How to separate absolute and relative error components: Interval case

Determining the surface temperature of materials with unknown emissivity is studied. A method for determining the surface temperature using a standard sample of average spectral normal emissivity in the wavelength range of 1,65–1,80 μm and an industrially produced Metis M322 pyrometer operating in the same wavelength range. The surface temperature of studied samples of the composite material and platinum was determined experimentally from the temperature of a standard sample located on the studied surfaces. The relative error in determining the surface temperature of the studied materials, introduced by the proposed method, was calculated taking into account the temperatures of the platinum and the composite material, determined from the temperature of the standard sample located on the studied surfaces, and from the temperature of the studied surfaces in the absence of the standard sample. The relative errors thus obtained did not exceed 1,7 % for the composite material and 0,5% for the platinum at surface temperatures of about 973 K. It was also found that: the inaccuracy of a priori data on the emissivity of the standard sample in the range (–0,01; 0,01) relative to the average emissivity increases the relative error in determining the temperature of the composite material by 0,68 %, and the installation of a standard sample on the studied materials leads to temperature changes on the periphery of the surface not exceeding 0,47 % for composite material and 0,05 % for platinum.

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Testing for Error Cross-Sectional Independence in a Two-Way Error Components Panel Data Model

SSRN Electronic Journal ◽

10.2139/ssrn.2708185 ◽

2015 ◽

Author(s):

Guangyu Mao

Keyword(s):

Panel Data ◽

Data Model ◽

Panel Data Model ◽

Cross Sectional ◽

Error Components

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Error-aware Design Procedure to Implement Energy-efficient Approximate Squaring Hardware

Nanoscience &Nanotechnology-Asia ◽

10.2174/2210681209666190807143557 ◽

2020 ◽

Vol 10 (4) ◽

pp. 471-477

Author(s):

Merin Loukrakpam ◽

Ch. Lison Singh ◽

Madhuchhanda Choudhury

Keyword(s):

Energy Saving ◽

Relative Error ◽

Energy Efficient ◽

Piecewise Linear ◽

Arithmetic Operation ◽

Design Procedure ◽

Digital Signal ◽

Maximum Relative Error ◽

Square Function ◽

Efficient Design

Background:: In recent years, there has been a high demand for executing digital signal processing and machine learning applications on energy-constrained devices. Squaring is a vital arithmetic operation used in such applications. Hence, improving the energy efficiency of squaring is crucial. Objective:: In this paper, a novel approximation method based on piecewise linear segmentation of the square function is proposed. Methods: Two-segment, four-segment and eight-segment accurate and energy-efficient 32-bit approximate designs for squaring were implemented using this method. The proposed 2-segment approximate squaring hardware showed 12.5% maximum relative error and delivered up to 55.6% energy saving when compared with state-of-the-art approximate multipliers used for squaring. Results: The proposed 4-segment hardware achieved a maximum relative error of 3.13% with up to 46.5% energy saving. Conclusion:: The proposed 8-segment design emerged as the most accurate squaring hardware with a maximum relative error of 0.78%. The comparison also revealed that the 8-segment design is the most efficient design in terms of error-area-delay-power product.

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Modeling Spatiotemporal Population Changes by Integrating DMSP-OLS and NPP-VIIRS Nighttime Light Data in Chongqing, China

Remote Sensing ◽

10.3390/rs13020284 ◽

2021 ◽

Vol 13 (2) ◽

pp. 284

Author(s):

Dan Lu ◽

Yahui Wang ◽

Qingyuan Yang ◽

Kangchuan Su ◽

Haozhe Zhang ◽

...

Keyword(s):

Spatial Distribution ◽

Relative Error ◽

Urban Areas ◽

Large Scale ◽

Population Distribution ◽

Spatial Optimization ◽

Distribution Data ◽

Mountainous Areas ◽

Mean Relative Error ◽

Nighttime Light

The sustained growth of non-farm wages has led to large-scale migration of rural population to cities in China, especially in mountainous areas. It is of great significance to study the spatial and temporal pattern of population migration mentioned above for guiding population spatial optimization and the effective supply of public services in the mountainous areas. Here, we determined the spatiotemporal evolution of population in the Chongqing municipality of China from 2000–2018 by employing multi-period spatial distribution data, including nighttime light (NTL) data from the Defense Meteorological Satellite Program’s Operational Linescan System (DMSP-OLS) and the Suomi National Polar-orbiting Partnership Visible Infrared Imaging Radiometer Suite (NPP-VIIRS). There was a power function relationship between the two datasets at the pixel scale, with a mean relative error of NTL integration of 8.19%, 4.78% less than achieved by a previous study at the provincial scale. The spatial simulations of population distribution achieved a mean relative error of 26.98%, improved the simulation accuracy for mountainous population by nearly 20% and confirmed the feasibility of this method in Chongqing. During the study period, the spatial distribution of Chongqing’s population has increased in the west and decreased in the east, while also increased in low-altitude areas and decreased in medium-high altitude areas. Population agglomeration was common in all of districts and counties and the population density of central urban areas and its surrounding areas significantly increased, while that of non-urban areas such as northeast Chongqing significantly decreased.

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Lightweight Blockchain Processing. Case Study: Scanned Document Tracking on Tezos Blockchain

Applied Sciences ◽

10.3390/app11157169 ◽

2021 ◽

Vol 11 (15) ◽

pp. 7169

Author(s):

Mohamed Allouche ◽

Tarek Frikha ◽

Mihai Mitrea ◽

Gérard Memmi ◽

Faten Chaabane

Keyword(s):

Load Balancing ◽

Relative Error ◽

Execution Time ◽

General Purpose ◽

Experimental Results ◽

Raspberry Pi ◽

Embedded Platform ◽

Memory Resources ◽

Processing Solution

To bridge the current gap between the Blockchain expectancies and their intensive computation constraints, the present paper advances a lightweight processing solution, based on a load-balancing architecture, compatible with the lightweight/embedding processing paradigms. In this way, the execution of complex operations is securely delegated to an off-chain general-purpose computing machine while the intimate Blockchain operations are kept on-chain. The illustrations correspond to an on-chain Tezos configuration and to a multiprocessor ARM embedded platform (integrated into a Raspberry Pi). The performances are assessed in terms of security, execution time, and CPU consumption when achieving a visual document fingerprint task. It is thus demonstrated that the advanced solution makes it possible for a computing intensive application to be deployed under severely constrained computation and memory resources, as set by a Raspberry Pi 3. The experimental results show that up to nine Tezos nodes can be deployed on a single Raspberry Pi 3 and that the limitation is not derived from the memory but from the computation resources. The execution time with a limited number of fingerprints is 40% higher than using a classical PC solution (value computed with 95% relative error lower than 5%).

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A modified physical model of high-strength water hydraulic artificial muscles considering the effects of geometry and material properties

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1177/0954406221999077 ◽

2021 ◽

pp. 095440622199907

Author(s):

Zengmeng Zhang ◽

Jinkai Che ◽

Peipei Liu ◽

Yunrui Jia ◽

Yongjun Gong

Keyword(s):

Physical Model ◽

Relative Error ◽

Wall Thickness ◽

Material Properties ◽

High Strength ◽

Artificial Muscles ◽

Operating Pressure ◽

Rubber Tube ◽

Contraction Ratio ◽

Water Hydraulic

Compared with pneumatic artificial muscles (PAMs), water hydraulic artificial muscles (WHAMs) have the advantages of high force/weight ratio, high stiffness, rapid response speed, large operating pressure range, low working noise, etc. Although the physical models of PAMs have been widely studied, the model of WHAMs still need to be researched for the different structure parameters and work conditions between PAMs and WHAMs. Therefore, the geometry and the material properties need to be considered in models, including the wall thickness of rubber tube, the geometry of ends, the elastic force of rubber tube, the elongation of fibers, and the friction among fiber strands. WHAMs with different wall thickness and fiber materials were manufactured, and static characteristic experiments were performed when the actuator is static and fixed on both ends, which reflects the relationship between contraction force and pressure under the different contraction ratio. The deviations between theoretical values and experimental results were analyzed to investigate the effect of each physical factor on the modified physical model accuracy at different operating pressures. The results show the relative error of the modified physical model was 7.1% and the relative error of the ideal model was 17.4%. When contraction ratio is below 10% and operating pressure is 4 MPa, the wall thickness of rubber tube was the strongest factor on the accuracy of modified model. When the WHAM contraction ratio from 3% to 20%, the relative error between the modified physical model and the experimental data was within ±10%. Considering the various physical factors, the accuracy of the modified physical model of WHAM is improved, which lays a foundation of non-linear control of the high-strength, tightly fiber-braided and thick-walled WHAMs.

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A fractional order epidemic model for the simulation of outbreaks of Ebola

Advances in Difference Equations ◽

10.1186/s13662-021-03272-5 ◽

2021 ◽

Vol 2021 (1) ◽

Author(s):

Weiqiu Pan ◽

Tianzeng Li ◽

Safdar Ali

Keyword(s):

Numerical Solution ◽

Root Mean Square ◽

Fractional Order ◽

Relative Error ◽

Numerical Solutions ◽

Real Data ◽

Mean Square ◽

Order Model ◽

The Real ◽

Fractional Orders

AbstractThe Ebola outbreak in 2014 caused many infections and deaths. Some literature works have proposed some models to study Ebola virus, such as SIR, SIS, SEIR, etc. It is proved that the fractional order model can describe epidemic dynamics better than the integer order model. In this paper, we propose a fractional order Ebola system and analyze the nonnegative solution, the basic reproduction number $R_{0}$ R 0 , and the stabilities of equilibrium points for the system firstly. In many studies, the numerical solutions of some models cannot fit very well with the real data. Thus, to show the dynamics of the Ebola epidemic, the Gorenflo–Mainardi–Moretti–Paradisi scheme (GMMP) is taken to get the numerical solution of the SEIR fractional order Ebola system and the modified grid approximation method (MGAM) is used to acquire the parameters of the SEIR fractional order Ebola system. We consider that the GMMP method may lead to absurd numerical solutions, so its stability and convergence are given. Then, the new fractional orders, parameters, and the root-mean-square relative error $g(U^{*})=0.4146$ g ( U ∗ ) = 0.4146 are obtained. With the new fractional orders and parameters, the numerical solution of the SEIR fractional order Ebola system is closer to the real data than those models in other literature works. Meanwhile, we find that most of the fractional order Ebola systems have the same order. Hence, the fractional order Ebola system with different orders using the Caputo derivatives is also studied. We also adopt the MGAM algorithm to obtain the new orders, parameters, and the root-mean-square relative error which is $g(U^{*})=0.2744$ g ( U ∗ ) = 0.2744 . With the new parameters and orders, the fractional order Ebola systems with different orders fit very well with the real data.

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Methodology for comprehensive cell-level analysis of wound healing experiments using deep learning in MATLAB

BMC Molecular and Cell Biology ◽

10.1186/s12860-021-00369-3 ◽

2021 ◽

Vol 22 (1) ◽

Author(s):

Jan Oldenburg ◽

Lisa Maletzki ◽

Anne Strohbach ◽

Paul Bellé ◽

Stefan Siewert ◽

...

Keyword(s):

Wound Healing ◽

Deep Learning ◽

Cell Density ◽

Relative Error ◽

Medical Image Analysis ◽

Learning Algorithms ◽

Cell Velocity ◽

Population Scale ◽

Conventional Methods

Abstract Background Endothelial healing after deployment of cardiovascular devices is particularly important in the context of clinical outcome. It is therefore of great interest to develop tools for a precise prediction of endothelial growth after injury in the process of implant deployment. For experimental investigation of re-endothelialization in vitro cell migration assays are routinely used. However, semi-automatic analyses of live cell images are often based on gray value distributions and are as such limited by image quality and user dependence. The rise of deep learning algorithms offers promising opportunities for application in medical image analysis. Here, we present an intelligent cell detection (iCD) approach for comprehensive assay analysis to obtain essential characteristics on cell and population scale. Results In an in vitro wound healing assay, we compared conventional analysis methods with our iCD approach. Therefore we determined cell density and cell velocity on cell scale and the movement of the cell layer as well as the gap closure between two cell monolayers on population scale. Our data demonstrate that cell density analysis based on deep learning algorithms is superior to an adaptive threshold method regarding robustness against image distortion. In addition, results on cell scale obtained with iCD are in agreement with manually velocity detection, while conventional methods, such as Cell Image Velocimetry (CIV), underestimate cell velocity by a factor of 0.5. Further, we found that iCD analysis of the monolayer movement gave results just as well as manual freehand detection, while conventional methods again shows more frayed leading edge detection compared to manual detection. Analysis of monolayer edge protrusion by ICD also produced results, which are close to manual estimation with an relative error of 11.7%. In comparison, the conventional Canny method gave a relative error of 76.4%. Conclusion The results of our experiments indicate that deep learning algorithms such as our iCD have the ability to outperform conventional methods in the field of wound healing analysis. The combined analysis on cell and population scale using iCD is very well suited for timesaving and high quality wound healing analysis enabling the research community to gain detailed understanding of endothelial movement.

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Optimisation Method for Determination of Crack Tip Position Based on Gauss-Newton Iterative Technique

Chinese Journal of Mechanical Engineering ◽

10.1186/s10033-021-00585-0 ◽

2021 ◽

Vol 34 (1) ◽

Author(s):

Bing Yang ◽

Zhanjiang Wei ◽

Zhen Liao ◽

Shuwei Zhou ◽

Shoune Xiao ◽

...

Keyword(s):

Stress Intensity Factor ◽

Stress Intensity ◽

Intensity Factor ◽

Plastic Zone ◽

Relative Error ◽

Crack Tip ◽

Image Correlation ◽

Preconditioned Conjugate Gradient ◽

Loading Process ◽

Tip Position

AbstractIn the digital image correlation research of fatigue crack growth rate, the accuracy of the crack tip position determines the accuracy of the calculation of the stress intensity factor, thereby affecting the life prediction. This paper proposes a Gauss-Newton iteration method for solving the crack tip position. The conventional linear fitting method provides an iterative initial solution for this method, and the preconditioned conjugate gradient method is used to solve the ill-conditioned matrix. A noise-added artificial displacement field is used to verify the feasibility of the method, which shows that all parameters can be solved with satisfactory results. The actual stress intensity factor solution case shows that the stress intensity factor value obtained by the method in this paper is very close to the finite element result, and the relative error between the two is only − 0.621%; The Williams coefficient obtained by this method can also better define the contour of the plastic zone at the crack tip, and the maximum relative error with the test plastic zone area is − 11.29%. The relative error between the contour of the plastic zone defined by the conventional method and the area of the experimental plastic zone reached a maximum of 26.05%. The crack tip coordinates, stress intensity factors, and plastic zone contour changes in the loading and unloading phases are explored. The results show that the crack tip change during the loading process is faster than the change during the unloading process; the stress intensity factor during the unloading process under the same load condition is larger than that during the loading process; under the same load, the theoretical plastic zone during the unloading process is higher than that during the loading process.

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Use of a membrane module for semi-direct air evaporative cooling

Indoor and Built Environment ◽

10.1177/1420326x19877510 ◽

2019 ◽

Vol 29 (10) ◽

pp. 1346-1358 ◽

Cited By ~ 1

Author(s):

Sebastian Englart

Keyword(s):

Moisture Content ◽

Relative Error ◽

Air Temperature ◽

Evaporative Cooling ◽

Cross Flow ◽

Membrane Module ◽

Transfer Model ◽

Air Cooling ◽

Heating Efficiency ◽

Circulating Water

This study discusses the use of a membrane module for semi-direct evaporative air cooling. A cross-flow membrane module was used to carry out this air treatment process. For such a flow, it was proposed to describe and solve the heat and mass transfer model as a one-dimensional problem. The mathematical model was used to determine the moisture content and air temperature at the outlet from the module and the temperature of the circulating water. Results obtained using the proposed model are in good agreement with the experimental data. The relative error for the air temperature at the module outlet did not exceed 0.5%. For the moisture content, the relative error did not exceed 4%. For the circulating water temperature, the relative error did not exceed 0.6%. This paper also discusses the heating efficiency of the evaporative cooling process. Methods for determining the unit cooling indicator and the energy efficiency ratio are also proposed.

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