First-order Differentiator Research Articles

A Stable Approach for Numerical Differentiation by Local Regularization Method with its Regularization Parameter Selection Strategies

The local regularization method for solving the first-order numerical differentiation problem is considered in this paper. The a-priori and a-posteriori selection strategy of the regularization parameter is introduced, and the convergence rate of local regularization solution under some assumption of the exact derivative is also given. Numerical comparison experiments show that the local regularization method can reflect sharp variations and oscillations of the exact derivative while suppress the noise of the given data effectively.

Reinforcement Learning-Based Nearly Optimal Control for Constrained-Input Partially Unknown Systems Using Differentiator

In this article, a synchronous reinforcement-learning-based algorithm is developed for input-constrained partially unknown systems. The proposed control also alleviates the need for an initial stabilizing control. A first-order robust exact differentiator is employed to approximate unknown drift dynamics. Critic, actor, and disturbance neural networks (NNs) are established to approximate the value function, the control policy, and the disturbance policy, respectively. The Hamilton-Jacobi-Isaacs equation is solved by applying the value function approximation technique. The stability of the closed-loop system can be ensured. The state and weight errors of the three NNs are all uniformly ultimately bounded. Finally, the simulation results are provided to verify the effectiveness of the proposed method.

On Goodness of WiFi Based Monitoring of Sleep Vital Signs in the Wild

WiFi channel state information (CSI) has emerged as a plausible modality for sensing different human vital signs, i.e., respiration and body motion, as a function of modulated wireless signals that travel between WiFi devices. Although a remarkable proposition, most of the existing research in this space struggles to withstand robust performance beyond experimental conditions. To this end, we take a careful look at the dynamics of WiFi signals under human respiration and body motions in the wild. We first characterize the WiFi signal components—multipath and signal subspace—that are modulated by human respiration and body motions. We extrapolate on a set of transformations, including first-order differentiation, max-min normalization and component projections, that faithfully explains and quantifies the dynamics of respiration and body motions on WiFi signals. Grounded in this characterization, we propose two methods: 1) a respiration tracking technique that models the peak dynamics observed in the time-varying signal subspace and 2) a body-motion tracking technique built with a multi-dimensional clustering of evolving signal subspace. Finally, we reflect on the manifestation of these techniques in a practical sleep monitoring application. Our systematic evaluation with over 550 hours of data from 5 users covering both line-of-sight (LOS) and non-line-of-sight (NLOS) settings shows that the proposed techniques can achieve comparable performance to purpose-built pulse-Doppler radar.

Nondestructive detection of sunset yellow in cream based on near-infrared spectroscopy and interval random forest.

Based on near-infrared spectrum and interval random forest, a fast quantitative analysis method for the content of sunset yellow content was established. The spectra of 132 cream pigment samples were obtained by FT-NIR spectrometer, and various preprocessing methods such as standard normal variable (SNV), wavelet transform (WT), and SG (Savitzky-Golay) were used to smooth and denoise the original spectrum. In this paper, WT and first-order differentiation were used as pretreatment and the Kennard-Stone algorithm was used to divide the data set. Finally interval partial least squares, partial least squares, interval random forest and random forest were used to construct an optimal quantitative analysis model. The experimental results show that the interval random forest can find the best sub-interval to achieve the prediction ability of the model. The R2 (the coefficient of determination) and RMSEP (root mean square error of the prediction) of the prediction set are 0.8965 and 0.2454, respectively. The research results show that near-infrared spectroscopy combined with interval random forest algorithm is a fast and non-destructive method to detect the content of sunset yellow in cream.

Hyperspectral remote sensing for extraction of soil salinization in the northern region of Ningxia

Soil salinization affects negatively on agricultural productivity in the semiarid region of Ningxia. In this study, the performance of inversion model to determine soil salinization was assessed using some analysis and reflectance of wavelength. About 42 vegetation samples and 42 soil samples were collected for model extraction. Hyper-spectral data processing method was used to analyze spectral characteristics of different levels of salinization area vegetation. Spectral data were transformed in 16 different approaches, including root mean squares, logarithm, inversion logarithm, and first-order differentiation. After the transformation, the obtained soil and vegetation characteristics spectra correlate well with soil salt content, built soil index, and many vegetation indices. Nonlinear regression was employed to establish soil salinization remote sensing monitoring model. By comparing various spectral transformations, the first-order differential of soil spectral was the most sensitive to soil salinization degrees. The model of the current research was based on salinity index (SI) and improved soil-adjusted vegetation index (MSAVI). The correlation between simulated values and measured values was 0.758. Therefore, remote sensing monitoring derived from MSAVI–SI can greatly improve the dynamic and periodical monitoring of soil salinity in the study area.

Ultra-wideband doublet signal generation with tunable notch band based on delay-line filter

ABSTRACT A novel and simple scheme to generate Ultra-wideband (UWB) doublet signal with tunable notch band based on a tunable delay-line filter is presented. The first-order differentiation is realized by a dual-drive Mach–Zehnder modulator (DD-MZM), which differentiates the Gaussian pulses to the monocycle pulses. Subsequently, the UWB monocycle pulses are transmitted to an optical delay-line filter implemented by a balanced photo-detector and a tunable delay line for both differentiation and photodetection. Consequently, the desired UWB doublet signal can be obtained with a 10-dB bandwidth of 8.75 GHz. Besides, the polarity reversibility of the generated doublet signal is demonstrated by changing the bias voltage of the DD-MZM. Moreover, the desired notch can be introduced in the generated frequency spectrum to eliminate the interference between the existing narrowband systems and the UWB systems. And the tunability of the band-notched position is implemented by simply adjusting the delay time of the delay-line filter. The feasibility of the presented scheme is investigated by mathematical models and simulations.

Study of a WO3 thin film based hydrogen gas sensor decorated with platinum nanoparticles

A simple platinum nanoparticle (Pt NP)/WO3 semiconducting metal oxide (SMO)-based structure is fabricated and completely studied as a hydrogen gas sensor. In this work, simple rapid thermal evaporation (RTE) was employed to fabricate Pt NPs. This approach could easily produce Pt NPs with a small grain size and uniformity on the WO3 thin film. Experimentally, at 200 °C, the studied device exhibited an excellent hydrogen sensing response of 1.41 × 106 (under a 1% H2/air gas), a very low detecting level of 1 ppm H2/air, and a relatively shorter response (recovery) time of 201 s (26) s. Moreover, first order differential (FOD) and shape-preserving piecewise cubic interpolation (SPPCI) were also employed to overcome the wireless transmission problem for the Internet of Things (IoTs). Furthermore, based on the thermodynamic analysis, the surface coverage performance was studied for this device. As the result, the studied device exhibited practically adsorption with hydrogen gas at 200 °C. The studied device is therefore promising for high-performance hydrogen sensing applications.

Efficient Optical Spatial First-Order Differentiator Based on Graphene-Based Metalines and Evolutionary Algorithms

We propose a novel optical spatial differentiator to perform the differentiation computation in terahertz region based on the graphene metalines, which consist of graphene layers with different widths and chemical potentials. The numerical simulation results show that when beam waist size w>1.9λ, the metalines perform the first-order differentiation in the reflection spectrum with efficiency>97%, which can be theoretically demonstrated by using transfer matrix method. In order to further improve the performance of the differentiator, evolutionary algorithm, such as genetic algorithm, is used to inversely design the structure parameters and chemical potentials of graphene metalines. The optimization results show that some performance metrics of the differentiator, for example normalized root-mean-square deviation, are better than the previous structures. Obviously, the proposed graphene metalines combined with inverse design technology can achieve a high-performance optical spatial differentiator in terahertz region and provide a new way to design the photonics devices.

Best Uniform Approximation of the Differentiation Operator by Operators Bounded in the Space L2

We give a solution of the problem on the best uniform approximation on the number axis of the first-order differentiation operator on the class of functions with bounded second derivative by linear operators bounded in the space L2. This is one of the few cases of the exact solution of the problem on the approximation of the differentiation operator in some space with the use of approximating operators that are bounded in another space. We obtain a related exact inequality between the uniform norm of the derivative of a function, the variation of the Fourier transform of the function, and the L∞-norm of its second derivative. This inequality can be regarded as a nonclassical variant of the Hadamard-Kolmogorov inequality.

Application of high-order numerical algorithm for two-fluid two-pressure model: Hydraulic load analysis

Hydraulic load analysis is of great importance in the design of pressurized water reactor. It provides load conditions for structural mechanics analysis of primary loop system and ensures the reliability of primary loop pipeline and main equipment. Currently common hydraulic load analysis software mainly includes RELAP5 and WAHA, both of which adopt the classical two-fluid six-equation single pressure model and the first-order differentiation algorithm. The single pressure model is not stable, and its numerical results are prone to oscillation under high-order precision schemes. Meanwhile, the low-order algorithm is not accurate enough, which is not conducive to the simulation of pressure wave problems. However, the two-fluid two-pressure model is unconditionally adaptive. In order to improve the accuracy of the numerical algorithm and ensure the stability of the numerical value, a high-order semi-implicit algorithm for solving the transient term and convection term is developed based on the two-fluid two-pressure model. Finally, the high-order algorithm is applied to the hydraulic load problems such as shock tube, water hammer and blowout. The results show that the algorithm can effectively reduce the numerical diffusion and improve the prediction accuracy.

Chebyshev spectral variational integrator and applications

The Chebyshev spectral variational integrator (CSVI) is presented in this paper. Spectral methods have aroused great interest in approximating numerically a smooth problem for their attractive geometric convergence rates. The geometric numerical methods are praised for their excellent long-time geometric structure-preserving properties. According to the generalized Galerkin framework, we combine two methods together to construct a variational integrator, which captures the merits of both methods. Since the interpolating points of the variational integrator are chosen as the Chebyshev points, the integration of Lagrangian can be approximated by the Clenshaw-Curtis quadrature rule, and the barycentric Lagrange interpolation is presented to substitute for the classic Lagrange interpolation in the approximation of configuration variables and the corresponding derivatives. The numerical float errors of the first-order spectral differentiation matrix can be alleviated by using a trigonometric identity especially when the number of Chebyshev points is large. Furthermore, the spectral variational integrator (SVI) constructed by the Gauss-Legendre quadrature rule and the multi-interval spectral method are carried out to compare with the CSVI, and the interesting kink phenomena for the Clenshaw-Curtis quadrature rule are discovered. The numerical results reveal that the CSVI has an advantage on the computing time over the whole progress and a higher accuracy than the SVI before the kink position. The effectiveness of the proposed method is demonstrated and verified perfectly through the numerical simulations for several classical mechanics examples and the orbital propagation for the planet systems and the Solar system.

A Highly Sensitive Ammonia (NH3) Sensor Based on a Tungsten Trioxide (WO3) Thin Film Decorated With Evaporated Platinum (Pt) Nanoparticles

An interesting ammonia (NH3) sensor based on a tungsten trioxide (WO3) thin film decorated with platinum (Pt) nanoparticles (NPs) is fabricated and demonstrated herein. Pt NPs are prepared by a rapid thermal evaporation (RTE) approach. The small size of these Pt NPs causes an increased surface area/volume ( ${S}_{A}/{V}$ ) ratio and enhanced sensing performance. The experimental results indicate good properties, including a higher sensing response of 72.61 under 1000 ppm NH3/air gas, a lower optimum operating temperature of 225 °C, and a lower detecting limit (≤ 1 ppm NH3/air). The studied device also has the advantages of a simple structure, easy fabrication, relatively low cost, a wide concentration detection range, and stable sensing performance. In addition, a first-order differential (FOD) and shape-preserving piecewise cubic interpolation (SPPCI) algorithms are employed to effectively reduce the redundant results and recover the reduced data for wireless transmission application. Thus, the studied Pt NP/WO3 thin film-based device shows a promise for high-performance ammonia sensing applications.

Arbitrary-order optical differentiation in refection by sequence of first-order differentiators

We propose a simple analytical method for designing arbitrary-order optical differentiators operating in reflection by successively arranging several first-order optical differentiators. The approach is based on the scattering matrix analysis, does not involve numerical optimization and is valid for differentiators of arbitrary configurations. The numerical simulation results demonstrate high-quality differentiation of a picosecond pulse for up to the fourth order. The proposed method can find application in the design of analogue optical computing and optical information processing systems.

Multi-Target Concurrent Vital Sign and Location Detection Using Metamaterial-Integrated Self-Injection-Locked Quadrature Radar Sensor

A new architecture of self-injection-locked (SIL) quadrature radar sensor based on a metamaterial (MTM) leaky-wave antenna (LWA) to detect multi-target vital sign and location simultaneously is proposed for the first time. The angular information of targets is obtained by a 1-D MTM LWA with −50° to +30° beam-steering angle when the frequency varies from 1.85 to 2.85 GHz. Furthermore, the distance from the radar sensor to the targets is obtained by imposing the frequency-shift keying (FSK) modulation on the radar waveforms. Meanwhile, the vital sign signals of multiple targets can be extracted from the Doppler frequency spectrum. For the proof of concept, two frequencies, 2.24 and 2.45 GHz, are chosen to detect two targets at different locations, which correspond to the scanning angle at −10° and −40°, respectively. A first-order microwave differentiator followed by a quadrature coupler is employed to convert the radio frequency (RF) signals from the output of the MTM LWA to in-phase (I) and quadrature (Q) RF signals with frequency-dependent amplitudes, thereby eliminating the null point issues for radar detection. Experimental results show that the proposed SIL MTM radar sensor can detect the target location accurately, while the obtained vital sign results agree well with the ground truth.

Contact Force/Torque Control Based on Viscoelastic Model for Stable Bipedal Walking on Indefinite Uneven Terrain

Humanoid robots are being designed to perform tasks currently carried out by human workers in industry, manufacturing, service, and disaster assistance. To this end, the humanoid robot should be able to walk stably across many types of terrain. However, when traversing a complex unknown environment, it is difficult to realize accurate terrain perception immediately through large data collected by the sensor system, leading to a difference between planned foot landing positions and actual foot landing positions. As a result, an unexpected contact force/torque may affect the stability of the robot. This paper adopts active contact perception instead of terrain perception and proposes a contact force/torque control method based on the viscoelastic model to address this problem. In addition, we design a body stability controller based on tracking the trajectories of the virtual repellent point (VRP) and the divergent component of motion (DCM) to restrain the disturbance caused by the unexpected contact force/torque. Simulations and experiments on the BHR-6P humanoid robot platform demonstrate the proposed contact force/torque control method for walking on indefinite uneven terrain. Note to Practitioners —This paper presents a contact force/torque controller based on a viscoelastic model, which unifies contact perception and adaptive reaction. Using the viscoelastic model, we get the relationship between the end position/posture and the first-order differential of the contact force/torque, from which a state equation can be established and used to design a state feedback controller. Combining with body stabilization, we adopt this controller to modify the trajectory of both landing and support feet simultaneously for humanoid robots to realize stable bipedal walking on indefinite uneven terrain, which is validated in both simulations and experiments on the BHR-6P humanoid robot. In addition, this method can be employed for other robots or equipment when the contact force/torque control is needed; e.g., industry manipulators and quadruped robots.

Optical analog computing devices designed by deep neural network

We proposed a multilayered spatial optical differentiator designing method by use of the deep neural network (DNN). After trained for approximately 30 h, the DNN is able to predict the reflection coefficient of a 12-layer multilayer film with high fidelity (validation mean squared error < 2.4×10−4). As a useful example, a second-order spatial optical differentiator was then designed. Compared with the general optimization method, the machine learning could help to quickly generate a wavefront computing device at an about 6-times faster speed. The performance of the designed device is confirmed from the comparison with the theoretical ideal operation output. Another first-order spatial optical differentiator was also designed to validate the generality of the method. The results indicate that the DNN may have a bright future in designing devices capable of all kinds of complex time-space wavefront mathematical operation, in particular based on the multilayer material systems.

Distributed Finite-Time Fault-Tolerant Containment Control for Multiple Unmanned Aerial Vehicles.

This paper investigates the distributed finite-time fault-tolerant containment control problem for multiple unmanned aerial vehicles (multi-UAVs) in the presence of actuator faults and input saturation. The distributed finite-time sliding-mode observer (SMO) is first developed to estimate the reference for each follower UAV. Then, based on the estimated knowledge, the distributed finite-time fault-tolerant controller is recursively designed to guide all follower UAVs into the convex hull spanned by the trajectories of leader UAVs with the help of a new set of error variables. Moreover, the unknown nonlinearities inherent in the multi-UAVs system, computational burden, and input saturation are simultaneously handled by utilizing neural network (NN), minimum parameter learning of NN (MPLNN), first-order sliding-mode differentiator (FOSMD) techniques, and a group of auxiliary systems. Furthermore, the graph theory and Lyapunov stability analysis methods are adopted to guarantee that all follower UAVs can converge to the convex hull spanned by the leader UAVs even in the event of actuator faults. Finally, extensive comparative simulations have been conducted to demonstrate the effectiveness of the proposed control scheme.

A Novel Approach for the Design of Optimum IIR Differentiators Using Fractional Interpolation

In this paper, a novel method for designing an optimum infinite impulse response digital differentiator of the first and second orders is presented. The proposed method interpolates bilinear transform and rectangular transform fractionally, and then, unknown variables of the generalized equation are optimized using the genetic algorithm. The results obtained by the proposed designs are superior to all state-of-the-art designs in terms of magnitude responses. The first-order and second-order differentiator attains mean relative magnitude error as low as $$-\,27.702$$ (dB) and $$-\,35.04$$ (dB), respectively, in the complete Nyquist range. Besides, suggested low-order, differentiator design equations can also be optimized of any desired Nyquist frequency range, which makes it suitable for real-time applications.

Photonic generation of MMW-UWB monocycle and doublet signals based on frequency up-conversion and delay-line filter

A photonic approach to generate millimeter-wave (MMW) ultra-wideband (UWB) monocycle and doublet signals using stimulated Brillouin scattering (SBS) selective sideband amplification technique and delay-line filter is proposed and theoretically analyzed. In the proposed approach, a dual-drive Mach–Zehnder modulator (DDMZM) is used as a first-order differentiator to produce a monocycle UWB signal. Then the generated monocycle signal is single-sideband (SSB) modulated by SBS effect for up-conversion. A balanced photodetector (BPD) is further employed for both photodetection and first-order differentiation. Consequently, an MMW-UWB monocycle signal or an MMW-UWB doublet signal can be attained in electrical field with controlling an optical switch. The frequency spectra of the generated MMW-UWB monocycle and doublet signals meet well with the Federal Communication Committee (FCC) mask with power efficiency of 50.63% and 40.53%. Besides, the produced MMW-UWB signals can be employed to realize multiple modulation formats, such as on–off keying modulation (OOK), pulse position modulation (PPM) and pulse amplitude modulation (PAM).

A First-Order Differentiator with First-Order Sliding Mode Filtering

This paper proposes a sliding mode differentiator for estimating the first-order derivatives of noisy signals. The proposed differentiator can be seen as a version of Slotine et al.’s sliding mode observer extended with additional non-Lipschitzness. It behaves exactly as a first-order low-pass filter in the sliding mode and is globally convergent. Its discrete-time implementation is based on the implicit (backward) Euler discretization, which does not result in chattering. The differentiator is validated through some numerical examples.