Nonlinear Method Research Articles

NONLINEAR DYNAMICS METHODS APPLICATIONS TO PRODUCT LIFECYCLE MANAGEMENT

The research being carried out is aimed at applying nonlinear dynamics methods in product life cycle management to improve communication between processes and achieve environmental sustainability. The purpose of the article is to create a nonlinear mathematical model for analysing product lifecycle management. Chaotic nonlinear dynamical processes of product lifecycle are deterministic but have the property that even small uncertainties in initial conditions lead to exponentially growing errors in the management that limit long-term forecasts. The emergence of chaotic behaviour in processes of product lifecycle was explored, focusing on fluctuations. The study employed methods such as systems analysis, correlation analysis, nonlinear dynamics, and the Surrogate model of chaotic Lorenz waterwheel. It was identified that sharp technological innovations as the primary drivers of short-term fluctuations impacting fixed efficiency and effectiveness of product life cycle process development. The resulting nonlinear dynamic model allowed for flexible operation, transitioning between equilibrium, periodic, and chaotic states based on coefficient values for asset growth rates and time constants reflecting product life cycle process dynamics. The research results are valuable for companies seeking to reduce their environmental impact and implement circular economy principles.

A deterministic mathematical model with non-linear least squares method for investigating the transmission dynamics of lumpy skin disease

Lumpy skin disease (LSD) is an economically significant viral disease of cattle caused by the lumpy disease virus (LSDV) which is primarily spread mechanically by blood feeding vectors such as particular species in flies, mosquitoes and ticks. Despite efforts to control its spread, LSD has been expanding geographically, posing challenges for effective control measures. This study develops a Susceptible-Exposed-Infectious-Recovered-Susceptible (SEIRS) model that incorporates cattle and vector populations to investigate LSD transmission dynamics. The model considers the waning rate of natural active immunity in recovered cattle, disease-induced mortality, and the biting rate. Using a standard dynamical system approach, we conducted a qualitative analysis of the model, defining the invariant region, establishing conditions for solution positivity, computing the basic reproduction number, and examining the stability of disease-free and endemic equilibria. We employ a non-linear least squares method for model calibration, fitting it to a synthetic dataset. We subsequently test it with actual infectious cases data. Results from the calibration and testing phases demonstrate the model’s validity and reliability for diverse settings. Local and global sensitivity analyses were conducted to determine the model’s robustness to parameter values. The biting rate emerged as the most significant parameter, followed by the probabilities of infection from either population and the recovery rate. Additionally, the waning rate of LSD infection-induced immunity gained positive significance in LSD prevalence from the beginning of the infectious period onward. Simulation results suggest reducing the biting rate as the most effective LSD control measure, which can be achieved by applying vector repellents in cattle farms/herds, thereby mitigating the disease’s prevalence in both cattle and vector populations and reducing the chances of infection from either population. Furthermore, measures aiming to boost LSD infection-induced immunity upon recovery are recommended to preserve the immune systems of the cattle population.

Hyperspectral remote sensing of forage stoichiometric ratios in the senescent stage of alpine grasslands

Senescence is an important phenological stage in the life cycle of grassland plants, and estimating grass senescence in alpine grasslands is particularly crucial for animal husbandry and grazing the utilization of grassland resources for grazing. However, the application of proximal sensing technologies to capture the variations in forage growth parameters in the senescent stage, especially regarding some key stoichiometric ratios, still faces challenges associated with indiscernible spectral properties and indeterminate absorption and reflectance features. The present study aims to demonstrate the potential and effectiveness of applying hyperspectral data to assess the forage carbon-nitrogen (C:N) ratio and calcium-phosphorus (Ca:P) ratio during the senescent stage (September to November). A progressive variable dimensionality reduction strategy based on a genetic algorithm (GA) and hybrid optimization method (ant optimization colony (ACO) and extreme learning machine (ELM)) coupled with multiple linear and nonlinear statistical methods is applied to develop C:N ratio and Ca:P ratio estimation models via combination with data from 205 sample sites collected from six field campaigns (2016-2019) on the eastern Tibetan Plateau. The results show that the important spectral bands favorable for forage C:N ratio and Ca:P ratio retrieval are generally in the red and shortwave infrared (SWIR) regions, and the proposed model presents satisfactory performance in the estimation of the forage C:N ratio (V-R2 = 0.81, V-RMSE = 6.44) and Ca:P ratio (V-R2 = 0.64, V-RMSE = 2.54) during senescence. Moreover, the model can effectively overcome the spatial differences among sampling areas and perform optimally in capturing the variations in the forage C:N ratio and Ca:P ratio in the early and middle stages of senescence. Overall, our study demonstrates that it is feasible and promising to estimate these stoichiometric ratios using hyperspectral feature bands during grass senescence at the canopy level, with potential applications that may further enhance the monitoring of forage quality and quantity.

Backstepping synchronization control for four-dimensional chaotic system based on DNA strand displacement

Backstepping control is an important nonlinear control design method, which realizes the control of complex systems by constructing control law step by step, and has significant advantages for dealing with complex nonlinear systems. This article proposes a synchronization technique for four-dimensional chaotic systems using a combination of backstepping control method and DNA strand displacement technology. By relying on theoretical knowledge of DNA molecules, five basic chemical reaction modules such as trigger reaction, reference reaction, catalytic reaction, annihilation reaction and degradation reaction are given to construct a four-dimensional DNA chaotic system. On the basis of the relevant theory of chaotic dynamics, the constructed system is analyzed by Lyapunov exponent diagram and spectral entropy complexity algorithm, and the results come to the conclusion that the system reveals extremely complex and varied dynamic behaviors. Combining DNA strand displacement technology with backstepping control method, four controllers are developed to ensure that the trajectories of two homogeneous chaotic systems are synchronized. The numerical simulation results validate the feasibility and applicability of the proposed method. The method proposed in this paper may provide some references in the field of DNA molecular chaos synchronization control.

Construction of multi-component finite element model to predict biomechanical behaviour of breasts during running and quantification of the stiffness impact of internal structure.

This study aims to investigate the biomechanical behaviour and the stiffness impact of the breast internal components during running. To achieve this, a novel nonlinear multi-component dynamic finite element method (FEM) has been established, which uses experimental data obtained via 4D scanning technology and a motion capture system. The data are used to construct a geometric model that comprises the rigid body, layers of soft tissues, skin, pectoralis major muscle, fat, ligaments and glandular tissues. The traditional point-to-point method has a relative mean absolute error of less than 7.92% while the latest surface-to-surface method has an average Euclidean distance (d) of 7.05mm, validating the simulated results. After simulating the motion of the different components of the breasts, the displacement analysis confirms that when the motion reaches the moment of largest displacement, the displacement of the breast components is proportional to their distance from the chest wall. A biomechanical analysis indicates that the stress sustained by the breast components in ascending order is the glandular tissues, pectoralis major muscle, adipose tissues, and ligaments. The ligaments provide the primary support during motion, followed by the pectoralis major muscle. In addition, specific stress points of the breast components are identified. The stiffness impact experiment indicates that compared with ligaments, the change of glandular tissue stiffness had a slightly more obvious effect on the breast surface. The findings serve as a valuable reference for the medical field and sports bra industry to enhance breast protection during motion.

Site index curves using the generalized algebraic difference approach – Gada in planted forests of Pinus taeda L. in the midwest of Santa Catarina, Brazil

One of the most widely used tools for assessing the productive potential of planted Pinus taeda L. forests is to generate site index curves. Site index is a measure of the productive potential of forests and is influenced by various factors such as soil, water, light, among others, representing the relationship between the dominant height of trees and age at a specific location. This relationship produces a curve and can be used for site classification, consequently estimating the productivity of the forest stand. The objective of this study was to evaluate the performance of dynamic equations, the Algebraic Difference Approach (ADA), and its generalization (GADA). The data were obtained from permanent plots of Continuous Forest Inventory (CFI), collected in forest stands, through a sequence of annual remeasurements from 5 to 17 years of age. Dominant height was estimated as a function of age using nonlinear equations, and subsequently, the ADA and GADA methods were applied using the Chapman-Richards basic equation. The results of the GADA method provided a substantial reduction in the root mean square error (RMSE), less than half when compared to the traditional guide curve method, and an increase from 0.95 to 0.99 in R2adj. Therefore, the GADA methodology proved to be suitable and efficient for site index classification, with noticeable flexibility and reliability on its estimates.

Non-linear Mendelian randomization: detection of biases using negative controls with a focus on BMI, Vitamin D and LDL cholesterol.

Mendelian randomisation (MR) is an established technique in epidemiological investigation, using the principle of random allocation of genetic variants at conception to estimate the causal linear effect of an exposure on an outcome. Extensions to this technique include non-linear approaches that allow for differential effects of the exposure on the outcome depending on the level of the exposure. A widely used non-linear method is the residual approach, which estimates the causal effect within different strata of the non-genetically predicted exposure (i.e. the "residual" exposure). These "local" causal estimates are then used to make inferences about non-linear effects. Recent work has identified that this method can lead to estimates that are seriously biased, and a new method-the doubly-ranked method-has been introduced as a possibly more robust approach. In this paper, we perform negative control outcome analyses in the MR context. These are analyses with outcomes onto which the exposure should have no predicted causal effect. Using both methods we find clearly biased estimates in certain situations. We additionally examined a situation for which there are robust randomised controlled trial estimates of effects-that of low-density lipoprotein cholesterol (LDL-C) reduction onto myocardial infarction, where randomised trials have provided strong evidence of the shape of the relationship. The doubly-ranked method did not identify the same shape as the trial data, and for LDL-C and other lipids they generated some highly implausible findings. Therefore, we suggest there should be extensive simulation and empirical methodological examination of performance of both methods for NLMR under different conditions before further use of these methods. In the interim, use of NLMR methods needs justification, and a number of sanity checks (such as analysis of negative and positive control outcomes, sensitivity analyses excluding removal of strata at the extremes of the distribution, examination of biological plausibility and triangulation of results) should be performed.

Formation Control of Autonomous Underwater Vehicles Using an Improved Nonlinear Backstepping Method

The characteristics of autonomous underwater vehicles include nonlinearity, strong coupling, multiple inputs and multiple outputs, uncertainty, strong disturbance, underdrive, and multiple constraints. Autonomous underwater vehicle cluster systems are associated with large-scale complex dynamic systems through local perception or network communication, which have the structural characteristics of “complex dynamic + association topology + interaction rules”. To solve the problem of formation trajectory tracking of underactuated autonomous underwater vehicles, a controller was designed on the basis of an improved nonlinear backstepping algorithm, cascade system theory, and the Lyapunov direct method. In this design, the formation is determined from the actual trajectory of the leader autonomous underwater vehicle. The formation control rate is determined using the backstepping method and Lyapunov theory. Nonlinear disturbance observers were added to ensure that the trajectory error of the formation control could be quickly reduced in a real case with interference. The stability and effectiveness of this method were verified through simulation experiments. The robustness of the control algorithm was verified using two simulation cases, and the simulation results show that the proposed control method can maintain the expected formation.

A retrospective view on non-linear methods in chemometrics, and future directions

This perspective article reviews how the chemometrics community approached non-linear methods in the early years. In addition to the basic chemometric methods, some methods that fall under the term “machine learning” are also mentioned. Thereafter, types of non-linearity are briefly presented, followed by discussions on important aspects of modeling related to non-linear data. Lastly, a simulated data set with non-linear properties is analyzed for quantitative prediction and batch monitoring. The conclusion is that the latent variable methods to a large extent handle non-linearities by adding more linear combinations of the original variables. Nevertheless, with strong non-linearities between the X and Y space, non-linear methods such as Support Vector Machines might improve prediction performance at the cost of interpretability into both the sample and variable space. Applying multiple local models can improve performance compared to a single global model, of both linear and non-linear nature. When non-linear methods are applied, the need for conservative model validation is even more important. Another approach is pre-processing of the data which can make the data more linear before the actual modeling and prediction phase.

The circadian pattern of atrial fibrillation onset

Abstract Background/Introduction Atrial fibrillation (AF) is the most common sustained cardiac arrhythmia affecting 2% of the population. Within the broad spectrum of AF symptomatology, there is a particular subset of patients that show a predominant or even exclusive nocturnal onset of paroxysmal AF. Purpose The aim of this study is to assess the timing of onset of AF in the 24-hour cycle and to assess whether a circadian rhythm is present in the onset of AF. Methods The MEDLINE, EMBASE, and CENTRAL databases, searched from inception to September 2023, provided 18 studies detailing the onset of AF in a 24-hour cycle. Patients had either paroxysmal or persistent AF. Studies performed in ICU populations (n=3) were omitted due to different triggers for AF. Time of AF onset was determined either by Cardiac Implantable Electronic Device (CIED) (n=5), Holter (n=7) or minute history taking (n=3). The presence and statistical significance of a 24-hour periodicity is tested using the cosinor analysis: Y(t)= A ⋅ sin(2πft + α) + β where the amplitude, frequency, phase and error (A, f, α and β, respectively) are computed by single harmonic regression using a nonlinear least-squares method. Goodness of fit is estimated using R2, the statistical significance of the model is tested using a zero-amplitude test. Results The 15 studies included 2.080 patients with 11.886 onsets of AF. The blue bars in Figure 1 represent the total of AF onsets from all studies per hour. The pattern of onset AF can be approximated well by a single sine function (Onset(t)= 95.7915 ⋅ sin((2π ⋅ 0.0417 ⋅ t) – 1.8386) + 510.5500, R2 0.77, P = 0.03) with a 24-hour period, clearly establishing the 24-hour rhythmicity in the onset of AF (Figure 1, red line). Hours with significantly more onset of AF compared to the mean, assessed by residual Chi2 testing, are exclusively nocturnal (22.00-7.00, indicated by a moon symbol in Figure 1) while hours with significantly less onset are exclusively during daytime (7.00-22.00, indicated by a sun symbol in Figure 1). Conclusion Despite the potential limitations due to the methods used, such as arrhythmia discrimination in CIED-studies and asymptomatic episodes in case of history taking, the overall picture of predominance of nocturnal AF onset is clearly established. Multiple pathophysiological mechanisms might underlie this circadian pattern and nocturnal predominance, like obstructive sleep apnea and increased vagal tone, which should be subject of further research.time of onset of AF over a 24h period

#2898 Exposure response model describing hematologic changes with chronic treatment of CKD anemia with vadadustat

Abstract Background and Aims Vadadustat (VADA) is an oral hypoxia-inducible factor (HIF) prolyl hydroxylase inhibitor, a class of drugs that stabilize HIF and stimulate endogenous erythropoietin production, increasing iron mobilization and red blood cell production. VADA is approved in 36 countries globally and is indicated in the European Union for the treatment of symptomatic anaemia associated with chronic kidney disease (CKD) in adults on chronic maintenance dialysis and is an alternative to treatment with erythropoiesis-stimulating agents (ESAs). The aim of this work was to develop a predictive, semi-mechanistic model to understand the effects of VADA and erythropoiesis-stimulating agents (ESAs) on hemoglobin response and to evaluate the impact of intrinsic and extrinsic patient characteristics on that response for non-dialysis dependent (NDD) and dialysis-dependent (DD) patient populations. Method A predictive semi-mechanistic pharmacokinetic/pharmacodynamic (PK/PD) model for VADA and ESA treatment was developed using nonlinear mixed effects methods. The model describes changes in reticulocyte count (RETICs), mature erythrocytes (RBCs) and hemoglobin (Hb) as a function of drug exposure and subject-specific characteristics. The dataset was based on data from 7 Phase 1 to Phase 3 studies (Table 1; N = 894 for VADA; N = 560 for ESA modeling) in healthy volunteers and subjects with NDD- or DD-CKD who were either ESA-naïve or ESA experienced but not receiving treatment at screening. Prior population PK modeling of VADA provided estimated drug exposures for VADA-treated subjects, while dose normalized to standard units (IU/kg/wk) was used as the exposure metric for subjects on ESA. Each of these exposure metrics could vary with time, as the dose was adjusted according to observed Hb response. This work evaluated alternative model structures, as well as covariate effects affecting Hb individual response. Results A predictive semi-mechanistic pharmacokinetic/pharmacodynamic (PK/PD) model for VADA and ESA treatment was developed using nonlinear mixed effects methods. The model describes changes in reticulocyte count (RETICs), mature erythrocytes (RBCs) and hemoglobin (Hb) as a function of drug exposure and subject-specific characteristics. The dataset was based on data from 7 Phase 1 to Phase 3 studies (Table 1; N = 894 for VADA; N = 560 for ESA modeling) in healthy volunteers and subjects with NDD- or DD-CKD who were either ESA-naïve or ESA experienced but not receiving treatment at screening. Prior population PK modeling of VADA provided estimated drug exposures for VADA-treated subjects, while dose normalized to standard units (IU/kg/wk) was used as the exposure metric for subjects on ESA. Each of these exposure metrics could vary with time, as the dose was adjusted according to observed Hb response. This work evaluated alternative model structures, as well as covariate effects affecting Hb individual response. A similar model structure was found to describe early changes in RETICs and longer-term changes in Hb for both VADA and ESAs. In each case, the magnitude of response increases with increased drug exposure up to a maximum value (Emax), and the Emax values were similar between VADA and ESAs. Subject intrinsic predictors of response included eGFR, subject age, BMI, and serum albumin, while extrinsic factors affecting response included geographic region, limits on acceptable Hb values (which also differ by geographic region) and the presence of previous ESA treatment. Interestingly, Hb responses were also correlated with changes in serum hepcidin, a key regulator of iron homeostasis, following both VADA and ESA treatment. Differences between the response to VADA and ESA were also described, including differences in temporal changes in RETICs and Hb. Conclusion This model showed an exposure-response relationship between VADA or ESA treatment and changes in RETICs and Hb for ESA naïve or ESA-experienced CKD subjects. The model will be used to inform dosage recommendations for VADA based on patient characteristics.

Precise Mass, Orbital Motion, and Stellar Properties of the M-dwarf Binary LP 349−25AB

LP 349−25 is a well-studied close stellar binary system comprised of two late M dwarf stars, where both stars are close to the limit between star and brown dwarf. This system was previously identified as a source of gigahertz radio emission. We observed LP 349−25AB over 11 epochs in 2020–2022, detecting both components in this nearby binary system using the Very Long Baseline Array (VLBA). We fit simultaneously the VLBA absolute astrometric positions together with existing relative astrometric observations derived from optical/infrared observations with a set of algorithms that use nonlinear least-squares, genetic algorithm, and Markov Chain Monte Carlo methods to determine the orbital parameters of the two components. We find the masses of the primary and secondary components to be 0.08188 ± 0.00061 M ⊙ and 0.06411 ± 0.00049 M ⊙, respectively, representing one of the most precise mass estimates of any ultracool dwarf (UCD) to date. The primary is a UCD of 85.71 ± 0.64 M Jup, while the secondary has a mass consistent with being a brown dwarf of 67.11 ± 0.51 M Jup. This is one of the very few direct detections of a brown dwarf with VLBA observations. We also find a distance to the binary system of 14.122 ± 0.057 pc. Using stellar evolutionary models, we find the model-derived stellar parameters of both stars. In particular, we obtain a model-derived age of 262 Myr for the system, which indicates that LP 349−25AB is composed of two pre–main-sequence stars. In addition, we find that the secondary star is significantly less evolved than the primary star.

A New Preconditioned Nonlinear Conjugate Gradient Method in Real Arithmetic for Computing the Ground States of Rotational Bose–Einstein Condensate

A New Preconditioned Nonlinear Conjugate Gradient Method in Real Arithmetic for Computing the Ground States of Rotational Bose–Einstein Condensate

The influence of lateral pressure on ultimate strength of ship structure

ABSTRACT The lateral pressure influences the ultimate strength of double-bottom structure. In the midship section of bulk carrier, upward bottom local loads typically exceed downward loads, resulting in increased longitudinal thrust in the outer bottom plating and a reduction in the ultimate strength of the hull girder during hogging conditions. In the present research, the typical stiffened plate and double bottom structures of the Kamsarmax type bulk carrier are taken as the research objects. The nonlinear finite element method is considered to analyze the collapse behaviour of the stiffened plate and double-bottom structure under the longitudinal thrust/bending and lateral pressure, respectively. The influence of lateral pressure on buckling modes, stress distribution, collapse mode and ultimate strength is systematically demonstrated and analyzed. This research contributes significantly to the safety design of hull structures.

Exact Nonlinear Decomposition of Ideal-MHD Waves Using Eigenenergies

In this paper, we introduce a new method for exact decomposition of propagating, nonlinear magnetohydrodynamic (MHD) disturbances into their component eigenenergies associated with the familiar slow, Alfvén, and fast wave eigenmodes, and the entropy and field-divergence pseudoeigenmodes. First, the mathematical formalism is introduced, where it is illustrated how the ideal-MHD eigensystem can be used to construct a decomposition of the time variation of the total energy density into contributions from the eigenmodes. The decomposition method is then demonstrated by applying it to the output of three separate nonlinear MHD simulations. The analysis of the simulations confirms that the component wave modes of a composite wavefield are uniquely identified by the method. The slow, Alfvén, and fast energy densities are shown to evolve in exactly the way expected from comparison with known linear solutions and nonlinear properties, including processes such as mode conversion. Along the way, some potential pitfalls for the numerical implementation of the decomposition method are identified and discussed. We conclude that the exact, nonlinear decomposition method introduced is a powerful and promising tool for understanding the nature of the decomposition of MHD waves as well as analyzing and interpreting the output of dynamic MHD simulations.

Efficient WENO Schemes for Nonuniform Grids

A set of arbitrarily high-order WENO schemes for reconstructions on nonuniform grids is presented. These non-linear interpolation methods use simple smoothness indicators with a linear cost with respect to the order, making them easy to implement and computationally efficient. The theoretical analysis to verify the accuracy and the essentially non-oscillatory properties are presented together with some numerical experiments involving algebraic problems in order to validate them. Also, these general schemes are applied for the solution of conservation laws and hyperbolic systems in the context of finite volume methods.

The Derivation of Vertical Damping Reduction Factors for the Design and Analysis of Structures Using Acceleration, Velocity, and Displacement Spectra

Damping reduction factors (DRFs) play a vital role in the seismic design of structures. DRFs have been widely studied due to their primary importance to the lateral resistance of structures subjected to earthquakes. On the other hand, devastating earthquakes have occurred all over the world, and recently, the Kahramanmaraş earthquakes in Turkey revealed the import of the vertical component of earthquakes and their impact on structures and infrastructures. Considering the importance of this parameter, this paper aims to develop new damping reduction factor (DRF) equations for the acceleration (DRFa), velocity (DRFv), and displacement spectra (DRFd) of the vertical components of earthquakes. For this purpose, 775 real ground motion records were selected from the Pacific Earthquake Engineering Research (PEER) strong motion database, and the vertical elastic response spectra of selected records were computed according to linear dynamic analysis. Taking the 5%-damped vertical response spectra as the target, the vertical spectral damping reduction factors (DRFa, DRFv, and DRFd) were computed for 1%, 3%, 10%, 15%, 20%, 30%, and 40% damping ratios. The effect of the earthquake magnitude, distance, and soil types on the DRFs was investigated. The results indicated that magnitude, distance, and soil type had no particular effect on the trend in the DRFs. Based on the evaluations, extensive statistical analyses were carried out, and new prediction equations were developed according to the nonlinear regression method. The developed equations were then compared to those found in the literature and seismic design codes. The comparisons proved that the proposed DRFa, DRFd, and DRFv models are strongly compatible with real DRFs and show strong robustness compared to existing models.

Socio-economic dimensions and human centricity in Industry 5.0: a study on manufacturing sectors in central and Eastern European economies

PurposeThis study aims to quantify the concept of Industry 5.0, with a focus on human-centricity in the manufacturing sector.Design/methodology/approachThe panel nonlinear autoregressive distributed lag method is applied to assess asymmetry and vulnerability in the food, textile, chemical manufacturing, high-tech and transportation sectors. The robustness of the results is tested using a panel Granger non-causality test and panel vector autoregressive models.FindingsThis study finds that financial unions, fair internal markets, gender and youth participation are significant factors for human centricity in the manufacturing sectors. The NARDL results suggest that both the chemical and high-tech industries human participation are insignificant in both the long run and short run. The results of the food industry are significant in both the sort run and the long run.Research limitations/implicationsManufacturing sectors need to create sustainable employment strategies that lead to stable, enduring and satisfying jobs in order to achieve human centricity. Involve skilled workers in important decision-making processes and empower them with technology.Originality/valueThis study differed from prior research in several ways. Firstly, it incorporates the social dimension as a control variable in the pursuit of I5.0 implementation across various manufacturing sectors. Secondly, it quantifies the human-centricity aspect of I5.0 within these sectors.

Distributed Formation Maneuvering Quantized Control of Under-Actuated Unmanned Surface Vehicles with Collision and Velocity Constraints

This paper focuses on a distributed cooperative time-varying formation maneuvering issue of under-actuated unmanned surface vehicles (USVs). A fleet of USVs is guided by a parameterized path with a time-varying formation while avoiding collisions and preserving the connectivity in the environment with multiple obstacles. In some surface missions, due to the obstacles in the external environment, the bandwidth limitations of the communication channel, and the hardware components/performance constraints of the USVs themselves, each vehicle is considered to be subject to model uncertainty, actuator quantization, sensor dead zone, and velocity constraints. During the control design process, the radial basis function (RBF) neural networks (NNs) are utilized to deal with nonlinear terms. Based on a nonlinear decomposition method, the relationship between the control signal and the quantization one is established, which overcomes the difficulty arising from actuator quantization. A Nussbaum function is introduced to handle the unknown output dead zone problem caused by reduced sensor sensitivity. Moreover, a universal-constrained function is employed to satisfy both the constrained and unconstrained requirements during formation keeping and obstacle avoidance. The Lyapunov stability theory confirmed that the error signals are uniformly ultimately bounded (UUB). The simulation results demonstrate the effectiveness of the proposed distributed formation control of multiple USVs.

Closed cracks characterization in a steel sample applying a pump probe waves ultrasonic method

Abstract Ultrasonic measurements are commonly used for crack sizing in industrial context, but due to potential partial crack closure, the crack depth can be underestimated. It could be of importance regarding the prediction of remaining service life and maintenance scheduling of industrial components. In the literature, nonlinear ultrasonic methods have proven efficient for this issue. Among them, a pump probe waves method is investigated here for possible use in an industrial context. In this paper, an industrial steel component with several partially closed fatigue cracks is studied. First, a three-point bending test associated with digital image correlation is performed with ultrasonic measurements to obtain reliable indications about the cracks closure state. A three-dimensional laser vibrometry experiment shows the possibility to open the crack using a pump wave. The pump probe waves method is conducted using a standard 45° shear wave transducer in echo mode as a probe. The results allow to discuss physical mechanism in play. It is also shown the possibility to detect the closed nature for all of the cracks even if the full opening state is not reached. Moreover, a coherent crack profile is found compared to mechanical test. The results are validated on a notched sample for which the nonlinear response is negligible. Industrial application as well as possible improvement are discussed.