Probabilistic Error Model Research Articles

Precision Sensitivity Optimization for Parallel Robotic System Based on Multi-Source Preventive Maintenance

This paper presents a multi-source preventive maintenance (MPM) based precision sensitivity optimization method for parallel robotic systems. Taking a parallel mechanism as an example, the input error can be divided into finite mutually independent uncertain error sources, and the probabilistic error model is established by the Monte Carlo stochastic method. Considering that several times of maintenance can lead to an increase of the accuracy degradation factor, a generalized hierarchy maintenance yield model is established, where the cost of preventive maintenance and failure replacement maintenance are distinguished between the independent error source and the overall error source. The nonlinear relationship between the maintenance yield per unit cost and influencing factors, including the error threshold and the maintenance times is obtained, which allows to develop an optimal maintenance strategy. Preventive maintenance is introduced to avoid unintended failure of the mechanism while extending the lifetime. The high-precision parallel mechanism has demonstrated promising applications in medical, industrial and other fields, and its economic benefits can be effectively improved by incorporating the MPM method. The experiment of manufacturing human lung models using a parallel 3D printing device demonstrates that the MPM method can improve the long-term precision and reliability of the parallel device, and the optimized human lung contour tracking precision can be improved by up to 55.56%.

Assembly precision design for parallel robotic mechanism based on uncertain hybrid tolerance allocation

PurposeThe coupling impact of hybrid uncertain errors on the machine precision is complex, as a result of which the designing method with multiple independent error sources under uncertainties remains a challenge. For the purpose of precision improvement, this paper focuses on the robot design and aims to present an assembly precision design method based on uncertain hybrid tolerance allocation (UHTA), to improve the positioning precision of the mechanized robot, as well as realize high precision positioning within the workspace.Design/methodology/approachThe fundamentals of the parallel mechanism are introduced first to implement concept design of a 3-R(4S) &3-SS parallel robot. The kinematic modeling of the robot is carried out, and the performance indexes of the robot are calculated via Jacobian matrix, on the basis of which, the 3D spatial overall workspace can be quantified and visualized, under the constraints of limited rod, to avoid the singular position. The error of the robot is described, and a probabilistic error model is hereby developed to classify the hybrid error sensitivity of each independent uncertain error source by Monte Carlo stochastic method. Most innovatively, a methodology called UHTA is proposed to optimize the robot precision, and the tolerance allocation approach is conducted to reduce the overall error amplitude and improve the robotized positioning precision, on the premise of not increasing assembly cost.FindingsThe proposed approach is validated by digital simulation of medical puncture robot. The experiment highlights the mathematical findings that the horizontal plane positioning error of the parallel robotic mechanism can be effectively reduced after using UHTA, and the average precision can be improved by up to 39.54%.Originality/valueThe originality lies in UHTA-based precision design method for parallel robots. The proposed method has widely expanding application scenarios in industrial robots, biomedical robots and other assembly automation fields.

Robust Design for Intelligent Reflecting Surface-Assisted Secrecy SWIPT Network

This paper investigates the robust beamforming design in a secrecy multiple-input single-output (MISO) network aided by the intelligent reflecting surface (IRS) with simultaneous wireless information and power transfer (SWIPT). Specifically, by considering that the energy receivers (ERs) are potential eavesdroppers (Eves) and imperfect channel state information (CSI) of the direct and cascaded channels can be obtained, we investigate the max-min fairness robust secrecy design. The objective is to maximize the minimum robust information rate among the legitimate information receivers (IRs). To solve the formulated non-convex design problem in bounded and probabilistic CSI error models, we utilize the alternating optimization (AO) and successive convex approximation (SCA) methods to obtain an approximate problem. Then, an iteration-based algorithm framework was proposed, where the unit modulus constraint (UMC) of the IRS is handled by the penalty dual decomposition (PDD) method. Moreover, a stochastic SCA method is proposed to handle the outage constrained design with statistical CSI. Finally, simulation results validate the promising performance of the proposed design.

Compliance error compensation of a robot end-effector with joint stiffness uncertainties for milling: An analytical model

This paper presents an analytical model to compensate for the compliance errors of a Delta parallel robot as the mini robot, which is mounted at the end effector of an articulated robot to form a macro-mini manipulator for milling operations. This model is derived from a passive compliance design with mechanical springs for the robot considering uncertainties in the joint stiffness. The significance of this design is that it allows determining the compliance parameters of the model by analytical formulas. Quantitative criteria, probabilistic error models, and numerical examples with milling-like trajectories are given to evaluate the effectiveness of the proposed model. Simulation analysis was performed for the Delta robot that identified the sensitivity of its compliance errors over the workspace. The positioning accuracy reliability of the robot was improved with the model, particularly its deflection accuracy along a prescribed trajectory was theoretically increased by 82.6 percent under an estimated process force. Lastly, the amplification of the compliance errors was diminished when the standard deviation of the joint stiffness was varied.

Characterizing distributed hydrological model residual errors using a probabilistic long short-term memory network

Errors in hydrological simulations have impacted their applications in flood prediction and water resources management. Properly characterizing the properties of errors such as heteroscedasticity and autocorrelation can provide improved hydrological predictions. Here, we present a probabilistic Long Short-Term Memory (LSTM) network for modeling hydrological residual errors. Three steps are undertaken to characterize uncertainty using the LSTM: (i) the network is trained with gradient optimization to obtain optimal predictions; (ii) the distribution of the errors for optimal predictions are estimated using a Bayesian Markov chain Monte Carlo (MCMC) algorithm; (iii) probabilistic predictions are made using the inferred error distribution and optimal predictions. We examine the model in the source of Yellow River, China over the period 1992–2015. A distributed hydrological model MIKE SHE is applied to simulate streamflows in the catchment. As benchmarks, we compare the results with a Bayesian linear regression model and a traditional probabilistic residual error model. Results show the probabilistic LSTM network reduces the heteroscedasticity and removes almost all autocorrelations in residual errors. Besides, compared with the other two methods, the proposed method produces more than 50% narrower uncertainty intervals with the best probability coverage. Our results highlight the potential ability of a deep learning approach integrated with a hydrological model to better characterize predictive uncertainty in hydrologic modeling.

GRACEfully Closing the Water Balance: A Data‐Driven Probabilistic Approach Applied to River Basins in Iran

AbstractTo fully benefit from remotely sensed observations of the terrestrial water cycle, bias and random errors in these data sets need to be quantified. This paper presents a Bayesian hierarchical model that fuses monthly water balance data and estimates the corresponding data errors and error‐corrected water balance components (precipitation, evaporation, river discharge, and water storage). The model combines monthly basin‐scale water balance constraints with probabilistic data error models for each water balance variable. Each data error model includes parameters that are in turn treated as unknown random variables to reflect uncertainty in the errors. Errors in precipitation and evaporation data are parameterized as a function of multiple data sources, while errors in GRACE storage observations are described by a noisy sine wave model with parameters controlling the phase, amplitude, and randomness of the sine wave. Error parameters and water balance variables are estimated using a combination of Markov Chain Monte Carlo sampling and iterative smoothing. Application to semiarid river basins in Iran yields (a) significant reductions in evaporation uncertainty during water‐stressed summers, (b) basin‐specific timing and amplitude corrections of the GRACE water storage dynamics, and (c) posterior water balance estimates with average standard errors of 4–12 mm/month for water storage, 3.5–7 mm/month for precipitation, 2–6 mm/month for evaporation, and 0–2 mm/month for river discharge. The approach is readily extended to other data sets and other (gauged) basins around the world, possibly using customized data error models. The resulting error‐filtered and bias‐corrected water balance estimates can be used to evaluate hydrological models.

Comprehensive framework for the hyper-robust Bayesian calibration of a nondestructive testing instrument

Reinforced concrete structures degrade due to rebar corrosion, leading to the loss of steel rebar volume. Nondestructive techniques (NDT) are employed for knowing the current state of a corroding structure. However, there are uncertainties in the reported values because of measurement error and noise. In this paper, probabilistic measurement error models (MEM) – relating the “true” value to the NDT reported value – are used, and instrument calibration is proposed to quantify the systematic error and random error. Additionally, there is uncertainty in choosing an appropriate MEM from an ensemble of possible models. This entire process is proposed here within a Bayesian framework of uncertainty quantification. A hyper-robust calibration approach is adopted to avoid the calibrated measurement’s sensitivity to the uncertainties in MEM parameters and in the model selection, such that the actual estimate of the corrosion rate is quantified in the form of a probability density function. The proposed procedure is demonstrated for a linear polarisation resistance based instrument. The proposed approach is found to be suitable for the study case and also general enough to be applied to other NDT instruments.

ESREEM: Efficient Short Reads Error Estimation Computational Model for Next-generation Genome Sequencing

Aims: To assess the error profile in NGS data, generated from high throughput sequencing machines. Background: Short-read sequencing data from Next Generation Sequencing (NGS) are currently being generated by a number of research projects. Depicting the errors produced by NGS platforms and expressing accurate genetic variation from reads are two inter-dependent phases. It has high significance in various analyses, such as genome sequence assembly, SNPs calling, evolutionary studies, and haplotype inference. The systematic and random errors show incidence profile for each of the sequencing platforms i.e. Illumina sequencing, Pacific Biosciences, 454 pyrosequencing, Complete Genomics DNA nanoball sequencing, Ion Torrent sequencing, and Oxford Nanopore sequencing. Advances in NGS deliver galactic data with the addition of errors. Some ratio of these errors may emulate genuine true biological signals i.e., mutation, and may subsequently negate the results. Various independent applications have been proposed to correct the sequencing errors. Systematic analysis of these algorithms shows that state-of-the-art models are missing. Objective: In this paper, an effcient error estimation computational model called ESREEM is proposed to assess the error rates in NGS data. Methods: The proposed model prospects the analysis that there exists a true linear regression association between the number of reads containing errors and the number of reads sequenced. The model is based on a probabilistic error model integrated with the Hidden Markov Model (HMM). Result: The proposed model is evaluated on several benchmark datasets and the results obtained are compared with state-of-the-art algorithms. Conclusions: Experimental results analyses show that the proposed model efficiently estimates errors and runs in less time as compared to others.

Fundamental Thermal Limits on Data Retention in Low-Voltage CMOS Latches and SRAM

Ultra-low-power systems with substantial computing capacity require latches and SRAMs to operate at extremely low supply voltages. However, with aggressive technology scaling, reliability becomes a major challenge due to unavoidable process variations and the presence of multiple noise sources, including intrinsic thermal noise. This paper provides a quantitative measure of reliability by calculating the probability distribution function (PDF) of errors induced by thermal noise in latches and SRAMs operating in subthreshold conditions. Implemented in a novel simulation tool for thermal-noise analysis of CMOS circuits (STTACC), our algorithm uses a stochastic differential equation circuit model that preserves the proper Poissonian statistics for thermal-noise-driven current fluctuations in MOSFETs. Our probabilistic error model can handle error rate analysis for arrays of latches or full SRAMs on time scales from seconds to years without excessive computational overhead. We demonstrate that the time-to-error (TTE) statistics of subthreshold SRAMs obey log-normal distributions that depend on parameters such as node and device capacitance, device threshold variations and operating conditions of supply voltage and temperature. This makes it possible to quantitatively evaluate the asymptotic behavior of extremely rare error events that are inaccessible to standard SPICE-based simulations.

Robust Secure Wireless Powered MISO Cognitive Mobile Edge Computing

Wireless power transfer (WPT) and cognitive radio (CR) are two promising techniques in designing mobile-edge computing (MEC) systems. In this paper, we study a robust secure wireless powered multiple-input single-output (MISO) cognitive MEC system, which integrates several techniques: physical-layer security, WPT, CR, underlay spectrum sharing and MEC. Three optimization problems are formulated to minimize the total transmission power (TTP) of the primary transmitter (PT) and the secondary base station (SBS) under perfect channel state information (CSI) model, bounded CSI error model and the probabilistic CSI error model, respectively. The formulated problems are nonconvex and hard to solve. Three two-phase iterative optimization algorithms combined with Lagrangian dual, semidefinite relaxation (SDR), S-Procedure and Bernstein-type inequalities are proposed to jointly optimize the beamforming vectors of the PT and the SBS, the central processing unit (CPU) frequency and the transmit power of the MD. Simulation results are provided to verify the effectiveness of the proposed algorithms.

Analysis and Improvements in AprilTag Based State Estimation.

In this paper, we analyzed the accuracy and precision of AprilTag as a visual fiducial marker in detail. We have analyzed error propagation along two horizontal axes along with the effect of angular rotation about the vertical axis. We have identified that the angular rotation of the camera (yaw angle) about its vertical axis is the primary source of error that decreases the precision to the point where the marker system is not potentially viable for sub-decimeter precise tasks. Other factors are the distance and viewing angle of the camera from the AprilTag. Based on these observations, three improvement steps have been proposed. One is the trigonometric correction of the yaw angle to point the camera towards the center of the tag. Second, the use of a custom-built yaw-axis gimbal, which tracks the center of the tag in real-time. Third, we have presented for the first time a pose-indexed probabilistic sensor error model of the AprilTag using a Gaussian Processes based regression of experimental data, validated by particle filter tracking. Our proposed approach, which can be deployed with all three improvement steps, increases the system’s overall accuracy and precision by manifolds with a slight trade-off with execution time over commonly available AprilTag library. These proposed improvements make AprilTag suitable to be used as precision localization systems for outdoor and indoor applications.

Robust Joint Hybrid Transceiver Design for Millimeter Wave Full-Duplex MIMO Relay Systems

The joint design of hybrid beamforming matrices is conceived for multiuser mm-wave full-duplex (FD) multiple-input multiple-output (MIMO) relay-aided systems in the presence of realistic channel state information (CSI) errors. Specifically, considering a probabilistic CSI error model, we maximize the system’s worst-case sum rate by jointly optimizing the base station’s (BS’s) analog and digital beamforming matrices, plus the analog receive and transmit beamforming matrices of the relay station (RS) as well as its digital amplify-and-forward beamforming matrix under practical constraints. Explicitly, the transmit power constraints of the BS and RS, the residual self-interference power constraint of the RS, the per-user quality of service constraints, and the unit-modulus constraints on the analog beamforming matrix elements are all taken into account. Since the resultant optimization problem is very challenging due to its highly nonlinear objective function and nonconvex coupling constraints, we first transform it into a more tractable form. We then develop a novel joint optimization algorithm based on the penalty dual decomposition (PDD) technique to solve the resultant problem. The proposed PDD-based algorithm performs double-loop iterations: the inner loop updates the optimization variables in a block coordinate descent fashion, while the outer loop adjusts the Lagrange multipliers and penalty parameter, hence ensuring convergence to the set of stationary solutions of the original problem. Our simulations show that the mm-wave FD hybrid MIMO relay systems relying on our new algorithm significantly outperform both their non-robust FD and conventional half-duplex counterparts.

High-resolution ISR amplicon sequencing reveals personalized oral microbiome

BackgroundSequencing of the 16S rRNA gene has been the standard for studying the composition of microbial communities. While it allows identification of bacteria at the level of species, this method does not usually provide sufficient information to resolve communities at the sub-species level. Species-level resolution is not adequate for studies of transmission or stability or for exploring subspecies variation in disease association. Strain level analysis using whole metagenome shotgun sequencing has significant limitations that can make it unsuitable for large-scale studies. Achieving sufficient depth of sequencing can be cost-prohibitive, and even with adequate coverage, deconvoluting complex communities such as the oral microbiota is computationally very challenging. Thus, there is a need for high-resolution, yet cost-effective, high-throughput methods for characterizing microbial communities.ResultsSignificant improvement in resolution for amplicon-based bacterial community analysis was achieved by combining amplicon sequencing of a high-diversity marker gene, the ribosomal 16-23S intergenic spacer region (ISR), with a probabilistic error modeling based denoising algorithm, DADA2. The resolving power of this new approach was compared to that of both standard and high-resolution 16S-based approaches using a set of longitudinal subgingival plaque samples. The ISR strategy resulted in a 5.2-fold increase in community resolution compared to reference-based 16S rRNA gene analysis and showed 100% accuracy in predicting the correct source of a clinical sample. Individuals’ microbial communities were highly personalized, and although they exhibited some drift in membership and levels over time, that difference was always smaller than the differences between any two subjects, even after 1 year. The construction of an ISR database from publicly available genomic sequences allowed us to explore genomic variation within species, resulting in the identification of multiple variants of the ISR for most species.ConclusionsThe ISR approach resulted in significantly improved resolution of communities and revealed a highly personalized human oral microbiota that was stable over 1 year. Multiple ISR types were observed for all species examined, demonstrating a high level of subspecies variation in the oral microbiota. The approach is high-throughput, high-resolution yet cost-effective, allowing subspecies-level community fingerprinting at a cost comparable to that of 16S rRNA gene amplicon sequencing. It will be useful for a range of applications that require high-resolution identification of organisms, including microbial tracking, community fingerprinting, and potentially for identification of virulence-associated strains.

Robust AN-Aided Beamforming and Power Splitting Design for Secure MISO Cognitive Radio With SWIPT

A multiple-input single-output cognitive radio downlink network is studied with simultaneous wireless information and power transfer. In this network, a secondary user coexists with multiple primary users and multiple energy harvesting receivers. In order to guarantee secure communication and energy harvesting, the problem of robust secure artificial noise-aided beamforming and power splitting design is investigated under imperfect channel state information (CSI). Specifically, the transmit power minimization problem and the max-min fairness energy harvesting problem are formulated for both the bounded CSI error model and the probabilistic CSI error model. These problems are non-convex and challenging to solve. A 1-D search algorithm is proposed to solve these problems based on S-Procedure under the bounded CSI error model and based on Bernstein-type inequalities under the probabilistic CSI error model. It is shown that the optimal robust secure beamforming can be achieved under the bounded CSI error model, whereas a suboptimal beamforming solution can be obtained under the probabilistic CSI error model. A tradeoff is elucidated between the secrecy rate of the secondary user receiver and the energy harvested by the energy harvesting receivers under a max-min fairness criterion.

Probabilistic Error Modeling for Approximate Adders

Approximate adders are widely being advocated as a means to achieve performance gain in error resilient applications. In this paper, a generic methodology for analytical modeling of probability of occurrence of error and the Probability Mass Function (PMF) of error value in a selected class of approximate adders is presented, which can serve as performance metrics for the comparative analysis of various adders and their configurations. The proposed model is applicable to approximate adders that comprise of sub-adder units of uniform as well as non-uniform lengths. Using a systematic methodology, we derive closed form expressions for the probability of error for a number of state-of-the-art high-performance approximate adders. The probabilistic analysis is carried out for arbitrary input distributions. It can be used to study the dependence of error statistics in an adder’s output on its configuration and input distribution. Moreover, it is shown that by building upon the proposed error model, we can estimate the probability of error in circuits with multiple approximate adders. We also demonstrate that, using the proposed analysis, the comparative performance of different approximate adders can be correctly predicted in practical applications of image processing.

Increasing Safety of a Robotic System for Inner Ear Surgery Using Probabilistic Error Modeling Near Vital Anatomy.

Safe and effective planning for robotic surgery that involves cutting or ablation of tissue must consider all potential sources of error when determining how close the tool may come to vital anatomy. A pre-operative plan that does not adequately consider potential deviations from ideal system behavior may lead to patient injury. Conversely, a plan that is overly conservative may result in ineffective or incomplete performance of the task. Thus, enforcing simple, uniform-thickness safety margins around vital anatomy is insufficient in the presence of spatially varying, anisotropic error. Prior work has used registration error to determine a variable-thickness safety margin around vital structures that must be approached during mastoidectomy but ultimately preserved. In this paper, these methods are extended to incorporate image distortion and physical robot errors, including kinematic errors and deflections of the robot. These additional sources of error are discussed and stochastic models for a bone-attached robot for otologic surgery are developed. An algorithm for generating appropriate safety margins based on a desired probability of preserving the underlying anatomical structure is presented. Simulations are performed on a CT scan of a cadaver head and safety margins are calculated around several critical structures for planning of a robotic mastoidectomy.

Sensor fusion in the epistemic situation calculus

Robot sensors are usually subject to error. Since in many practical scenarios a probabilistic error model is not available, sensor readings are often dealt with in a hard-coded, heuristic fashion. In this paper, we propose a logic to address the problem from a KR perspective. In this logic, the epistemic effect of sensing actions is deferred to so-called fusion actions, which may resolve discrepancies and inconsistencies of recent sensing results. Moreover, a local closed-world assumption can be applied dynamically. When needed, this assumption can be revoked and fusions can be undone using a form of forgetting.

Random Error Modeling and Analysis of Airborne Lidar Systems

When airborne lidar is used to produce digital elevation models, the random error of airborne lidar systems is often the limiting factor. To improve the overall 3-D expected accuracy of airborne lidar systems, we develop random error models of airborne lidar systems. First, we present a footprint geolocation equation for the airborne lidar that describes an ideal system, followed by a modified footprint geolocation equation that contains systematic and random errors. To better constrain these uncertainties, we describe the mathematical characteristics of the random error in detail by modeling it as a stochastic process. The probabilistic random error models are developed by analyzing the differences between the errorless equation and the equation with errors. This paper also addresses the issue of recovering the errors and presents an error recovery model. Finally, based on a linear scanner and a new coordinate system, we simulate the geometric processes of point positioning of airborne lidar systems and study the impacts of the random measurement errors on the 3-D coordinate accuracy of airborne lidar systems.

Probabilistic Error Modeling and Topology-Based Smoothing of Indoor Localization and Tracking Data, Based on the IEEE 802.15.4a Chirp Spread Spectrum Specification

Location awareness is a core capability in many context-aware computing platforms. Multiple existing systems either provide inadequate accuracy or require extensive calibration or preexisting measurements in order to be functional. This work presents an extensive study of indoor tracking based on the chirp spread spectrum (CSS) specification and an associated analytical framework that allows comparisons to be made between different deployments. CSS provides resilience to fading, while being rapidly deployable. Wireless CSS modules are used to provide time of arrival measurements, necessary to infer the coordinates of a mobile user through trilateration. CSS resilience is tested in four deployments: an indoor space where line of sight (LoS) conditions are always satisfied, an indoor site that includes concrete, nonreflective obstructions, an industrial space with metallic, reflective obstacles, and a Tunnel. Empirical data are discussed in conjunction with the geometric dilution of precision (GDoP) metric, which depends on the system's deployment topology. The probabilistic modeling of the normalized localization error provides insight into the underlying distribution and is utilized in the context of a novel topology-based smoothing technique. Results indicate that CSS can provide accurate tracking. The application of the smoothing algorithm, however, further reduces the normalized error by a considerable amount.

Accurate indoor localization with ultra-wideband using spatial models and collaboration

Ultra-wideband (UWB) localization is a recent technology that performs competitively with many indoor localization methods currently available. Despite its desirable traits, such as potential high accuracy and high material penetrability, the resolution of non-line-of-sight signals remains a very hard problem and has a significant impact on the localization performance. In this work, we address the peculiarities of UWB error behavior by building models that capture the spatiality as well as the multimodal statistics of the error behavior. Our framework utilizes tessellated maps that associate probabilistic error models to localities in space. In addition to our UWB localization strategy (which provides absolute position estimates), we investigate the effects of collaboration in the form of relative positioning. To this end, we develop a relative range and bearing model and, together with the UWB model, present a unified localization technique based on a particle filter framework. We test our approach experimentally on a group of 10 mobile robots equipped with UWB emitters and extension modules providing inter-robot relative range and bearing measurements. Our experimental insights highlight the benefits of collaboration, which are consistent over numerous experimental scenarios. Also, we show the relevance, in terms of positioning accuracy, of our multimodal UWB measurement model by performing systematic comparisons with two alternative measurement models. Our final results show median localization errors below 10 cm in cluttered environments, using a modest set of 50 particles in our filter.