Polynomial Regression Equation Research Articles

Equations for estimating the static supportive torque provided by upper-limb exoskeletons

Upper-limb exoskeletons are gaining traction in industrial work environments. However, other than advertised general specifications (e.g., peak support angle), the support torque provided throughout the reach envelope is largely unknown to end users. As such, this paper describes a methodology for measuring the specific supportive torque provided by upper-limb exoskeletons. The support of four commercially available passive upper-limb exoskeletons was quantified using an isokinetic dynamometer for all support ranges and levels (n = 68). Tests were repeated four times to determine between-session reliability. Intraclass correlation coefficients demonstrated ‘Good’ to ‘Excellent’ reliability, except for one condition. Polynomial regression equations were developed for each condition to predict exoskeleton support for any upper-limb elevation angle between 10° and 180°. These equations can be used to approximate upper-limb exoskeleton support in digital human modeling assessments, or to aid selection of exoskeleton settings specific to a worker's anthropometry and work task location.

Role of different natural materials in reducing nitrogen loss during industrial sludge composting: Modelling and optimization

In this study, the effects of pumice, expanded perlite, and expanded vermiculite on nitrogen loss were examined for industrial sludge composting using the Box-Behnken experimental design. The independent factors and their levels were selected as amendment type, amendment ratio, and aeration rate, and codded as x1, x2, and x3 at 3 levels (low, center, and high). The statistical significance of independent variables and their interactions were determined at 95% confidence limits by Analysis of Variance. The quadratic polynomial regression equation produced to predict the responses was solved and the optimum values of the variables were predicted by analyzing the three-dimensional response surfaces plots. The optimum conditions for minimum nitrogen loss by the regression model were as pumice of amendment type, 40% of amendment ratio, and 6 L/min of aeration rate. In this study, it was observed that time-consuming and laborious laboratory work can be minimized with the Box-Behnken experimental design.

PyDigitizer – A Python module for digitizing 2D curves

The paper presents a PyDigitizer application designed to extract numerical coordinates of existing curves from image format. The application is created in the Python programming language and offers the possibility of manual extraction of curve coordinates, intersection of curves with user-specified abscissa or ordinate, generation of polynomial regression equations of curves. All generated information (coordinates, intersection points, regression curves) can be exported to Microsoft Excel. Also, point coordinates of Excel curves can be loaded into PyDigitizer to obtain polynomial regression curves or intersections.

Multivariate polynomial regression based selection and analysis of process parameters for X-ray inspection of pipeline containing medium

Pressure pipelines use pressure to transport gas, liquefied gas, and steam in the process of use. If there are defects in the pipeline, it is easy to leak or burst, and even cause secondary accidents. To ensure safety, it is necessary to inspect the pressure pipelines in use regularly. However, it is difficult for the pressure pipeline in use to empty the internal medium. Therefore, it is of great significance to inspect the defects of the industrial pressure pipeline under operating conditions. In this paper, X-ray testing experiments are carried out for weld defects of pipelines with the medium. Using the experimental data, multivariate polynomial regression equations of negative blackness and tube voltage, and other variables are established, which provides an effective tool for the formulation of the optimal process route for testing pressure pipelines containing medium.

Determination of Optimum Gamma Ray Irradiation Doses for Hulless Barley (Hordeum vulgare var. nudum L. Hook. f.) Genotypes

The limited germplasm resources of hulless barley restrict the breeding of hulless barley with improved traits. Mutation techniques are an effective tool for generating variation for plant breeding studies. This study aimed to evaluate the impact of gamma-ray at different doses on certain seedling properties of M1 plants of two hulless barley genotypes, as well as determine the effective dose (ED50). The seeds of two hulless two-row barley genotypes, cv. Yalin and hulless barley line YAA7050-14, were irradiated with 100, 150, 200, 250, and 300 gray Gamma-rays delivered by a Cobalt 60 source along with non-irradiated control samples. Gamma-ray irradiation affects the seedling properties of M1 plants of both hulless barley genotypes significantly. The significant effect varied based on the doses, traits, and genotypes. While lower doses were found statistically identical to the control in the majority of qualities in the M1 generation, 250-300 gray gamma ray doses caused statistically significant decreases in the majority of characteristics studied in both genotypes. The effective doses (ED50) for hulless barley genotypes were determined by plotting growth reduction values of seedling lengths, then the polynomial regression equations were calculated for each genotype. It was determined that 50% growth reduction in shoot length was reached at 214.1 Gy and 253.4 Gy for cv. Yalin and line YAA7050-14, respectively.

LiDAR Point Cloud Data Combined Structural Analysis Based on Strong Form Meshless Method Using Essential Boundary Condition Capturing.

This study proposes a novel hybrid simulation technique for analyzing structural deformation and stress using light detection and ranging (LiDAR)-scanned point cloud data (PCD) and polynomial regression processing. The method estimates the edge and corner points of the deformed structure from the PCD. It transforms into a Dirichlet boundary condition for the numerical simulation using the particle difference method (PDM), which utilizes nodes only based on the strong formulation, and it is advantageous for handling essential boundaries and nodal rearrangement, including node generation and deletion between analysis steps. Unlike previous studies, which relied on digital images with attached targets, this research uses PCD acquired through LiDAR scanning during the loading process without any target. Essential boundary condition implementation naturally builds a boundary value problem for the PDM simulation. The developed hybrid simulation technique was validated through an elastic beam problem and a three-point bending test on a rubber beam. The results were compared with those of ANSYS analysis, showing that the technique accurately approximates the deformed edge shape leading to accurate stress calculations. The accuracy improved when using a linear strain model and increasing the number of PDM model nodes. Additionally, the error that occurred during PCD processing and edge point extraction was affected by the order of polynomial regression equation. The simulation technique offers advantages in cases where linking numerical analysis with digital images is challenging and when direct mechanical gauge measurement is difficult. In addition, it has potential applications in structural health monitoring and smart construction involving machine leading techniques.

Effects of Sodium Butyrate Supplementation in Milk on the Growth Performance and Intestinal Microbiota of Preweaning Holstein Calves.

The aim of the present study was to investigate the effects of sodium butyrate (SB) supplementation on the growth and intestinal microbiota of preweaning dairy calves. Eighty newborn Holstein calves (56 female and 24 male) were randomly allocated to four treatment groups with 20 calves each (14 female and 6 male). The suckling milk for the four treatments was supplemented with 0, 4.4, 8.8, or 17.6 g/d SB. During the 6-week experiment, dry matter intake was recorded daily, body weight was measured weekly, and rectal fecal samples were collected in the 2nd week. The V3-V4 hypervariable regions of the microbial 16S rRNA were amplified and then sequenced. SB supplementation elevated average daily gains (ADGs) in the first and second weeks. The optimal SB supplementation level for the whole preweaning period was 8.78 g/d, as revealed by analyzing the whole preweaning period ADG using second-order polynomial regression (quadratic) equations. The alpha diversity (Shannon diversity index), beta diversity, core phyla and genera, and function of the intestinal microbiota were affected by SB supplementation. In addition, the Shannon diversity index and core phyla and genera of the intestinal microbiota were correlated with calf growth-related indices. Overall, SB supplementation in suckling milk improved the growth performance and intestinal microbiota development of dairy calves in a quadratic manner, and regression analysis indicated an optimal supplementation level of 8.78 g/d.

Plant stress prediction model on nutrient film technique hydroponic in a natural greenhouse

This study aimed to identify plant stress on the NFT hydroponic module in the greenhouse using the mathematical model of the 4th-order polynomial regression equation. The artificial Neural Network (ANN) approach was also conducted to analyze factors affecting plant growth and yield. Tatsoi plants (Brassica rapa subsp. Narinosa) were grown in the NFT hydroponic module with three treatments of irrigation time, i.e., 6 hours (A6), 12 hours (A12), and 24 hours (A24). Measured parameters include microclimate (temperature, relative humidity, and light intensity) and plant morphology (leaf canopy area, root length, leaf number, and plant weight). The value of the resulting model’s coefficient of determination (R2) for A6, A12, and A24 were 0.9986, 0.994, and 0.9988, respectively. The results of the validation test also show that the prediction data built from the model is very close to the actual data of tatsoi plant’s leaf canopy area. Based on the ANN approach, the MAPE value (0.240) and error (0.00116) A6 treatment were the smallest, whereas the largest R2 value (0.979) was also obtained in this treatment. Furthermore, analysis of the plant weight showed that changes in the leaf canopy area due to water stress ultimately affect plant yield.

Linking the Perceived Strength Supports Both From Organization and Supervisor to Performances: The Roles of Strengths-Based Climate and Meaningful Task

Although employee strengths use has gained popularity in academia and practice, our understanding of its effective application for maximizing employee performance remains insufficient. This study investigates the interaction between perceived organizational and supervisor support for strengths use and employees’ strengths-based psychological climate and job performance. Using multi-wave data from 241 employee–supervisor dyads, the results of polynomial regression equations with a response surface analysis show that the higher the congruence between perceived organizational and supervisor support for strengths use, the better the strengths-based psychological climate. The congruence between these two forms of support has indirect effects on task performance and organizational citizenship behaviors (OCB) via the strengths-based psychological climate. Furthermore, while meaningful work is found to enhance the indirect effect of congruence on task performance through the strengths-based psychological climate, task interdependence does not strengthen the indirect effect of congruence on OCB. This study highlights the importance of the congruence between perceived organizational and supervisor support for strengths use in promoting employee performance and provides several useful practical implications for both organizations and career counselors.

An Experimental Study on the Elbow Pressure Drop and Conveying Stability of Pneumatic Conveying for Stiff Shotcrete Based on Response Surface Methodology

The pressure drop and conveying stability caused by the bend significantly affect the pneumatic conveying process of stiff shotcrete, which is the key to solving the problem of long-distance transportation. In this paper, the effects of different air velocities (32 m/s, 36 m/s, 40 m/s), water-cement ratios (0.1, 0.2, and 0.3), and bending-diameter ratios (4, 12, and 20) on the pressure drop of the elbow R1 and conveying stability R2 are studied using the response surface method. The conveying stability is characterized by the pressure variation coefficient (C.V). The response surface graph aids in the intuitive analysis of the effects of these variables. The results show that the impact of air velocity on R1 and R2 is exceptionally significant, and the interaction of each factor on the response value is analyzed. The response value and the quadratic polynomial regression equation between the various factors are obtained in addition to the flow characteristics of stiff shotcrete under different working conditions. The relationship established by the statistical processing of the experimental results can provide some reference for specifying the pressure loss model of stiff shotcrete.

Development of a potassium-based soil washing solution using response surface methodology for efficient removal of cesium contamination in soil

The overuse of chelating soil washing agents for removal of heavy metal can release soil nutrients and negatively affect organisms. Therefore, developing novel washing agents that can overcome these shortcomings is necessary. In this study, we tested potassium as a main solute of novel washing agent for cesium-contaminated field soil, owing to the physicochemical similarities between potassium and cesium. Response surface methodology was combined with a four-factor, three-level Box–Behnken design to determine the superlative washing conditions of the potassium-based solution for the removal of cesium from the soil. The parameters that were considered were the following: potassium concentration, liquid-to-soil ratio, washing time, and pH. Twenty-seven sets of experiments were conducted using the Box–Behnken design, and a second-order polynomial regression equation model was obtained from the results. Analysis of variance proved the significance and goodness of fit of the derived model. Three-dimensional response surface plots displayed the results of each parameter and their reciprocal interactions. The washing conditions that achieved the highest cesium removal efficiency (81.3%) in field soil contaminated at 1.47 mg/kg were determined to be the following: a potassium concentration of 1 M, a liquid-to-soil ratio of 20, washing time of 2 h, and a pH of 2.

The development of the normal Schirmer tear test results during the dog's first year of life.

To evaluate the relationship between lacrimation and age in a homogeneous group of healthy beagle dogs during the first year of life. Schirmer tear test I (STT I) was performed at an interval of 12-15 days in both eyes of 16 clinically healthy beagle dogs (eight males and eight females) from 94 to 361 days of age. Three different quadratic polynomial regression equations were estimated for the variation in lacrimation: (1) for the entire period (19 observations), (2) for observations 1-4 (days 94-136), and (3) for observations 5-19 (days 150-361). By fitting quadratic regression equations to different phases of tear production during the dog's first year of life, it was possible to see that with each day of life, lacrimation increased 0.08 times (8%). From days 94 to 136, however, lacrimal production fell 1.1 times with each day of life. From day 150 to 361, production increased by 0.02 (2%) each day of life. In addition, there was a positive significant and moderate linear correlation between body weight and STT I values (p=.01). In dogs, during the first year of life, STT I data distribution is parabolic in shape. Age significantly affected tear production. STT I decreased at approximately 108-121 days of age and increased thereafter. Body weight was a significant factor for STT I in young dogs. The establishment of this normal pattern of lacrimation is important for both clinical practitioners and laboratory studies.

Buildability Analysis of 3D Concrete Printing Process: A Parametric Study Using Design of Experiment Approach

Plastic collapse and buckling are the key structural failure criteria in 3D concrete printing (3DCP). This study aims to analyze the effect of different geometrical designs and printing factors on the buildability performance of 3DCP structures. Due to the high number of variables involved, the Design of Experiment (DOE) has been used to reduce the number of simulations. In geometrical design parameters, the structure’s design is more sensitive, followed by the width and length of the printed design. The buildability increases when we move from sharp corners to more stable structures like fillets and circular geometry. For geometrical design parameters, a maximum buildability of 74% of the designed height is achieved for circular design with the highest width and lowest diameter. For printing parameters, the highest buildability of 486 mm (81%) is achieved for the lower values of printing speed and layer height. The study analyzed failure phenomena of buckling and yield strength for the tested combination of parameters. The study analyzed the sensitivity analysis of individual parameters and their combination for maximum buildability and developed the low order polynomial regression equation for each printing parameter and geometrical factors. Based on the analysis of the results, the study also proposed different new printing strategies to increase the overall performance of the printing process.

Adsorption removal of arsenic from Aqueous solution by carboxy methyl Cellulose(CMC) modified with montmorillonite

In this research, CMC/MMT nano composite was prepared using the free radical polymerization method and evaluated as Arsenic ions removal adsorption from an aqueous solution. We used the Design expert (CCD) to remove Arsenic Ions optimally. SEM, XRD and FTIR analyses were used to determine the adsorbent properties. The experimental design was done with four time variables (25–40min), Arsenic concentration (0.5–2 ppm), adsorbent dose (0.05-2gr) and pH (4–8). The interaction and combined effects of the variables were evaluated by the analysis of variance (ANOVA) table. A quadratic polynomial regression equation was developed to predict the response under optimal conditions. The results of kinetic studies and adsorption isotherms present that the kinetics of Arsenic ion adsorption by CMS/MMT adsorbent follows the quadratic equation and the Langmuir isotherm with a better correlation coefficient than the Freundlich equation. Furthermore, under optimal conditions (pH = 5.6, t = 34 min), 1.9 ppm Arsenic is adsorbed per 0.09 g of the adsorbent with 85% efficiency which indicates that the carboxymethyl cellulose hydrogel modified with Montmorillonite is a suitable adsorbent to remove Arsenic ions from aqueous solution.

Cooling performance and optimization of a tubular indirect evaporative cooler based on response surface methodology

To optimize the cooling effectiveness of the tubular indirect evaporative cooler (TIEC), an experimental design was conducted using the response surface methodology (RSM). In this work, the wet-bulb effectiveness was selected as the response value, while the influencing factors included six operation parameters, namely, the spray water flow rate (Qw), secondary-to-primary air flow rate ratio (Rsp), primary air resistance (R1), secondary air resistance (R2), inlet air dry bulb temperature (tg1) and air relative humidity (RH). The operation conditions of a TIEC with a tube diameter of 10 mm were optimized. The second-order model fitting of the RSM was used to obtain the polynomial regression equation between the wet-bulb effectiveness and each factor. The wet-bulb effectiveness can be achieved up to 78 % under the optimized conditions with Qw of 1.2 m3/h, Rsp of 0.5, R1 of 89 Pa, R2 of 100 Pa, tg1 of 17.3 °C, and RH of 79.6 %.

Predictability of Proximal Enamel Thickness Assessment using Intraoral Periapical Radiographs: A Cross-sectional Study

Introduction: Measurements of tooth crown dimensions and enamel thickness are useful guides for interproximal stripping procedures aimed at creating space. In borderline non extraction orthodontic treatment cases, interproximal stripping is performed to gain space. Intraoral periapical radiographs and bitewing radiographs are commonly used to determine Proximal Enamel Thickness (PET). Aim: To determine the predictability of using IOPA-based PET measurements for assessing real/anatomic PET. Materials and Methods: This was a single-centre, crosssectional study conducted at Saveetha Dental College and Hospital, Chennai, Tamil Nadu, India, between March 2022 and April 2022. Digital Intraoral Periapical Radiographs (IOPAs) of 40 premolar teeth with intact crown structures were obtained using the paralleling technique. The PET of both the mesial and distal sides of the same teeth was measured using Carestream Imaging software. Subsequently, the extracted teeth were sectioned and examined under a Stereomicroscope (SM), and PET measurements of the mesial and distal surfaces were obtained along the heights of contour using ImageJ analysis software. Pearson’s correlation, along with linear and polynomial regression analyses, was performed using International Business Machines (IBM) Statistical Package for Social Sciences (SPSS) software. Results: A low but significant positive correlation between the PET of the sectioned teeth and the PET measured from IOPAs was observed (p=0.002, R=0.55). A significant difference in PET between the two methods for both sides was noted (p<0.05). The mean distal enamel thickness was significantly greater than the mean mesial enamel thickness for both the IOPA and SM methods (p<0.05). A polynomial regression equation, Y=2.084- 1.234X+0.318X3 , was established to predict PET of the sectioned teeth (Y) based on PET measured from IOPAs (X). Conclusion: The present study establishes a correlation between the true PET of teeth measured using cut-sections and PET measured from IOPAs, which are readily available in clinical practice. A correlation coefficient was determined, and PET can be predicted using IOPAs, although not with absolute accuracy. Distal PET was found to be higher than mesial PET, with no significant difference in enamel thickness between the two sides.

Effect of GA3 and NAA on tomato production under protected cultivation in Kaski, Nepal

A field experiment was carried out under naturally ventilated greenhouse to assess the performance of tomato cv. Srijana as influenced by GA 3 and NAA during the summer season of 2018–2019 at Kham Ghale Krishi farm, Pokhara, Kaski, Nepal. The treatments comprised of four levels of Gibberellic Acid (GA 3 ) (i.e., 0 ppm, 25 ppm, 50 ppm and 75 ppm) combined with four different levels of Naphthalene Acetic Acid (NAA) (i.e., 0 ppm, 25 ppm, 50 ppm and 75 ppm). Treatments were replicated thrice in the two factorial RCBD. The results revealed that the fruit yield was significantly influenced by the levels of GA 3 , NAA and their interactions. Among four levels of NAA, the highest yield (109.91metric ton ha-1) of tomato was recorded with NAA @ 25 ppm which was 10.37%, 17.47% and 24.78% higher over NAA @ 0 ppm, NAA @ 50 ppm and NAA @ 75 ppm, respectively. Similarly, a significantly higher yield (103.46metric ton ha-1) of tomato was attained with GA 3 @ 50 ppm and it was 13.91%, 10.31% and 6.74% higher over GA 3 @ 0 ppm, GA 3 @ 25 ppm and GA 3 @ 75 ppm, respectively. Interactions between GA 3 and NAA levels were significant for all yield attributes. Regression analysis on the effect of GA 3 and NAA on the yield of tomato exhibited a polynomial regression equation, while the physical dose of GA 3 and NAA was observed to be 52.65 ppm and 20.29 ppm, respectively. It could be suggested that the production of tomato could be improved by the combined application of GA 3 @ 50 ppm and NAA @ 25 ppm under the controlled condition of Kaski, Nepal. • Average yield per hectare for tomato is very low in summer season particularly due to poor fruit set and flower drop. • GA3 and NAA can be used to address the problem of poor fruiting and flower drop. • Application of GA3 @50 ppm and NAA@25 ppm led to better fruit set and yield under protected condition. • This can boost the yield and encourage tomato growers to use PGR's at proper concentration under protected condition.

Parametric mathematical modeling and 3D response surface analysis for rod to plate friction welding of AISI 1020 steel/AISI 1018 steel

PurposeRotary friction welding (RFW) was used to solve the issues in fusion welding of rod to plate joints of low carbon steel (AISI 1020 steel/AISI 1018 steel) such solidification cracking, wider heat affected zone (HAZ), lower HAZ hardness, high residual stresses and distortion. The main objective of this investigation is to develop parametric mathematic models (PMMs), 3D response surface analysis to predict tensile strength (TS) and weld interface hardness (WIH) of rod to plate joints and correlate microstructure with TS and WIH of rod to plate joints.Design/methodology/approachThe three-factor x five-level central composite design (CCD) consisting fewer experiments was employed for designing experimental matrix. The tensile and microhardness tests were performed to evaluate mechanical performance of joints. The PMMs of TS and WIH of rod to plate joints were developed using polynomial regression equations incorporating the RFW parameters. The 3D response surfaces were developed using response surface methodology (RSM) to optimize RFW parameters for joining AISI 1020/AISI 1018 rod to plate.FindingsThe joints made using friction pressure/friction time (FRNP/FRNT) of 3.71 MPa/s, forging pressure/forging time (FRGP/FRGT) of 3.71 MPa/s and rotational speed (RTSP) of 19.99 rps exhibited higher TS and WIH of 452 MPa and 252 HV0.5. The PMMs accurately predicted TS and WIH of rod to plate joints at less than 1.5% error and 95% confidence. The RTSP revealed greater effect on TS and WIH of rod to plate joints followed by FRGP/FRGT and FRNP/FRNT. The superior TS and WIH of joints developed using optimized process parameters is correlated to the evolution of finer bainitic microstructure in weld interface due to the dynamic recrystallization of grains ensued by optimum frictional heating and plastic deformation.Originality/valueThe PMMs were developed for predicting TS and WIH of joints. The RFW parameters were optimized to enhance TS and WIH of joints. Low carbon steel rod to plates joints were developed using RFW for automotive applications without fusion welding defects. The microstructural features of low strength and high strength rod to plate joints were correlated to the TS and WIH of rod to plate joints.

Investigation on the machinability of TiN nano particulate reinforced magnesium matrix composite

In the present work, the machinability of magnesium matrix nanocomposite was investigated. The nanocomposite consists of pure Mg as matrix and TiN Nano particulate as reinforcement. The composite was fabricated through powder metallurgy process for three different compositions such as 1.5, 2.5 and 5% by weight of TiN Nano particulates. Machinability behavior of the nanocomposite was studied through milling process with process parameters, feed rate of 5, 10 and 15 mm/min, depth of cut of 0.15, 0.3 and 0.45 mm and spindle speed of end mill remain constant of about 2000 rpm. The performance measures considered in this study are cutting forces, material removal rate, surface roughness and tool tip temperature. The milling process was carried out at room temperature for normal atmospheric conditions. Poly crystalline diamond (PCD) coated solid carbide flat type end mill was used in the study. L27 orthogonal array was used to conduct the experiments. The results from the study revealed the fact that the performance measures like cutting force, tool tip temperature and surface roughness are significantly influenced by TiN Nano particulate in the composite, whereas the material removal rate is greatly influenced by the machining parameter feed rate. High hardness, heat resistance and excellent wear resistance of TiN Nano particulate resulted in the influence of the performance measures. Main effect plots and interaction plots were generated for the performance measures which was further followed by ANOVA and second order polynomial regression equation to test the level of significance with least error.

How to avoid errors when computing reference interval tables and graphs using regression equations for cross-sectional studies of fetal biometry.

While visualization of fetal anatomy is one of the primary purposes of diagnostic ultrasound, the application of statistical analysis to biological measurements of fetal structures such as the head, abdomen, long bones, and heart, requires equations that compute changes in these measurements over time. One of the challenges for the investigator who desires to compute reference intervals for a fetal measurement is selecting the best equation for the measurements of interest. Fractional polynomial regression equations have been used to describe changes in fetal measurements over time and consists of 44 equations for the investigator to select. Since it would be laborious to analyze each equation to identify the best fit of the data, software programs have been developed for such analysis. However, depending upon the software program, potential errors can occur when translating the coefficients of a complex equation to a format that can be used by the clinician to create reference interval tables and graphs. This study reviews the requirements for statistical output that allows the investigator to generate reference interval tables and graphs using Excel. A step-by-step sequence is explained that enables the investigator to minimize the possibility of errors when reporting complex equations and their associated graphs that result from fractional polynomial regression analysis. Using the techniques described in this opinion paper should decrease the potential for reporting erroneous equations used to compute reference interval tables and graphs. This article is protected by copyright. All rights reserved.