Development of Prediction Model to Predict the Compressive Strength of Eco-Friendly Concrete Using Multivariate Polynomial Regression Combined with Stepwise Method

Concrete is the most widely used building material, but it is also a recognized pollutant, causing significant issues for sustainability in terms of resource depletion, energy use, and greenhouse gas emissions. As a result, efforts should be concentrated on reducing concrete’s environmental consequences in order to increase its long-term viability. In order to design environmentally friendly concrete mixtures, this research intended to create a prediction model for the compressive strength of those mixtures. The concrete mixtures that were used in this study to build our proposed prediction model are concrete mixtures that contain both recycled aggregate concrete (RAC) and ground granulated blast-furnace slag (GGBFS). A white-box machine learning model known as multivariate polynomial regression (MPR) was developed to predict the compressive strength of eco-friendly concrete. The model was compared with the other two machine learning models, where one is also a white-box machine learning model, namely linear regression (LR), and the other is the black-box machine learning model, which is a support vector machine (SVM). The newly suggested model shows robust estimation capabilities and outperforms the other two models in terms of R2 (coefficient of determination) and RMSE (root mean absolute error) measurements.

ESTIMATING WITH A GIVEN ACCURACY OF THE COEFFICIENTS AT NONLINEAR TERMS OF UNIVARIATE POLYNOMIAL REGRESSION USING A SMALL NUMBER OF TESTS IN AN ARBITRARY LIMITED ACTIVE EXPERIMENT

We substantiate the structure of the efficient numerical axis segment an active experiment on which allows finding estimates of the coefficients fornonlinear terms of univariate polynomial regression with high accuracy using normalized orthogonal Forsyth polynomials with a sufficiently smallnumber of experiments. For the case when an active experiment can be executed on a numerical axis segment that does not satisfy these conditions, wesubstantiate the possibility of conducting a virtual active experiment on an efficient interval of the numerical axis. According to the results of the experiment, we find estimates for nonlinear terms of the univariate polynomial regression under research as a solution of a linear equalities system withan upper non-degenerate triangular matrix of constraints. Thus, to solve the problem of estimating the coefficients for nonlinear terms of univariatepolynomial regression, it is necessary to choose an efficient interval of the numerical axis, set the minimum required number of values of the scalarvariable which belong to this segment and guarantee a given value of the variance of estimates for nonlinear terms of univariate polynomial regressionusing normalized orthogonal polynomials of Forsythe. Next, it is necessary to find with sufficient accuracy all the coefficients of the normalized orthogonal polynomials of Forsythe for the given values of the scalar variable. The resulting set of normalized orthogonal polynomials of Forsythe allows us to estimate with a given accuracy the coefficients of nonlinear terms of univariate polynomial regression in an arbitrary limited active experiment: the range of the scalar variable values can be an arbitrary segment of the numerical axis. We propose to find an estimate of the constant and ofthe coefficient at the linear term of univariate polynomial regression by solving the linear univariate regression problem using ordinary least squaresmethod in active experiment conditions. Author and his students shown in previous publications that the estimation of the coefficients for nonlinearterms of multivariate polynomial regression is reduced to the sequential construction of univariate regressions and the solution of the correspondingsystems of linear equalities. Thus, the results of the paper qualitatively increase the efficiency of finding estimates of the coefficients for nonlinearterms of multivariate polynomial regression given by a redundant representation.

Design of Petroleum Physical Properties Prediction Application

Based on the results of previous studies regarding the modeling of the physical properties of petroleum, a mathematical model has been built to calculate the prediction of the physical properties of petroleum. The prediction is based on viscosity, interfacial tension, and density data from the EOR laboratory in UPN Veteran Yogyakarta. The model still cannot be used independently without the Python environment, so to be used easily by more users, the model must be built into an independent application that can be installed on the user's device. In this research, the application design for the physical properties of petroleum prediction application will be carried out. The application is built using the Multivariate Polynomial Regression method according to the model to predict the physical properties of petroleum, and uses Naïve Bayes to classify the petroleum, and will be the changing result of the physical properties of petroleum modeling that has been made in a previous study. The shift from model to the application requires several adjustments, including user interface, system, and database adjustments which are implemented as the designs of application. . The design is done before the application is built to suit user needs as the result of the research.

Constrained global optimization of multivariate polynomials using polynomial B-spline form and B-spline consistency prune approach

In this paper, we propose basic and improved algorithms based on polynomial B-spline form for constrained global optimization of multivariate polynomial functions. The proposed algorithms are based on a branch-and-bound framework. In improved algorithm we introduce several new ingredients, such as B-spline box consistency and B-spline hull consistency algorithm to prune the search regions and make the search more efficient. The performance of the basic and improved algorithm is tested and compared on set of test problems. The results of the tests show the superiority of the improved algorithm over the basic algorithm in terms of the chosen performance metrics. We compare optimal value of global minimum obtained using the proposed algorithms with CENSO, GloptiPoly and several state-of-the-art NLP solvers, on set of $11$ test problems. The results of the tests show the superiority of the proposed algorithm and CENSO solver (open source solver for global optimization of B-spline constrained problem) in that it always captures the global minimum to the user-specified accuracy.

Petroleum Physical Properties Prediction Application in Enhanced Oil Recovery Process

The Enhanced Oil Recovery (EOR) process is one of the ways in the petroleum exploitation process so that thick oil can be lifted to the surface and produced. The EOR process referred to in this study is the EOR process carried out in previous studies at the EOR laboratory of UPN Veteran Yogyakarta Indonesia by adding biosurfactants and adjusting the temperature. In laboratory experiments, each time an amount of biosurfactant concentration is added and the temperature is adjusted, the calculation must be done repeatedly to determine the amount of viscosity, interfacial tension (IFT), and density. This experiments takes a long time, requires high cost and variety limitation of the condition. The previous research has succeeded in building a model with multivariate polynomial regression equations to predict the value of the physical properties of crude oil from existing data then classify it into three categories using Naive Bayes, i.e., light oil, medium oil, and heavy oil. The physical properties of petroleum measured in the research are viscosity, interfacial tension, and density. The model uses laboratory data which are taken from the test results of Pertamina's KW-55 well as validation. The validation result shows that Multivariate Polynomial Regression has succeeded in predicting the value of viscosity, interfacial tension, and density with error values ranging from 0% to 1% from the sample data. With a low error value, the application can make forecasting with more variable conditions. The model still cannot be used independently without the Python environment, so to be used easily by more users, the model must be built into an independent application that can be installed on the user's device. In this research, the prediction application of petroleum physical properties has been built. The application is made using the Multivariate Polynomial Regression method according to the model in the previous study to predict the physical properties of petroleum, then uses Naïve Bayes to classify the oil. The application completed the several adjustment to shift from model to application, including user interface, system, and database adjustments.

A Multivariate Polynomial Regression to Reconstruct Ground Contact and Flight Times Based on a Sine Wave Model for Vertical Ground Reaction Force and Measured Effective Timings

Effective contact (tce) and flight (tfe) times, instead of ground contact (tc) and flight (tf) times, are usually collected outside the laboratory using inertial sensors. Unfortunately, tce and tfe cannot be related to tc and tf because the exact shape of vertical ground reaction force is unknown. However, using a sine wave approximation for vertical force, tce and tc as well as tfe and tf could be related. Indeed, under this approximation, a transcendental equation was obtained and solved numerically over a tce x tfe grid. Then, a multivariate polynomial regression was applied to the numerical outcome. In order to reach a root-mean-square error of 0.5 ms, the final model was given by an eighth-order polynomial. As a direct application, this model was applied to experimentally measured tce values. Then, reconstructed tc (using the model) was compared to corresponding experimental ground truth. A systematic bias of 35 ms was depicted, demonstrating that ground truth tc values were larger than reconstructed ones. Nonetheless, error in the reconstruction of tc from tce was coming from the sine wave approximation, while the polynomial regression did not introduce further error. The presented model could be added to algorithms within sports watches to provide robust estimations of tc and tf in real time, which would allow coaches and practitioners to better evaluate running performance and to prevent running-related injuries.

Factorization of Polynomials Given by Arithmetic Branching Programs

Given a multivariate polynomial computed by an arithmetic branching program (ABP) of size s, we show that all its factors can be computed by arithmetic branching programs of size poly(s). Kaltofen gave a similar result for polynomials computed by arithmetic circuits. The previously known best upper bound for ABP-factors was poly $$ (s^{ {\rm \log} s}) $$ ( s log s ) .