Search Results (8)

In this study, a regression model was developed using the thermo-regulated residual refinement regression model (TRRM) analysis method based on three years and four months of in situ data collected from two water-cooled centrifugal chillers installed in A Tower, Seoul, South Korea. The primary objective of this study was to predict the coefficient of performance (COP) of water-cooled chillers under various operating conditions using only the chilled water outlet temperature ($T_2$) and the cooling water inlet temperature ($T_3$). The secondary objective was to estimate the COP under standard temperature conditions, which is essential for the absolute performance evaluation of chillers. The collected dataset was refined through thermodynamic preprocessing, including the removal of missing values and outliers, to ensure high data reliability. Based on this refined dataset, regression analyses were conducted separately for four cases: daytime (09:00–21:00) and nighttime (21:00–09:00) operations of chiller #1 and chiller #2, resulting in the derivation of four final regression equations. The reliability of the final dataset was further validated by applying other regression models, including simple linear (SL), bi-quadratic (BQ), and multivariate polynomial (MP) regression. The performance of each model was evaluated by calculating the coefficient of determination ($R^2$), coefficient of variation of root mean square error (CVRMSE), and the p-values of each coefficient. Additionally, the predicted COP values under the design and standard temperature conditions were compared with the measured COP values to assess the accuracy of the model. Error rates were also analyzed under scenarios where $T_2$ and $T_3$ were each varied by ±1 °C. To ensure robust validation, a final comparison was performed between the predicted and measured COP values. The results demonstrated that the TRRM exhibited high reliability and predictive accuracy, with most regression equations achieving $R^2$ values exceeding 90%, CVRMSE below 5%, and p-values below 0.05. Furthermore, the predicted COP values closely matched the actual measured COP values, further confirming the reliability of the regression model and equations. This study provides a practical method for estimating the COP of water-cooled chillers under standard temperature conditions or other operational conditions using only $T_2$ and $T_3$. This methodology can be utilized for objective performance assessments of chillers at various sites, supporting the development of effective maintenance strategies and performance optimization plans. Full article

A new algorithm is developed to automatically detect rebar locations and diameters of reinforced concrete structures using the ground penetrating radar technique. The study uses two-way travel time and biquadratic equations to formulate electromagnetic wave speed in reinforced concrete structures where hyperbolic signatures are approximated. Leveraging an established algorithm, a computer code has been developed to offer automated analysis of ground-penetrating radar data obtained from survey grids. Four reinforced concrete slabs were designed, fabricated, and tested to validate the developed evaluation approach. The proposed methodology demonstrates outstanding signal processing proficiency and reliably and effectively identifies rebar information. Full article

We discuss the weighted complementarity problem, extending the nonlinear complementarity problem on $R^n$. In contrast to the NCP, many equilibrium problems in science, engineering, and economics can be transformed into WCPs for more efficient methods. Smoothing Newton algorithms, known for their at least locally superlinear convergence properties, have been widely applied to solve WCPs. We suggest a two-step Newton approach with a local biquadratic order convergence rate to solve the WCP. The new method needs to calculate two Newton equations at each iteration. We also insert a new term, which is of crucial importance for the local biquadratic convergence properties when solving the Newton equation. We demonstrate that the solution to the WCP is the accumulation point of the iterative sequence produced by the approach. We further demonstrate that the algorithm possesses local biquadratic convergence properties. Numerical results indicate the method to be practical and efficient. Full article

In order to propose a deeper analysis of the general quartic equation with real coefficients, the analytical solutions for all cubic and quartic equations were reviewed here; then, it was found that there can only be one form of the resolvent cubic that satisfies the following two conditions at the same time: (1) Its discriminant is identical to the discriminant of the general quartic equation. (2) It has at least one positive real root whenever the general quartic equation is non-biquadratic. This unique special form of the resolvent cubic is defined here as the “Standard Form of the Resolvent Cubic”, which becomes relevant since it allows us to reveal the relationship between the nature of the roots of the general quartic equation and the nature of the roots of all the forms of the resolvent cubic. Finally, this new analysis is the basis for designing and programming efficient algorithms that analytically solve all algebraic equations of the fourth and lower degree with real coefficients, always avoiding the application of complex arithmetic operations, even when these equations have non-real complex roots. Full article

This paper presents a general analysis of all the quartic equations with real coefficients and multiple roots; this analysis revealed some unknown formulae to solve each kind of these equations and some precisions about the relation between these ones and the Resolvent Cubic; for example, it is well-known that any quartic equation has multiple roots whenever its Resolvent Cubic also has multiple roots; however, this analysis reveals that any non-biquadratic quartic equation and its Resolvent Cubic always have the same number of multiple roots; additionally, the four roots of any quartic equation with multiple roots are real whenever some specific forms of its Resolvent Cubic have three non-negative real roots. This analysis also proves that any method to solve third-degree equations is unnecessary to solve quartic equations with multiple roots, despite the existence of the Resolvent Cubic; finally, here is developed a generalized variation of the Ferrari Method and the Descartes Method, which help to avoid complex arithmetic operations during the resolution of any quartic equation with real coefficients, even though this equation has non-real roots; and a new, more simplified form of the discriminant of the quartic equations is also featured here. Full article

In this paper, based on the modified block-by-block method, we propose a higher-order numerical scheme for two-dimensional nonlinear fractional Volterra integral equations with uniform accuracy. This approach involves discretizing the domain into a large number of subdomains and using biquadratic Lagrangian interpolation on each subdomain. The convergence of the high-order numerical scheme is rigorously established. We prove that the numerical solution converges to the exact solution with the optimal convergence order $O(h_x^{4-\alpha }+h_y^{4-\beta })$ for $0<\alpha ,\beta <1$. Finally, experiments with four numerical examples are shown, to support the theoretical findings and to illustrate the efficiency of our proposed method. Full article

In this note, we study the Ulam stability of a general functional equation in four variables. Since its particular case is a known equation characterizing the so-called bi-quadratic mappings (i.e., mappings which are quadratic in each of their both arguments), we get in consequence its stability, too. We deal with the stability of the considered functional equations not only in classical Banach spaces, but also in 2-Banach and complete non-Archimedean normed spaces. To obtain our outcomes, the direct method is applied. Full article

Active filter design is a mature topic that provides good solutions that can be implemented using discrete devices or integrated circuit technology. For instance, when the filter topologies are implemented using commercially available operational amplifiers (opamps), one can explore varying circuit parameters to tune the central frequency or enhance the quality (Q) factor. We show the addition of a feedback loop in the signal flow graph of a biquadratic filter topology, which enhances Q and highlights that a sensitivity analysis can be performed to identify which circuit elements influence central frequency, Q, or both. In this manner, we show the opamp-based implementation of a biquadratic bandpass filter, in which Q is enhanced through performing a sensitivity analysis for each circuit element. Equations for the central frequency and Q are provided to observe that there is not a direct parameter that enhances them, but we show that from sensitivity analysis one can identify the circuit elements that better enhance Q-factor. Full article