were explored to identify regime 2 rear-end crashes. The performance of individual neural network models was improved by hybridizing their outputs. Individual and hybrid PNN (probabilistic neural network) models were also explored along with matched case control logistic regression. The stepwise selection procedure yielded the matched logistic regression model indicating the difference between average speeds upstream and downstream as significant. Even though the model provided good interpretation, its classification accuracy over the validation dataset was far inferior to the hybrid MLP/NRBF and PNN models. Hybrid neural network models along with classification tree model (developed to identify the traffic regimes) were able to identify about 60% of the regime 2 rear-end crashes in addition to all regime 1 rear-end crashes with a reasonable number of positive decisions (warnings). It translates into identification of more than ¾ (77%) of all rear-end crashes. Classification models were then developed for the next most frequent type, i.e., lane change related crashes. Based on preliminary analysis, it was concluded that the location specific characteristics, such as presence of ramps, mile-post location, etc. were not significantly associated with these crashes. Average difference between occupancies of adjacent lanes and average speeds upstream and downstream of the crash location were found significant. The significant variables were then subjected as inputs to MLP and NRBF based classifiers. The best models in each category were hybridized by averaging their respective outputs. The hybrid model significantly improved on the crash identification achieved through individual models and 57% of the crashes in the validation dataset could be identified with 30% warnings. Although the hybrid models in this research were developed with corresponding data for rear-end and lane-change related crashes only, it was observed that about 60% of the historical single vehicle crashes (other than rollovers) could also be identified using these models. The majority of the identified single vehicle crashes, according to the crash reports, were caused due to evasive actions by the drivers in order to avoid another vehicle in front or in the other lane. Vehicle rollover crashes were found to be associated with speeding and curvature of the freeway section; the established relationship, however, was not sufficient to identify occurrence of these crashes in real-time. Based on the results from modeling procedure, a framework for parallel real-time application of these two sets of models (rear-end and lane-change) in the form of a system was proposed. To identify rear-end crashes, the data are first subjected to classification tree based rules to identify traffic regimes. If traffic patterns belong to regime 1, a rear-end crash warning is issued for the location. If the patterns are identified to be regime 2, then they are subjected to hybrid MLP/NRBF model employing traffic data from five surrounding traffic stations. If the model identifies the patterns as crash prone then the location may be flagged for rear-end crash, otherwise final check for a regime 2 rear-end crash is applied on the data through the hybrid PNN model. If data from five stations are not available due to intermittent loop failures, the system is provided with the flexibility to switch to models with more tolerant data requirements (i.e., model using traffic data from only one station or three stations). To assess the risk of a lane-change related crash, if all three lanes at the immediate upstream station are functioning, the hybrid of the two of the best individual neural network models (NRBF with three hidden neurons and MLP with four hidden neurons) is applied to the input data. A warning for a lane-change related crash may be issued based on its output. The proposed strategy is demonstrated over a complete day of loop data in a virtual real-time application. It was shown that the system of models may be used to continuously assess and update the risk for rear-end and lane-change related crashes. The system developed in this research should be perceived as the primary component of proactive traffic management strategy. Output of the system along with the knowledge of variables critically associated with specific types of crashes identified in this research can be used to formulate ways for avoiding impending crashes. However, specific crash prevention strategies e.g., variable speed limit and warnings to the commuters demand separate attention and should be addressed through thorough future research

Radial basis approximation of tensor fields on manifolds: From operator estimation to manifold learning

In this paper, we study the Radial Basis Function (RBF) approximation to differential operators on smooth tensor fields defined on closed Riemannian submanifolds of Euclidean space, identified by randomly sampled point cloud data. {The formulation in this paper leverages a fundamental fact that the covariant derivative on a submanifold is the projection of the directional derivative in the ambient Euclidean space onto the tangent space of the submanifold. To differentiate a test function (or vector field) on the submanifold with respect to the Euclidean metric, the RBF interpolation is applied to extend the function (or vector field) in the ambient Euclidean space. When the manifolds are unknown, we develop an improved second-order local SVD technique for estimating local tangent spaces on the manifold. When the classical pointwise non-symmetric RBF formulation is used to solve Laplacian eigenvalue problems, we found that while accurate estimation of the leading spectra can be obtained with large enough data, such an approximation often produces irrelevant complex-valued spectra (or pollution) as the true spectra are real-valued and positive. To avoid such an issue,} we introduce a symmetric RBF discrete approximation of the Laplacians induced by a weak formulation on appropriate Hilbert spaces. Unlike the non-symmetric approximation, this formulation guarantees non-negative real-valued spectra and the orthogonality of the eigenvectors. Theoretically, we establish the convergence of the eigenpairs of both the Laplace-Beltrami operator and Bochner Laplacian {for the symmetric formulation} in the limit of large data with convergence rates. Numerically, we provide supporting examples for approximations of the Laplace-Beltrami operator and various vector Laplacians, including the Bochner, Hodge, and Lichnerowicz Laplacians.Comment: 17 figure

Co-Fathering With Nonresident Biological Fathers: A Phenomenological Study on Stepfathers

The purpose of this phenomenological study is to understand the experiences of stepfathers when both the non-resident biological father (NRBF) and stepfather are involved in the parenting efforts. This study will explore the stepfather’s co-fathering experiences with the NRBF and its overall effect on stepfamily functioning and marital satisfaction. The theories guiding this study are the family stress theory and the family systems theory. These two theories will help to explain how stressful events, such as stepfamily formation and the presence of the NRBF, disrupt the family’s equilibrium and challenge the stepfamily to find adaptive ways to reestablish their balance. Stepfathers were recruited and participated in a semi-structured interview, in which they discussed the challenges they experienced with co-fathering with a NRBF. The results of the study showed that stepfathers had four unmet needs which prevented a healthy co-fathering relationship with the NRBF: (a) a need to be accepted, (b) a need to establish authority, (c) a need for communication, and (d) a need for guidance. This study paves the way for premarital and postmarital stepfamily educational programs which may increase the possibility for fathers to engage in a collaborative approach to parenting

Content-Specific Broadcast Cellular Networks based on User Demand Prediction: A Revenue Perspective

The Long Term Evolution (LTE) broadcast is a promising solution to cope with exponentially increasing user traffic by broadcasting common user requests over the same frequency channels. In this paper, we propose a novel network framework provisioning broadcast and unicast services simultaneously. For each serving file to users, a cellular base station determines either to broadcast or unicast the file based on user demand prediction examining the file's content specific characteristics such as: file size, delay tolerance, price sensitivity. In a network operator's revenue maximization perspective while not inflicting any user payoff degradation, we jointly optimize resource allocation, pricing, and file scheduling. In accordance with the state of the art LTE specifications, the proposed network demonstrates up to 32% increase in revenue for a single cell and more than a 7-fold increase for a 7 cell coordinated LTE broadcast network, compared to the conventional unicast cellular networks.Comment: 6 pages; This paper will appear in the Proc. of IEEE WCNC 201

Assessment of Freeway Traffic Parameters Leading to Lane-Change Related Collisions

This study aims at ‘predicting’ the occurrence of lane-change related freeway crashes using the traffic surveillance data collected from a pair of dual loop detectors. The approach adopted here involves developing classification models using the historical crash data and corresponding information on real-time traffic parameters obtained from loop detectors. The historical crash and loop detector data to calibrate the neural network models (corresponding to crash and non-crash cases to set up a binary classification problem) were collected from the Interstate-4 corridor in Orlando (FL) metropolitan area. Through a careful examination of crash data, it was concluded that all sideswipe collisions and the angle crashes that occur on the inner lanes (left most and center lanes) of the freeway may be attributed to lane-changing maneuvers. These crashes are referred to as lane-change related crashes in this study. The factors explored as independent variables include the parameters formulated to capture the overall measure of lane-changing and between-lane variations of speed, volume and occupancy at the station located upstream of crash locations. Classification tree based variable selection procedure showed that average speeds upstream and downstream of crash location, difference in occupancy on adjacent lanes and standard deviation of volume and speed downstream of the crash location were found to be significantly associated with the binary variable (crash versus non-crash). The classification models based on data mining approach achieved satisfactory classification accuracy over the validation dataset. The results indicate that these models may be applied for identifying real-time traffic conditions prone to lane-change related crashes

Catch-22s of reservoir computing

Reservoir Computing (RC) is a simple and efficient model-free framework for forecasting the behavior of nonlinear dynamical systems from data. Here, we show that there exist commonly-studied systems for which leading RC frameworks struggle to learn the dynamics unless key information about the underlying system is already known. We focus on the important problem of basin prediction -- determining which attractor a system will converge to from its initial conditions. First, we show that the predictions of standard RC models (echo state networks) depend critically on warm-up time, requiring a warm-up trajectory containing almost the entire transient in order to identify the correct attractor. Accordingly, we turn to Next-Generation Reservoir Computing (NGRC), an attractive variant of RC that requires negligible warm-up time. By incorporating the exact nonlinearities in the original equations, we show that NGRC can accurately reconstruct intricate and high-dimensional basins of attraction, even with sparse training data (e.g., a single transient trajectory). Yet, a tiny uncertainty in the exact nonlinearity can render prediction accuracy no better than chance. Our results highlight the challenges faced by data-driven methods in learning the dynamics of multistable systems and suggest potential avenues to make these approaches more robust.Comment: Published version (slight change to the title due to journal policy). Code at https://github.com/spcornelius/RCBasin

A Method of Topology Optimization for Curvature Continuous Designs

Recently, there have been many developments made in the field of topology optimization. Specifically, the structural dynamics community has been the leader of the engineering disciplines in using these methods to improve the designs of various structures, ranging from bridges to motor vehicle frames, as well as aerospace structures like the ribs and spars of an airplane. The representation of these designs, however, are usually stair-stepped or faceted throughout the optimization process and require post-process smoothing in the final design stages. Designs with these low-order representations are insufficient for use in higher-order computational fluid dynamics methods, which are becoming more and more popular. With the push for the development of higher-order infrastructures, including higher-order grid generation methods, there exists a need for techniques that handle curvature continuous boundary representations throughout an optimization process. Herein a method has been developed for topology optimization for high-Reynolds number flows that represents smooth bodies, that is, bodies that have continuous curvature. The specific objective function used herein is to match specified x-rays, which are a surrogate for the wake profile of a body in cross-flow. The parameterized level-set method is combined with a boundary extraction technique that incorporates a modified adaptive 4th-order Runge-Kutta algorithm, together with a classical cubic spline curve-fitting method, to produce curvature-continuous boundaries throughout the optimization process. The level-set function is parameterized by the locations and coefficients of Wendland C2 radial basis functions. Topology optimization is achieved by implementing a conjugate gradient optimization algorithm that simultaneously changes the locations of the radial basis function centers and their respective coefficients. To demonstrate the method several test cases are shown where the objective is to generate a smooth representation of a body or bodies that match specified x-rays. First, multiple examples of shape optimization are presented for different topologies. Then topology optimization is demonstrated with an example of two bodies merging and several examples of a single body splitting into separate bodies