Local Transfer Function Research Articles

Neural Network Layer Algebra: A Framework to Measure Capacity and Compression in Deep Learning.

We present a new framework to measure the intrinsic properties of (deep) neural networks. While we focus on convolutional networks, our framework can be extrapolated to any network architecture. In particular, we evaluate two network properties, namely, capacity, which is related to expressivity, and compression, which is related to learnability. Both these properties depend only on the network structure and are independent of the network parameters. To this end, we propose two metrics: the first one, called layer complexity, captures the architectural complexity of any network layer; and, the second one, called layer intrinsic power, encodes how data are compressed along the network. The metrics are based on the concept of layer algebra, which is also introduced in this article. This concept is based on the idea that the global properties depend on the network topology, and the leaf nodes of any neural network can be approximated using local transfer functions, thereby allowing a simple computation of the global metrics. We show that our global complexity metric can be calculated and represented more conveniently than the widely used Vapnik-Chervonenkis (VC) dimension. We also compare the properties of various state-of-the-art architectures using our metrics and use the properties to analyze their accuracy on benchmark image classification datasets.

On the spatial characteristics of the flame transfer function for a GCH4-GO2 swirl coaxial flame

In this study, the combustion instability characteristics of gaseous methane–gaseous oxygen atmospheric flame were investigated. A swirl coaxial injector was used under external modulation with a central methane flow and a loudspeaker. The flame transfer function with a photomultiplier tube was examined for possible errors, and an injector transfer function was defined to study the influence of the input perturbation on the cold gas flow without combustion. Both the results of flame transfer function and injector transfer function were affected by acoustic resonance. However, a higher mode of resonance did not appear in the flame transfer function. To analyze this difference, the flame movement was visualized using a high-speed camera by capturing the OH* chemiluminescence signal. Furthermore, a local flame transfer function was defined to examine the flame response zone-by-zone through a light signal. A higher-mode reaction appeared again in the local flame transfer function. It was found that flame separation due to modulation was the cause of the difference among the flame transfer function, injector transfer function, and local flame transfer function. By capturing the entire flame, its periodicity could be lost; hence, the local flame transfer function could prevent misinterpretation of the flame fluctuation.

Learning an optimised stable Taylor-Galerkin convection scheme based on a local spectral model for the numerical error dynamics

We present a new spectral framework to design and optimise numerical methods for convection problems termed Local Transfer function Analysis (LTA), which improves the state-of-art model for error dynamics due to numerical discretisation. LTA converts the numerical discretisation into a network of transfer function blocks in the spectral space, where optimisation of the solution error becomes an impedance matching problem. In addition, a machine learning model based on the graph neural network is employed to learn the optimal coefficients of the transfer function leading to the matched impedance by examining both the local physical field and the local mesh topology. We demonstrate applications of this technique to design Taylor-Galerkin finite element numerical schemes for solving linear convection on irregular meshes in 1D. Using the LTA, we identify and constrain the neural network predictions to the numerically stable design space, thus improving the stability and generalisation of the optimal parameters that lead to a matched impedance.

Calculation of Deformation-Related Quantities in a Hot-Rolling Process

The hot deformation of metal as a nonlinear system is mathematically described by a local linear model associated with the working conditions using a transfer function (TF) in the Laplace domain. Experimental data (true stress vs. true strain curves) are obtained using the established compressive uniaxial deformation test, where experimental conditions (strain rate and temperature) define the working conditions of the local linear TF model, which is intrinsically a function of strain. Based on the TF model, three important physical quantities of the tested metal are determined exactly: the work done per unit deformation, the average flow stress, and the flow-stress derivative with respect to the strain based on a particular TF. The exactly determined quantities, determined as a function of strain, can replace the previously used approximations in some rolling force and torque calculations.

Signal selection for local module identification in linear dynamic networks: A graphical approach

In a dynamic network of interconnected transfer functions, it is not necessary to use all the node signals for estimating a local transfer function. Given the network topology, detailed conditions are available for selecting inputs and outputs in a (MIMO) predictor model that warrants consistent and minimum variance estimation of a target module through the so-called local direct method. Motivated by the existing minimum-input signal selection approach that gradually incorporates additional signals, an alternative graphical algorithm for signal selection is developed in this work by directly exploiting the complete network graph. Then, as a straightforward application of existing analytical results, graphical conditions for consistent identification are derived for the novel signal selection approach. We show by an example that in some cases, for the consistent estimation of the target module, the developed method leads to fewer selected signals than the original minimum-input method.

LTF-NSI: a novel local transfer function based on neighborhood similarity index for medical image enhancement

Medical image is an essential tool used in quantitative and qualitative evaluation of different diseases. Medical imaging methods such as fluorescein angiography (FA), optical coherence tomography angiography (OCTA), computed tomography (CT), optical coherence tomography (OCT), and X-ray are used for diagnosis. These imaging modalities suffer from low contrast, which leads to deterioration in the image quality. Consequently, this causes limitation in the usage of medical images in clinical routine and hindered its potential by depriving clinicians from assessing useful information that are needed in disease monitoring, treatment, progression, and decision-making. To overcome this limitation, we propose a novel local transfer function for medical image enhancement algorithm using the pixel neighborhood constraint. The proposed algorithm uses block-wise intensity distribution to generate the regional similarity index. The regional similarity index transformed each centered pixel in the block, to generate a new similarity image. An intuitive optimization algorithm is utilized to optimize the proposed algorithm parameters. Experimentation results show that the proposed LTF-NSI performs better than the state-of-the-art methods and improves the interpretability and perception of the medical images, which can provide clinicians and computer vision program with good quantitative and qualitative information.

Data-driven local average room transfer function estimation for multi-point equalization.

Multi-point room equalization (EQ) aims to achieve a desired sound quality within a wider listening area than single-point EQ. However, multi-point EQ necessitates the measurement of multiple room impulse responses at a listener position, which may be a laborious task for an end-user. This article presents a data-driven method that estimates a spatially averaged room transfer function (RTF) from a single-point RTF in the low-frequency region. A deep neural network (DNN) is trained using only simulated RTFs and tested with both simulated and measured RTFs. It is demonstrated that the DNN learns a spatial smoothing operation: notches across the spectrum are smoothed out while the peaks of the single-point RTF are preserved. An EQ framework based on a finite impulse response filter is used to evaluate the room EQ performance. The results show that while not fully reaching the level of multi-point EQ performance, the proposed data-driven local average RTF estimation method generally brings improvement over single-point EQ.

Derivation of a near-surface damping model for the Groningen gas field

SUMMARY Seismic damping of near-surface deposits is an important input to site-response analysis for seismic hazard assessment. In Groningen, the Netherlands, gas production from a reservoir at 3 km depth causes seismicity. Above the gas field, an 800 m thick layer of unconsolidated sediments exist, which consists of a mixture of sand, gravel, clay and peat strata. Shear waves induced at 3 km depth experience most of their anelastic attenuation in these loose sediments. A good estimate of damping is therefore crucial for modelling realistic ground-motion levels. In Groningen, we take advantage of a large network of 200 m deep vertical arrays to estimate damping from recordings of the induced events. As a first step, we apply seismic interferometry by deconvolution to estimate local transfer functions over these vertical arrays. Subsequently, two different methods are employed. The first is the ‘upgoing’ method, where the amplitude decay of the retrieved upgoing wave is used. The second is the ‘up-down’ method, where the amplitude difference between retrieved up- and downgoing waves is utilized. For the upgoing method, the amplitude of the upgoing direct wave is affected by both elastic and anelastic effects. In order to estimate the anelastic attenuation, it is necessary to remove the elastic amplification first. Despite the fact that elastic compensation could be determined quite accurately, non-physical damping values were estimated for a number of boreholes. Likely, the underlying cause was small differences in effective response functions of geophones at different depths. It was found that the up-down method is more robust. With this method, elastic propagation corrections are not needed. In addition, small differences in in situ geophone response are irrelevant because the up- and downgoing waves retrieved at the same geophone are used. For the 1-D case, we showed that for estimating the local transfer function, the complex reverberations need to be included in the interferometric process. Only when this is done, the transfer function does not contain elastic transmission loss and Q estimation can be made without knowing the soil profile in detail. Uncertainty in the estimated damping was found from the signal-to-noise ratio of the estimated transfer function. The Q profiles estimated with the up-down method were used to derive a damping model for the top 200 m of the entire Groningen field. A scaling relation was derived by comparing estimated Q profiles with low-strain damping profiles that were constructed using published models for low-strain damping linked to soil properties. This scaling relation, together with the soil-property-based damping model, allowed up-scaling of the model to each grid-cell in the Groningen field. For depths below 200 m, damping was derived from the attenuation of the microseism over Groningen. The mean damping model, over a frequency band between 2 and 20 Hz, was estimated to be 2.0 per cent (0–50 m depth), 1.3 per cent (50–100 m), 0.66 per cent (100–150 m), 0.57 per cent (150–200 m) and 0.5 per cent (200–580 m).

Robust probability model based on variational Bayes for point set registration

Point set registration is widely used in various fields, but because the current registration algorithms suffer from the complexities of point set distributions, it has become a challenging problem. To solve this problem, we propose a probabilistic model based on variational Bayes. Specifically, we propose to build an asymmetric generalized Gaussian mixture probability model to evaluate the correspondence between point sets and eliminate outliers, by controlling the mixing ratio of the corresponding points to deal with the missing correspondence and using intermediate variable to simulate the transition from the model point set to the target point set. We propose a local variation to speed up the accurate update of the parameters to obtain a more compact lower bound of the change. In addition, a global–local strategy constraint transfer function is proposed, and coarse-to-fine registration is achieved by simulating the degradation scheme. Experimental results show that our method has the best robustness compared with the state-of-the-art registration algorithms.

Interaction of equivalence ratio fluctuations and flow fluctuations in acoustically forced swirl flames

The generation and turbulent transport of temporal equivalence ratio fluctuations in a swirl combustor are experimentally investigated and compared to a one-dimensional transport model. These fluctuations are generated by acoustic perturbations at the fuel injector and play a crucial role in the feedback loop leading to thermoacoustic instabilities. The focus of this investigation lies on the interplay between fuel fluctuations and coherent vortical structures that are both affected by the acoustic forcing. To this end, optical diagnostics are applied inside the mixing duct and in the combustion chamber, housing a turbulent swirl flame. The flame was acoustically perturbed to obtain phase-averaged spatially resolved flow and equivalence ratio fluctuations, which allow the determination of flux-based local and global mixing transfer functions. Measurements show that the mode-conversion model that predicts the generation of equivalence ratio fluctuations at the injector holds for linear acoustic forcing amplitudes, but it fails for non-linear amplitudes. The global (radially integrated) transport of fuel fluctuations from the injector to the flame is reasonably well approximated by a one-dimensional transport model with an effective diffusivity that accounts for turbulent diffusion and dispersion. This approach however, fails to recover critical details of the mixing transfer function, which is caused by non-local interaction of flow and fuel fluctuations. This effect becomes even more pronounced for non-linear forcing amplitudes where strong coherent fluctuations induce a non-trivial frequency dependence of the mixing process. The mechanisms resolved in this study suggest that non-local interference of fuel fluctuations and coherent flow fluctuations is significant for the transport of global equivalence ratio fluctuations at linear acoustic amplitudes and crucial for non-linear amplitudes. To improve future predictions and facilitate a satisfactory modelling, a non-local, two-dimensional approach is necessary.

A New Recurrent Radial Basis Function Network-based Model Predictive Control for a Power Plant Boiler Temperature Control

In this paper, a new radial basis function network-based model predictive control (RBFN-MPC) is presented to control the steam temperature of a power plant boiler. For the first time in this paper the Laguerre polynomials are used to obtain local boiler models based on different load modes. Recursive least square (RLS) method is used as observer of the Laguerre polynomials coefficient. Then a new locally recurrent radial basis function neural network with self-organizing mechanism is used to model these local transfer function and it used to estimate the boiler future behavior. The recurrent RBFN tracks system is dynamic online and updates the model. In this recurrent RBFN, the output of hidden layer nodes at the past moment is used in modelling, So the boiler model behaves exactly like a real boiler. Various uncertainties have been added to the boiler and these uncertainties are immediately recognized by the recurrent RBFN. In the simulation, the proposed method has been compared with traditional MPC (based on boiler mathematical model). Simulation results showed that the recurrent RBFN-based MPC perform better than mathematical model-based MPC. This is due to the neural network's online tracking of boiler dynamics, while in the traditional way the model is always constant. As the amount of uncertainty increases, the difference between our proposed method and existing methods can clearly be observed.

Rough Set Approach toward Data Modelling and User Knowledge for Extracting Insights

Information is considered to be the major part of an organization. With the enhancement of technology, the knowledge level is increasing with the passage of time. This increase of information is in volume, velocity, and variety. Extracting meaningful insights is the dire need of an individual from such information and knowledge. Visualization is a key tool and has become one of the most significant platforms for interpreting, extracting, and communicating information. The current study is an endeavour toward data modelling and user knowledge by using a rough set approach for extracting meaningful insights. The technique has used different rough set algorithms such as K-nearest neighbours (KNN), decision rules (DR), decomposition tree (DT), and local transfer function classifier (LTF-C) for an experimental setup. The approach has found its accuracy for the optimal use of data modelling and user knowledge. The experimental setup of the proposed method is validated by using the dataset available in the UCI web repository. Results of the proposed study show that the model is effective and efficient with an accuracy of 96% for KNN, 87% for decision rules, 91% for decision trees, 85.04% for cross validation architecture, and 94.3% for local transfer function classifier. The validity of the proposed classification algorithms is tested using different performance metrics such as F-score, precision, accuracy, recall, specificity, and misclassification rates. For all these performance metrics, the KNN classifier outperformed, and this high performance shows the applicability of the KNN classifier in the proposed problem.

A multiple-model based internal model control method for power control of small pressurized water reactors

Small pressurized water reactors (PWRs) usually have variable operating conditions and complex operating environments. It is significant to design a robust control system to ensure stable and satisfactory reactor power maneuvers under large uncertainties. This paper purposes a multiple-model based internal model control (IMC) method for power control of small PWRs. Six local transfer function models are first developed from a nonlinear reactor core model over the entire operating range. Then, six local power controllers are designed for a small PWR based on these local models using the IMC scheme. The IMC filter time constant is determined by the genetic algorithm based multi-objective optimization to keep good balance between the control performance and cost. The local controllers are connected by a probability-weighted multiple model approach to generate a global IMC system for the reactor. Dynamic simulation results of the small PWR under the IMC scheme as well as performance assessments of the IMC scheme against the PID control scheme during typical transient operations have shown good reference tracking performances and strong disturbance rejection capabilities of the multiple-model based IMC system, demonstrating the feasibility and effectiveness of the proposed method for the power control of small PWRs.

Heat-release dynamics in a doubly-transcritical LO2/LCH4 cryogenic coaxial jet flame subjected to fuel inflow acoustic modulation

Large Eddy Simulations are used to study the heat-release response to fuel inflow acoustic harmonic oscillations, in a coaxial jet flame where both reactants (O2 and CH4) are injected in a dense cryogenic state. The geometry is that of the academic test rig Mascotte, operated by ONERA (France), which high pressure operating conditions are relevant for the characterization of flame dynamics in Liquid Rocket Engines (LREs). The simulations, which are carried out with a real-gas fluid solver using a detailed kinetic scheme for CH4 high-pressure oxycombustion, provide a thorough insight into the flame response for a wide range of forcing frequencies, spanning from approximately 1kHz to 20kHz. Local Flame Transfer Functions (FTF) are computed and analyzed: regions of preferential heat-release response are observed to be highly dependent on the forcing frequency. An analysis based on a flame sheet assumption is conducted to distinguish the main sources of heat release fluctuations: the primary contribution comes from the species diffusivity oscillations, while the density variations have a negligible effect. The second largest contributor is either the mixture fraction gradient or the flame surface area, depending on the forcing frequency. The FTFs are expected to be useful for thermoacoustic Low-Order Models or Helmholtz solvers, and the subsequent analysis has the potential to guide future development of analytical models for flame dynamics in LREs.

Numerical investigation on combustion instability modeling in a lean premixed gas turbine combustor combining finite element analysis with local flame transfer function

The present work suggests a numerical approach using an FEM (finite element method) code for the eigenvalue calculation of the thermoacoustic combustion instabilities coupling with the local flame transfer function in a generic lean premixed combustor. The URANS (unsteady Reynolds average Navier-Stokes) simulation shows a good agreement in capturing steady and unsteady flame geometries with the measurement in the literature. Also, global and local parameters of flame responses to acoustic velocity fluctuations undergo quantitatively similar changes in prediction and in the experiment. The numerically determined flame transfer function and gas properties are incorporated in an in-house Helmholtz solver to compute eigenvalues of the target combustor. In the solver, the Helmholtz equation is discretized with a Galerkin FEM on a multi-dimensional hybrid unstructured mesh. The nonlinearity related with the heat release source term is treated with an iterative methodology, and the large scale eigenvalue calculation is performed using the shift-invert approach available in the ARPACK (ARnoldi PACKage) library. The predictive capabilities of the current modeling approach are validated against the measured mode frequency and instability growth rate. In addition, the prediction results show the effect of spatially-distributed heat release on the thermoacoustic model accuracy.

Analysis of the Dynamics of Premixed Methane and Biogas Flames Based on Cross-correlation Maps

ABSTRACT In this study, the cross-correlation method (CCM) has been investigated in detail and applied to analyze the dynamic response of premixed methane and biogas flames. CCM mapping was proposed in a recent study as an effective, and notably simple, method to evaluate the actual contribution of different flame zones to its global dynamic response. The physical interpretation of cross-correlation maps has been further investigated and validated by means of spatially resolved measurements of the local flame transfer function along the flame. The results obtained are consistent with vortex shedding being the phenomenon governing the dynamics of the flames studied. Methane and biogas flames exhibited different response to fluctuations. The analysis of cross-correlation maps revealed changes in the location of regions with strongest response to velocity fluctuations. Furthermore, this method was applied to determine the variations in the convective length associated with the phase delay between the oscillations in velocity and in heat release rate. In spite of the broad differences among the flames studied, all of them were consistent with the perturbations traveling along the flame at approximately one half of the flow velocity, in coincidence with the findings of some recent works.

Dynamics identification and control of nonlinear MIMO coupled plant using supervised neural gas and comparison with recurrent neural controller

The dynamics identification and subsequent control of a nonlinear system is not a trivial issue. The application of a neural gas network that is trained with a supervised batch version of the algorithm can produce identification models in a robust way. In this paper, the neural model identifies each local transfer function, demonstrating that the local linear approximation can be done. Moreover, other parameters are analyzed in order to obtain a correct modeling. Furthermore, the algorithm is applied to control a nonlinear multi-input multi-output system composed of tanks. In addition, this plant is a coupled system where the manipulated input variables are influencing all the output variables. The aim of the work is to demonstrate that the supervised neural gas algorithm is able to obtain linear models to be used in a state space design scenario to control nonlinear coupled systems and guarantee a robust control method. The results are compared with the common approach of using a recurrent neural controller trained with a dynamic backpropagation algorithm. Regarding the steady-state errors in disturbance rejection, reference tracking and sensitivity to simple process changes, the proposed approach shows an interesting application to control nonlinear plants.

Interactive geological visualization based on quadratic-surface distance query

Seismic data visualization and analysis can help the domain experts, e.g., geologists and oil or gas exploration experts, to explore the distribution of petroleum or gas. It assists them to get a better understanding of stratigraphic structures and the distribution of the geological materials, e.g., underground flow path (UFP) and the contexts of UFPs (river delta, floodplain, slump fan, oil well, etc.). UFPs are one of the significant stratigraphic structures according to the domain experts, because they are closely related to the distribution and the migration of oil or gas. We design a quadratic-surface distance query scheme to explore UFPs and their contexts within a local region. First, it just needs to share parameters of quadratic surfaces to the rendering modules instead of all volume data or all subvolume data to conduct distance queries, and it is flexible to perform multiple complex logic operations through the quadratic surface-based queries. Second, it enables one to perform domain-specific interactions after distance queries such as the flexible switching of multiple display modes. Third, it enables one to perform local transfer function on different subvolumes different query results or their arbitrary combinations. We have evaluated the approach by comparing them with existing methods by performance evaluation and result evaluation. Results show that the proposed approach is capable of performing complex distance queries and fulfilling the domain-specific interactions getting better results and timing performance.

A programmable metasurface for real time control of broadband elastic rays

Real-time engineering of elastic rays in solid materials is crucial for several applications relevant to active noise and vibration cancellation and to inverse methods aiming to either reveal or dissimulate the presence of foreign bodies. Here, we introduce a programmable elastic metasurface for the first time with sensing-and-actuating units, allowing to adapt and reprogram its wave control functionalities in real time. The active units behave following decoupled ‘feedforward’ sensor-to-actuator control loops governed by local transfer functions encoded into a digital circuit and offering highly flexible phase and amplitude engineering of transmitted and/or scattered waves. The proposed metasurface is concretized numerically and experimentally by achieving, for the first time, real-time tunable ray steering of flexural waves in a host plate. Various other significant demonstrations have been included to strongly illustrate the multifunctional adaptability of the design. In particular, one-way non-reciprocal blocking of waves is observed experimentally whereas skin cloaking of voids is tested numerically. Finally, operability across broad wave frequency ranges is demonstrated (5–45 kHz). The design will pave a new efficient way in the field of sensing and actuation of elastic waves.

Precise Analytical Model of Power Supply Induced Jitter Transfer Function at Inverter Chains

Precise analytical models of power supply noise induced jitter (PSIJ) at inverter chains are proposed. Based on the piecewise linear approximated I–V curve model, analytical models of local PSIJ transfer functions at local rising and falling edges are derived. The total PSIJ transfer function of an inverter chain output is then estimated by alternately accumulating the local PSIJ transfer function at local rising and falling edges. Based on several assumptions, the full PSIJ transfer function model is significantly simplified, which provides physical insights of PSIJ at inverter chains. Accuracy of the proposed analytical model is successfully validated by SPICE simulations with 130 nm CMOS technology. In addition, properties of the PSIJ transfer function at inverter chains are analyzed based on the proposed model.