Proposed Uncertainty Model Research Articles

Uncertainty model for automated gunshot residue particle length measurements obtained from electron microscopy images.

Currently, the use of algorithms and computer vision systems for metrological purposes has increased in different areas of knowledge to reduce human error and process deviations, consequently increasing reliability and reducing measurement uncertainties. This study presents a model for estimating the uncertainty of Feret's diameter (DF ) measurements of scanning electron microscopy (SEM) images from regular and irregular gunshot residue (GSR) particles at different magnifications. The data were extracted using the automatic measurement algorithm developed by the Brazilian Institute of Metrology, Quality and Technology (Inmetro). The proposed uncertainty model was based on the recommendations of the guide to the expression of uncertainty in measurement (GUM). The gold standard technique to identify and detect GSR particles is the SEM coupled to energy dispersive X-ray spectroscopy (SEM/EDS), which was used in the study. The low uncertainty values obtained in this study are justified by the refinement of the measurements performed at each stage of digital image procedures. The proposed uncertainty model contributes in an innovative way to the metrological evaluation of regular and irregular GSR particles at different images magnifications. The correct morphometry definition of these particles allows to study their distinction from other possible sources of GSR and, above all, their correlation with the type of ammunition used when firing the firearm. These measurement uncertainty calculations can be applied to any object images acquired by SEM, which provides more confidence in the results of measurements of the object of interest.

Model-based and model-free collision detection and identification for a parallel Delta robot with uncertainties

This paper presents two methods for human collision detection and identification for a parallel Delta robot considering uncertainties. In the model-based, a generalized momentum observer based on the explicit model of the Delta robot is used to estimate a proposed uncertainty model without collision. A linear regression algorithm is approached to recognize actuator hysteresis friction models and modeling error parameters, constructing the uncertainty model. The boundary and convergence of the identification parameters are guaranteed based on a least square method. Then, the estimated uncertainty is compared with the generalized momentum observer to detect and identify collision impacts as external torques. In the model-free, the neural network model for actuated torque prediction controlling the Delta robot is developed based on a model-driven and data-driven approach. The training procedure of the proposed network only uses no collision datasets. The model-free method uses a neural network to provide detection signals and external torques identified by comparing its conservative predictions to the measured torques when a collision occurs. In this work, only low-cost current sensors and low-resolution encoders are attached to the Delta robot system for generating the datasets. Finally, the identification capacity of the proposed methods is also compared with a force sensor to verify the effectiveness in real-time implementation.

Average Rician K-Factor-Based Uncertainty Model of Measured Antenna Efficiency Using the Reference Antenna Method in Reverberation Chambers

Along several decades of development, many methods based on reverberation chambers (RCs) have been proposed for accurate and efficient measurement of antenna efficiency. The standard reference antenna method (RAM) is applicable for almost all frequency bands of interest and all types of antennas, and thus, it may well be the most widely applied method in the industry. In this article, an average Rician <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula> -factor-based uncertainty model for the standard RAM is proposed. It takes both the number of independent samples and the nonideality of the RC into consideration. Extensive measurements are performed for different RC configurations. It is shown that the newly proposed uncertainty model provides good and stable estimations of the measurement uncertainties for both unloaded and loaded RCs. Moreover, it is experimentally verified that the differences in the radiation characteristics between the reference antenna and the antenna under test (AUT) have little effect on measurement uncertainty regardless of the loading conditions of the RC. The findings of this work allow more flexible and efficient antenna efficiency measurements, including estimation of the associated uncertainty.

Variability of Mechanical Properties of Cellular Lightweight Concrete Infill and Its Effect on Seismic Safety

Cellular lightweight concrete (CLC) block masonry has gained popularity in the masonry market with the growing demand in the modern construction industry due to its various advantages, including a positive impact on the environment. Subsequently, the detailed characterization of its vital engineering properties should be studied for the development of the mathematical model, analysis, evaluation, and design of structures made of CLC block masonry. The present study investigates the variability in two important strength properties of CLC block masonry and proposes the most appropriate models for their statistical distribution to support probability-based structural analysis and design. This study shows that the assumption of a normal distribution in the absence of an appropriate uncertainty model can result in an inaccurate estimate of the seismic risk of an RC frame building infilled with CLC block masonry. The paper further assesses the seismic safety of a typical RC framed building infilled with CLC block masonry in relation to traditional brick masonry, considering the proposed uncertainty model. Although CLC block masonry results in a higher seismic risk compared with traditional brick masonry, it can be used as an infill material in high seismic areas because it results in a probability of failure within the acceptable limit.

Modeling and Investigation of Demand Response Uncertainty on Reliability Assessment

Demand Response (DR) provides an opportunity for customers to reduce their loads during times of high prices and therefore to shave the peak loads. The power outputs of large-scale generator units can be predicted and controlled easily; therefore, the pricing and reliability of conventional power utilities can be assessed straightforwardly. However, the customer loads are very variable and difficult to predict and control; therefore, the integration of DR might cause uncertainty issues on pricing and reliability and is essential to be further investigated. A novel uncertainty model for load reduction is proposed in this paper. The probability intensities of load reduction are first estimated from the measured load reduction variations. A multi-state probability model is then proposed for load reduction and the Markov process is used to calculate the state probabilities. A stochastic analysis scheme using Monte Carlo simulation for pricing and reliability taking the DR uncertainty into account is then investigated. Several cases are designed to compare the effects of DR uncertainty. Simulation results show that the proposed uncertainty model can be integrated into conventional economic dispatch to precisely evaluate the DR uncertainty on system operation and reliability.

A Nonstationary Uncertainty Model and Bayesian Calibration of Strain-Life Models

Abstract The Coffin–Manson–Basquin–Haford (CMBH) model is a well-accepted strain-life relationship to model fatigue life as a function of applied strain. In this paper, we propose a nonstationary uncertainty model for the CMBH model, alongside a Bayesian framework for model calibration and estimation of confidence and prediction intervals. Using Inconel 617 coupon test data, we compared our approach to traditional stationary variance models. The proposed uncertainty model successfully captures the fact that the variance of strain amplitude decreases with increasing fatigue life. Additionally, a discussion on how to use the proposed Bayesian framework to compensate for the lack of data by using prior information coming from similar alloys is also presented considering Hastealloy-X and Inconel 617 coupon data.

Propagated Uncertainty Models Arising From Device, Environment, and Target for a Small Laser Spot Airborne LiDAR Bathymetry and its Verification in the South China Sea

This contribution identifies the uncertainty sources influencing the component uncertainties for an airborne LiDAR bathymetry (ALB) measurement and presents the models for various component uncertainties (arising from the device, environment, and target for ALBs). Since various instrumental and environmental factors introduce vertical and horizontal uncertainties in ALB data, these uncertainties should be first analyzed and then precisely modeled to ensure the accuracy of the measurements. For this purpose, ten different effects that influence the accuracy of ALB data are systematically analyzed and modeled for four aspects in this article: the device aspect (laser pointing deflection, trajectory uncertainty, and boresight/lever arm offset), environmental aspect (atmospheric limitation, refraction on the sea surface, refraction in water, scattering in water, and water level fluctuation), target aspect (irregular bottom), and other aspect (accuracy of coordinate transformation model). In addition, the effect of the laser spot size is also discussed. To verify the presented uncertainty models, an ALB survey was operated around Yuanzhi Island in the South China Sea. For a water depth of 10 m, the theoretical overall root-sum-squares (RSS) for ten different effects of an ALB system (approximately 34 cm calculated using the total vertical uncertainty (TVU) models) is generally in accordance with the actual performance of the ALB data (approximately 39 cm) performance. The difference is mainly attributed to the limited accuracy of the ground truth data, and the difference between the water depth and laser ranging is reasonable. In this process, the topography data in the same region captured by a shipborne multibeam echo sounder (MBES) were used as the ground truth. The results indicated that for the typical ALB system, the laser pointing uncertainty and refraction uncertainty on the sea surface are primary uncertainty sources and should be corrected in a higher priority to meet the seafloor topographic accuracy demand of the International Hydrographic Organization (IHO) Standards for Hydrographic Surveys (S-44). The proposed uncertainty models can be used not only to guide the actual measurement of an ALB system but also to provide the uncertainty correction reference for ALB data postprocessing.

Robust optimization for a multiple-priority emergency evacuation problem under demand uncertainty

This study examines a multiple-priority emergency evacuation optimization problem with time-dependent demand uncertainty. A multiple-priority dynamic traffic model—namely, the multiple-priority cell transmission model (MPCTM) —is developed to simulate the priority of network flows for emergency evacuation response. Moreover, a robust optimization approach is applied to formulate such an emergency evacuation response problem. The robust counterpart solutions of the proposed uncertainty model have been shown to be tractable, using the duality theorem. Finally, a real example of Ya’an earthquake emergency evacuation planning verifies the effectiveness of the proposed MPCTM.

LFT-Structured Uncertainty State-Space Modeling for State Feedback Robust Control of the Ultra-Precision Wafer Stage

This paper presents linear-fractional-trans-formation (LFT)-structured uncertainty state-space modeling for robust control of the multiple-input multiple-output (MIMO) ultra-precision wafer stage with flexible structures to meet the challenges of vibration-dependent model uncertainties. Specifically, based on the modal MIMO state-space model, a parametric uncertainty model related with flexible modes is presented, and the uncertainty parameters are structured to a diagonal matrix with the LFT method. Meanwhile, a multiplicative uncertainty model is employed to express the uncertainty in high frequency with respect to ignored high-order modes. Thus, the final uncertainty model is structured with uncertainty parameters and high-frequency uncertainty. Based on the proposed uncertainty model, a comprehensive robust control scheme is proposed. Specifically, the weighting function matrixes are designed by the loop-shaping approach, and a $\mu$ analysis is employed to achieve a nonconservative solution with respect to the structured uncertainty. A standard stability criterion of a $\bf{M} \boldsymbol{\Delta}$ structure system is then utilized to determine the system stability by the largest structure singular value. Comparative experiments on a developed ultra-precision wafer stage are finally conducted, and the results validate that the proposed method achieves significant improvements on control performance, robustness, and robust stability in all exposure fields.

Technical Note: Monte Carlo methods to comprehensively evaluate the robustness of 4D treatments in proton therapy.

Proton therapy is very sensitive to treatment uncertainties. These uncertainties can induce proton range variations and may lead to severe dose distortions. However, most commercial tools only offer a limited integration of these uncertainties during treatment planning. In order to verify the robustness of a treatment plan, this study aims at developing a comprehensive Monte Carlo simulation of the treatment delivery, including the simulation of setup and range errors, variation of the breathing motion, and interplay effect. Most clinically relevant uncertainties have been modeled and implemented in the fast Monte Carlo dose engine MCsquare. Especially, variation of the breathing motion is taken into account by deforming the initial Four-dimensional computed tomography (4DCT) series and generating multiple new 4DCT series with scaled motion. Systematic and random errors are randomly sampled, following a Monte Carlo approach, to generate individual erroneous treatment scenarios. The robustness of treatment plans is analyzed and reported with dose-volume histogram(DVH) bands. The statistical uncertainty coming from the Monte Carlo scenario sampling is studied. A validation demonstrated the ability of the motion model to generate new 4DCT series with scaled motion amplitude and improved image quality in comparison to the initial 4DCT. The robustness analysis is applied to a lung tumor treatment. Considering the proposed uncertainty model, the simulation of 300 treatment scenarios was necessary to reach an acceptable level of statistical uncertainty on the DVH band. A comprehensive and statistically sound method of treatment plan robustness verification is proposed. The uncertainty model presented in this paper is not specific to protons and can also be applied to photon treatments. Moreover, the generated 4DCT series, with scaled motion, can be imported in commercial TPSs.

The effect of price responsive loads uncertainty on the risk-constrained optimal operation of a smart micro-grid

The financial and technical decisions of a smart micro-grid energy management system have always been affected by the existence of uncertainty in various parameters, such as electric load, electricity price, and renewable generation. Especially when the behavior of price and load is influenced by each other in a smart micro-grid. In this paper, we describe the uncertainty issue in the consumption behavior of price responsive loads and we utilize a model based on robust optimization to consider this uncertainty. The effects of considering the uncertainty of price responsive loads with the proposed model on a typical risk-constrained optimal operation of a smart micro-grid are illustrated through two case studies. The first case involves solving the considered optimal operation problem without considering the proposed uncertainty model while the second one shows the effects of proposed uncertainty model on the optimal solutions. The operation optimization problem is formed as a mixed-integer two-stage stochastic framework. Results show that with this uncertainty model the manager of smart micro-grid can increase its bids in day-ahead market at peak and mid-peak time slots while it can decrease them in off-peak time slots. Also, considering the impacts of this uncertainty model on profitability and system reliability, the smart micro-grid manager needs a trade-off between increasing its profit and increasing the system operation risk.

Probabilistic assessment of performance under uncertain information using a generalized maximum entropy principle

When information about a distribution consists of statistical moments only, a self-consistent approach to deriving a subjective probability density function (pdf) is Maximum Entropy. Nonetheless, the available information may have uncertainty, and statistical moments maybe known only to lie in a certain domain. If Maximum Entropy is used to find the distribution with the largest entropy whose statistical moments lie within the domain, the information at only a single point in the domain would be used and other information would be discarded. In this paper, the bounded information on statistical moments is used to construct a family of Maximum Entropy distributions, leading to an uncertain probability function. This uncertainty description enables the investigation of how the uncertainty in the probabilistic assignment affects the predicted performance of an engineering system with respect to safety, quality and design constraints. It is shown that the pdf which maximizes (or equivalently minimizes) an engineering metric is potentially different from the pdf which maximizes the entropy. The feasibility of the proposed uncertainty model is shown through its application to: (i) fatigue failure analysis of a structural joint; (ii) evaluation of the probability that a response variable of an engineering system exceeds a critical level, and (iii) random vibration.

Metrological Validation of a Measurement Procedure for the Characterization of a Biological Ultrasound Tissue-Mimicking Material

The speed of sound and attenuation are important properties for characterizing reference materials such as biological phantoms used in ultrasound applications. There are many publications on the manufacture of ultrasonic phantoms and the characterization of their properties. However, few studies have applied the principles of metrology, such as the expression of the uncertainty of measurement. The objective of this study is to validate a method for characterizing the speed of sound and the attenuation coefficient of tissue-mimicking material (TMM) based on the expression of the measurement of uncertainty. Six 60-mm-diameter TMMs were fabricated, three 10 mm thick and three 20 mm thick. The experimental setup comprised two ultrasonic transducers, acting as transmitter or receiver depending on the stage of the measurement protocol, both with a nominal center frequency of 5 MHz and an element diameter of 12.7 mm. A sine burst of 20 cycles and 20-V peak-to-peak amplitude at 5 MHz excited the transmitter transducer, producing a maximum pressure of 0.06 MPa. The measurement method was based on the through-transmission substitution immersion technique. The speed of sound measurement system was validated using a calibrated stainless-steel cylinder as reference material, and normalized errors were <0.8. The attenuation coefficient measurement method was validated using replicated measurements under repeatability conditions. The normalized error between the two measurement sets was <1. The proposed uncertainty models for the measurements of the speed of sound and the attenuation coefficient can help other laboratories develop their own uncertainty models. These validated measurement methods can be used to certify a TMM as a reference material for biotechnological applications.

Uncertainty evaluation of dead zone of diagnostic ultrasound equipment

This paper presents a model for evaluating measurement uncertainty of a feature used in the assessment of ultrasound images: dead zone. The dead zone was measured by two technicians of the INMETRO's Laboratory of Ultrasound using a phantom and following the standard IEC/TS 61390. The uncertainty model was proposed based on the Guide to the Expression of Uncertainty in Measurement. For the tested equipment, results indicate a dead zone of 1.01 mm, and based on the proposed model, the expanded uncertainty was 0.17 mm. The proposed uncertainty model contributes as a novel way for metrological evaluation of diagnostic imaging by ultrasound.

RGB–D terrain perception and dense mapping for legged robots

Abstract This paper addresses the issues of unstructured terrain modeling for the purpose of navigation with legged robots. We present an improved elevation grid concept adopted to the specific requirements of a small legged robot with limited perceptual capabilities. We propose an extension of the elevation grid update mechanism by incorporating a formal treatment of the spatial uncertainty. Moreover, this paper presents uncertainty models for a structured light RGB-D sensor and a stereo vision camera used to produce a dense depth map. The model for the uncertainty of the stereo vision camera is based on uncertainty propagation from calibration, through undistortion and rectification algorithms, allowing calculation of the uncertainty of measured 3D point coordinates. The proposed uncertainty models were used for the construction of a terrain elevation map using the Videre Design STOC stereo vision camera and Kinect-like range sensors. We provide experimental verification of the proposed mapping method, and a comparison with another recently published terrain mapping method for walking robots.

A QUALITY ANALYSIS AND UNCERTAINTY MODELING APPROACH FOR CROWD-SOURCING LOCATION CHECK-IN DATA

Abstract. The location check-in data, developing along with social network, are considered as user-generated crowd-sourcing geospatial data. With massive data volume, abundance in contained information, and high up-to-date status, the check-in data provide a new data source for geographic information service represented by location-based service. However, there is a significant quality issue regarding to crowd-sourcing data, which has a direct influence to data availability. In this paper, a data quality analysis approach is designed for the location check-in data and a check-in data uncertainty model is proposed. First of all, the quality issue of location check-in data is discussed. Then, according to the characteristics of check-in data, a location check-in data quality analysis and data processing approach is proposed, using certain standard dataset as reference to conduct an affine transformation for the check-in dataset, during which the RANSAC algorithm is adopted for outlier elimination. Subsequently, combining GIS data uncertainty theory, an uncertainty model of processed check-in data is set up. At last, using location check-in data obtained from jiepang.com as experimental data and selected navigation data as data standard, multiple location check-in data quality analysis and uncertainty modeling experiments are conducted. By comprehensive analysis of experimental results, the feasibility of proposed location checkin data quality analysis and process approach and the availability of proposed uncertainty model are verified. The novel approach is proved to have a certain practical significance to the study of the quality issue of crowd-sourcing geographic data.

A second-order uncertainty model for target classification using kinematic data

When kinematic data is used for target classification, traditional Bayesian methods often lead to unreasonable results, especially when the target is not maneuvering. We find that this is due to the poor modeling of the uncertain mapping from the target class space to the maneuver feature space. Our proposed second-order uncertainty model gives both a preferable description of the uncertain mapping from the feature space to the class space and a more practical method to calculate the class likelihood under a relaxed dependence assumption. It is also clarified when the classifying features are extracted from a multiple-model filter, the real dynamic mode of a target should be determined to prevent the classifier from being degraded since it is in fact not a stochastic process and cannot be correctly described by multiple models simultaneously. A numerical example demonstrates that a well-formulated Bayesian classifier can produce results as expected.

A probabilistic model for the assessment of uncertainties in the shear strength of rock discontinuities

Discontinuity shear strength plays a critical role in many problems encountered in rock engineering, especially in the design of rock slopes. Since its precise estimation is generally not possible, it is crucial that the errors and uncertainties associated with its estimate be quantified and reflected in the design procedure. In this study, the uncertainties underlying discontinuity shear strength are thoroughly examined and an uncertainty analysis model is developed for the estimation of in situ discontinuity shear strength with a special emphasis on rock slopes. An extensive literature survey on shear behavior of unfilled rock discontinuities has been carried out and the necessary data for the quantification of uncertainties are extracted from this survey. These uncertainties stem from the discrepancies between laboratory-measured and in situ discontinuity shear strength values, as well as from the inherent variability of shear strength within a rock medium. The main causes of discrepancies, namely, scale, anisotropy and water saturation are considered. For each source of discrepancy a correction factor, treated as a random variable, is assigned and guidelines for the quantification of the statistical parameters of these correction factors are presented within the framework of the proposed uncertainty analysis model. The proposed uncertainty model provides an analytical tool for the systematic treatment of uncertainties involved in the estimation of the in situ value of peak friction angle from the laboratory test results.