Nonlinear Noise Source Research Articles

Marine propeller underwater radiated noise prediction with the FWH acoustic analogy part 3: Assessment of full-scale propeller hydroacoustic performance versus sea trial data

This paper assesses the full-scale The Princess Royal vessel Underwater Radiated Noise (URN) characteristics using a CFD method. Also, the cavitation extensions and propeller hydrodynamic characteristics are explored over a wide range of operating conditions. The numerical calculations were carried out using a hybrid method combining the DES and permeable formulation of the FWH equation. In the numerical calculations, two different permeable noise surfaces encapsulating the complete hull and only the propeller and its slipstream were utilised. In order to accurately solve the tip vortex flow and model the tip vortex cavitation (TVC) in the propeller slipstream, the developed V-AMR technique was applied in the numerical calculations together with the Schnerr-Sauer mass transfer model to model the cavitation. The results were validated with the full-scale measurements in terms of propeller hydrodynamic characteristics, cavitation extension and URN. The results showed that the sheet cavitation extensions predicted in the numerical calculations agreed with the sea trial observations despite the differences in the violent cavitation dynamics. Similarly, TVC was somewhat observed in the numerical calculations using the V-AMR technique with a lack of dynamics and extension in the propeller slipstream compared to the full-scale observations. The comparison of noise spectra at two different operating conditions, where similar cavitations were observed between the numerical calculations and full-scale observations, showed an agreement with the full-scale measurements. The lack of TVC and possible bursting phenomena predicted in the numerical calculations caused the underprediction of propeller URN levels up to 20 dB at certain frequencies over the noise spectrum at the lowest blade loading conditions. When the two different permeable noise surfaces were compared, it can be concluded that the permeable noise surface, encapsulating the complete hull, captures more noise information in the noise spectrum than the permeable surface, encapsulating only the propeller and its slipstream. Also, a more distinct spectral hump triggered by the tip vortex was observed using the permeable noise surface around the complete hull compared to one around the propeller. The results showed that the interaction between the cavitation and nonlinear noise sources occurring around the hull might influence the amplitude of the characteristic hump, apart from the possible hull interference on the ship hull and appendages induced by the propeller.

Numerical investigation into the effects of tip vortex cavitation on propeller underwater radiated noise (URN) using a hybrid CFD method

This study explores the influence of tip vortex cavitation (TVC) on propeller induced URN using a hybrid CFD method. The cavitating flow around the model and full-scale benchmark propeller belong to the Newcastle University's research vessel, The Princess Royal, operating under uniform, inclined and non-uniform flow conditions were solved using DES and mass transfer model. The recently developed advanced mesh refinement (V-AMR) technique was incorporated into the calculations for better modelling tip vortex flow and realising the TVC in the propeller slipstream. This technique enabled the inclusion of the nonlinear noise sources, mainly represented by turbulence and vorticity, including TVC, effectively for the accurate prediction of propeller URN. The numerical calculations were conducted in conditions where only the sheet cavitation was modelled without the V-AMR technique and where the sheet and tip vortex cavitation was modelled together using the V-AMR technique to understand the contribution of TVC to the overall propeller URN. The results were first validated with the available experimental data obtained in the model scale test campaign in the cavitation tunnel and sea-trial data for the propeller's hydrodynamic performance characteristics, cavitation extensions and URN. The results showed that the contribution of TVC to the overall propeller URN was minimal in conditions where the stable and structured TVC was present (i.e., under uniform flow conditions). However, when the propeller was operating under inclined and non-uniform flow conditions where the cavitation dynamics and vortex pulsation were dominant, the unstructured and unstable TVC was observed compared to the observations of TVC under uniform flow conditions. The unstructured TVC created several spikes, which can be associated with its strong cavitation dynamics and possible collapsing/bursting phenomena. These spikes created by the TVC and observed in the time domain acoustic pressure signal consequently contributed to the propeller URN at the different frequency ranges of the noise spectrum and increased the URN levels up to 15 dB under non-uniform flow conditions compared to the propeller URN predictions when only the sheet cavitation was present.

Numerical investigation of marine propeller Underwater Radiated Noise using acoustic analogy part 1: The influence of grid resolution

This study investigates the effects of grid resolution on hydroacoustic performance of the benchmark INSEAN E779A propeller operated in uniform flow, open water and non-cavitating conditions. In the numerical calculations, an incompressible hydrodynamic solver together with the porous FW-H (Ffowcs-Williams Hawkings) equation is used to predict the propeller URN (Underwater Radiated Noise). The first aim within this study is to explore the sensitivity of the grid resolution on the prediction of propeller hydroacoustic performance. Furthermore, amongst the contribution of nonlinear noise sources on overall acoustic pressure, the role of the tip vortex is believed to be dominant under non-cavitating conditions. The inadequate extension of the tip vortex is one of the drawbacks in the RANS (Reynolds-averaged Navier-Stokes) solver for accurate prediction of propeller URN, especially at the receivers located in the propeller's slipstream. Thus, the second aim within this study is to examine the contribution of tip vortex on overall acoustic pressure. In order to visualise the numerical noise and determine the realistic extension of the vortex distributions in the propeller's slipstream, the time derivative of the pressure technique is proposed in this study. The results indicate that insufficient grid resolution in the numerical simulations causes unphysical numerical noise which is attributed to the sliding interfaces, and it leads to contamination of the overall acoustic pressures. Moreover, an increase in grid resolution reduces numerical diffusion in the RANS solver, allowing for an extended tip vortex distribution. However, an increase in tip vortex extension and intensity alongside the downstream of the propeller is not adequate itself to make a reliable prediction of propeller URN by using RANS. Consequently, a more realistic prediction of propeller URN requires the use of advanced models (i.e. LES (Large Eddy Simulation) and DES (Detached Eddy Simulation)) together with the porous FW-H equation, particularly if the receivers located in the downstream are of great interest.

Numerical investigation of marine propeller underwater radiated noise using acoustic analogy Part 2: The influence of eddy viscosity turbulence models

The present study focuses on the impact of eddy viscosity turbulence models on the benchmark INSEAN E779A marine propeller hydroacoustic performance under non-cavitating and open water conditions. In the numerical calculations, Realisable k-epsilon (k-ε), k-ω Shear Stress Transport (k-ω SST) and Spalart-Allmaras turbulence models, which are widely used in hydrodynamic fields, are selected. Hydroacoustic performance of the model propeller is predicted with the porous FW-H formulation coupled with Reynolds-averaged Navier Stokes (RANS) solver. This study aims to show the effects of different turbulence models on marine propeller hydroacoustic performance at high and low blade loading conditions both in the near and far-fields. The numerical results show that the underwater radiated noise (URN) levels, which are predicted by using different eddy viscosity turbulence models together with the porous FW-H formulation, are found to be similar at low blade loading conditions. The reason behind this similarity is due to the analogous wake structure and hydrodynamic field. However, when the propeller loading is high, the propeller's wake loses its stability; hence, the coherent vortex structures break-up and evolve into the far-field of the propeller's slipstream. The instability process of the propeller's wake is predicted in a different manner by eddy viscosity turbulence models, and these differences cause dissimilar prediction of the URN in the far-field. Consequently, the underwater pressure field is considerably affected by the instability of the vortex structures (as a non-linear noise source) for far-field noise estimations. As a result, vortex instability in the propeller's slipstream might be the main noise source of the URN for far-field noise estimations under non-cavitating and high blade loading conditions.

Investigation into the Tip-Gap Flow and Its Influence on Ducted Propeller Tip-Gap Noise Using Acoustic Analogies

Ducted propellers are commonly used on naval vessels such as submarines and increasingly more in omnipresent autonomous underwater vehicles. Understanding the noise signature of these vessels is of critical importance from both detection and concealment perspective, but the detailed physics of how the tip of the propeller blade interacts with the boundary layer on the duct is not sufficiently well understood. The present study introduces a series of simulations in which tip vortices formed over finite-span lifting surfaces are investigated with the aim of better understanding interactions of tip-gap flow and its interaction with incident boundary layers on radiated noise. Particular attention is devoted to characterizing the nature of the incipient complex flow features and their effect on the force coefficients, surface pressure fluctuations. These reveal that variations of force coefficients with tip-gap height may be used as an early indicator of tip vortex being suppressed as the gap is reduced. Use of the λ2 criterion identifies the formation of strong coherent vortical structures in the tip-gap region. It is suggested that the interaction of these structures with the tip edges is likely to be an important source of noise, with a similar generation mechanism to trailing edge noise. Preliminary analysis of the acoustic signatures computed using the Ffowcs Williams-Hawkings acoustic analogy indicates high levels of directivity, with most of the noise being generated by the foil rather than the duct. The presence of substantial amounts of vorticity in the flow also suggests that accounting for the nonlinear quadrupole noise sources within the fluid might be necessary to fully describe the noise pattern developed.

Noise reduction in gravitational-wave data via deep learning

With the advent of gravitational wave astronomy, techniques to extend the reach of gravitational wave detectors are desired. In addition to the stellar-mass black hole and neutron star mergers already detected, many more are below the surface of the noise, available for detection if the noise is reduced enough. Our method (DeepClean) applies machine learning algorithms to gravitational wave detector data and data from on-site sensors monitoring the instrument to reduce the noise in the time-series due to instrumental artifacts and environmental contamination. This framework is generic enough to subtract linear, non-linear, and non-stationary coupling mechanisms. It may also provide handles in learning about the mechanisms which are not currently understood to be limiting detector sensitivities. The robustness of the noise reduction technique in its ability to efficiently remove noise with no unintended effects on gravitational-wave signals is also addressed through software signal injection and parameter estimation of the recovered signal. It is shown that the optimal SNR ratio of the injected signal is enhanced by $\sim 21.6\%$ and the recovered parameters are consistent with the injected set. We present the performance of this algorithm on linear and non-linear noise sources and discuss its impact on astrophysical searches by gravitational wave detectors.

3D Multiple Input Multiple Output Large-Scale Antenna Systems

The channel could be evaluated by utilizing several estimation algorithms. The various patterns of pilot arrangements for the channel appreciation are a huge problem in channel appreciation techniques since all the processes depends on it; this paper discusses improvements in channel selection. The Least Square and Least Square Mean methods are common, simple ways to begin to estimate a channel; however, they are less efficient than more complex approaches. Due to the boost in demand with high data rates in communications, developers continue to invent new methods and mechanisms to adjust the capacity and the accuracy of the communication network. One of the primary troubles in wireless communication is the communication channel, which is affected by nonlinear and random noise sources, which decrease the quality of the service on the network; in this case, the channel must be equalized to increase performance with minimal error. In this paper, a Massive Multiple Input Multiple Output was designed and simulated in order to estimate the channel and the performance of the network through using Least Square and Least Square Mean.

Aerofoil broadband and tonal noise modelling using stochastic sound sources and incorporated large scale fluctuations

The present work discusses modifications to the stochastic Fast Random Particle Mesh (FRPM) method featuring both tonal and broadband noise sources. The technique relies on the combination of incorporated vortex-shedding resolved flow available from Unsteady Reynolds-Averaged Navier-Stokes (URANS) simulation with the fine-scale turbulence FRPM solution generated via the stochastic velocity fluctuations in the context of vortex sound theory. In contrast to the existing literature, our method encompasses a unified treatment for broadband and tonal acoustic noise sources at the source level, thus, accounting for linear source interference as well as possible non-linear source interaction effects. When sound sources are determined, for the sound propagation, Acoustic Perturbation Equations (APE-4) are solved in the time-domain. Results of the method's application for two aerofoil benchmark cases, with both sharp and blunt trailing edges are presented. In each case, the importance of individual linear and non-linear noise sources was investigated. Several new key features related to the unsteady implementation of the method were tested and brought into the equation. Encouraging results have been obtained for benchmark test cases using the new technique which is believed to be potentially applicable to other airframe noise problems where both tonal and broadband parts are important.

Nonlinear secondary noise sources for passive defect detection using ultrasound sensors

This paper introduces the concept of secondary noise sources for passive defect detection and localization in structures. The proposed solution allows for the exploitation of the principle of Green's function reconstruction from noise correlation, even in the absence of an adequate ambient noise. The main principle is to convert a part of low-frequency modal vibrations into high-frequency noise by exploiting the frictional contact nonlinearities. The device consists of a mass-spring resonator coupled to a flexible beam by a rough frictional interface. The extremity of the beam, attached to the surface of a plate, excites efficiently flexural waves in the plate up to 30kHz when the primary resonator vibrates around its natural frequency, i.e. a few dozens Hz. A set of such devices is placed at random positions on the plate surface, and low-frequency excitation is provided by a shaker. The generated high-frequency noise is recorded by an array of eight piezoelectric transducers attached to the plate. A differential correlation matrix is constructed by subtracting correlation functions computed from noise signals at each sensor pairs, before and after the introduction of a local heterogeneity mimicking a defect. A simple array processing then allows for the detection and estimation of the defect location from this differential correlation matrix. Beyond the successful proof of concept, influence of experimental parameters, such as the number of secondary sources or the variability of the position of the shaker application point, is also investigated.

Advanced lithium ion battery modeling and nonlinear analysis based on robust method in frequency domain: Nonlinear characterization and non-parametric modeling

Due to the importance of battery modeling and characterization and lack of an accurate and comprehensive method, which considers battery as a nonlinear model, this paper introduces a novel methodology for analysis in the frequency domain. This methodology looks to the battery from a different point of view and covers aspects of the battery that is often neglected in the previous work and research studies. Using periodic signals for system identification, allows separating noise and nonlinear distortions from the linear part of the system. Meanwhile random phase multisine signals are very popular as an arbitrary number of frequencies can be added together and applied to the battery at once. In addition to a shorter test time in comparison with conventional single sine EIS (electrochemical impedance spectroscopy), by performing extra periods and different phase realizations, transients are eliminated and noise disturbance and also nonlinear distortion is detected, quantified and qualified. Thanks to the statistical and averaging methods, the linear part of the system can be identified and distinguished from nonlinear noise source, which helps to improve model quality and accuracy. Furthermore this method is used for battery characterization and for evaluating the battery performance and its nonlinear behavior at different current rms values as well as at various state of charge levels.

Readout for intersatellite laser interferometry: Measuring low frequency phase fluctuations of high-frequency signals with microradian precision

Precision phase readout of optical beat note signals is one of the core techniques required for intersatellite laser interferometry. Future space based gravitational wave detectors like eLISA require such a readout over a wide range of MHz frequencies, due to orbit induced Doppler shifts, with a precision in the order of μrad/√Hz at frequencies between 0.1 mHz and 1 Hz. In this paper, we present phase readout systems, so-called phasemeters, that are able to achieve such precisions and we discuss various means that have been employed to reduce noise in the analogue circuit domain and during digitisation. We also discuss the influence of some non-linear noise sources in the analogue domain of such phasemeters. And finally, we present the performance that was achieved during testing of the elegant breadboard model of the LISA phasemeter, which was developed in the scope of a European Space Agency technology development activity.

Comprehensive noise characterisation of magnetic tunnel junction sensors for optimising sensor performance and temperature detection

Noise performance of magnetic tunnel junction (MTJ) sensors is impacted by various factors including junction structure, post-deposition treatment, and operating parameters. The optimisation of these factors can lead to a better MTJ sensor design with minimised noise level and enhanced detectivity for functioning as a magnetometer. In this paper, the authors studied the influence of several parameters (bias voltage, temperature, magnetic field, and junction area) on the noise performance of MTJ sensors. Relatively high bias voltage and low ambient temperature were suggested to be helpful in reducing the electronic 1/f noise. A mechanism of utilising MTJ as a temperature sensor by making use of the mid-frequency noise (from 10.0 kHz to 22.8 kHz) was proposed. The relation between temperature and noise power was obtained by numerically fitting the measured noise power with an equation composing of three components representing background noise, intertwined thermal and shot noise, and non-linear noise source, respectively. Temperature of the junction could be determined by measuring the mid-frequency noise power at certain bias voltage and substituting it into the equation. This provides a possible route of using a MTJ as a multifunctional sensor for sensing both magnetic field and temperature.

Advanced phasemeter for deep phase modulation interferometry.

We present the development of an advanced phasemeter for the deep phase modulation interferometry technique. This technique aims for precise length measurements with a high dynamic range using little optical hardware. The advanced phasemeter uses fast ADCs and an FPGA to implement a design of multiple single-bin Fourier transforms running at high sampling rates. Non-linear noise sources in the design were analyzed and suppressed. A null measurement with an optical beatnote signal using λ = 1064nm was conducted. It showed a sensitivity of 0.8μrad/√Hz below 10Hz and 13.3μrad/√Hz above, with a large dynamic range. The shown performance could enable the measuring of optical path lengths with sensitivities down to 0.14pm/√Hz and 2.3pm/√Hz, respectively, over several fringes in an interferometric setup.

Ship underwater noise assessment by the acoustic analogy. Part I: nonlinear analysis of a marine propeller in a uniform flow

The aim of this work is to analyze the hydroacoustic behavior of a marine propeller through the acoustic analogy and to test the versatility and effectiveness of this approach in dealing with the many (and relatively unexplored) issues concerning the underwater noise and its numerical prediction. In particular, a propeller in a noncavitating open water condition is examined here by coupling a Reynolds averaged Navier–Stokes hydrodynamic solver to a hydroacoustic code implementing different resolution forms of the Ffowcs Williams–Hawkings (FWH) equation. The numerical results suggest that unlike the analogous aeronautical problem, where the role played by the nonlinear quadrupole sources is known to be relevant just at high transonic or supersonic regime, the pressure field underwater seems to be significantly affected by the flow nonlinearities, while the contribution from the linear terms (the thickness and loading noise components) is dominant only in a spatially very limited region. Then, contrary to popular belief and regardless of the low blade rotational speed, a reliable hydroacoustic analysis of a marine propeller cannot put aside the contribution of the nonlinear noise sources represented by the turbulence and vorticity three-dimensional fields and requires the computation of the FWH quadrupole source terms.

On Acoustic Radiation by Rotating Body Sources in Frequency Domain

For the complexity of the sound generated mechanism of rotating body source, this paper describes a frequency-domain numerical method for predicting sound radiation of rotating body sources based on the Kirchhoff integral equation with analytical Green's function of rotating monopole and dipole source in free space. The sound radiation model is established in free space and the relationship between characteristics of sound field and acoustic nature frequency of source, angular frequency and its harmonics can be revealed by the mathematical solution. Numerical simulation shows that sound field has a strong directivity, fundamental frequency transmitting in the rotary shaft direction and harmonics spreading along radial direction and frequency shift phenomena appearing clearly in higher rotating speed of source. The method has a theoretical significance for exploring the low-noise rotating machinery. Research about sound radiation of moving source originates from Lighthill. The first integral approach for acoustic propagation is the acoustic analogy. In the acoustic analogy, the governing Navier-Stokes equations are rearranged to be in wave-type form. There is some question as to which terms should be identified as part of the sound source and retained in the right-hand side of the equation and which terms should be in the left-hand side as part of the operator. The far-field sound pressure is then given in terms of a volume integral over the domain containing the sound source. However the major difficulty with the acoustic analogy is that the sound source is not compact in supersonic flows. Several modifications to Lighthill's original theory have been proposed to account for the moving sound source or other effects. The Ffowcs Williams and Hawkings (FW-H) equation was introduced to extend acoustic analogy in the case of solid surfaces. However, when acoustic sources are present in the flowfield a volume integration is needed. This volume integration of the quadrupole source term is difficult to compute and is usually neglected in most acoustic analogy codes. Errors could be encountered in calculating the sound field. Another alternative is the Kirchhoff method which assumes that the sound transmission is governed by the simple wave equation. Kirchhoff's method consists of the calculation of the nonlinear near- and mid-field, usually numerically, with the far-field solutions found from a linear Kirchhoff formulation evaluated on a control surface surrounding the nonlinear-field. The control surface is assumed to enclose all the nonlinear flow effects and noise sources. The sound pressure can be obtained in terms of a surface integral of the surface pressure and its normal and time derivatives. This approach has the potential to overcome some of the difficulties associated with the traditional acoustic analogy approach. The method is simple and accurate and accounts for the nonlinear quadrupole noise in the far-field. Full diffraction and focusing effects are included while eliminating the propagation of the reactive near-field. Kirchhoff's formula, published in 1882, is used in the theory of diffraction of light and in other electromaqnetic problems. It also has many applications to problems of wave in acoustics. One of the novel uses of this formula was proposed by Hawkinqs for predicting

Upper Bounding Variations of Best Linear Approximations of Nonlinear Systems in Power Sweep Measurements

In many engineering applications, linear models are preferred, even if it is known that the system is nonlinear. A large class of nonlinear systems can be represented as Y = G BLA U + YS, with G BLA being the best linear approximation and YS being a nonlinear noise source that represents that part of the output that is not captured by the linear approximation. Because G BLA not only depends upon the linear dynamics but also on the nonlinear distortions, it will vary if the input power is changed. In this paper, we study under what conditions (class of excitations and class of nonlinear systems) these variations of G BLA can be bounded, starting from the knowledge of the power spectrum SYS. In general, without a restriction of the class of systems, no upper bound can be given. However, for some important classes of systems, the variations can be bounded by selecting a well-defined criterion. Since SYS can easily be measured using well-designed measurement procedures, it becomes possible to provide the designer with an upper bound for the variations of G BLA, leading to more robust design procedures.

Robustness Issues of the Best Linear Approximation of a Nonlinear System

In many engineering applications, linear models are preferred, even if it is known that the system is disturbed by nonlinear distortions. A large class of nonlinear systems, which are excited with a ldquoGaussianrdquo random excitation, can be represented as a linear system G BLA plus a nonlinear noise source Y S . The nonlinear noise source represents that part of the output that is not captured by the linear approximation. In this paper, it is shown that the best linear approximation G BLA and the power spectrum S Y S of the nonlinear noise source Y S are invariants for a wide class of excitations with a user-specified power spectrum. This shows that the alternative ldquolinear representationrdquo of a nonlinear system is robust, making its use in the daily engineering practice very attractive. This result also opens perspectives to a new generation of dynamic system analyzers that also provide information on the nonlinear behavior of the tested system without increasing the measurement time.

Application of RANS modelling and LES to the prediction of noise from a simple cold propane jet

Numerical simulation, combining computational fluid dynamic and acoustic models, is useful as an aeroacoustic tool that is effective in identifying components or surfaces that generate significant amounts of noise, and can thereby provide opportunities for early design changes. In this work, numerical solutions of a cold turbulent jet of propane issuing from a circular nozzle are used to provide velocity information at a Reynolds number of 68,000. Predictions provided by large eddy simulation are compared with Reynolds‐averaged Navier‐Stokes solutions derived using a second‐moment turbulence closure, as well as with experimental data available in the literature. Reasonable agreement with data is found, and these solutions are used subsequently as the basis for noise predictions. The first acoustic model employed is based on Lighthill's theory using the Goldstein broadband noise source formalisation that postulates axisymmetric turbulence superposed on the mean flow. The second approach is based on Ffowcs‐Williams and Hawkings theory which implies that the far field sound is computed from an integral formulation with all quantities evaluated on a control surface, with the control surface itself assumed to enclose all nonlinear flow effects and noise sources. The simulation results reported in this paper confirm previous experimental works presented in the literature demonstrating that jet noise is modified by inlet conditions.

Linear Approximation of Weakly Nonlinear MIMO Systems

A nonlinear multiple-input-multiple-output (MIMO) Volterra system, measured with random multisine signals, can be replaced by an approximating linear MIMO system followed by nonlinear-noise sources. This approximation is a straightforward extension of the approximation to single-input-single-output Volterra systems. For a two-input-two-output cubic system, an optimized measurement strategy is also proposed to reduce as much as possible the influence of nonlinear noise on the measurement of the nonparametric frequency-response function

Initial estimates for the dynamics of a Hammerstein system

This paper studies the generation of initial estimates for the dynamic part of a Hammerstein model. It will be shown that ARMAX or Box–Jenkins models result in better initial estimates than ARX or output-error (OE) models even in the absence of disturbing noise. This will be proven by noticing that a static nonlinear system can be replaced by a static gain plus a nonlinear noise source that acts in a completely similar way to disturbing noise for the study of the second-order properties of the estimators in the prediction error framework.