Evaluation Formula Research Articles

Error analysis and accuracy evaluation method for coordinate measurement in transformed coordinate system

Multiple coordinate system transformations are required for engineering measurements of multi-faceted components. Traditional engineering measurements neglect coordinate errors after transformations, leading to inaccurate accuracy evaluations for coordinates. In this study, the effects of angular deviation and coordinate value magnitude on coordinate errors during transformations are first analyzed. Additionally, the transformation deviation of the three-point method is examined. Subsequently, an accuracy evaluation method for coordinate measurements is proposed to determine the scale scaling factor and the formula for calculating the variance of measuring coordinate errors. Finally, a coordinate accuracy evaluation method and evaluation formula that consider coordinate system transformation errors are proposed by self-checking. The validity of the proposed accuracy evaluation formula is confirmed through experiments. The coordinate measurement accuracy of the low-cost binocular camera is higher than that of the total station, whether or not coordinate system transformations are considered. Stereo-vision measurement technology is more suitable for small-scale engineering measurements.

Application of edge computing and IoT technology in supply chain finance

This study proposes an IoT data management framework based on blockchain and edge computing and conducts detailed simulation experiment design and performance evaluation for the field of supply chain finance. Previous methods often struggled with high latency, limited scalability, and inadequate risk management, and to address these issues, the experimental platform includes traditional centralized systems, distributed systems, blockchain-based systems, and edge computing + blockchain systems. By monitoring indicators such as data processing delay, data transmission delay, data retrieval time, system throughput, and data integrity of each platform, and introducing evaluation formulas for credit risk, operational risk, and market risk, the performance of different systems in processing supply chain financial data is comprehensively analyzed. The experimental results show that the edge computing + blockchain system performs well in data processing efficiency, security, real-time, and system throughput, especially under high load conditions. Our market risk value is reduced to 0.015. This framework improves the efficiency and security of data transmission and effectively reduces credit risk and operational risk, providing an efficient and reliable solution for data management in supply chain finance.

Phase classification and transient effects of the start-up process of multi-functional pump station in pump mode

In the context of achieving the goal of carbon neutrality, multi-functional pump stations (MFPS) have been greatly developed as a new energy system in recent years. The MFPS can operate in forward direction in pump mode to pump water and in turbine mode in reverse direction to generate electricity. At present, the instability of the MFPS during start-up process (SUP) in pump mode has become the key to restricting the operating life and further development of MFPS. In this paper, based on the motion characteristics of the pump and the cut-off facility (COF), the SUP of the MFPS in pump mode is clearly classified. In order to reveal the transient effect during the SUP, the steady-state full characteristic experiment (SFCE) of the pump was carried out. The occurrence phase of the transient effect during the SUP is analyzed, and the deviation between the steady-state external characteristics and the transient characteristics is revealed. In this study, the evaluation formula of the start-up completion degree (SUCD) of the MFPS in pump mode is proposed for the first time, and the evaluation and identification of the start-up progress at different phases are completed. The results show that the water flow in the system is in a reverse flow state in the Phase I. The SUCD of Phase I is 17 %. In the Phase II, The high-speed jet flow in the pump flows to the inlet of the guide vane (GV), which gradually changes the mainstream direction in the GV. A certain vortex structure can be observed at the exit of the flap gate (FG). The SUCD of Phase II is 61 %. In the Phase I and II, the dimensionless head of transient simulation is much larger than that of SFCE. In the Phase III, the flow state in the impeller will gradually stabilize. The transient effect disappears and the pressure fluctuation intensity decreases. The SUCD of Phase III is 93 %. In the Phase IV, the separation vortex that persists from Phase I-III at the tail of the GV blades disappears. The diversion capacity at the gate increases, and significant annular flow can be observed near the FG.

Study on Fault Diagnosis of Single-Group Springs of Mining Vibrating Screen

In the mining vibrating screen’s working process, the support spring often fails due to alternating loads and a poor working environment. The six-degrees-of-freedom simplified rigid body dynamic model is established to obtain the vibration response of the mining vibrating screen with a faulty single-group spring and is verified using the ABAQUS (2020) simulation in this paper. Unlike previous studies focusing on multiple-group spring failures or using lower-degree-of-freedom models, this study addresses the common single-group spring failure with the comprehensive model capturing complex spatial motion. This study also reveals that the vibration angle can be used to diagnose the failure location, while the vibration displacement can be used to evaluate the health state of single-group springs. Based on these rules, the novel method for locating a faulty spring group and new evaluation formulas for their health states are validated by the simulations. The results indicate that the failure location is accurately diagnosed, and the errors of the health state evaluation are minimal. The evaluated values are 66.12% and 85.56% when the health states of the spring groups at the feed side and the out-feed side are 65% and 85%, respectively. Therefore, this diagnostic model provides significant theoretical assistance for diagnosing single-group spring failure in the mining vibrating screen, enhancing maintenance strategies and operational reliability.

On Some General Tornheim-Type Series

In this paper, we solve the open problem posed by Kuba by expressing ∑j,k≥1Hk(u)Hj(v)Hj+k(w)jrks(j+k)t as a linear combination of multiple zeta values. These sums include Tornheim’s double series as a special case. Our approach is based on employing two distinct methods to evaluate the specific integral proposed by Yamamoto, which is associated with the two-poset Hasse diagram. We also provide a new evaluation formula for the general Mordell–Tornheim series and some similar types of double and triple series.

New Formulas for Evaluation of Cyclohexanol Solidification on Substrates with Surface Nanostructures.

In semiconductor manufacturing, the sublimation drying process is crucial but poorly understood-particularly regarding the solidification of agents such as cyclohexanol on Si substrates. This knowledge gap results in inconsistent film properties and risks such as structural collapse. To address this critical gap in knowledge, the present study focused on an in-depth examination of the nucleation behavior exhibited by cyclohexanol during its cooling and solidification on Si substrates. Using a digital camera (GoPro10), the solidification process in experiments was recorded for a range of cooling rates and using substrates with distinct surface patterns. To evaluate temporal changes in crystal nucleation, video images were visually checked, and the temporal changes in the number of nuclei were examined. For a more quantitative analysis, the least-squares method was successfully employed to correlate mathematical equations to time-dependent nucleation data. Interestingly, the outcomes revealed significant correlations between the nucleation rate, cooling rate, and substrate pattern. In summary, this research offers a robust experimental framework for understanding the complex solidification behavior of cyclohexanol on Si substrates. The study contributes both qualitative and quantitative analyses, enriching our understanding of the variables that govern the solidification process, which has significant implications for enhancing the overall reliability and efficiency of semiconductor manufacturing.

Establishment of a cholangiocarcinoma risk evaluation model based on mucin expression levels.

Cholangiocarcinoma (CCA) is a highly malignant cancer, characterized by frequent mucin overexpression. MUC1 has been identified as a critical oncogene in the progression of CCA. However, the comprehensive understanding of how the mucin family influences CCA progression and prognosis is still incomplete. To investigate the functions of mucins on the progression of CCA and to establish a risk evaluation formula for stratifying CCA patients. Single-cell RNA sequencing data from 14 CCA samples were employed for elucidating the roles of mucins, complemented by bioinformatic analyses. Subsequent validations were conducted through spatial transcriptomics and immunohistochemistry. The construction of a risk evaluation model utilized the least absolute shrinkage and selection operator regression algorithm, which was further confirmed by independent cohorts and diverse data types. CCA tumor cells with elevated levels of MUC1 and MUC4 showed activated nucleotide metabolic pathways and increased invasiveness. MUC5AC-high cells were found to promote CCA progression through WNT signaling. MUC5B-high cells exhibited robust cellular oxidation activities, leading to resistance against antitumoral treatments. MUC13-high cells were observed to secret chemokines, recruiting and transforming macrophages into the M2-polarized state, thereby suppressing antitumor immunity. MUC16-high cells were found to promote tumor progression through interleukin-1/nuclear factor kappa-light-chain-enhancer of activated B cells signaling upon interaction with neutrophils. Utilizing the expression levels of these mucins, a risk factor evaluation formula for CCA was developed and validated across multiple cohorts. CCA samples with higher risk factors exhibited stronger metastatic potential, chemotherapy resistance, and poorer prognosis. Our study elucidates the functional mechanisms through which mucins contribute to CCA development, and provides tools for risk stratification in CCA.

Uncrewed Boat Path Planning Algorithm based on Evolutionary Potential Field Model in Dense Obstacle Environment

In the trajectory planning of crewless ships, the artificial potential field method is commonly used. The results obtained using the classic potential field model for path design are not optimal and cannot fully meet the trajectory design requirements of uncrewed ships. This paper uses the evolutionary potential field model for trajectory planning. The evaluation formula of the potential path is combined with the differential evolution algorithm to evaluate and optimize the potential. A quadratic optimization smoothing algorithm is designed to limit the maximum turning angle of the uncrewed ship. Simulation experiments show that this method is effective and reliable.

A Series Approximation for the Analytic Fourier–Feynman Transform on Wiener Space

In this paper, we first establish an evaluation formula to calculate Wiener integrals of functionals on Wiener space. We then apply our evaluation formula to carry out easy an calculation for the analytic Fourier–Feynman transform of the functionals. Some examples are furnished to illustrate the usefulness of the evaluation formula. Finally, using the evaluation formula, we establish the series approximation for the analytic Fourier–Feynman transform.

Development of Sample Size Formulas for Least Square Regression-Based Consistency Evaluation of Quantitative Indicators

Objective To develop and verify the sample size formulas for quantitative data consistency evaluation based on the least square regression method. Methods According to the principle of least square regression-based quantitative consistency evaluation,statistical inference,and formula derivation,we developed the formulas for calculating sample size based on regression constant and regression coefficient.Furthermore,the accuracy of the formulas was verified by the data of three examples,and the results were compared with those of the sample size formula established based on the Bland-Altman(BA)method. Results The sample size formulas for regression-based quantitative consistency evaluation were deduced,and the accuracy of the formulas was verified by three examples.In addition,the results obtained with this formula had differences compared with those of the sample size formula established based on the BA method.Furthermore,consistent conclusions could be obtained by regression analysis and BA analysis with the sample size calculated with the regression method.However,with the sample size calculated based on the BA method,the consistency conclusion of regression analysis and BA analysis was sometimes not valid. Conclusion A sample size formula for quantitative consistency evaluation based on the regression method was proposed for the first time,which provided methodological support for the research in this field.

Tensile resistance and shear-tension interaction relationship of T-type perfobond rid shear connectors

This study aims to investigate the mechanical performance of T-type perfobond rib (T-type PBL) shear connectors under complex load cases. Initially, the experimental tests were conducted and finite element analyses (FEA) were performed. Subsequently, a parametric study was carried out to assess the impact of geometric parameters on tensile resistance and the effect of tension ratio on the shear-tension interaction resistance of T-type PBL connectors. Finally, based on the test and FEA results, prediction methods were developed for evaluating the tensile resistance and shear-tension interaction relationship of T-type PBL connectors. The test results showed that the pull-out of the concrete below the flange led to the failure of T-type PBL shear connectors under tension. The concrete failure angles were approximately 33°. The failure under shear was manifested as concrete collapse and connector yielding. The ultimate capacity decreased with the increase in tension ratio. The specimens with tension ratios of 25%, 45%, and 65% decreased 7.9%, 16.3%, and 24.2%, respectively, compared to the specimen under pure shear. The parametric study suggested that the rib height and perforated rebars were the main factors impacting the tensile resistance of T-type PBL shear connectors. When the tension ratio reached 55% of the ultimate, the failure mode of the shear connectors was dominated by the pull-out of the concrete. The tensile resistance evaluation formula was verified by the test and FEA results, demonstrating an average calculated-to-FE-results ratio of 0.99 with a standard deviation of 0.04. The suggested shear and tension interaction relationship for T-type PBL connectors had reliable predictive outcomes, with a coefficient of variation of 0.02. This study could provide guidance for the design of T-type PBL shear connectors and promote the application in long-span composite structures.

Virtual source approach for maximizing resolution in high-penetration gamma-ray imaging

High-energy gamma-ray radiography has exceptional penetration ability and has become an indispensable nondestructive testing (NDT) tool in various fields. For high-energy photons, point projection radiography is almost the only feasible imaging method, and its spatial resolution is primarily constrained by the size of the gamma-ray source. In conventional industrial applications, gamma-ray sources are commonly based on electron beams driven by accelerators, utilizing the process of bremsstrahlung radiation. The size of the gamma-ray source is dependent on the dimensional characteristics of the electron beam. Extensive research has been conducted on various advanced accelerator technologies that have the potential to greatly improve spatial resolution in NDT. In our investigation of laser-driven gamma-ray sources, a spatial resolution of about 90 µm is achieved when the areal density of the penetrated object is 120 g/cm2. A virtual source approach is proposed to optimize the size of the gamma-ray source used for imaging, with the aim of maximizing spatial resolution. In this virtual source approach, the gamma ray can be considered as being emitted from a virtual source within the convertor, where the equivalent gamma-ray source size in imaging is much smaller than the actual emission area. On the basis of Monte Carlo simulations, we derive a set of evaluation formulas for virtual source scale and gamma-ray emission angle. Under optimal conditions, the virtual source size can be as small as 15 µm, which can significantly improve the spatial resolution of high-penetration imaging to less than 50 µm.

Dazzling Evaluation of the Impact of a High-Repetition-Rate CO2 Pulsed Laser on Infrared Imaging Systems.

This article utilizes the Canny edge extraction algorithm based on contour curvature and the cross-correlation template matching algorithm to extensively study the impact of a high-repetition-rate CO2 pulsed laser on the target extraction and tracking performance of an infrared imaging detector. It establishes a quantified dazzling pattern for lasers on infrared imaging systems. By conducting laser dazzling and damage experiments, a detailed analysis of the normalized correlation between the target and the dazzling images is performed to quantitatively describe the laser dazzling effects. Simultaneously, an evaluation system, including target distance and laser power evaluation factors, is established to determine the dazzling level and whether the target is recognizable. The research results reveal that the laser power and target position are crucial factors affecting the detection performance of infrared imaging detector systems under laser dazzling. Different laser powers are required to successfully interfere with the recognition algorithm of the infrared imaging detector at different distances. And laser dazzling produces a considerable quantity of false edge information, which seriously affects the performance of the pattern recognition algorithm. In laser damage experiments, the detector experienced functional damage, with a quarter of the image displaying as completely black. The energy density threshold required for the functional damage of the detector is approximately 3 J/cm2. The dazzling assessment conclusions also apply to the evaluation of the damage results. Finally, the proposed evaluation formula aligns with the experimental results, objectively reflecting the actual impact of laser dazzling on the target extraction and the tracking performance of infrared imaging systems. This study provides an in-depth and accurate analysis for understanding the influence of lasers on the performance of infrared imaging detectors.

Radioprotection issues in uraniferous minerals collections with reference to an actual case.

Our work investigated the radioprotection implications associated with the possession of a collection of uraniferous minerals. Considering different scenarios, we developed (and applied to an actual collection) specific formulas for radiation doses evaluation. We discussed the shielding necessary to reduce the gamma irradiation down to the required values. A mathematical model was developed to estimate the minimum air flow rate to reduce the radon air concentration below the reference values. The radiation risks associated to the handling of single specimens was also addressed, including hand skin irradiation and shielding capabilities of surgical lead gloves. Finally, we discussed the radiation risks associated to the exhibition of a single specimen. The results, compared to the safety standards of the EU Directive 13/59, show that the exhibition of uraniferous samples with activity of a few MBq do not need specific radioprotection requirements nor for the involved personnel nor for visitors.

Physicochemical properties of carbonized grass (CG): Implications for soft clay improvement

In global environmental governance, effectively and sustainably treating soft clay remains a key challenge. The production of traditional soil stabilizers, like cement, not only consumes vast non-renewable resources but also poses issues related to high energy consumption and environmental burdens. Hence, there is an urgent need to identify sustainable alternatives. This study introduces carbonized grass (CG) prepared from waste cutting grass as a sustainable material, experiments on soft clay and research on its physical and chemical properties, and adds wood charcoal (WC) and carbonized cow dung compost (CC) as controls. The study assesses the impact of carbonization temperature (500–1000 °C) on the water absorption properties of WC, CC, and CG. Using CG produced by a homemade dry distillation gasifier (SDDG) as raw material, it is added directly or together with calcined oyster shell waste (COS) into the soft clay, and a cone penetration test is conducted. The impact of different initial moisture contents (30%, 50% and 70%) of soft clay and the blending amounts of CG and CG-COS on the strength of the samples was studied, and an evaluation formula was proposed. Test results showed that CG exhibited a significant advantage in stabilizing high-moisture clay compared to CC and WC. After 28 days, the incorporation of CG significantly reduces the amount of COS (about 40%). Employing Scanning Electron Microscopy (SEM) and Energy-Dispersive X-ray Spectroscopy (EDS), the physical and chemical properties of the samples were analyzed. The analysis confirmed CG's unique honeycomb structure, acting as nucleation sites between particles. Additionally, its strong water absorbency aided in shortening the distance between particles, promoting the bonding of hydrated calcium silicate (C-S-H) with soil particles, leading to an improvement in sample strength. The results showed that improving soft clay with CG-COS significantly reduces the use of traditional stabilizers while leading to a substantial increase in soil strength. Additionally, this approach contributes to a noteworthy reduction in greenhouse gas emissions. Therefore, recycling cutting grass for CG preparation as a substitute for conventional soil stabilizers emerges as a green and viable method.

Kinetics formulation for Two-Dimensional Growth Behavior of Water/Ice Interface on Si Substrate.

Sublimation drying is used in the drying process of semiconductor device manufacturing. However, the solidification behavior mechanics of sublimation agents on substrates has not been clarified. Therefore, the properties of solidified films within substrate surfaces can become nonuniform, leading to their collapse. This study aimed to analyze the interface growth behavior during the cooling and solidification of a water/ice system as a basic case and to clarify the dynamic mechanism of the solidification behavior of liquid films on Si substrates. The solidification behavior of a water/ice system on Si substrates was captured on a video at different cooling rates. The recorded video was subjected to a digital image analysis to examine the crystal morphology and quantify the interface growth rate. The least-squares method with kinetic formulas was used to evaluate the feasibility of fitting the temperature variation to the interface growth rate. A visual examination of the morphology of interfacial growth revealed that it can be classified into four morphologies. The proposed kinetic equation describes the experimental results regarding the temperature dependence of the interfacial growth rate. Through image analysis, the interface growth rate of water and ice was quantified, and an evaluation formula was proposed.

A design method of bipolar junction transistor for high-precision remote temperature sensing

A design method of BJTs for high-precision temperature-sensing is studied. The effects of non-idealities in the BJT on temperature-sensing accuracy are analyzed, and an accuracy evaluation formula containing the non-idealities is derived. We have proposed a novel parameter criteria of high-precision temperature-sensing BJT which constrains the influenced error of each non-ideality below ±0.1 °C using the variable-controlling procedure. The conversion approach from the proposed parameter criteria to electrical characteristics is also developed to guide the high-precision temperature-sensing BJT design. According to the proposed method, temperature-sensing BJTs are designed and fabricated. The test results showed that the temperature-sensing accuracy is within ±0.5 °C in temperature range of −55 °C to 125 °C, which meets the need for high-precision temperature sensing.

Bandgap analysis of partial-interaction composite beams periodically attached vibration absorbers

Elastic metamaterials with local resonant components exhibit unique bandgap behavior that can be utilized to control the vibration and noise of mechanical structures. This study aims to introduce the bandgap characteristics into the vibroacoustic control of partial-interaction composite beams (PICBs) widely adopted in civil engineering, aviation, and marine fields. Vibration absorbers are arranged periodically on the beam to generate a bandgap in PICBs, thereby transforming a conventional PICB into a metamaterial beam. An analytical approach is proposed to establish the spectral element (SE) matrix of a metamaterial beam based on the Timoshenko–Ehrenfest beam theory. Specifically, the governing equations of motion for PICBs follow Hamilton's principle. This model considers the effects of shear slip between two-layer sub-beams, shear deformations, and rotary inertia. The SE matrix of PICBs is then constructed and applied to obtain the SE matrix of the metamaterial beam by assembling the SE matrix of the vibration absorbers. Subsequently, the wave finite element (WFE) method is employed to predict the dispersion curve of the infinite metamaterial beam and the dynamic response of the finite metamaterial beam. In a benchmark example, the complex band structure and transmission indicated by the proposed approach are validated compared to those calculated by evaluation formulas of the literature and the finite element method. Lastly, the bandgap behavior for the vibration absorber parameters, lattice constants, and shear connector stiffness is investigated based on the defined dimensionless parameters. These results are valuable for optimizing vibration and noise reduction in PICBs equipped with attached vibration absorbers.

Flexural Buckling Strength of Steel Angle with Reinforcement in Electric Transmission Towers

In Japan, mid-sized electric transmission towers are made of steel angle members connected by high-strength bolts and are mainly designed to withstand wind loads. However, recent collapses due to the increasing wind intensity caused by climate change have led to a high demand for the reinforcement of conventional towers currently in operation. This paper reports the flexural buckling strength evaluation method for reinforced steel angle members under eccentric load. The study utilizes a theoretical approach to derive the evaluation formula, considering the effect of the eccentric load and the amount of reinforcement. Finally, small-scale experiments validate the proposed design formula, which can reasonably evaluate the strength of reinforced steel angle members.

Study of Rapid Evaluation Method for Structural Load‐Bearing Capacity of Typical Rural Masonry Residential Buildings in Shandong Province, China

Typical rural masonry residential buildings mainly include brick–wood and brick–concrete structures, and they occupy a significant proportion among individual buildings in Shandong Province, and their structural reliability directly affects the safety of life and property. Structural load‐bearing capacity can be used for quantitative judgment of structural reliability level. For evaluating the structural load‐bearing capacity of rural masonry residential buildings rapidly, factors affecting the structural bearing capacity and positions with weak structural bearing capacity are determined by field investigation and modeling analysis with software for structural calculation. The ratio of structural resistance to action effect is taken as the evaluation index of structural bearing capacity, and the quantitative relationships between this index and the masonry compressive strength, mortar strength, window–hole ratio, and the cantilever width are established through regression analysis. The accuracy and applicability are verified by Elman neural network model as well as comparison results between rapid evaluation formula and modeling analysis. The results show that the rapid evaluation model for structural load‐bearing capacity in this paper can be used to accurately describe the relationships between the ratio of structural resistance to action effect with affecting factors, and it can play a role in screening structural monomers with irregular load‐bearing capacity in group evaluation of structural bearing capacity.