Search results for: Broyden method

Authors: M. Y. Waziri, M. A. Aliyu

Abstract:

The paper proposes an approach to improve the performance of Broyden’s method for solving systems of nonlinear equations. In this work, we consider the information from two preceding iterates rather than a single preceding iterate to update the Broyden’s matrix that will produce a better approximation of the Jacobian matrix in each iteration. The numerical results verify that the proposed method has clearly enhanced the numerical performance of Broyden’s Method.

Keywords: mulit-step Broyden, nonlinear systems of equations, computational efficiency, iterate

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Authors: Adel Mohsen

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A direct method based on the good Broyden's updates for evaluating the inverse of a nonsingular square matrix of full rank and solving related system of linear algebraic equations is studied. For a matrix A of order n whose LU-decomposition is A = LU, the multiplication count is O (n3). This includes the evaluation of the LU-decompositions of the inverse, the lower triangular decomposition of A as well as a “reduced matrix inverse”. If an explicit value of the inverse is not needed the order reduces to O (n3/2) to compute to compute inv(U) and the reduced inverse. For a symmetric matrix only O (n3/3) operations are required to compute inv(L) and the reduced inverse. An example is presented to demonstrate the capability of using the reduced matrix inverse in treating ill-conditioned systems. Besides the simplicity of Broyden's update, the method provides a mean to exploit the possible sparsity in the matrix and to derive a suitable preconditioner.

Keywords: Broyden's updates, matrix inverse, inverse factorization, solution of linear algebraic equations, ill-conditioned matrices, preconditioning

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Authors: Mohamed Hafid, Marcel Lacroix

Abstract:

This study presents an inverse analysis for predicting the thermal conductivities and the heat flux of a high-temperature metallurgical reactor simultaneously. Once these thermal parameters are predicted, the time-varying thickness of the protective phase-change bank that covers the inside surface of the brick walls of a metallurgical reactor can be calculated. The enthalpy method is used to solve the melting/solidification process of the protective bank. The inverse model rests on the Levenberg-Marquardt Method (LMM) combined with the Broyden method (BM). A statistical analysis for the thermal parameter estimation is carried out. The effect of the position of the temperature sensors, total number of measurements and measurement noise on the accuracy of inverse predictions is investigated. Recommendations are made concerning the location of temperature sensors.

Keywords: inverse heat transfer, phase change, metallurgical reactor, Levenberg–Marquardt method, Broyden method, bank thickness

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Authors: Dewi Retno Sari Saputro, Purnami Widyaningsih, Hendrika Handayani

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Extreme data on an observation can occur due to unusual circumstances in the observation. The data can provide important information that can’t be provided by other data so that its existence needs to be further investigated. The method for obtaining extreme data is one of them using maxima block method. The distribution of extreme data sets taken with the maxima block method is called the distribution of extreme values. Distribution of extreme values is Gumbel distribution with two parameters. The parameter estimation of Gumbel distribution with maximum likelihood method (ML) is difficult to determine its exact value so that it is necessary to solve the approach. The purpose of this study was to determine the parameter estimation of Gumbel distribution with quasi-Newton BFGS method. The quasi-Newton BFGS method is a numerical method used for nonlinear function optimization without constraint so that the method can be used for parameter estimation from Gumbel distribution whose distribution function is in the form of exponential doubel function. The quasi-New BFGS method is a development of the Newton method. The Newton method uses the second derivative to calculate the parameter value changes on each iteration. Newton's method is then modified with the addition of a step length to provide a guarantee of convergence when the second derivative requires complex calculations. In the quasi-Newton BFGS method, Newton's method is modified by updating both derivatives on each iteration. The parameter estimation of the Gumbel distribution by a numerical approach using the quasi-Newton BFGS method is done by calculating the parameter values that make the distribution function maximum. In this method, we need gradient vector and hessian matrix. This research is a theory research and application by studying several journals and textbooks. The results of this study obtained the quasi-Newton BFGS algorithm and estimation of Gumbel distribution parameters. The estimation method is then applied to daily rainfall data in Purworejo District to estimate the distribution parameters. This indicates that the high rainfall that occurred in Purworejo District decreased its intensity and the range of rainfall that occurred decreased.

Keywords: parameter estimation, Gumbel distribution, maximum likelihood, broyden fletcher goldfarb shanno (BFGS)quasi newton

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Authors: Mohamed Hafid, Marcel Lacroix

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This study presents a simple inverse heat transfer procedure for predicting the wall erosion and the time-varying thickness of the protective bank that covers the inside surface of the refractory brick wall of a melting furnace. The direct problem is solved by using the Finite-Volume model. The melting/solidification process is modeled using the enthalpy method. The inverse procedure rests on the Levenberg-Marquardt method combined with the Broyden method. The effect of the location of the temperature sensors and of the measurement noise on the inverse predictions is investigated. Recommendations are made concerning the location of the temperature sensor.

Keywords: melting furnace, inverse heat transfer, enthalpy method, levenberg–marquardt method

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Authors: Mohamed Hafid, Marcel Lacroix

Abstract:

This study aimed at developing an inverse heat transfer approach for predicting the time-varying freezing front and the temperature distribution of tumors during cryosurgery. Using a temperature probe pressed against the layer of tumor, the inverse approach is able to predict simultaneously the metabolic heat generation and the blood perfusion rate of the tumor. Once these parameters are predicted, the temperature-field and time-varying freezing fronts are determined with the direct model. The direct model rests on one-dimensional Pennes bioheat equation. The phase change problem is handled with the enthalpy method. The Levenberg-Marquardt Method (LMM) combined to the Broyden Method (BM) is used to solve the inverse model. The effect (a) of the thermal properties of the diseased tissues; (b) of the initial guesses for the unknown thermal properties; (c) of the data capture frequency; and (d) of the noise on the recorded temperatures is examined. It is shown that the proposed inverse approach remains accurate for all the cases investigated.

Keywords: cryosurgery, inverse heat transfer, Levenberg-Marquardt method, thermal properties, Pennes model, enthalpy method

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Authors: Strahinja Kovačević, Jelena Vladić, Senka Vidović, Zoran Zeković, Lidija Jevrić, Sanja Podunavac Kuzmanović

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Supercritical extracts of highly valuated medicinal plant Satureja montana were prepared by application of supercritical carbon dioxide extraction in the carbon dioxide pressure range from 125 to 350 bar and temperature range from 40 to 60°C. Using GC/MS method of analysis chemical profiles (aromatic constituents) of S. montana extracts were obtained. Self-training artificial neural networks were applied to predict the retention time of the analyzed terpenes in GC/MS system. The best ANN model obtained was multilayer perceptron (MLP 11-11-1). Hidden activation was tanh and output activation was identity with Broyden–Fletcher–Goldfarb–Shanno training algorithm. Correlation measures of the obtained network were the following: R(training) = 0.9975, R(test) = 0.9971 and R(validation) = 0.9999. The comparison of the experimental and predicted retention times of the analyzed compounds showed very high correlation (R = 0.9913) and significant predictive power of the established neural network.

Keywords: ANN regression, GC/MS, Satureja montana, terpenes

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Authors: Gautam Kumar Saharia, Sagardeep Talukdar, Riki Dutta, Sudipta Nandy

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The physics informed neural network (PINN) method opens up an approach for numerically solving nonlinear partial differential equations leveraging fast calculating speed and high precession of modern computing systems. We construct the PINN based on strong universal approximation theorem and apply the initial-boundary value data and residual collocation points to weekly impose initial and boundary condition to the neural network and choose the optimization algorithms adaptive moment estimation (ADAM) and Limited-memory Broyden-Fletcher-Golfard-Shanno (L-BFGS) algorithm to optimize learnable parameter of the neural network. Next, we improve the PINN with a weighted loss function to obtain both the bright and dark soliton solutions of Fokas-Lenells equation (FLE). We find the proposed scheme of adjustable weight coefficients into PINN has a better convergence rate and generalizability than the basic PINN algorithm. We believe that the PINN approach to solve the partial differential equation appearing in nonlinear optics would be useful to study various optical phenomena.

Keywords: deep learning, optical Soliton, neural network, partial differential equation

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Authors: Gautam Kumar Saharia, Sagardeep Talukdar, Riki Dutta, Sudipta Nandy

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The physics-informed neural network (PINN) method opens up an approach for numerically solving nonlinear partial differential equations leveraging fast calculating speed and high precession of modern computing systems. We construct the PINN based on a strong universal approximation theorem and apply the initial-boundary value data and residual collocation points to weekly impose initial and boundary conditions to the neural network and choose the optimization algorithms adaptive moment estimation (ADAM) and Limited-memory Broyden-Fletcher-Golfard-Shanno (L-BFGS) algorithm to optimize learnable parameter of the neural network. Next, we improve the PINN with a weighted loss function to obtain both the bright and dark soliton solutions of the Fokas-Lenells equation (FLE). We find the proposed scheme of adjustable weight coefficients into PINN has a better convergence rate and generalizability than the basic PINN algorithm. We believe that the PINN approach to solve the partial differential equation appearing in nonlinear optics would be useful in studying various optical phenomena.

Keywords: deep learning, optical soliton, physics informed neural network, partial differential equation

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Authors: Muhammad Jawwad, Riffat Iqbal

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The Socratic method, also known as the dialectical method and elenctic method, has significant relevance in the contemporary educational system. It can be incorporated into modern-day educational systems theoretically as well as practically. Being interactive and dialogue-based in nature, this teaching approach is followed by critical thinking and innovation. The pragmatic value of the Dialectical Method has been discussed in this article, and the limitations of the Socratic method have also been highlighted. The interactive Method of Socrates can be used in many subjects for students of different grades. The Limitations and delimitations of the Method have also been discussed for its proper implementation. This article has attempted to elaborate and analyze the teaching method of Socrates with all its pre-suppositions and Epistemological character.

Keywords: Socratic method, dialectical method, knowledge, teaching, virtue

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Authors: Mohammad Reza Akhavan Khaleghi

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This paper shows changes done to the Reduced Finite Element Method (RFEM) that its result will be the most powerful numerical method that has been proposed so far (some forms of this method are so powerful that they can approximate the most complex equations simply Laplace equation!). Finite Element Method (FEM) is a powerful numerical method that has been used successfully for the solution of the existing problems in various scientific and engineering fields such as its application in CFD. Many algorithms have been expressed based on FEM, but none have been used in popular CFD software. In this section, full monopoly is according to Finite Volume Method (FVM) due to better efficiency and adaptability with the physics of problems in comparison with FEM. It doesn't seem that FEM could compete with FVM unless it was fundamentally changed. This paper shows those changes and its result will be a powerful method that has much better performance in all subjects in comparison with FVM and another computational method. This method is not to compete with the finite volume method but to replace it.

Keywords: reduced finite element method, new computational package, new finite element formulation, new higher-order form, new isogeometric analysis

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Authors: O. Acan, Y. Keskin

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In this study, we will carry out a comparative study between the reduced differential transform method, the adomian decomposition method, the variational iteration method and the homotopy analysis method. These methods are used in many fields of engineering. This is been achieved by handling a kind of 2-Dimensional and forth-order partial differential equations called the Kuramoto–Sivashinsky equations. Three numerical examples have also been carried out to validate and demonstrate efficiency of the four methods. Furthermost, it is shown that the reduced differential transform method has advantage over other methods. This method is very effective and simple and could be applied for nonlinear problems which used in engineering.

Keywords: reduced differential transform method, adomian decomposition method, variational iteration method, homotopy analysis method

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Authors: Elvis Adam Alhassan, Kaiyu Tian, Akos Konadu, Ernest Zamanah, Michael Jackson Adjabui, Ibrahim Justice Musah, Esther Agyeiwaa Owusu, Emmanuel K. A. Agyeman

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In this paper, how to solve simultaneous equations using the Elvis improved method is shown. The Elvis improved method says; to make one variable in the first equation the subject; make the same variable in the second equation the subject; equate the results and simplify to obtain the value of the unknown variable; put the value of the variable found into one equation from the first or second steps and simplify for the remaining unknown variable. The difference between our Elvis improved method and the substitution method is that: with Elvis improved method, the same variable is made the subject in both equations, and the two resulting equations equated, unlike the substitution method where one variable is made the subject of only one equation and substituted into the other equation. After describing the Elvis improved method, findings from 100 secondary students and the views of 5 secondary tutors to demonstrate the effectiveness of the method are presented. The study's purpose is proved by hypothetical examples.

Keywords: simultaneous equations, substitution method, elimination method, graphical method, Elvis improved method

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Authors: Arezoo Hakimi, Afshin Farahbakhsh

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Herein, we comparison synthesized Fe3O4 using, hydrothermal method, Mechanochemical processes and solvent thermal method. The Hydrothermal Technique has been the most popular one, gathering interest from scientists and technologists of different disciplines, particularly in the last fifteen years. In the hydrothermal method Fe3O4 microspheres, in which many nearly monodisperse spherical particles with diameters of about 400nm, in the mechanochemical method regular morphology indicates that the particles are well crystallized and in the solvent thermal method Fe3O4 nanoparticles have good properties of uniform size and good dispersion.

Keywords: Fe3O4 nanoparticles, hydrothermal method, mechanochemical processes, solvent thermal method

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Authors: Autcha Araveeporn

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This paper presents a study about a nonparametric regression model consisting of a smoothing spline method and a penalized spline regression method. We also compare the techniques used for estimation and prediction of nonparametric regression model. We tried both methods with crude oil prices in dollars per barrel and the Stock Exchange of Thailand (SET) index. According to the results, it is concluded that smoothing spline method performs better than that of penalized spline regression method.

Keywords: nonparametric regression model, penalized spline regression method, smoothing spline method, Stock Exchange of Thailand (SET)

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Authors: Bale Baidi Blaise, Gilles Marckmann, Liman Kaoye, Talaka Dya, Moustapha Bachirou, Gambo Betchewe, Tibi Beda

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This work highlights the capabilities of particles swarm optimization (PSO) method to identify parameters of hyperelastic models. The study compares this method with Genetic Algorithm (GA) method, Least Squares (LS) method, Pattern Search Algorithm (PSA) method, Beda-Chevalier (BC) method and the Levenberg-Marquardt (LM) method. Four classic hyperelastic models are used to test the different methods through parameters identification. Then, the study compares the ability of these models to reproduce experimental Treloar data in simple tension, biaxial tension and pure shear.

Keywords: particle swarm optimization, identification, hyperelastic, model

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Authors: M. K. Balyan

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The main principles of X-ray Fourier interferometric holography method are discussed. The object image is reconstructed by the mathematical method of Fourier transformation. The three methods are presented – method of approximation, iteration method and step by step method. As an example the complex amplitude transmission coefficient reconstruction of a beryllium wire is considered. The results reconstructed by three presented methods are compared. The best results are obtained by means of step by step method.

Keywords: dynamical diffraction, hologram, object image, X-ray holography

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Authors: N. Guruprasad

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This paper presents a modification of approximation method for transportation problems. The initial basic feasible solution can be computed using either Russel's or Vogel's approximation methods. Russell’s approximation method provides another excellent criterion that is still quick to implement on a computer (not manually) In most cases Russel's method yields a better initial solution, though it takes longer than Vogel's method (finding the next entering variable in Russel's method is in O(n1*n2), and in O(n1+n2) for Vogel's method). However, Russel's method normally has a lesser total running time because less pivots are required to reach the optimum for all but small problem sizes (n1+n2=~20). With this motivation behind we have incorporated a variation of the same – what we have proposed it has TMC (Total Modified Cost) to obtain fast and efficient solutions.

Keywords: computation, efficiency, modified cost, Russell’s approximation method, transportation, Vogel’s approximation method

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Authors: Bib Paruhum Silalahi, Djihad Wungguli, Sugi Guritman

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Steepest descent method is a simple gradient method for optimization. This method has a slow convergence in heading to the optimal solution, which occurs because of the zigzag form of the steps. Barzilai and Borwein modified this algorithm so that it performs well for problems with large dimensions. Barzilai and Borwein method results have sparked a lot of research on the method of steepest descent, including alternate minimization gradient method and Yuan method. Inspired by previous works, we modified the step size of the steepest descent method. We then compare the modification results against the Barzilai and Borwein method, alternate minimization gradient method and Yuan method for quadratic function cases in terms of the iterations number and the running time. The average results indicate that the steepest descent method with the new step sizes provide good results for small dimensions and able to compete with the results of Barzilai and Borwein method and the alternate minimization gradient method for large dimensions. The new step sizes have faster convergence compared to the other methods, especially for cases with large dimensions.

Keywords: steepest descent, line search, iteration, running time, unconstrained optimization, convergence

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Authors: S. Shahrooi, A. Talavari

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Numeral study on the crack and discontinuity using element-free methods has been widely spread in recent years. In this study, for stress intensity factor calculation of the cracked axis under torsional loading has been used from a new element-free method as MLPG method. Region range is discretized by some dispersed nodal points. From method of moving least square (MLS) utilized to create the functions using these nodal points. Then, results of meshless method and finite element method (FEM) were compared. The results is shown which the element-free method was of good accuracy.

Keywords: stress intensity factor, crack, torsional loading, meshless method

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Authors: Abu Hashan Md Mashud, M. Sharif Uddin, Aminur Rahman Khan

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In this paper, we formulate a new problem as a linear programming and Integer Programming problem and maximize profit within the limited budget and limited resources based on the construction of a tea garden problem. It describes a new idea about how to optimize profit and focuses on the practical aspects of modeling and the challenges of providing a solution to a complex real life problem. Finally, a comparative study is carried out among Graphical method, Simplex method and Branch and bound method.

Keywords: integer programming, tea garden, graphical method, simplex method, branch and bound method

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Authors: Osamu Igawa, Hiroshi Kouchiwa, Yuji Ito

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In recent years, a reconstruction project for sewer pipelines has been progressing in Japan with the aim of renewing old sewer culverts. However, it is difficult to secure a sufficient base area for shafts in an urban area because many streets are narrow with a complex layout. As a result, construction in such urban areas is generally very demanding. In urban areas, there is a strong requirement for a safe, reliable and economical construction method that does not disturb the public’s daily life and urban activities. With this in mind, we developed a new construction method called the 'shield switching type micro-tunneling method' which integrates the micro-tunneling method and shield method. In this method, pipeline is constructed first for sections that are gently curved or straight using the economical micro-tunneling method, and then the method is switched to the shield method for sections with a sharp curve or a series of curves without establishing an intermediate shaft. This paper provides the information, features and construction examples of this newly developed method.

Keywords: micro-tunneling method, secondary lining applied RC segment, sharp curve, shield method, switching type

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Authors: E. Popov, N. Yorino, Y. Zoka, Y. Sasaki, H. Sugihara

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This paper discusses the performance of critical trajectory method (CTrj) for power system transient stability analysis under various loading settings and heavy fault condition. The method obtains Controlling Unstable Equilibrium Point (CUEP) which is essential for estimation of power system stability margins. The CUEP is computed by applying the CTrjto the boundary controlling unstable equilibrium point (BCU) method. The Proposed method computes a trajectory on the stability boundary that starts from the exit point and reaches CUEP under certain assumptions. The robustness and effectiveness of the method are demonstrated via six power system models and five loading conditions. As benchmark is used conventional simulation method whereas the performance is compared with and BCU Shadowing method.

Keywords: power system, transient stability, critical trajectory method, energy function method

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Authors: A. A. James, A. O. Adesanya, M. R. Odekunle, D. G. Yakubu

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This paper examines the development of one step, five hybrid point method for the solution of first order initial value problems. We adopted the method of collocation and interpolation of power series approximate solution to generate a continuous linear multistep method. The continuous linear multistep method was evaluated at selected grid points to give the discrete linear multistep method. The method was implemented using a constant order predictor of order seven over an overlapping interval. The basic properties of the derived corrector was investigated and found to be zero stable, consistent and convergent. The region of absolute stability was also investigated. The method was tested on some numerical experiments and found to compete favorably with the existing methods.

Keywords: interpolation, approximate solution, collocation, differential system, half step, converges, block method, efficiency

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Authors: Abraham Castellanos, Christophe Durville, Sophie Echenim

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In this article, a portfolio optimization problem is performed in a Solvency II context: it illustrates how advanced optimization techniques can help to tackle complex operational pain points around the monitoring, control, and stability of Solvency Capital Requirement (SCR). The market SCR of a portfolio is calculated as a combination of SCR sub-modules. These sub-modules are the results of stress-tests on interest rate, equity, property, credit and FX factors, as well as concentration on counter-parties. The market SCR is non convex and non differentiable, which does not make it a natural optimization criteria candidate. In the SCR formulation, correlations between sub-modules are fixed, whereas risk-driven portfolio allocation is usually driven by the dynamics of the actual correlations. Implementing a portfolio construction approach that is efficient on both a regulatory and economic standpoint is not straightforward. Moreover, the challenge for insurance portfolio managers is not only to achieve a minimal SCR to reduce non-invested capital but also to ensure stability of the SCR. Some optimizations have already been performed in the literature, simplifying the standard formula into a quadratic function. But to our knowledge, it is the first time that the standard formula of the market SCR is used in an optimization problem. Two solvers are combined: a bundle algorithm for convex non- differentiable problems, and a BFGS (Broyden-Fletcher-Goldfarb- Shanno)-SQP (Sequential Quadratic Programming) algorithm, to cope with non-convex cases. A market SCR minimization is then performed with historical data. This approach results in significant reduction of the capital requirement, compared to a classical Markowitz approach based on the historical volatility. A comparative analysis of different optimization models (equi-risk-contribution portfolio, minimizing volatility portfolio and minimizing value-at-risk portfolio) is performed and the impact of these strategies on risk measures including market SCR and its sub-modules is evaluated. A lack of diversification of market SCR is observed, specially for equities. This was expected since the market SCR strongly penalizes this type of financial instrument. It was shown that this direct effect of the regulation can be attenuated by implementing constraints in the optimization process or minimizing the market SCR together with the historical volatility, proving the interest of having a portfolio construction approach that can incorporate such features. The present results are further explained by the Market SCR modelling.

Keywords: financial risk, numerical optimization, portfolio management, solvency capital requirement

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Authors: Sung-Sik Park, Han Chang, Kyung-Hun Chae, Sae-Byeok Lee

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In this study, a three-dimensional (3D) Particle method without using grid was developed for analyzing large deformation of soils instead of using ordinary finite element method (FEM) or finite difference method (FDM). In the 3D Particle method, the governing equations were discretized by various particle interaction models corresponding to differential operators such as gradient, divergence, and Laplacian. The Mohr-Coulomb failure criterion was incorporated into the 3D Particle method to determine soil failure. The yielding and hardening behavior of soil before failure was also considered by varying viscosity of soil. First of all, an unconfined compression test was carried out and the large deformation following soil yielding or failure was simulated by the developed 3D Particle method. The results were also compared with those of a commercial FEM software PLAXIS 3D. The developed 3D Particle method was able to simulate the 3D large deformation of soils due to soil yielding and calculate the variation of normal and shear stresses following clay deformation.

Keywords: particle method, large deformation, soil column, confined compressive stress

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Authors: Nur Rokhman

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A mathematical function gives relationship between the variables composing the function. Interpolation can be viewed as a process of finding mathematical function which goes through some specified points. There are many interpolation methods, namely: Lagrange method, Newton method, Spline method etc. For some specific condition, such as, big amount of interpolation points, the interpolation function can not be written explicitly. This such function consist of computational steps. The solution of equations involving the interpolation function is a problem of solution of non linear equation. Newton method will not work on the interpolation function, for the derivative of the interpolation function cannot be written explicitly. This paper shows the use of Secton method to determine the numerical solution of the function involving the interpolation function. The experiment shows the fact that Secton method works better than Newton method in finding the root of Lagrange interpolation function.

Keywords: Secton method, interpolation, non linear function, numerical solution

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Authors: B. Chikh, L. Moussa, H. Bechtoula, Y. Mehani, A. Zerzour

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This study presents a new method, applicable to evaluation and design of structures has been developed and illustrated by comparison with the capacity spectrum method (CSM, ATC-40). This method uses inelastic spectra and gives peak responses consistent with those obtained when using the nonlinear time history analysis. Hereafter, the seismic demands assessment method is called in this paper DSM, Ductility Spectrum Method. It is used to estimate the seismic deformation of Single-Degree-Of-Freedom (SDOF) systems based on DDRS, Ductility Demand Response Spectrum, developed by the author.

Keywords: seismic demand, capacity, inelastic spectra, design and structure

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Authors: Hadi Rouhi Belvirdi

Abstract:

The construction of underground structures using the traditional method, which begins with excavation and the implementation of the foundation of the underground structure, continues with the construction of the main structure from the ground up, and concludes with the completion of the final ceiling, is known as the Bottom-Up Method. In contrast to this method, there is an advanced technique called the Top-Down Method, which has practically replaced the traditional construction method in large projects in industrialized countries in recent years. Unlike the traditional approach, this method starts with the construction of surrounding walls, columns, and the final ceiling and is completed with the excavation and construction of the foundation of the underground structure. Some of the most significant advantages of this method include the elimination or minimization of formwork surfaces, the removal of temporary bracing during excavation, the creation of some traffic facilities during the construction of the structure, and the possibility of using it in limited and high-traffic urban spaces. Despite these numerous advantages, unfortunately, there is still insufficient awareness of this method in our country, to the extent that it can be confidently stated that most stakeholders in the construction industry are unaware of the existence of such a construction method. However, it can be utilized as a very important execution option alongside other conventional methods in the construction of underground structures. Therefore, due to the extensive practical capabilities of this method, this article aims to present a methodology for constructing underground structures based on the aforementioned advanced method to the scientific community of the country, examine the advantages and limitations of this method and their impacts on time and costs, and discuss its application in urban spaces. Finally, some underground structures executed in the Ahvaz urban rail, which are being implemented using this advanced method to the best of our best knowledge, will be introduced.

Keywords: top-down method, bottom-up method, underground structure, construction method

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Authors: Saheed A. Gbadegeshin

Abstract:

Commercialization method is a means to make inventions available at the market for final consumption. It is described as an important tool for keeping business enterprises sustainable and improving national economic growth. Thus, there are several scholarly publications on it, either presenting or testing different methods for commercialization. However, young entrepreneurs, technologists and scientists would like to know the best method to commercialize their innovations. Then, this question arises: What is the best commercialization method? To answer the question, a systematic literature review was conducted, and practitioners were interviewed. The literary results revealed that there are many methods but new methods are needed to improve commercialization especially during these times of economic crisis and political uncertainty. Similarly, the empirical results showed there are several methods, but the best method is the one that reduces costs, reduces the risks associated with uncertainty, and improves customer participation and acceptability. Therefore, it was concluded that new commercialization method is essential for today's high technologies and a method was presented.

Keywords: commercialization method, technology, knowledge, intellectual property, innovation, invention

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