New Robust Projection to Latent Structure

In many actual nonlinear systems, especially near the equilibrium point, linearity is the primary feature and nonlinearity is the secondary feature. For the system that deviates from the equilibrium point, the secondary nonlinearity or local structure feature can also be regarded as the small uncertainty part, just as the nonlinearity can be used to represent the uncertainty of a system (Wang et al. 2019). So this chapter also focuses on how to deal with the nonlinearity in PLS series method, but starts from an different view, i.e., robust PLS. Here the system nonlinearity is considered as uncertainty and a new robust $$\mathrm{L}_1$$ L 1 -PLS is proposed.

Wavelet Characterizations for Investigating Nonlinear Oscillators

This study investigates the wavelet-based system identification capabilities on determining the system nonlinearity based on the system impulse response function. Wavelet estimates of the instantaneous envelopes and instantaneous frequency are used to plot the system backbone curve. This wavelet estimate is then used to estimate the values of the parameter for the system. Two weakly nonlinear oscillators, which are the Duffing and the Van der Pol oscillators, have been analyzed using this wavelet approach. A case study based on a model of an oscillating flap wave energy converter (OFWEC) was also discussed in this study. Based on the results, it was shown that this technique is recommended for nonlinear system identification provided the impulse response of the system can be captured. This technique is also suitable when the system's form is unknown and for estimating the instantaneous frequency even when the impulse responses were polluted with noise.

Measure of nonlinearity for underwater target tracking using hull-mounted sensor

PurposeDoppler-Bearing Tracking (DBT) is commonly used in target tracking applications for the underwater environment using the Hull-Mounted Sensor (HMS). It is an important and challenging problem in an underwater environment.Design/methodology/approachThe system nonlinearity in an underwater environment increases due to several reasons such as the type of measurements taken, the speeds of target and observer, environmental conditions, number of sensors considered for measurements and so on. Degrees of nonlinearity (DoNL) for these problems are analyzed using a proposed measure of nonlinearity (MoNL) for state estimation.FindingsIn this research, the authors analyzed MoNL for state estimation and computed the conditional MoNL (normalized) using different filtering algorithms where measurements are obtained from a single sensor array (i.e. HMS). MoNL is implemented to find out the system nonlinearity for different filtering algorithms and identified how much nonlinear the system is, that is, to measure nonlinearity of a problem.Originality/valueAlgorithms are evaluated for various scenarios with different angles on the target bow (ATB) in Monte-Carlo simulation. Computation of root mean squared (RMS) errors in position and velocity is carried out to assess the state estimation accuracy using MATLAB.

Comparative study between chaos theory and the innovation process

This article aims to make a correlation between chaos theory and the innovation process. Unlike what the name seems to be, chaos theory is linked to discovering simple patterns and laws that govern several complex phenomena. The complex is also innovation; therefore, this article makes an analogy of the innovation process from its conception to its implementation in the market with three principles of chaos theory: system, nonlinearity, and complexity. The innovative organization is characterized by constant innovation and complexity in nature. Uncertainty is an essential feature of innovation, which means an inability to predict the prospecting processor's outcome to set the best way to achieve a goal. Unpredictability is one of the characteristics of chaotic systems in which any minimal initial change in their conditions causes drastic changes in their course. Based on these premises, analogies were made to serve as a basis for further studies.

Application of Cubature Information Filter for Underwater Target Path Estimation

Bearings-only tracking plays a pivotal role in passive underwater surveillance. Using noisy sonar bearing measurements, the target motion parameters (TMP) are extensively estimated using the extended Kalman filter (EKF) because of its simplicity and low computational load. The EKF utilizes the first order approximation of the nonlinear system in estimation of the TMP that degrades the accuracy of estimation due to the elimination of the higher order terms. In this paper, the cubature Kalman filter (CKF) that captures the system nonlinearity upto third order is proposed to estimate the TMP. The CKF is further extended using the information filter (IF) to provide decentralized data fusion, hence the filter is termed as cubature information filter (CIF). The results are generated using Matlab with Gaussian assumption of noise in measurements. Monte-Carlo simulation is done and the results demonstrate that the CIF accuracy is same as that of UKF and this indicates the usefulness of the algorithm for state estimation in underwater with the required accuracy.

A Feasibility Study for a Nonlinear Guided Wave Mixing Technique

Ultrasonic non-destructive testing is an effective means of examining objects without destroying them. Among such testing, ultrasonic nonlinear evaluation is used to detect micro-damage, such as corrosion or plastic deformation. In terms of micro-damage evaluation, the data that comes from amplitude comparison in the frequency domain plays a significant role. Its technique and parameter are called ultrasonic nonlinear technique and nonlinearity. A certain portion of nonlinearity comes from the equipment system, while the other portion of nonlinearity comes from the material. The former is system nonlinearity, while the latter is material nonlinearity. System nonlinearity interferes with interpretation, because its source is not from the material. In this study, in order to minimize system effects, a mixing technique is implemented. To use the large area inspection ability of the guided wave, the main research issue in this paper is focused on the guided wave mixing technique. Moreover, several bulk wave mixing theory equations become good concepts for guided wave mixing theoretical study, and the conventional nonlinear technique and guided wave mixing experimental results are compared in this study to confirm the reliability. This technique can play an important role in quantitatively discriminating fine damage by minimizing the nonlinearity of the equipment system.

Diffusion-induced blowup solutions for the shadow limit model of a singular Gierer–Meinhardt system

In this paper, we provide a thorough investigation of the blowing up behavior induced via diffusion of the solution of the following non-local problem: [Formula: see text] where [Formula: see text] is a bounded domain in [Formula: see text] with smooth boundary [Formula: see text] such problem is derived as the shadow limit of a singular Gierer–Meinhardt system, Kavallaris and Suzuki [On the dynamics of a non-local parabolic equation arising from the Gierer–Meinhardt system, Nonlinearity (2017) 1734–1761; Non-Local Partial Differential Equations for Engineering and Biology: Mathematical Modeling and Analysis, Mathematics for Industry, Vol. 31 (Springer, 2018)]. Under the Turing type condition [Formula: see text] we construct a solution which blows up in finite time and only at an interior point [Formula: see text] of [Formula: see text] i.e. [Formula: see text] where [Formula: see text] More precisely, we also give a description on the final asymptotic profile at the blowup point [Formula: see text] and thus we unveil the form of the Turing patterns occurring in that case due to driven-diffusion instability. The applied technique for the construction of the preceding blowing up solution mainly relies on the approach developed in [F. Merle and H. Zaag, Reconnection of vortex with the boundary and finite time quenching, Nonlinearity 10 (1997) 1497–1550] and [G. K. Duong and H. Zaag, Profile of a touch-down solution to a nonlocal MEMS model, Math. Models Methods Appl. Sci. 29 (2019) 1279–1348].

Feedback Control for a Drone with a Suspended Load via Hierarchical Linearization

As a possible extension of a drone application, transportation of a cable-suspended load is expected. The model of a drone with a suspended load is a nonlinear underactuated system that is known to be difficult to analyze and control. This paper applies the linearization method, known as hierarchical linearization, to the system. We observed that, via the hierarchical linearization scheme, the system can be linearized exactly and the controller can be designed simultaneously. There are two features of this approach. First, the controller exactly considers the system nonlinearity, and the feedback controller is based on the linear control theory. Second, it is possible to derive the analytical solution of the closed-loop system. We have demonstrated these features via numerical simulations.

Geometric control of quadrotor UAVs using integral backstepping

The traditional quadcopter control systems should deal with two common problems. Namely, the singularities related to the inverse kinematics and the ambiguity linked to the quaternion representation of the dynamic model. Moreover, the stability problem due to the system nonlinearity and high degree of coupling. This paper provides a solution to the two issues by employing a geometrical integral-backstepping control system. The integral terms were added to improve system ability to track desired trajectories. The high-level control laws are considered as a virtual control and transmitted to the low-level to track the high-level commands. The proposed control system along with the quadcopter dynamic model were expressed in the special Euclidean group SE(3). Finally, the control system robustness against mismatching parameters was studied while tracking various paths.

Accelerated Controller Tuning for Wind Turbines Under Multiple Hazards

During their lifecycle, wind turbines can be subjected to multiple hazard loads, such as high-intensity wind, earthquake, wave, and mechanical unbalance. Excessive vibrations, due to these loads, can have detrimental effects on energy production, structural lifecycle, and the initial cost of wind turbines. Vibration control by various means, such as passive, active, and semi-active control systems provide crucial solutions to these issues. We developed a novel control theory that enables semi-active controller tuning under the complex structural behavior and inherent system nonlinearity. The proposed theory enables the evaluation of semi-active controllers’ performance of multi-degrees-of-freedom systems, without the need for time-consuming simulations. A wide range of controllers can be tested in a fraction of a second, and their parameters can be tuned to achieve system-level performance for different optimization objectives.