Nonlinear Sensor Research Articles

A large calibrated database of hand movements and grasps kinematics

Modelling hand kinematics is a challenging problem, crucial for several domains including robotics, 3D modelling, rehabilitation medicine and neuroscience. Currently available datasets are few and limited in the number of subjects and movements. The objective of this work is to advance the modelling of hand kinematics by releasing and validating a large publicly available kinematic dataset of hand movements and grasp kinematics. The dataset is based on the harmonization and calibration of the kinematics data of three multimodal datasets previously released (Ninapro DB1, DB2 and DB5, that include electromyography, inertial and dynamic data). The novelty of the dataset is related to the high number of subjects (77) and movements (40 movements, each repeated several times) for which we release for the first time calibrated kinematic data, resulting in the largest available kinematic dataset. Differently from the previous datasets, the data are also calibrated to avoid sensor nonlinearities. The validation confirms that the data are not affected by experimental procedures and that they are similar to data acquired in real-life conditions.

Nonlinear optical effect and nonlinear optical mass sensor based on graphene optomechanical system

Graphene, atomically thin two-dimensional (2D) nanomaterial consisting of a single layer of carbon atoms, has received tremendous attention in the past few decades. Graphene may be considered as an excellent nanomaterial for fabricating nanomechanical resonator systems to investigate the quantum behavior of the motion of micromechanical resonators because of its unique properties of low mass density, high frequency, high quality-factor, and intrinsically small size. Additionally, graphene optomechanics based on a bilayer graphene resonator coupled to a microwave on-chip cavity, where light and micromechanical motion interact via the radiation pressure, has been demonstrtated experimentally recently. In this work, we demonstrate theoretically the nonlinear optical effect including optical bistability and four-wave mixing under the regimes woth different parameters and detunings in a graphene resonator-microwave cavity system. When the graphene optomechanics is driven by one strong pump laser beam, we find that the optical bistability can be controlled by tuning the power and the frequency of the pump beam. The four-wave mixing (FWM) phenomenon is also investigated and we find that sharp peaks in the FWM spectrum exactly are located at the resonant frequency of graphene resonator. Therefore, a straight nonlinear optical means for determining the resonant frequency of the graphene resonator is presented. Setting the cavity field resonating with pump field, and then scanning the probe frequency across the cavity frequency, one can easily and exactly obtain the resonant frequency of the resonator from the FWM spectrum. We further theoretically propose a mass sensor based on the graphene optomechanical system. The mass of external nanoparticles deposited onto the graphene resonator can be measured conveniently by tracking the shift of resonant frequency due to mass changing in the FWM spectrum. Compared with optomechanical mass sensors in linear regime, the nonlinear optical mass sensor may be immune to the detection noise. The system may have potential applications in communication networks for frequency conversion and provide a new platform for high sensitive sensing devices.

Optimal Estimation and Feedforward Control of Strip-Longitudinal Hardness for Thickness Hunting Suppression of Tandem Cold Mill Process

Following the recent trend of weight reduction in car industry, producing high quality cold-rolled AHSS (advanced high-strength steel) strip becomes important. Thickness hunting (or fluctuation) problem can be more prominent for this cold-rolled AHSS strip making, which can stem from the non-uniformity of hot-rolled strip and can severely degrade product quality. In this paper, we propose a novel framework to estimate the strip-longitudinal hardness of the TCM (tandem cold mill) process and its feedforward control to substantially reduce the thickness hunting, while fully incorporating the interconnected nature and sensing sparsity of the TCM process. In particular, our estimator consists of the following two complementary loops: 1) fast real-time hardness estimation loop, which optimally fuses the process model and sensing information; and 2) slower constant process-parameter estimation loop via optimization utilizing the nonlinear process model and (stored/measured) sensor data. Efficacy of the proposed estimation and control frameworks are then validated with high-precision TCM process physics simulator.

Data-based Identifiability and Observability Assessment for Nonlinear Control Systems using the Profile Likelihood Method

This paper introduces the profile likelihood method in order to assess simultaneously the parameter identifiability and the state observability for nonlinear dynamic state-space models with constant parameters. While a formal definition of a parameter’s identifiability has been used before, the novel idea is to investigate also the state’s observability by the identifiability of its initial value. Using the profile likelihood, both qualitative as well as quantitative statements are drawn from the analysis based on the nonlinear model and (possibly noisy) sensor data. A simplified wind turbine model is presented and used as an application example for the profile likelihood approach in order to investigate the model’s usability for state and parameter estimation. It is shown that the critical model parameters and initial states are identifiable in principle. The analysis with more complex models and realistic data reveals the limitations when assumptions are deliberately violated in order to meet reality.

Developing Variational Autoencoders with Differential Entropy Soft Sensor Models for Nonlinear Processes

Developing a good soft sensor for prediction has been a major interest, given the time lag to obtain quality data. Deep learning based variational autoencoders (VAE) have been implemented in industrial plants because of their capacities in dealing with the complex stochastic nonlinearity with better probabilistic interpretation. However, unsupervised VAE is inapplicable to the prediction. This article proposes a nonlinear soft sensor, which is an extension of the VAE framework with differential entropy (VAE_DE) loss function to construct a prediction model. The proposed VAE_DE model structure allows all the available data to be used for training although the data consist of process-quality data pairs and/or solely process data. Also, VAE DE enhances the prediction performance and its robustness through capturing the inter-correlations between process data and quality data in the nonlinear probabilistic model. Under the proposed framework, VAE DE model can be used for quick quality estimates of process data with unavailable quality data. The prediction quality of the proposed method is testified through a numerical case and an industrial case.

Data-Based Identifiability and Observability Assessment for Nonlinear Control Systems Using the Profile Likelihood Method

Abstract This paper introduces the profile likelihood method in order to assess simultaneously the parameter identifiability and the state observability for nonlinear dynamic state-space models with constant parameters. While a formal definition of a parameter’s identifiability has been used before, the novel idea is to investigate also the state’s observability by the identifiability of its initial value. Using the profile likelihood, both qualitative as well as quantitative statements are drawn from the analysis based on the nonlinear model and (possibly noisy) sensor data. A simplified wind turbine model is presented and used as an application example for the profile likelihood approach in order to investigate the model’s usability for state and parameter estimation. It is shown that the critical model parameters and initial states are identifiable in principle. The analysis with more complex models and realistic data reveals the limitations when assumptions are deliberately violated in order to meet reality.

Soft Sensor Modeling for Unobserved Multimode Nonlinear Processes Based on Modified Kernel Partial Least Squares With Latent Factor Clustering

To cope with the soft sensor modeling of unobserved multimode nonlinear processes, this paper proposes a modified kernel partial least squares (KPLS) by integrating latent factor clustering (LFC), called LFC-KPLS. In the proposed method, the process data are first divided into several batches orderly, and then projected onto the latent space by using the nonlinear functional expansion technology. In the latent space, partial least squares method is applied to compute the regression coefficients between the input variables and output variable of each batch. These regression coefficients, called the latent factors, can describe the functional relationships in the unobserved multimode data. Therefore, the latent factors are used for mode clustering so that the process data with similar functional relations can be clustered in one mode together. For each mode, the nonlinear soft sensor is established based on KPLS. To assign the mode of the online query sample, a mode identification strategy based on Bayesian inference is designed for the soft sensor online prediction. Finally, two cases studies are adopted to validate the proposed method.

Validating the Critical Point of Spontaneous Parametric Downconversion for Over 600 Scanning MEMS Micromirrors on Wafer Level

Sensors and actuators based on resonant micro-electro-mechanical systems (MEMS), such as scanning micro mirrors, are well-established in automotive and consumer products. As the areas of application broaden, the requirements for the MEMS are increasing. Devices outside of the performance specifications have to be rejected which is costly due to the high processing times of MEMS technologies. In particular, nonlinear system behavior is often found to cause unexpected device failure or performance issues. Thus, accurate simulation or rather system models which account for nonlinear sensor dynamics can not only increase process yield, but more importantly, lead to a comprehensive understanding of the underlying physics and to improved MEMS design. We have studied [1] the possibility of a rather drastic device failure induced by nonlinearities on the example of a resonant scanning MEMS micro mirror. On the level of a few selected chips, we have carefully measured the complex nonlinear system behavior and modeled it by a nonlinear mode-coupling phenomenon known as spontaneous parametric down-conversion (SPDC). The most intriguing feature of SPDC is the sudden change from a rather linear to a nonlinear system behavior at the critical oscillation amplitude. However, the threshold only lies within the range of the mirror's operational amplitude, if certain frequency resonance conditions regarding the mechanical modes are met. Thus, the critical amplitude strongly depends on the frequency spectrum of the MEMS design which in turn is largely influenced by fabrication imperfections. We validate the dependence of the critical amplitude on the resonance condition by measuring it for over 600 micro mirrors on wafer-level. Our work does not only validate the theory of SPDC with measurements on such a large scale, but also demonstrates modeling strategies which are essential for MEMS product design.

A Continuous-discrete Adaptive Observer Design for Nonlinear Systems Subject to Sensor Nonlinearities

In this paper, we address the problem of nonlinear continuous-discrete adaptive observer design for a class of system with sampled data measurements subject to sensor nonlinearities. The main difficulty of the considered class of system is coming from the fact that the output equation contains unknown parameters which renders the design of a classical sampled data observer difficult. To overcome this difficulty, we propose a new online continuous-discrete adaptive observer which ensures a simultaneous exponential convergence of both states and parameters. Comparing to other observer structures, our design is characterized by a simpler structure thanks to the introduction of a parametric adaptation law. To show the efficiency of our proposed approach, numerical simulations have been performed for different values of sampling time. In addition, the delayed-sampled measurements case is also illustrated.

Quantized Nonstationary Filtering of Networked Markov Switching RSNSs: A Multiple Hierarchical Structure Strategy

This article addresses the quantized nonstationary filtering problem for networked Markov switching repeated scalar nonlinear systems (MSRSNSs). A more general issue is explored for MSRSNSs, where the measurement outputs are characterized by packet losses, nonstationary quantized output, and randomly occurred sensor nonlinearities (ROSNs) simultaneously. Note that both packet losses and ROSNSs are depicted by Bernoulli distributed sequences. By utilizing a multiple hierarchical structure strategy, the nonstationary filters are designed for MSRSNSs, in which the correlation among modes of systems, quantizer, and controller are presented in terms of nonstationary Markov process. A practical example is provided to verify the proposed theoretical results.

Anti-Symmetric Mode Vibration of Electrostatically Actuated Clamped-Clamped Microbeams for Mass Sensing.

This paper details study of the anti-symmetric response to the symmetrical electrostatic excitation of a Micro-electro-mechanical-systems (MEMS) resonant mass sensor. Under higher order mode excitation, two nonlinear coupled flexural modes to describe MEMS mass sensors are obtained by using Hamilton’s principle and Galerkin method. Static analysis is introduced to investigate the effect of added mass on the natural frequency of the resonant sensor. Then, the perturbation method is applied to determine the response and stability of the system for small amplitude vibration. Through bifurcation analysis, the physical conditions of the anti-symmetric mode vibration are obtained. The corresponding stability analysis is carried out. Results show that the added mass can change the bifurcation behaviors of the anti-symmetric mode and affect the voltage and frequency of the bifurcation jump point. Typically, we propose a mass parameter identification method based on the dynamic jump motion of the anti-symmetric mode. Numerical studies are introduced to verify the validity of mass detection method. Finally, the influence of physical parameters on the sensitivity of mass sensor is analyzed. It is found that the DC voltage and mass adsorption position are critical to the sensitivity of the sensor. The results of this paper can be potentially useful in nonlinear mass sensors.

Establishing Meaningful Limits of Detection for Ion-Selective Electrodes and Other Nonlinear Sensors.

Although IUPAC has recommended a probabilistic approach to determining limit of detection (LOD) based on false-positive and false-negative rates for more than 20 years, the LOD definition for ion-selective electrodes (ISEs) long predates these recommendations and conflicts substantively with them. Although it is well known that the ISE LOD definition does not follow best practice, it continues to be used due to simplicity and a lack of available methods for estimating LOD for nonlinear sensors. Here, we use ISEs as a model system for estimation of LOD for nonlinear sensors that is consistent with broad IUPAC recommendations and justified using statistical theory. Using freely available software, the new approach and updated definition is demonstrated through theory, simulation, and an environmental application. The results show that the current LOD definition for ISEs performs substantially worse than the proposed definition when assessed against IUPAC recommendations, including ignoring sensor noise and LOD uncertainty, leading to bias of an order of magnitude or more. Further, the environmental application shows that the new definition, which includes estimates of LOD uncertainty, allows more objective assessment of sensor response and fitness for purpose. The growing demand for ultrasensitive sensors that operate in complex matrices has pushed the boundaries of traditional calibration approaches. These sensors often operate near their limit of detection (LOD), with additional challenges created if their response is nonlinear. These challenges are amplified when assessing new sensors, since they may be less reproducible and noisier than benchmark techniques.

Finite-time event-triggered non-fragile state estimation for discrete-time delayed neural networks with randomly occurring sensor nonlinearity and energy constraints

In this paper, the problem of event-triggered non-fragile state estimator design for discrete-time delayed neural networks (DNNs) is investigated over finite-time span. In consideration of the changes of environment and high sensitivity, external disturbances and/or parameter uncertainties might be involved in estimator parameters of the concerned DNNs. Therefore, it is one of our main objectives to design a non-fragile state estimator subject to the norm bounded gain variation. The sensor nonlinearity is supposed to occur in a random way. In the meanwhile, the event-triggered scheme and energy constraints are adopted in state estimator design for the purpose of energy and resource saving. By using the Lyapunov stability theory and some analytical techniques, sufficient conditions are established to guarantee that the estimation error system is finite-time bounded and meet a prescribed mixed H∞ and passivity performance constraint. Furthermore, the estimator gains are obtained via solving a set of linear matrix inequalities (LMIs). Finally, two numerical examples are exploited to demonstrate the effectiveness of the developed technique.

Adaptive digital PID control of first‐order‐lag‐plus‐dead‐time dynamics with sensor, actuator, and feedback nonlinearities

AbstractProportional‐integral‐derivative (PID) control is one of the most widely used feedback control strategies because of its ability to follow step commands and reject constant disturbances with zero asymptotic error, as well as the ease of tuning. This paper presents an adaptive digital PID controller for sampled‐data systems with sensor, actuator, and feedback nonlinearities. The linear continuous‐time dynamics are assumed to be first‐order lag with dead time (ie, delay). The plant gain is assumed to have known sign but unknown magnitude, and the dead time is assumed to be unknown. The sensor and actuator nonlinearities are assumed to be monotonic, with known trend but are otherwise unknown, and the feedback nonlinearity is assumed to be monotonic, but is otherwise unknown. A numerical investigation is presented to support a simulation‐based conjecture, which concerns closed‐loop stability and performance. Numerical examples illustrate the effect of initialization on the rate of adaptation and investigate failure modes in cases where the assumptions of the simulation‐based conjecture are violated.

Isolated frequencies at which nonlinear materials behave linearly.

In this Rapid Communication, we demonstrate that specific frequencies in weakly nonlinear lattices avoid the generation of higher harmonics, and thus the lattices behave linearly. Using a multiple scales analysis, we present plane-wave solutions that persist at only a single frequency and wave number; i.e., whose spatiotemporal production of higher harmonics is remarkably small. We study monatomic and diatomic chains with quadratic and cubic stiffness nonlinearities as example systems. Direct numerical integration of the equations of motion confirms that finite amplitude plane waves assigned to these special frequencies produce negligible higher harmonics when injected into the lattices. Such findings provide new considerations for the operating frequency of nonlinear communications devices, sensors, and transducers for enhanced signal-to-noise ratios.

Modeling and implementation of 1-D inverted magnetic needle system using a robust sliding mode controller

In this paper, we propose a novel problem in control systems area involving the control of a magnetic needle in the presence of an external magnetic field. A magnetic needle when restricted to rotate about a single axis in an external magnetic field, by pivoting its center will produce a stable and unstable equilibrium. Here, we present the detailed mathematical modeling of the 1-D inverted magnetic needle system and its control in the unstable equilibrium point. We use sliding mode controller (SMC) to achieve the control objectives. The simulation results are validated with the experimental results. For achieving a close match, we consider sensor and actuator nonlinearities. Further, its robust performance is compared with proportional-derivative (PD), proportional-integral-derivative (PID) controllers in the presence of system parameter uncertainty, disturbance, and sensor delay. We also study the effect of change in SMC parameters, proportional and derivative gains on the system performance. It is to be noted that the proposed experimental setup can be extended to a much more general and complex system, both in modeling as well as control design leading to a new benchmark problem in the control system.

An array of coupled nonlinear oscillators as a model for amplitude variations in intermodulation distortions from the auditory system

The response of a nonlinear oscillator driven by two or more forces displays several frequency components corresponding to the linear combinations of the driving frequencies, known as intermodulation distortions (IMDs). The auditory system of all classes of vertebrates produces strong IMDs in the presence of sounds of two tones. This phenomenon is attributed to the nonlinearity of the biological acoustic sensors within the inner ear. In this work, we developed a numerical model to investigate the total IMDs generated by a chain of coupled nonlinear oscillators. Total nonlinear distortions exhibited variations in amplitudes with respect to the stimulus frequency. The variation profile was sensitive to the magnitude of the driving forces and the difference in the two driving frequencies. We found that the arrangement of the oscillators’ characteristic frequencies was necessary for the variations in total IMD level. Results from the numerical model agreed with measurements of IMDs from Chinese edible frog (Hoplobatrachus Rugulosus), whose inner ear is constituted by arrays of acoustic receptors with progressively increasing natural frequencies. In response to sounds of two tones, IMDs produced by the inner ear of Chinese edible frog exhibited variations in amplitudes with respect to the driving frequencies. The third-order distortion level displayed several peaks at high stimulating sound pressure level, and at large differences between the stimulus frequencies. Our findings suggest that an array of coupled nonlinear oscillator can serve as a simple model for the generation of nonlinear distortions by the inner ear.

Optimal compressed sensing strategies for an array of nonlinear olfactory receptor neurons with and without spontaneous activity

There are numerous different odorant molecules in nature but only a relatively small number of olfactory receptor neurons (ORNs) in brains. This "compressed sensing" challenge is compounded by the constraint that ORNs are nonlinear sensors with a finite dynamic range. Here, we investigate possible optimal olfactory coding strategies by maximizing mutual information between odor mixtures and ORNs' responses with respect to the bipartite odor-receptor interaction network (ORIN) characterized by sensitivities between all odorant-ORN pairs. For ORNs without spontaneous (basal) activity, we find that the optimal ORIN is sparse-a finite fraction of sensitives are zero, and the nonzero sensitivities follow a broad distribution that depends on the odor statistics. We show analytically that sparsity in the optimal ORIN originates from a trade-off between the broad tuning of ORNs and possible interference. Furthermore, we show that the optimal ORIN enhances performances of downstream learning tasks (reconstruction and classification). For ORNs with a finite basal activity, we find that having inhibitory odor-receptor interactions increases the coding capacity and the fraction of inhibitory interactions increases with the ORN basal activity. We argue that basal activities in sensory receptors in different organisms are due to the trade-off between the increase in coding capacity and the cost of maintaining the spontaneous basal activity. Our theoretical findings are consistent with existing experiments and predictions are made to further test our theory. The optimal coding model provides a unifying framework to understand the peripheral olfactory systems across different organisms.

Study on the propagation characteristics of SH wave in piemagnetic piezoeletric structures

Propagation of SH wave in layered magnetoelectric structure consisting of piezomagnetic layer and piezoelectric substrate is theoretically investigated in this paper. Since the parameters of the piezomagnetic material change with the variety of the external magnetic field, the piezomagnetic material exhibits nonlinearity. The dispersion characteristics of elastic waves propagation in the magnetoelectric composites is more complex and presents many new physical phenomena under different external magnetic field. The elastic parameter, piezomagnetic parameter and permeability of the piezomagnetic material Terfenol-D varied nonlinearly with external magnetic field. Combining with four different electro-magnetic boundary conditions, the dispersion equations of SH wave satisfying quasi-linear wave equations in the Terfenol-D layer and piezoelectric substrate were derived in matrix form. The results show that the SH wave dispersion curves are influenced by external magnetic fields and geometric configurations. Moreover, the elastic displacement, stress, potential and magnetic potential varied with the external magnetic field are presented graphically. It turns out that no matter how the external magnetic field changes, the displacement, stress and potential satisfy the boundary conditions. The research can provide theoretical reference for the applications of piezomagnetic material Terfenol-D in the nonlinear magnetoelectric sensors and engineering.

A novel chromophore containing a Michler’s donor and a tricyanofuran acceptor with enhanced nonlinear optical properties

Abstract Organic dyes have received extensive attention due to their broad applications related to nonlinear optics, biological and chemical sensors. Herein, a novel chromophore based on double donors and tricyanofuran acceptor was prepared and studied. This new chromophore displayed excellent thermal stability showing the onset decomposition temperature higher than 230 °C. Moreover, density functional theory calculation shows that chromophore y1 presented a lower HOMO-LUMO energy gap and a much larger hyperpolarizability (β) than the single donor chromophore. These results showed that the double donors can increase the donor ability and thus enhance nonlinear optical properties.