Search Results (8)

We consider general higher-order matrix elliptic differential–difference operators in arbitrary domains with small variable translations in lower-order terms. The operators are introduced by means of general higher-order quadratic forms on arbitrary domains. Each lower-order term depends on its own translation and all translations are governed by a small multi-dimensional parameter. The operators are considered either on the entire space or an arbitrary multi-dimensional domain with a regular boundary. The boundary conditions are also arbitrary and general and involve small variable translations. Our main results state that the considered operators converge in the norm resolvent sense to ones with zero translations in the best possible operator norm. Estimates for the convergence rates are established as well. We also prove the convergence of the spectra and pseudospectra. Full article

To resolve the problem of high-precision trajectory tracking control under interference conditions in a missile’s mid-guidance phase, according to the constructed nominal trajectory, an improved adaptive high-order sliding mode trajectory tracking controller (AHSTC) is proposed. In this method, the open-loop nominal trajectories are established according to the nonlinear programming and Gaussian pseudospectra method. A high-precision trajectory tracking controller is developed by designing a nonlinear sliding mode surface and an adaptive high-order sliding mode approaching law combined with the trajectory tracking nonlinear error model. To verify the effectiveness and superiority of the proposed method, analysis and simulation are carried out through the example of a missile mid-guidance phase tracking control. Compared to the linear quadratic regulator (LQR) and active disturbance rejection controller (ADRC) method, the simulation results show that the proposed AHSTC method shows faster convergence and improved tracking effect. Therefore, the proposed AHSTC method has a good results and engineering application value. Full article

Thermal microstructure profiling is an established technique for investigating turbulent mixing and stratification in lakes and oceans. However, it provides only quasi-instantaneous, 1-D snapshots. Other approaches to measuring these phenomena exist, but each has logistic and/or quality weaknesses. Hence, turbulent mixing and stratification processes remain greatly under-sampled. This paper contributes to addressing this problem by presenting a novel analysis of thermal microstructure profiles, focusing on their multi-scale stratification structure. Profiles taken in two small lakes using a Self-Contained Automated Micro-Profiler (SCAMP) were analysed. For each profile, buoyancy frequency (N), Thorpe scales (L_T), and the coefficient of vertical turbulent diffusivity (K_Z) were determined. To characterize the multi-scale stratification, profiles of d²T/dz² at a spectrum of scales were calculated and the number of turning points in them counted. Plotting these counts against the scale gave pseudo-spectra, which were characterized by the index D of their power law regression lines. Scale-dependent correlations of D with N, L_T and K_Z were found, and suggest that this approach may be useful for providing alternative estimates of the efficiency of turbulent mixing and measures of longer-term averages of K_Z than current methods provide. Testing these potential uses will require comparison of field measurements of D with time-integrated K_Z values and numerical simulations. Full article

In this note, given a matrix $A\in {\mathbb{C}}^{n\times n}$ (or a general matrix polynomial $P\left(z\right)$, $z\in \mathbb{C}$) and an arbitrary scalar ${\lambda }_0\in \mathbb{C}$, we show how to define a sequence ${\left\{{\mu }_k\right\}}_{k\in \mathbb{N}}$ which converges to some element of its spectrum. The scalar ${\lambda }_0$ serves as initial term (${\mu }_0={\lambda }_0$), while additional terms are constructed through a recursive procedure, exploiting the fact that each term ${\mu }_k$ of this sequence is in fact a point lying on the boundary curve of some pseudospectral set of A (or $P\left(z\right)$). Then, the next term in the sequence is detected in the direction which is normal to this curve at the point ${\mu }_k$. Repeating the construction for additional initial points, it is possible to approximate peripheral eigenvalues, localize the spectrum and even obtain spectral enclosures. Hence, as a by-product of our method, a computationally cheap procedure for approximate pseudospectra computations emerges. An advantage of the proposed approach is that it does not make any assumptions on the location of the spectrum. The fact that all computations are performed on some dynamically chosen locations on the complex plane which converge to the eigenvalues, rather than on a large number of predefined points on a rigid grid, can be used to accelerate conventional grid algorithms. Parallel implementation of the method or use in conjunction with randomization techniques can lead to further computational savings when applied to large-scale matrices. Full article

Accurate direction of arrival (DOA) estimation of wideband, low-power nonstationary signals is important in many radio frequency (RF) applications. This article analyses the performance of two incoherent aggregation techniques for the DOA estimation of high chirp-rate linear frequency modulated (LFM) signals used in modern radar and electronic warfare (EW) applications. The aim is to determine suitable aggregation techniques for blind DOA estimation for real-time implementation with a frequency channelised signal. The first technique calculates a single pseudospectrum by directly combining the spatial covariance matrices from each of the frequency bins. The second technique first calculates the spatial pseudospectra from the spatial covariance matrix (SCM) from each frequency bin and then combines the spatial pseudospectra into one single estimate. Firstly, for single and multiple signal emitters, we compare the DOA estimation performance of incoherent SCM-based aggregation with that of the incoherent spatial pseudospectra-based aggregation using the root mean-squared error (RMSE). Secondly, we determine the types of signals and conditions for which these incoherent aggregation techniques are more suited. We demonstrate that the low-complexity SCM-based aggregation technique can achieve relatively good estimation performance compared to the pseudospectra-based aggregation technique for multiple narrowband signal detection. However, pseudospectra aggregation is better suited for single wideband emitter detection. Both the incoherent aggregation techniques presented in this article offer a computational advantage over the coherent processing techniques and hence are better suited for real-time implementation. Full article

Low-frequency multi-source direction-of-arrival (DOA) estimation has been challenging for micro-aperture arrays. Deep learning (DL)-based models have been introduced to this problem. Generally, existing DL-based methods formulate DOA estimation as a multi-label multi-classification problem. However, the accuracy of these methods is limited by the number of grids, and the performance is overly dependent on the training data set. In this paper, we propose an off-grid DL-based DOA estimation. The backbone is based on circularly fully convolutional networks (CFCN), trained by the data set labeled by space-frequency pseudo-spectra, and provides on-grid DOA proposals. Then, the regressor is developed to estimate the precise DOAs according to corresponding proposals and features. In this framework, spatial phase features are extracted by the circular convolution calculation. The improvement in spatial resolution is converted to increasing the dimensionality of features by rotating convolutional networks. This model ensures that the DOA estimations at different sub-bands have the same interpretation ability and effectively reduce network model parameters. The simulation and semi-anechoic chamber experiment results show that CFCN-based DOA is superior to existing methods in terms of generalization ability, resolution, and accuracy. Full article

A new multiple signal classification (MUSIC)-based methodology is presented for detecting and locating multiple damage types in a truss-type structure subjected to dynamic excitations. The methodology is based mainly on two steps: in step 1, the MUSIC method is employed to obtain the pseudo-spectra of vibration signatures, healthy and damaged, to be used for damage detection. In step 2, a new damage index, based on the obtained pseudo-spectra, is proposed to measure the structure condition. Furthermore, the damage location is estimated according to the variation in the amplitudes of the estimated pseudo-spectra. The presented results show that the proposed methodology can make an accurate and reliable estimation of the condition and location of three specific damage conditions, i.e., loosened bolts, internal corrosion, and external corrosion. Full article

High-altitude long-duration (HALE) flight capability is one of the ultimate goals pursued by human aviation technology, and the high-altitude solar-powered aircraft (SPA) is the most promising technical approach to achieve this target as well as wide application prospects. Due to the particularity of the energy system, the flight strategy optimization through the storage of gravity potential energy and other methods is a significant way to enhance the flight and application abilities for the SPA. In this study, a flight strategy optimization model has been proposed for the aim of HALE flight capability, which is based on the gravity energy reserving and mission altitude in practical engineering applications. This integrated model contains the five flight path phase model, the three-dimensional kinematic model, aerodynamic model, solar irradiation model and energy store and loss model. To solve the optimization problem of three-dimensional flight strategy, the Gauss pseudo-spectral Method (GPM) was employed to establish and calculate the optimal target as its advantages in treating process constraints and terminal constraints for the multiphase optimization problem. At last, the flight trajectory optimization with minimal battery mass for Zephyr 7 was studied by the GPOPS with some function files in MATLAB. The results indicate that the Zephyr 7 can reduce the battery mass from 16 kg to 12.61 kg for the day and night cycle flight and missions, which equals to increasing the battery specific energy by 23.1%. Meanwhile, the optimization results also show that the attitude angel may contribute to increasing the energy gained by photovoltaic cells. In addition, this optimized flight strategy brings the possibility of monthly or annual continuous flight for SPA as the simulation date is set to the autumnal day. Full article