Fourth-order Polynomial Regression Research Articles

Barrel Distortion Correction for Digital Optic-Based Motion Tracking in Ship Hydrodynamic Model Experiments

In hydrodynamic ship-model experiments, motion tracking of ship model trajectory is employed to predict the maneuverability of the ship when operating in its actual environment. There are some systems for motion tracking, such as inertial measurement unit, radar, laser, and infrared sensors. The system has proven reliable, however, the disadvantage is that they are all relatively expensive. This paper proposes a low-cost digital optic-based motion tracking system using consumer-grade video camera. In order to examine the accuracy of the system, some experiments to apply the method were carried out in maneuvering offshore engineering basin at the Indonesian Hydrodynamics Laboratory, The National Agency for Research and Innovation. To cover a broader area of the trajectory, a wide-angle camera lens was utilized, consequently, the image recorded by the camera experienced a barrel distortion. As a reference for the measurements, gridlines spaced 2 meters apart were drawn on the floor of the basin. Using the grid pattern, the distortion was corrected by finding the relationship between the grid pattern in the object space and in the distorted image. A fourth-order polynomial regression was applied to solve the problem. The results showed that the method was effective for correcting distorted images with a relative standard error of 0.42%.

Influence of electrode to cochlear duct length ratio on post-operative speech understanding outcomes

Objective To assess whether the pre-operative electrode to cochlear duct length ratio (ECDLR), is associated with post-operative speech recognition outcomes. Study Design A retrospective chart review study. Setting: Tertiary referral center. Patients The study included sixty-one adult CI recipients with a pre-operative computed tomography scan and a speech recognition test 12 months after implantation. Interventions The average of two raters’ cochlear duct length (CDL) measurements and the length of the recipient’s cochlear implant electrode array formed the basis for the electrode-to-cochlear duct length ratio (ECLDR). Speech recognition tests were compared as a function of ECDLR and electrode array length itself. Main outcome measures The relationship between ECDLR and percent correct on speech recognition tests. Results A second order polynomial regression relating ECDLR to percent correct on the CNC words speech recognition test was statistically significant, as was a fourth order polynomial regression for the AzBio Quiet test. In contrast, there was no statistically significant relationship between speech recognition scores and electrode array length. Conclusions ECDLR values can be statistically associated to speech-recognition outcomes. However, these ECDLR values cannot be predicted by the electrode length alone, and must include a measure of CDL.

Prediction and mathematical analysis of the outbreak of coronavirus (COVID-19) in Bangladesh

In this study based on Bangladesh, a modified SIR model is produced and analysed for COVID-19. We have theoretically investigated the model along with numerical simulations. The reproduction number (R0) has been calculated by using the method of the next-generation matrix. Due to the basic reproduction number, we have analysed the local stability of the model for disease-free and endemic equilibria. We have investigated the sensitivity of the reproduction number to parameters and calculate the sensitivity indices to determine the dominance of the parameters. Furthermore, we simulate the system in MATLAB by using the fourth-order Runge–Kutta (RK4) method and validate the results using fourth order polynomial regression (John Hopkins Hospital (JHH), 2020). Finally, the numerical simulation depicts the clear picture of the upward, and the downward trend of the spread of this disease along with time in a particular place, and the parameters in the mathematical model indicate this change of intensity. This result represents, the effect of COVID-19 from Bangladesh’s perspective.

Modular force approximating soft robotic pneumatic actuator.

Soft robots are highly flexible and adaptable instruments that have proven extremely useful, especially in the surgical environment where compliance allows for improved maneuverability throughout the body. Endoscopic devices are a primary example of an instrument that physicians use to navigate to difficult-to-reach areas inside the body. This paper presents a modular soft robotic pneumatic actuator as a proof of concept for a compliant endoscopic device. The actuator is 3D printed using an FDM printer. Maximum bending angle is measured using image processing in MATLAB at a gauge pressure level of 35psi. End-effector displacement is measured using electromagnetic tracking as gauge pressure ranges from 10 to 35psi, and uniaxial tensile loading ranges from 0 to 120g. The actuator achieves a maximum bending angle of 145°. Fourth-order polynomial regression is used to model the actuator displacement upon inflation and tensile loading with an average coefficient of correlation value of 0.998. We also develop a feedforward neural network as a robust computer-assisted method for controlling the actuator that achieves a coefficient of correlation value of 0.996. We propose a novel modular soft robotic pneumatic actuator that is developed via rapid prototyping and evaluated using image processing and machine learning models. The curled resting shape allows for simple manufacturing and achieves a greater range of bending than other actuators of its kind. A feedforward neural network provides accurate prediction of end-effector displacement upon inflation and loading to deliver precise manipulation and control.

Omnidirectional thermal anemometer for low airspeed and multi-point measurement applications

Current control strategies for livestock and poultry facilities need to improve their interpretation of the Thermal Environment (TE) that the animals are experiencing in order to provide an optimum TE that is uniformly distributed throughout the facility; hence, airspeed, a critical parameter influencing evaporative and convective heat exchange must be measured. An omnidirectional, constant temperature, Thermal Anemometer (TA) with ambient dry-bulb temperature (tdb) compensation was designed and developed for measuring airspeeds between 0 and 6.0ms−1. An Arduino measured two analog voltages to determine the thermistor temperature and subsequently the power being dissipated from a near-spherical overheated thermistor in a bridge circuit with a transistor and operational amplifier. A custom wind tunnel featuring a 0.1m diameter pipe with an access for TA insertion was constructed to calibrate the TA at different temperatures and airspeeds, at a constant relative humidity. The heat dissipation factor was calculated for a given airspeed at different ambient temperatures ranging from 18°C to 34°C and used in a unique fourth-order polynomial regression that compensates for temperature using the fluid properties evaluated at the film temperature. A detailed uncertainty analysis was performed on all key measurement inputs, such as the microcontroller analog to digital converter, TA and tdb thermistor regression statistics, and the calibration standard, that were propagated through the calibration regression. Absolute combined standard uncertainty associated with temperature corrected airspeed measurements ranged from 0.11ms−1 (at 0.47ms−1; 30.3% relative) to 0.71ms−1 (at 5.52ms−1; 12.8% relative). The TA system cost less than $35USD in components and due to the simple hardware, this thermal anemometer is well-suited for integration into multi-point data acquisition systems analyzing spatial and temporal variability inside livestock and poultry housing.

Comparative Experiment of Color Reproduction Methods

Digital camera which has the advantage of real-time image transferring and easily processing is more and more widely used in the packaging and printing industry with the rapid development of high-tech electronics industry. However, the color in digital camera is not accurate which affect the application. To minimize the color difference between the color in the digital camera and the real color, the color reproduction methods is developing. The field comparative experiment is carried out to compare the performance of color reproduction methods, such as polynomial regression algorithm in different color space, and color checker passport. The results show that fourth order polynomial regression color reproduction in XYZ color space has the best performance.

Estimation of fabric opacity by scanner

Purpose– This study aimed to use a scanner as a low-cost method for measuring the opacity of textile fabric. Textile fabrics must have specific ranges of opacity according to their uses for shirting, curtaining, etc. In this way, opacity is an important property in the textile industry. Conventionally, textile opacity is estimated using a spectrophotometer, which is an expensive method.Design/methodology/approach– In this study a scanner was used as a low-cost method for measuring the opacity of textile fabric. The opacity was estimated by using red, green and blue (RGB) parameters of images of fabric against white and black background.Findings– The accuracy of opacity estimation was improved by converting RGB into several color spaces. The best opacity estimation was obtained by using the XYZ color space. In addition, using a regression method, the best estimation was obtained by using a fourth-order polynomial regression with the LSLM color space.Originality/value– The opacity of fabric has been measured by spectrophotometer, but in this study, the opacity of fabric was measured by scanner as a low cost device and also with novel and simple method. This method achieved acceptable accuracy for opacity estimation. The obtained result is comparable with spectrophotometer results.

Moisture Content Prediction of Dried Longan Aril from Dielectric Constant Using Multilayer Perceptrons and Support Vector Regression

Problem statement: Estimation of moisture contents of dried food products from their dielectric constants was an important step in moisture measurement systems. The regression models that provide good prediction performance are desirable. Approach: The Multilayer Perceptrons (MLP) and Support Vector Regression (SVR) were applied in this research to predict the moisture contents of dried longan arils from their dielectric constants. The data set was collected from 1500 samples of dried longan aril with five different moisture contents of 10, 14, 18, 22 and 25% Wet basis (Wb.) Dielectric constant of dried longan aril was measured by using our previously proposed electrical capacitance-based system. The results from the MLP and SVR models were compared to that from the linear regression and polynomial regression models. To take into account the generalization of the models, the four-fold cross validation was applied. Results: For the training sets, the average mean absolute errors over three bulk densities of 1.30, 1.45 and 1.60 g cm-3 were 1.7578, 0.6157, 0.3812, 0.3113, 0.0103 and 0.0044% Wb for the linear regression, second-, third-, fourth-order polynomial regression, MLP and SVR models, respectively. For the validation sets, the average mean absolute errors over the three bulk densities were 1.7616, 0.6192, 0.3844, 0.3146, 0.0126 and 0.0093% Wb for the linear regression, 2nd, 3rd and 4th-order polynomial regression, MLP and SVR models, respectively. Conclusion: The regression models based on MLP and SVR yielded better performances than the models based on linear regression and polynomial regression on both training and validation sets. The models based on MLP and SVR also provided robustness to the variation of bulk density. Not only for dried longan aril, the proposed models can also be adapted and applied to other materials or dried food products.

Fetal Growth Curves for an Ethnically Diverse Military Population: The American Institute of Ultrasound in Medicine-Accredited Platform Experience

To determine which fetal growth curve provided the best estimates of fetal weight for a cohort of ethnically diverse patients at sea level. The study consisted of a population of 1,729 fetuses examined at sea level between January 1, 1997, and June 30, 2000, at 18 weeks, 28 weeks, and term. Gestational age (GA) based on menstrual dates was confirmed or adjusted by crown-rump length or early second-trimester biometry. Fetal weight was estimated by using biparietal diameter, head circumference, abdominal circumference, and femur length. Our fetal growth curves were analyzed with fourth-order polynomial regression analysis, applying four previously defined formulae for fetal growth. Fetal growth curves for estimated fetal weight demonstrated the expected parabolic shape, which varied according to the formulae used. Our curve best fit the following equation: estimated fetal weight = 4.522 - 0.22 x GA age + 0.25 x GA(2) - 0.001 x GA(3) + 5.248 x 10(-6) x GA(4) (R2 = 0.976). SD increased in concordance with GA. Madigan Army Medical Center serves a racially mixed, culturally diverse, military community with unrestricted access to prenatal care. Determination of the optimal population-appropriate growth curve at the correct GA assists clinicians in identifying fetuses at risk for growth restriction or macrosomia and therefore at risk for increased perinatal morbidity and death.

Fourth-order rotatable designs: A-optimal measures

The A-optimal rotatable design measures are derived for fourth-order polynomial regression on hyperspheres. The application of the association algebra of triangular association scheme is helpful in the derivation of the objective function.