Ellipsoidal Approximation Research Articles

Development of a true density-based automated quality grading device for unboiled arecanut kernels

The automated sorting of arecanut kernels is a significant challenge that has not been effectively addressed thus far. Scientific grading techniques are necessary given the paradigm change toward investigating alternative uses for arecanuts in industry and the medical field. This research work emphasizes the relatively unexplored aspect of the post-harvest process; quality grading of kernels based on physical properties. It aimed to develop a novel approach for classifying unboiled (Chali) arecanut kernels cultivated in Goa, India based on their true density, using a combination of mechanical and visual techniques. The study explored the potential of true density as a quality indicator for real-time grading of the kernels. To achieve this, automated grading equipment was devised, utilizing a load cell to measure the kernel's mass and the ellipsoid approximation method to estimate its volume. A machine vision system captured the top and side images of the kernels to measure their volume. Python programs were created to enable image acquisition, processing, object detection, measurement and kernel segregation. Real-time kernel classification was accomplished by establishing serial data communication between the Python code and the Arduino board. The kernel segregation process was facilitated by servomechanism and a stepper motor. The kernels were classified into acceptable and non-acceptable categories based on a threshold value of true density. The research successfully established a method that utilizes the physical attributes of arecanut kernels as parameters for quality grading. However, the study encountered challenges with the density measurements, as the paired t-test results revealed significant differences between the kernel true density measured by the device and the true density estimated using the weighing scale-water displacement method, indicating a percentage error of 13.2%. Addressing these challenges would lead to more accurate density calculations, thereby enhancing the overall effectiveness of the kernel classification process. Furthermore, the technique allowed for the offline estimation of the kernels' porosity, which was found to be 45.3%. In future research, the integration of density and porosity measurement systems could be explored for real-time quality evaluation based on porosity, offering potential opportunities for further enhancement and optimization of the grading process. The technology could be further applied to other types of nuts and agricultural products, thereby overcoming the limitations of color-based sorting using image processing. Key words: Quality grading, True density, Machine vision, Arecanut kernel, Python

Mathematical modeling of meningioma volume change after radiation treatment

ObjectiveMeningiomas are the most common primary central nervous tumor and are often treated with radiation therapy. This study examines the long-term volumetric changes of intracranial meningiomas in response to radiation therapy. The objective is to analyze and model the volumetric changes following treatment. MethodsData from a retrospective single-institution database (2005–2015) were used, with inclusion criteria being patients with a diagnosis of meningiomas, along with additional inclusion criteria consisting of treatment with radiation, having at least three magnetic resonance imaging (MRI) scans with one or more before and after radiation treatment, and the patients following up for at least eighteen months. Exclusion criteria consisted of patients less than 18 years old, patients receiving surgery and/or adjuvant chemotherapy following radiation, and patients without any available details regarding radiation treatment parameters. Tumor volumes were measured via T1-weighted post-contrast MRI and calculated using the ABC/2 ellipsoidal approximation, a method allowing for the measurement of non-linear growth volume reduction. ResultsOf 48 meningioma patients considered, 10 % experienced post-radiation growth, while 75 % witnessed a ≥50 % decrease in volume over a follow-up period of 0.3–14.9 years. Median decay rate was 0.81, and within 1.17 years, 90 % achieved the predicted volume reduction. Predicted vs. actual volumes showed a mean difference of 0.009 ± 0.347 cc. Initial tumor volumes strongly correlated (Pearson’s R=0.98, R-squared=0.96) with final asymptotic volumes, which had a median of 1.50 cc, with interquartile range (IQR) = [0.39, 3.67]. Conclusion90 % of patients achieved tumor-volume reduction at 1.17 years post-treatment, reaching a non-zero asymptote strongly correlated with initial tumor volume, and 75 % experienced at least a 50 % volume decrease. Individual volume changes for responsive meningiomas can be modeled and predicted using exponential decay curves.

Event-Based Distributed Set-Membership Estimation for Complex Networks Under Deception Attacks

This paper addresses the problem of event-based distributed set-membership estimation for complex networks with unknown but bounded (UBB) disturbances. To reflect the compromised data transmissions in cyber security, deception attacks are taken into consideration. Meanwhile, a novel estimation model is proposed against UBB disturbances. In order to schedule the signal transmissions between nodes and remote estimators, a novel decentralized dynamic periodic event-triggered mechanism (DPETM) with a time-varying threshold is developed for each node of the complex networks, which reduces the waste of communication resources and the complexity of computation. Thereafter, a series of distributed set-membership estimators are designed, whose parameters are explicitly determined in terms of the resolution of a particular linear matrix inequality (LMI) related to the information of the communication topology. An optimized ellipsoid estimation set is obtained by applying a recursive optimization algorithm. Finally, the simulation results are shown to demonstrate the viability of the proposed method. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This paper is motivated by set-membership state estimation problem of complex networks in practical missions, such as military, environment, industry, etc. The set-membership estimation of complex networks provides a reliable confidence region for each system node. Event-triggered control is an effective method for the design of set-membership estimator. But the common results require the systems to monitor the measurements point-to-point, which leads to the huge consumption of calculation and communication resources. For this reason, this paper originally extends the DPETM to the discrete-time version from the field of continuous-time systems. Meanwhile, this paper considers the deception attacks in communication channels, and the generic framework established earlier can tackle simultaneously sector-bounded nonlinearity, UBB disturbances, and deception attacks. The main difficulty of this paper lies in the analysis for the sawtooth constraint of periodic samplings. For this difficulty, we introduce a piecewise auxiliary function, which is similar with the loop-function in the field of continuous-time systems. Together with recursive optimization algorithm, the detailed analysis method is proposed for the reliable confidence regions of each set-membership estimator.

Ellipsoidal estimation of motion parameters of a non-cooperative space vehicle from visual information

The use of near-Earth space is currently complicated by presence of space debris objects in Earth’s orbit, which include spent stages of launch vehicles, inoperative satellites, and other large and small artificial objects. One approach to solving the problem of space debris involves docking and capturing a non-cooperative space object or spacecraft (target) with a so-called service spacecraft (chaser) for further actions to repair, refuel or change its orbit. Rendezvous and docking are complicated by the rotation of uncontrolled space objects caused by various factors. To perform this task, it is necessary to know the parameters of the orbital, rotational and relative motion of the target. The parameters of the orbital motion of such objects are usually known quite accurately from measurements from the Earth. This paper examines the case of a tumbling non-cooperative target located in an elliptical orbit. It is assumed that the target relative position and orientation are measured by the computer vision system (CVS) of the chaser. In this case, the position and orientation of the graphical reference frame (GRF) associated with the known 3-D graphical model of the target are determined relative to the reference frame associated with the chaser. The specific type of CVS is not considered. It is assumed that the chaser can carry out some maneuvers near the target and all parameters of the chaser angular motion are known. Thus, the attitude of the GRF relative to inertial reference frame (IRF) can be determined. The measured parameters are not enough to ensure safe rendezvous and docking with the target. To complete this task, it is necessary to determine all kinematic and dynamic parameters of the relative motion between the spacecraft. The rest of the required parameters are estimated. Orientation and rotation parameterization is done using quaternions. The angular motion equation of the target is considered in the GRF. This makes the angular velocity estimation faster and the inertia tensor estimation more stable. Stochastic characteristics of measurement errors are considered to be unknown and are not used. The only information about the errors is the bounds of their values. To determine the relative motion parameters, we use a new dynamic set-membership filter with ellipsoidal estimates. The filter can be successfully implemented on low-power on-board processors. The properties of the proposed algorithm are demonstrated using numerical simulation. The results obtained are expected to be used in the development of a navigation system for the rendezvous and docking, developed by a group of Ukrainian space industry enterprises under the leadership of the LLC “Kurs-orbital” (https://kursorbital.com/).

Detecting outliers in the multivariate control charts for dispersion monitoring

AbstractOutlier detection is an important aspect of statistical process monitoring (SPM) because outliers affect the performance of control charts. SPM researchers study the negative impact of outliers on control charts for monitoring location parameters. However, there is little research on outlier detection in multivariate charts for monitoring process dispersion. This study aims to investigate the impact of outliers in multivariate control charts for monitoring covariance matrix of a process, and then to recommend techniques for detecting potential outliers present from Phase I samples. We propose a new multivariate dispersion chart that employs the determinant of logarithm of estimated covariance matrix as the monitoring statistic. Through Monte Carlo simulations, the results show how outliers from the first phase affect the overall performance of multivariate charts. The results also demonstrate that the minimum volume ellipsoid (MVE) estimator is effective in reducing the effect of outliers on the proposed control scheme than the other compared estimators.

Sequential centralized fusion of multiple passive acoustic sensors with unknown propagation delays

In this paper, we address the problem of target tracking using multiple acoustic sensors to observe the target state with unknown propagation delays. This problem occurs because the measurements received by multiple acoustic sensors located at different positions are from different unknown emission times of the acoustic signal even if the sensors receive measurements simultaneously; thus, they cannot be stacked up directly for centralized fusion as usual. However, the target states at different unknown emission times can be aligned to a common measurement received time by the retrodiction of state prediction. On this basis, herein we propose the centralized fusion of multiple acoustic sensors via sequential processing, namely, sequential centralized fusion (SCF). First, the measurement received time is chosen as the target state time, and the target state is predicted to this time for tracking. Second, state prediction is retrodicted to the signal emission times by solving augmented implicit nonlinear equations through Wegstein's method. Third, the state prediction is updated with acoustic measurements sequentially at measurement received time. Compared with the existing distributed fusion methods, our proposed SCF method has smaller computational complexity and better tracking performance. Illustrative examples demonstrate that SCF outperforms covariance intersection and the largest ellipsoid approximation.

Local stabilization of networked linear systems with decentralized switching controllers

In this paper, we consider the decentralized control design problem for a particular case of networked switched affine systems. The considered network consists of interconnected (identical) linear systems with the controlled input switching among a finite set of values. We address a challenging case where the network can be only locally stabilized. Scalable Lyapunov based conditions are proposed for designing such decentralized controllers. The derived conditions (theoretical and linear matrix inequalities) do not depend on the number of subsystems. Ellipsoidal estimates of the domain of attraction are given.

Frequency domain identifiability and sloppiness of descriptor systems with an LFT structure

Identifiability and sloppiness are investigated in this paper for the parameters of a descriptor system based on its frequency responses. Two metrics are suggested respectively for measuring absolute and relative sloppiness of the parameter vector. In this descriptor system, system matrices are assumed to depend on its parameters through a linear fractional transformation, which enables it to include a large class of networked dynamic systems as a special case. When an associated transfer function matrix is of full normal row rank, a matrix rank based necessary and sufficient condition is derived for parameter identifiability. This condition can be verified recursively. An algorithm is suggested to find a set of frequencies, at which system frequency responses are capable to uniquely determine its parameter values. An ellipsoid approximation is given for the set consisting of all the parameter values of the descriptor system, whose frequency response deviates within a prescribed distance from that associated with a globally identifiable parameter vector value. Explicit formulas are also derived for the suggested absolute and relative sloppiness metrics for some application significant cases.

Image-guided surgical planning of percutaneous nephrolithotomy with patient-specific CTRs.

We propose the utilization of patient-specific concentric-tube robots (CTRs) whose designs are optimized to enhance their volumetric reachability of the renal stone, thus reducing the morbidities associated with percutaneous nephrolithotomy procedures. By employing a nested optimization-driven scheme, this work aims to determine a single surgical tract through which the patient-tailored CTR is deployed. We carry out a sensitivity analysis on the combined percutaneous access and optimized CTR design with respect to breathing-induced excursion of the kidneys based on preoperative images. Further, an investigation is also performed of the appropriateness and effectiveness of the percutaneous access provided by the proposed algorithm compared to that of an expert urologist. The method is based on an ellipsoidal approximation to the renal calculi and a grid search over candidate skin areas and available renal calyces using an anatomically constrained kinematic mapping of the CTR. Percutaneous access is selected for collision-free CTR deployment to the centroid of the stones with minimal positional error at the renal calyx. Further optimization of the CTR design results in a robot tailored to the therapeutic anatomical features of each clinical case. The study examined 14 sets of clinical data of PCNL patients, analyzing stone reachability using preoperative images and breathing-induced motions of the kidney. An experienced urologist qualitatively assessed the adequacy of percutaneous access generated by the algorithm. An assessment conducted by an expert urologist found that the percutaneous accesses produced by the proposed approach were found to be comparable to those chosen by the expert surgeon in most clinical cases. The simulated results demonstrated a mean volume coverage of for static anatomy and and when considering a 1cm excursion of the kidney in the craniocaudal directions due to respiration or tool-tissue interaction. The optimization-driven scheme for determining a single tract surgical plan, coupled with the use of a patient-specific CTR, shows promising results for improving percutaneous access in PCNL procedures. This approach clearly shows the potential for enhancing the quality and suitability of percutaneous accesses, addressing the challenges posed by staghorn and non-staghorn stones during PCNL procedures. Further research involving clinical validation is necessary to confirm these findings and explore the potential clinical benefits of the approach.

Analytical Optimal Solution for the Reachable Domain of Low-Thrust Spacecraft

Low-thrust electric propulsion system has drawn increasing attention from researchers because of its high propellant efficiency. The reachable domain of low-thrust spacecraft can provide a geometric insight for space mission planning. In this paper, analytical solutions of the envelope of reachable domain are obtained by employing the Pontryagin’s maximum principle in the well-known linearized model of relative motion, the Tschauner–Hempel equations. Specifically, this study focuses on two contributions. First, an analytical solution of the envelope of reachable domain is obtained, and the associated optimal control profile is derived. Second, an ellipsoid approximation of the reachable domain is proposed to represent the envelope directly based on the analytical solution. Numerical simulations are conducted to demonstrate the accuracy of the proposed solutions. The results show that the reachable domain obtained analytically coincides well with that solved by the numerical indirect method based on the two-body model with low thrust.

Mesoscopic pore characteristics analysis of aged bridge concrete based on X-ray computed tomography

The characteristics of mesoscopic pores in concrete bridges have significant influence on structural mechanical properties. In this study, 18 core specimens, taken from three decommissioned concrete bridges serving for about 25 years, were investigated using X-ray computed tomography (X-ray CT). After segmentation and 3D reconstruction with CT scanning images, the spatial characteristics for the porosity, volume, and shape of the concrete mesoscopic pores were analysed. The mesoscopic porosity decreases with the increase of concrete strength. The logarithm of the pore volume obeyed the Gumbel extreme value distribution, whose location and scale parameters had obvious bilinear degradation with depth. Ellipsoidal approximation was employed to precisely characterise the individual pore structure, and the Gaussian copula function could describe the joint distribution among the pore shape parameters. It was found that correlation coefficients of ellipsoidal shape parameters remained stable with depth. The proposed model quantitatively describes the mesoscopic pores in decommissioned concrete bridges and can shed certain light on concrete pore simulation.

Three-Dimensional Angularity Characterization of Coarse Aggregates by the Optimal Ellipsoid Approximation Algorithm

The three-dimensional (3D) angularity of coarse aggregates was investigated in this study by an optimal ellipsoid approximation algorithm. The minimum volume enclosing ellipsoid (MVEE) of the 3D coarse aggregate particle represented by the surface point cloud was computed by a Python program. An algorithm was proposed to compute the optimal ellipsoid that is inscribed in the aggregate particle as far as possible. In the algorithm, a fitting index was proposed and a cycle program was coded to search the optimal ellipsoid. Based on the optimal ellipsoid and the point cloud of the coarse aggregate particle, a 3D angularity index was proposed. The critical discriminant coefficient was introduced into the angularity index to filter out the tiny convex parts on the particle. Six 3D geometric models were generated and five 3D aggregate particles were randomly selected to verify the effectiveness of the angularity index. The results demonstrate that the angularity index proposed in this study can effectively distinguish the angularity of different geometric models. The effect of mesh precision on the angularity index was analyzed and the critical discriminant coefficient was studied by the parameter analysis method and Delphi expert investigation method.

Incorporating species-specific morphology improves model predictions of thermal and hydric stress in the sand fiddler crab, Leptuca pugilator

Understanding where and why organisms are experiencing thermal and hydric stress is critical for predicting species' responses to climate change. Biophysical models that explicitly link organismal functional traits like morphology, physiology, and behavior to environmental conditions can provide valuable insight into determinants of thermal and hydric stress. Here we use a combination of direct measurements, 3D modeling, and computational fluid dynamics to develop a detailed biophysical model of the sand fiddler crab, Leptuca pugilator. We compare the detailed model's performance to a model using a simpler ellipsoidal approximation of a crab. The detailed model predicted crab body temperatures within 1 °C of observed in both laboratory and field settings; the ellipsoidal approximation model predicted body temperatures within 2 °C of observed body temperatures. Model predictions are meaningfully improved through efforts to incorporate species-specific morphological properties rather than relying on simple geometric approximations. Experimental evaporative water loss (EWL) measurements indicate that L. pugilator can modify its permeability to EWL as a function of vapor density gradients, providing novel insight into physiological thermoregulation in the species. Body temperature and EWL predictions made over the course of a year at a single site demonstrate how such biophysical models can be used to explore mechanistic drivers and spatiotemporal patterns of thermal and hydric stress, providing insight into current and future distributions in the face of climate change.

Ellipsoidal approximations of the minimal robust positively invariant set

An optimization algorithm is presented in this paper for the minimal robust positively invariant (mRPI) set approximations via sums-of-squares (SOS) optimization. The mRPI set is an effective tool for robust analysis of uncertain systems under bounded disturbances. The approximation of the mRPI set is always characterized by a polyhedron computed after finite time iterations. In this paper, an mRPI set is characterized by an ellipsoidal set while bounded parametric uncertainties act on states. The proposed algorithm optimizes the shape matrix of the ellipsoidal set approximation by minimizing the volume of the ellipsoidal set. The algorithm is designed for discrete-time and continuous-time nonlinear systems respectively. The algorithm has the ability to further minimize the mRPI set by optimizing the state-feedback control law. Examples are employed to validate the effectiveness of the proposed algorithms.

Detect Orientation of Symmetric Objects from Monocular Camera to Enhance Landmark Estimations in Object SLAM

Object simultaneous localization and mapping (SLAM) introduces object-level landmarks to the map and helps robots to further perceive their surroundings. As one of the most preferred landmark representations, ellipsoid has a dense mathematical expression and can represent the occupied space of objects with high accuracy. However, the orientations of ellipsoid approximations often fail to coincide with the orientation of objects. To further improve the performance of object SLAM systems with ellipsoid landmarks, we innovatively propose a strategy that first extracts the orientations of those symmetric human-made objects in a single frame and then implements the results of the orientation as a back-end constraint factor of the ellipsoid landmarks. Experimental results obtained show that, compared with the baseline, the proposed orientation detection method can reduce the orientation error by more than 46.5% in most tested datasets and improves the accuracy of mapping. The average translation, rotation and shape error improved by 63.4%, 61.7% and 42.4%, respectively, compared with quadric-SLAM. With only 9 ms additional time cost of each frame, the object SLAM system integrated with our proposed method can still run in real time.

Real-Time Robust Receding Horizon Planning Using Hamilton–Jacobi Reachability Analysis

Safety guarantee prior to the deployment of robots can be difficult due to unexpected disturbances in runtime. This article presents a real-time receding-horizon robust trajectory planning algorithm for nonlinear closed-loop systems, which guarantees the safety of the system under unknown but bounded disturbances. We characterize the forward reachable sets (FRSs) of the system based on the Hamilton–Jacobi reachability analysis as a means for safety verification. For the online computation of the FRSs, we approximate nonlinear systems as LTV systems with linearization errors and compute ellipsoids that encompass the FRSs in continuous time. Using the proposed ellipsoidal approximation of the FRSs, we formulate a computationally tractable robust planning problem that can be solved online. Consequently, the proposed method enables real-time replanning of a reference trajectory with safety guarantees even when the system encounters unexpected disturbances in runtime. The flight experiment of obstacle avoidance in a windy environment validates the proposed robust planning algorithm.

A quantized set‐membership estimation‐based heading control method of unmanned surface vessels under unknown‐but‐bounded wave‐induced disturbances

AbstractThis paper is concerned with the heading tracking control problem for a network‐based unmanned surface vessel (USV) under wave‐induced disturbances. Considering the characteristics of the wave‐induced disturbances, the unknown‐but‐bounded (UBB) noise model is adopted. Meanwhile, signal quantization is taken into account due to the limited capacity of the communication channel. Based on these considerations, a novel set‐membership based control scheme is proposed, which consists of a set‐membership filter (SMF) and a set‐membership controller (SMC). In the proposed control scheme, the SMF is designed for providing an ellipsoidal estimation set for the USV at each sampling step, and then the SMC uses the estimation set for producing control input for the USV in order to track the reference. Sufficient conditions are derived for the considered USV system to be asymptotically stable and satisfy the modified set‐membership performance constraint. Simulation results verifies the effectiveness of the proposed control scheme.

Reachability of Linear Time-Invariant Systems via Ellipsoidal Approximations

Reachability analysis is a powerful tool when it comes to capturing the behaviour, thus verifying the safety, of autonomous systems. However, general-purpose methods, such as Hamilton-Jacobi approaches, exhibit exponential computational complexity with respect to the state dimension. In this paper, we show that supersolutions and subsolutions of a Hamilton-Jacobi-Bellman equation can be used to generate under- and over-approximating reachable sets for nonlinear systems, and based on this, we develop a scheme for approximating reachable sets of linear time-invariant systems via ellipsoids with polynomial computational complexity.

Nonlinear Analysis of Stability and Safety of Optimal Velocity Model Vehicle Groups on Ring Roads

In this work, we study a group of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> homogeneous vehicles travelling on a ring road by describing the collective vehicle dynamics via the so-called Optimal Velocity Model (OVM). We analyze the stability of the equilibrium motion regime in which all vehicles drive at the same speed and keep the same headway. First, stability is studied through linearization, thereby highlighting the roles of the model parameters. Next, we tackle the full nonlinear model and we determine ellipsoidal estimates of the equilibrium’s region of attraction by defining and solving suitable Linear Matrix Inequalities (LMIs). Finally, safety aspects are discussed, incorporated in our LMI formulation as lower bounds of the inter-vehicle distances, and illustrated via simulations.

Shape matters: Lagrangian tracking of complex nonspherical microparticles in superellipsoidal approximation

Humans are constantly exposed to airborne pollutants such as pollen, exhaust residues, microplastics, fabrics, aerosols, or, as recently, ash particles from volcanic eruptions, which are rarely perfectly spherical. In order to reduce the impact of harmful particles or, on the contrary, to improve the targeted delivery of drugs, understanding the motion of complex shaped particles in fluid flows is of key interest. Common models mainly use shape factors to account for deviations from spherical shape, but these often fail to accurately predict particle motion. We advocate a more accurate modeling of complex particles by a superellipsoidal shape approximation, which allows covering a wide range of particle geometries. Superellipsoidal particle shapes allow for a novel approximation of translational and rotational resistance tensors, derived based on data from dedicated DNS computations. Our surrogate approach for convex bodies (ϵ1,ϵ2∈(0,2)), implemented in OpenFOAM® based on Lagrangian particle tracking, is first validated based on experimental and in-silico results from the literature, followed by a comparison of the effects of non-sphericity for some well known fluid flow cases, such as a lid-driven cavity (validated for Re=470, St=0.0023), pipe flow (validated for Re=137, St=0.01) and a simplified bifurcation (validated for Re=500, St=0.5×10−2−0.5). We show that using shape factor assisted spherical or ellipsoidal approximations of the particles leads to insufficient accuracy of computation of the particle’s trajectory, whereas the newly derived superellipsoidal drag and torque models proved to provide a superior accuracy of the Lagrangian particle tracking over simplified non-spherical particle approximations.