Gait Assessment Using Three-Dimensional Acceleration of the Trunk in Idiopathic Normal Pressure Hydrocephalus

Background: The subjective evaluation of pathological gait exhibits a low inter-rater reliability. Therefore, we developed a three-dimensional acceleration of the trunk during walking to assess the pathological gait quantitatively.Methods: We evaluated 97 patients who underwent the cerebrospinal tap test and were diagnosed with idiopathic normal pressure hydrocephalus (iNPH) and 68 healthy elderlies. The gait features of all patients were evaluated and classified as one of the following: freezing of gait, wide-based gait, short-stepped gait, shuffling gait, instability, gait festination, difficulty in changing direction, and balance disorder in standing up. All gait features of 68 healthy elderlies were treated as normal. Trunk acceleration was recorded automatically by a smartphone placed on the umbilicus during a 15-foot walking test. Two novel indices were created. The first index was a trunk acceleration index, which was defined as (forward acceleration fluctuation) + (vertical acceleration fluctuation) – (lateral acceleration fluctuation) based on the multivariate logistics regression model, and the second index was created by multiplying the forward acceleration with the vertical acceleration. Additionally, 95% confidence ellipsoid volume of the three-dimensional accelerations was assessed.Results: Forward and vertical acceleration fluctuations were significantly associated with the probability of an iNPH-specific pathological gait. The trunk acceleration index demonstrated the strongest association with the probability of an iNPH-specific pathological gait. The areas under the receiver-operating characteristic curves for detecting 100% probability of an iNPH-specific pathological gait were 86.9% for forward acceleration fluctuation, 88.0% for vertical acceleration fluctuation, 82.8% for lateral acceleration fluctuation, 89.0% for trunk acceleration index, 88.8% for forward × vertical acceleration fluctuation, and 87.8% for 95% confidence ellipsoid volume of the three-dimensional accelerations.Conclusions: The probability of a pathological gait specific to iNPH is high at the trunk acceleration fluctuation, reduced in the forward and vertical directions, and increased in the lateral direction.

Multiway PCA for Early Leak Detection in a Pipeline System of a Steam Boiler—Selected Case Studies

In the paper the usability of the Multiway PCA (MPCA) method for early detection of leakages in the pipeline system of a steam boiler in a thermal-electrical power plant is presented. A long segment of measurements of selected process variables was divided into a series of “batches” (representing daily recordings of normal behavior of the plant) and used to create the MPCA model of a “healthy” system in a reduced space of three principal components (PC). The periodically updated MPCA model was used to establish the confidence ellipsoid for the “healthy” system in the PC coordinates. The staff’s decision of the probable leak detection is supported by comparison of the current location of the operating point (on the “fault trajectory”) with the boundaries of the confidence ellipsoid. It must be emphasized that due to daily and seasonal changes of heat/electricity demands, the process variables have substantially greater variability than in the examples of batch processes studied in literature. Despite those real challenges for the MPCA method, numerical examples confirmed that the presented approach was able to foresee the leaks earlier than the operator, typically 3–5 days before the boiler shutdown. The presented methodology may be useful in implementation of an on-line system, developed to improve safety and maintenance of boilers in a thermal-electrical power plant.

The partial banana mapping: a robust linear method for impact probability estimation

ABSTRACT This paper presents a robust linear method for impact probability estimation of near-Earth asteroids with the Earth. This method is a significantly modified and improved method, which uses a special curvilinear coordinate system associated with the nominal orbit of an asteroid. One of the coordinates of this system is the mean anomaly in the osculating orbit of an asteroid. A normal distribution of errors of coordinates and velocities of this system is assumed. Because of the usage of the curvilinear coordinate system, the fact that the confidence region is curved and stretched mainly along the nominal asteroid orbit is taken into account. On the main axis of the curvilinear confidence ellipsoid the virtual asteroid, which is the closest to the Earth, is found. The part of the curvilinear confidence ellipsoid, around the found virtual asteroid, is obtained and mapped on to its target plane. The impact probability is calculated as the probability of the asteroid being in the region of the found virtual asteroid multiplied by the probability of a collision of the found virtual asteroid with the Earth. This approach is shown to give more accurate and trustworthy results than the target plane method.

Monitoring Deformation along Railway Systems Combining Multi-Temporal InSAR and LiDAR Data

Multi-temporal interferometric synthetic aperture radar (MT-InSAR) can be applied to monitor the structural health of infrastructure such as railways, bridges, and highways. However, for the successful interpretation of the observed deformation within a structure, or between structures, it is imperative to associate a radar scatterer unambiguously with an actual physical object. Unfortunately, the limited positioning accuracy of the radar scatterers hampers this attribution, which limits the applicability of MT-InSAR. In this study, we propose an approach for health monitoring of railway system combining MT-InSAR and LiDAR (laser scanning) data. An amplitude-augmented interferometric processing approach is applied to extract continuously coherent scatterers (CCS) and temporary coherent scatterers (TCS), and estimate the parameters of interest. Based on the 3D confidence ellipsoid and a decorrelation transformation, all radar scatterers are linked to points in the point cloud and their coordinates are corrected as well. Additionally, several quality metrics defined using both the covariance matrix and the radar geometry are introduced to evaluate the results. Experimental results show that most radar scatterers match well with laser points and that LiDAR data are valuable as auxiliary data to classify the radar scatterers.

Systematic Effects in Laser Scanning and Visualization by Confidence Regions

A new method for dealing with systematic effects in laser scanning and visualizing them by confidence regions is derived. The standard deviations of the systematic effects are obtained by repeatedly measuring three-dimensional coordinates by the laser scanner. In addition, autocovariance and cross-covariance functions are computed by the repeated measurements and give the correlations of the systematic effects. The normal distribution for the measurements and the multivariate uniform distribution for the systematic effects are applied to generate random variates for the measurements and random variates for the measurements plus systematic effects. Monte Carlo estimates of the expectations and the covariance matrix of the measurements with systematic effects are computed. The densities for the confidence ellipsoid for the measurements and the confidence region for the measurements with systematic effects are obtained by relative frequencies. They only depend on the size of the rectangular volume elements for which the densities are determined. The problem of sorting the densities is solved by sorting distances together with the densities. This allows a visualization of the confidence ellipsoid for the measurements and the confidence region for the measurements with systematic effects.

Confidence regions in singular weakly nonlinear regression models with constraints

It is rather complicated to construct the confidence region in nonlinear regression model mainly when number of parameters is large. If the nonlinearity of the model is weak, then it is possible, after some modification, to approximate the confidence region by a confidence ellipsoid in the linearized model. The aim of the paper is to propose a solution in singular models with constraints.

ASSESSMENT OF POSTURAL INSTABILITY IN PATIENTS WITH A NEUROLOGICAL DISORDER USING A TRI-AXIAL ACCELEROMETER

<span lang="EN-US">Current techniques for quantifying human postural stability during quiet standing have several limitations. The main problem is that only two movement variables are evaluated, though a better description of complex three-dimensional (3-D) movements can be provided with the use of three variables. A single tri-axial accelerometer placed on the trunk was used to measure 3-D data.<br />We are able to evaluate 3-D movements using a method based on the volume of confidence ellipsoid (VE) of the set of points obtained by plotting three accelerations against each other. Our method was used to identify and evaluate pathological balance control. In this study, measurements were made of patients with progressive cerebellar ataxia, and also control measurements of healthy subjects, and a statistical analysis was performed. The results show that the VEs of the neurological disorder patients are significantly larger than the VEs of the healthy subjects. It can be seen that the quantitative method based on VE is very sensitive for identifying changes in stability, and that it is able to distinguish between neurological disorder patients and healthy subjects.<br /></span>

Volume of confidence ellipsoid: a technique for quantifying trunk sway during stance

The position of the trunk can be negatively affected by many diseases. This work focuses on a noninvasive method of quantifying human postural stability and identifying defects in balance and coordination as a result of the nervous system pathology. We used a three-degree-of-freedom orientation tracker (Xsens MTx unit) placed on a patient’s trunk and measured three-dimensional (3-D) data (pitch, roll, and yaw) during quiet stance. The principal component analysis was used to analyze the data and to determine the volume of 3-D 95% confidence ellipsoid. Using this method, we were able to model the distribution of the measured 3-D data (pitch, roll, and yaw). Eight patients with degenerative cerebellar disease and eight healthy subjects in this study were measured during stance, with eyes open and eyes closed, and statistical analysis was performed. The results of the new method based on the 3-D confidence ellipsoid show that the volumes related to the patients are significantly larger than the volumes related to the healthy subjects. The concept of confidence ellipsoid volume, although known to the biomechanics community, has not been used before to study the postural balance problems. The method can also be used to study, for example, head and pelvis movements or alignments during stance.

Bayesian survey design to optimize resolution in waveform inversion

We describe a Bayesian methodology for designing seismic experiments that optimally maximize model-parameter resolution for imaging purposes. The proposed optimal experiment design algorithm finds the measurements that are likely to optimally reduce the expected uncertainty on the model parameters. This Bayesian [Formula: see text]-optimality-based algorithm minimizes the volume of the expected confidence ellipsoid and leads to the maximization of the expected resolution of the model parameters. Computational efficiency is achieved by a greedy algorithm in which the design is sequentially improved. In contrast to minimizing the uncertainty volume over the entire subsurface simultaneously, a refinement of the algorithm minimizes the marginal uncertainties in a region of interest. Minimizing marginal uncertainties simultaneously accounts for quantitative prior model uncertainties while honoring a qualitative focus on particular regions of interest. The benefits of the proposed method over traditional non-Bayesian ones are demonstrated with several geophysical examples. These include reducing large seismic data volumes for real-time imaging and solving the problem of designing seismic surveys that account for source bandwidth, signal-to-noise ratio, and attenuation.