Nonlinear Approaches in Engineering Applications

Analysis of vehicles’ handling behavior in turning maneuvers requires a proper mathematical model. There are several factors affecting a vehicle’s response in a turning maneuver. Apart from variations in vehicle and tire parameters, external factors such as air resistance and slope of the road make it quite a complicated task to consider all parameters in the vehicle model. The majority of the most important features of the vehicle behavior in maneuvers are observable using fairly simplified planar vehicle models. In planar modeling, we ignore the roll, pitch, and vertical motions of the vehicle and only emphasize on the longitudinal, lateral, and yaw motions.

The most famous and basic planar vehicle model is known as the bicycle model. Many of the vehicle handling analyses and all the basic characterizations have been derived using bicycle model throughout the course of vehicle dynamics studies (Ellis, Vehicle dynamics. Business Books, 1969; Milliken and Milliken, Race car vehicle dynamics. Society of Automotive Engineers, Warrendale, PA 1995; Jazar, Vehicle dynamics: Theory and application. Springer, Berlin 2017). Bicycle model is accurate enough to represent the real car behavior to a reasonable extent in normal driving conditions. This characteristic of the bicycle model makes it useful in designing and investigating new ideas on dynamics and control of vehicles, such as defining the nominal vehicle response for yaw-rate and/or side-slip angle (Van Zanten, Bosch esp systems: 5 years of experience. SAE Technical Paper 2000; Rajamani, Vehicle dynamics and control. Springer, Berlin 2011).

In this article, the bicycle model is presented in detail and the underlying assumptions are discussed. In the rest of the chapter, the importance of steady-state responses of the bicycle model is discussed by comparing the steady-state and transient vehicle behaviors, characteristics of maneuvering vehicles including steady-state charts are presented, and finally, application of such an analysis on a path following strategy is explained and two examples are given to evaluate the proposed idea.

Artificial Intelligence (AI) is a machine intelligence tool providing enormous possibilities for smart industrial revolution. Internet of Things (IoT) is the axiom of industry 4.0 revolution, including a worldwide infrastructure for collecting and processing of the data/information from storage, actuation, sensing, advanced services and communication technologies. The combination of high-speed, resilient, low-latency connectivity, and technologies of AI and IoT will enable the transformation towards fully smart Autonomous Vehicle (AV) that illustrate the complementary between real world and digital knowledge for industry 4.0. The purpose of this articla is to examine how the latest approaches in AI and IoT can assist in the search for the Autonomous Vehicles. It has been shown that human errors are the source of 90% of automotive crashes, and the safest drivers drive ten times better than the average (Wu et al. Accident Analysis and Prevention, 117, 21–31, 2018). The automated vehicle safety is significant, and users are requiring 1000 times smaller acceptable risk level. Some of the incredible benefits of AVs are: (1) increasing vehicle safety, (2) reduction of accidents, (3) reduction of fuel consumption, (4) releasing of driver time and business opportunities, (5) new potential market opportunities, and (6) reduced emissions and dust particles. However, AVs must use large-scale data/information from their sensors and devices.

Drill string dynamics research is one of the important research directions in modern oil and gas drilling technology. Aiming at axial vibration, radial vibration, nonlinear vibration with the consideration of stochastic friction and the tooth wear under the action of torsional loads during the drilling process, theoretical analysis, and example calculation are carried out to obtain the parameter influence result of the drilling dynamics research.

The drilling dynamics under axial load is studied. With the combination of the force analysis of the horizontal drill string, the axial vibration analysis model is established. According to the axial vibration dynamic model, example analysis is conducted and vibration displacement, vibration velocity, and spectrum results in different drill string nodes are obtained.

The radial inertia effect on vertical vibration of drill string under whether considering the radial inertia or not is analyzed and compared. On the basis of theoretical analysis, according to the real working condition of drill string and based on the Rayleigh–Love model and one-dimensional viscoelastic model, vertical vibration equations of drill string are derived. According to the Laplace transform method and the relationships between parameters of the model, the solutions to complex impedance at the bottom of drill string are obtained, and then the comparison result of radial inertia effect on vertical vibration characteristics of drill string are analyzed.

In order to research the dynamic characteristics of drill string with wellbore stochastic friction forces, vibration characteristics analysis of drill string is conducted. On the basis of the wellbore random friction forces, the analysis models of drill string vibration and drilling efficiency of horizontal well are established under the background of shale gas. Then, the wellbore friction randomness is studied to obtain the method of constructing the wellbore friction random field. Combined with solution expressions of each force in the vibration equation, the discrete method of drill string dynamic model is established. According to the result of example analysis, the influence of key parameters on the dynamic characteristics of drill string is analyzed.

In actual drilling process, the torsion of the drill string generates torsional load, which acts on the drill bit. The force condition of the cutting teeth is affected by the torsional load, which causes the failure of the cutting teeth. The normal failure of the cutting tooth is due to the tooth wear. Therefore, the effect of torsional load on the cutting teeth wear is studied. According to the force condition with the consideration of the torsional load, a geometric model of the PDC cutter is established and the cutter wear model under the action of the torsional load is obtained by further derivation research.

Micro-/nanorobots have the potential to revolutionize medicine by specific applications, such as targeted drug delivery, biopsy, hyperthermia, brachytherapy, scaffolding, in vivo ablation, sensing, marking, and stem cell therapy. Application of microrobots can move us to the stage that monitoring diseases, precise localized drug delivery, minimally invasive surgery, and novel therapies such as stem cell therapy are done using the tools inside the human body.

Since size is small and velocity is low, microrobots have a very low Reynolds (Re) number. A low Re number indicates the dominance of viscous forces and hence, swimming methodologies at microscale are different from those at the macroscale. Although motion of these microrobots is linear at Stokes flow, hydrodynamics of flagella and cilia involve nonlinear models that should be addressed for precise actuation and control of micro-/nanorobots. Nonlinear modeling is of great significance especially when the artificial filaments are fabricated from soft materials to mimic natural flagella and cilia and provide enhanced propulsion.

A great challenge in developing an autonomous microrobotic system is to provide power and control for the microrobot. Since untethered microrobots can be used as implants and have a higher maneuverability, the control system should benefit from a wireless actuation mechanism. Magnetic actuation can transfer a reasonable amount of power wirelessly. There are different systems for generating magnetic field and gradients:

• Permanent magnets

• Helmholtz coils, Maxwell coils, or a combination thereof

• Magnetic resonance imaging (MRI) systems

• Customized sets of electromagnetic coils

Here I analyze the relative sea level signals from the tide gauges of North America. Linear and parabolic fittings are used to compute relative rates of rise and accelerations. There are 20 long-term-trend (LTT) tide gauges along the (Pacific) West Coast of North America. The average relative rate of rise is −0.38 mm/year, and the average acceleration is +0.0012 mm/year². There are 33 LTT tide gauges of the (Atlantic) East Coast of North America. The average relative sea level rise is 2.22 mm/year, and the average acceleration is +0.0027 mm/year².

The mathematical modelling and simulation of natural phenomena is considered the art of science. In this investigation, we review the modelling and simulation of dynamic system from the very beginning steps to the complicated and more advanced systems. This chapter may serve as a concise supplementary learning material for any course related to dynamic systems, modelling and simulations, deterministic dynamics, system of linear ordinary differential equations, etc. It will present guidelines and recommendations for modelling of various engineering systems. The basic concepts are illustrated with selection of several illustrative case studies with detailed diagrams and associate MATLAB scripts. This work will show that, with use of modern simulation tools and computer environments, modelling and simulation process of complex systems is structurally doable. The wide spectrum of the presented examples in mechanical, aerospace, civil, electrical, environmental and other engineering areas makes this work useful for a very wide audience, including engineers, scientists, students and enthusiasts of science and technology.

This chapter presents a description of the large deformation of solids in a curvilinear coordinate system with the application to the elastic–plastic deformation of thick-walled cylinders under simultaneous radial and axial loading. The tensor-based presentation is founded on the continuum theory. Both tensor and component notations are adopted. The analysis assumes the material to be a homogeneous and isotropic continuous medium. Material-independent fundamentals are first discussed in detail, including strain, deformation, and velocity gradients. Different forms of stress tensor in different space- or material-based coordinate systems are presented and discussed. The stress and strain definitions are used to derive the equilibrium equations and constitutive laws for elastic–plastic material behavior. The presented definitions have been used to develop a solution of radially and axially loaded thick-walled elastic–plastic cylinders with nonlinear hardening, adopting an associative constitutive law. The solution is capable of accurately providing continuous distribution of stress and strain gradients throughout the cylinder. It can be used therefore to calculate the current state in the bifurcation analysis of radially and axially loaded thick-walled cylinders and to establish the basis for further research on the safety of pressurized thick-walled cylindrical structures.

Engineering is intrinsically a field in which the application of science and mathematics is utilized to solve problems in pursuit of the design, operation, maintenance, and other faculties of systems in complex systems. Many of these systems contain nonlinear interactions and as such, require tools of varying robustness and power to describe them. Forecasting of future states or designing such systems is very costly, time consuming, and computationally intensive, due to finite project timelines and technical constraints within industry. Increasing the calculation power will provide us with daily data production in modeling and analysis of complex dynamic systems to exceed 2.5 exabyte by 2020, which is a 44-fold increase from those seen in 2010, illustrating the rapid changes in this area. “Big data” is a relatively amorphous term used to describe the rise in data volumes that are difficult to capture, store, manage, process, and analyze, using traditional database methods and tools. The new reality of big data has and shall continue to have profound implications on modeling, as new and highly valuable information can be extracted for decision-making.

Volume, often considered to be the primary characteristic of big data, refers to the absolute size of the dataset being considered. Variety in big datasets also provides additional challenges. Given the great diversity of data sources, including sensors, images, video feeds, financial transactions, location data, text documents, and others, reconciling these sources into unified modeling strategies is not straightforward. When considering so many different types of data, big data modeling strategies typically address three distinct types of data: structures data, semi-structured data, and unstructured data.

In this chapter, a review of classical machine learning methods will be provided, including a selection of clustering, classification, and regression methods. Then it will detail the six approaches for applying scalable machine learning solutions to big data, specifically, representation learning methods for data reduction. Deep learning for capturing highly nonlinear behavior, distributed and parallel learning, transfer learning for cross-domain and cross-task learning activities, active learning, and kernel-based learning will address the challenges associated with big data.

The development of modern engineering systems has introduced increasing levels of complexity and uncertainty over time. Combined with the design philosophy of engineering itself, this has given rise to many studies addressing the simple or multi-objective optimization problems present in these complex systems. Although conventional approaches can be applied to engineering optimization depends largely on the nature of problem, but they suffered to provide some quick and reasonable feedback to designers and cannot be challenging to further possible problems. Nevertheless, heuristic approaches that apply mixtures of different exploratory with or without traditional search and optimization methods are proposed to solve such complex problems. This chapter briefly provides the conventional optimizations and basic knowledge about the most widely implemented heuristic optimization techniques, as well as their application in optimization problems in mechanical engineering systems. It also presents the genetic programming that searches the space of possible computer programs which is extremely fit for solving the complex problem in truss structure design and optimization of mechanical engineering. Genetic programming employs tree structure of computer programs as individuals in its initial population, which gets evolved through generations by the algorithm operators to reach the optimum solution. To prove the ability of the genetic programming to solve complex mechanical engineering problems, a case study in design of truss with discrete design variables will be examined. In this example, genetic programming employs to find the optimum topology and discrete cross-section sizes of 10-bar truss problem which is a nonlinear problem subjected to different constraints such as the stability, maximum allowable stress and displacement in the truss nodes, and critical buckling load. As results and in comparison, with other state-of-art approaches, genetic programming finds a lighter truss structure with fewer elements because it could be constructed a tree-based expression to explore the search space.

Optimization is one of the important subjects in various engineering fields. Until now, not much work has been done in optimizing the dynamic response of mechanical structures with large amplitude of vibration.

In recent years, genetic algorithm has been introduced in many engineering areas (robotics, neural networks, fuzzy control, etc.) and has found numerous applications. In this chapter, this method is used for optimization, by maximizing the tip velocity of cantilever beam with constraints of stress and constant volume. In order to increase the optimization power of this algorithm, a penalty function is used along with nonconventional operators (fuzzy crossover operator, artificial selection, and dynamic mutation operator).

Also, the results obtained by the above-mentioned method are compared with the results of other solutions acquired by different optimization methods. It can be concluded that genetic algorithm can be used as a powerful and reliable method to achieve the global optimum for dynamic response of structures.