Amplitudes of characteristic waves and non-reflecting outflow conditions for high-fidelity numerical simulations

Non-reflecting boundary conditions are crucial for aeroacoustic simulations to prevent non-physical reflections at boundaries from contaminating the interior acoustic solutions. Various non-reflecting outflow conditions, mainly based on the characteristic theory, have been developed. By using a locally one-dimensional inviscid approximation, the characteristic wave amplitudes are identified as the projection of flow solutions into the eigenspace of the flux Jacobian matrix. When the weighted transverse terms are included, the definitions are essentially changed and produce different levels of non-physical reflections. This study aims to resolve the ambiguity in defining the amplitudes of characteristic waves. A new analysis in the frequency and wave number domain is proposed to identify the characteristic wave amplitudes in multidimensional space, and a second order in terms of the lateral wave number non-reflecting outflow condition that is more physically reasonable is derived. Numerical experiments are carried out to evaluate the performances of these non-reflecting conditions.

Dynamic characteristics of infinite-length and finite-length rods with high-wave-number periodic parameters

The dynamic characteristics of the infinite-length and finite-length rods with periodic distribution parameters are studied. The differential equation of longitudinal motion of the period-parametric rod is given. The algebraic matrix equation for the wave motion characteristics of the infinite-length periodic rod is derived based on the Bloch theorem and Fourier series. The characteristic frequencies are determined by the matrix eigenvalues which depend on the characteristic wave number and parametric wave number. Then the algebraic matrix equation for the dynamic characteristics of the finite-length periodic rod is derived based on the Galerkin method. The natural frequencies are determined by the matrix eigenvalues which depend on only the parametric wave number. An improving approach algorithm for solving the eigenvalue problem of high degree-of-freedom systems is developed based on the Rayleigh quotient. Finally, the circular cross-section rod with period-varying diameter is considered and numerical results on the dynamic characteristics are given. Large characteristic wave number and parametric wave number are considered for the infinite-length and finite-length periodic rods. The characteristic frequencies varying with the characteristic wave number and parametric wave number are shown, and the band gaps vanishing are revealed for increasing characteristic wave number. The finite-length periodic rod has the dynamic characteristics different from the infinite-length periodic rod. The effect of the term number of the displacement expansion on the natural frequencies and the natural frequencies varying with the parametric wave number and wave amplitude are shown for the finite-length periodic rod. The local resonance and periodical short descent of the natural frequencies with the increase of the parametric wave number and the different changes of the natural frequencies with the parametric wave amplitude are revealed. The above new dynamic characteristics of the infinite-length and finite-length rods with periodic distribution parameters have a potential application to period-structural design and optimization.

Application of Permutation Entropy in Feature Extraction for Near-Infrared Spectroscopy Noninvasive Blood Glucose Detection

Diabetes has been one of the four major diseases threatening human life. Accurate blood glucose detection became an important part in controlling the state of diabetes patients. Excellent linear correlation existed between blood glucose concentration and near-infrared spectral absorption. A new feature extraction method based on permutation entropy is proposed to solve the noise and information redundancy in near-infrared spectral noninvasive blood glucose measurement, which affects the accuracy of the calibration model. With the near-infrared spectral data of glucose solution as the research object, the concepts of approximate entropy, sample entropy, fuzzy entropy, and permutation entropy are introduced. The spectra are then segmented, and the characteristic wave bands with abundant glucose information are selected in terms of permutation entropy, fractal dimension, and mutual information. Finally, the support vector regression and partial least square regression are used to establish the mathematical model between the characteristic spectral data and glucose concentration, and the results are compared with conventional feature extraction methods. Results show that the proposed new method can extract useful information from near-infrared spectra, effectively solve the problem of characteristic wave band extraction, and improve the analytical accuracy of spectral and model stability.