The fifth edition of "Numerical Methods for Engineers" continues its tradition of excellence. Instructors love this text because it is a comprehensive text that is easy to teach from. Students love it because it is written for them--with great pedagogy and clear explanations and examples throughout. The text features a broad array of applications, including all engineering disciplines. The revision retains the successful pedagogy of the prior editions. Chapra and Canale's unique approach opens each part of the text with sections called Motivation, Mathematical Background, and Orientation, preparing the student for what is to come in a motivating and engaging manner. Each part closes with an Epilogue containing sections called Trade-Offs, Important Relationships and Formulas, and Advanced Methods and Additional References. Much more than a summary, the Epilogue deepens understanding of what has been learned and provides a peek into more advanced methods. Approximately 80% of the end-of-chapter problems are revised or new to this edition. The expanded breadth of engineering disciplines covered is especially evident in the problems, which now cover such areas as biotechnology and biomedical engineering. Users will find use of software packages, specifically MATLAB and Excel with VBA. This includes material on developing MATLAB m-files and VBA macros.

Numerical methods for engineers

One of the main concerns in geotechnical engineering is slope stability prediction during the earthquake. In this study, two intelligent systems namely artificial neural network (ANN) and particle swarm optimization (PSO)---ANN models were developed to predict factor of safety (FOS) of homogeneous slopes. Geostudio program based on limit equilibrium method was utilized to obtain 699 FOS values with different conditions. The most influential factors on FOS such as slope height, gradient, cohesion, friction angle and peak ground acceleration were considered as model inputs in the present study. A series of sensitivity analyses were performed in modeling procedures of both intelligent systems. All 699 datasets were randomly selected to 5 different datasets based on training and testing. Considering some model performance indices, i.e., root mean square error, coefficient of determination (R2) and value account for (VAF) and using simple ranking method, the best ANN and PSO---ANN models were selected. It was found that the PSO---ANN technique can predict FOS with higher performance capacities compared to ANN. R2 values of testing datasets equal to 0.915 and 0.986 for ANN and PSO---ANN techniques, respectively, suggest the superiority of the PSO---ANN technique.

Prediction of seismic slope stability through combination of particle swarm optimization and neural network

The potential surface settlement, especially in urban areas, is one of the most hazardous factors in subway and other infrastructure tunnel excavations. Therefore, accurate prediction of maximum surface settlement (MSS) is essential to minimize the possible risk of damage. This paper presents a new hybrid model of artificial neural network (ANN) optimized by particle swarm optimization (PSO) for prediction of MSS. Here, this combination is abbreviated using PSO-ANN. To indicate the performance capacity of the PSO-ANN model in predicting MSS, a pre-developed ANN model was also developed. To construct the mentioned models, horizontal to vertical stress ratio, cohesion and Young's modulus were set as input parameters, whereas MSS was considered as system output. A database consisting of 143 data sets, obtained from the line No. 2 of Karaj subway, in Iran, was used to develop the predictive models. The performance of the predictive models was evaluated by comparing performance prediction parameters, including root mean square error (RMSE), variance account for (VAF) and coefficient correlation (R2). The results indicate that the proposed PSO-ANN model is able to predict MSS with a higher degree of accuracy in comparison with the ANN results. In addition, the results of sensitivity analysis show that the horizontal to vertical stress ratio has slightly higher effect of MSS compared to other model inputs.

Feasibility of PSO-ANN model for predicting surface settlement caused by tunneling

Application of back-propagation (BP) artificial neural network (ANN) as an accurate, practical and quick tool in indirect estimation of uniaxial compressive strength (UCS) of rocks has recently been highlighted in the literature. This is mainly due to difficulty in direct determination of UCS in laboratory as preparing the core samples for this test is troublesome and time-consuming. However, ANN technique has some limitations such as getting trapped in local minima. These limitations can be minimized by combining the ANNs with robust optimization algorithms like particle swarm optimization (PSO). This paper gives insight into development of a hybrid PSO–BP predictive model of UCS. For this reason, dataset comprising the results of 228 laboratory tests including dry density, moisture content, P wave velocity, point load index test, slake durability index and UCS was prepared. These tests were conducted on 38 sandstone samples which were taken from two excavation sites in Malaysia. Findings showed that PSO–BP model performs well in predicting UCS. Nevertheless, to compare the prediction performance of the PSO–BP model, the UCS is predicted using ANN-based PSO and BP models. The correlation coefficient, R, values equal to 0.988 and 0.999 for training and testing datasets, respectively, suggest that the PSO–BP model outperforms the other predictive models.

Rock strength estimation: a PSO-based BP approach

In this work, we are interested to the PID control of nonlinear systems and more specially the control of a robot manipulator. The idea is to determine the optimal parameters ($$K_{p}, K_{i}$$ and $$K_{d}$$) of the controller using a novel algorithm of optimization called whale optimizer algorithm (WOA). To study the effectiveness of WOA-PID controller, its performance is compared with other controllers such as particle swarm optimization-PID (PSO-PID) and grey wolf optimizer-PID (GWO-PID). The model of robot manipulator and all controllers were tested using Simulink/MATLAB. Simulation results obtained clearly indicate the superiority of WOA-PID controller over the other controllers for trajectory tracking, better settling time, and ITAE errors.

Whale optimizer algorithm to tune PID controller for the trajectory tracking control of robot manipulator

Mathematical modelling, simulation and experimental verification of a scara robot

Signature verification (SV) toolbox: Application of PSO-NN

Swarm Intelligence (SI) is inspired from the study of colonies of swarms in Nature. This paper introduces a study originated on swarm intelligence, Particle Swarm Optimization (PSO). Three case studies on one link arm, a SCARA robot and a electrohydraulic robot - are presented on both simulation and experimental base to show effectiveness and simplicity of application. Convergence results of the cases are shown on robot trajectory control (PSO-PID) and robotic system identification (PSO-NN).

Robotic applications with Particle Swarm Optimization (PSO)

Experimental modal analysis of curved composite beam with transverse open crack

This paper presents an approach where the Particle swarm optimization (PSO) is employed to get optimum PID controller parameters to control of a SCARA robot. PSO is an evolutionary technique which is originated from swarm intelligence. A practical application of the PSO-PID controller is performed with the system dynamics. A simulation study is also included with the proposed controller by using the systems dynamic equations with the actuator dynamics and optimum PID parameters. Different trajectories are studied. Performances of the traditional controllers; PD, PID and the application of PSO-PID controller are then compared. Simulation results are presented. The numerical results definitely enforced the potential use of PSO-PID controller herein.

M. Taylan Das

Papers

Mathematical modelling, simulation and experimental verification of a scara robot

Signature verification (SV) toolbox: Application of PSO-NN

Robotic applications with Particle Swarm Optimization (PSO)

Experimental modal analysis of curved composite beam with transverse open crack

Control of a scara robot: pso-pid approach