Nonlinear Transformation Model Research Articles

Predicting Effluent Quality in Full-Scale Wastewater Treatment Plants Using Shallow and Deep Artificial Neural Networks

This research focuses on applying artificial neural networks with nonlinear transformation (ANNs) models to predict the performance of wastewater treatment plant (WWTP) processes. The paper presents a novel machine learning (ML)-based approach for predicting effluent quality in WWTPs through explaining the relationships between the multiple influent and effluent pollution variables of an existing WWTP. We developed AI models such as feed-forward neural network (FFNN) and random forest (RF) as well as deep learning methods such as convolutional neural network (CNN), recurrent neural network (RNN), and pre-train stacked auto-encoder (SAE) in order to avoid various shortcomings of conventional mechanistic models. The developed models focus on providing an adaptive, functional, and alternative methodology for modeling the performance of the WWTP. They are based on pollution data collected over three years. It includes chemical oxygen demand (COD), biochemical oxygen demand (BOD5), phosphates (PO₄−3), and nitrates (NO₃−), as well as auxiliary indicators including the temperature (T), degree of acidity or alkalinity (pH), electric conductivity (EC), and the total dissolved solids (TDS). The paper presents the results of using SNN- and DNN-based models to predict the effluent concentrations. Our results show that SNN can predict plant performance with a correlation coefficient (R) up to 88%, 90%, 93%, and 96% for the single models COD, BOD5, NO₃−, and PO₄−3, respectively, and up to 88%, 96%, and 93% for the ensemble models (BOD5 and COD), (PO₄−3 and NO₃−), and (COD, BOD5, NO₃−, PO₄−3), respectively. The results also show that the two-hidden-layers model outperforms the one-hidden-layer model (SNN). Moreover, increasing the input parameters improves the performance of models with one and two hidden layers. We applied DNN (CNN, RNN, SAE) with three, four, and five hidden layers for WWTP modeling, but due to the small datasets, it gave a low performance and accuracy. In sum, this paper shows that SNN (one and two hidden layers) and the random forest (RF) machine learning technique provide effective modeling of the WWTP process and could be used in the WWTP management.

Accurate Current Drive Modeling on EAST

A nonlinear transformer model is used for describing the tokamak discharge with fraction of noninductive current. The nonlinear model accurately identifies the tokamak as a toroidal transformer by a voltage balance equation. In order to verify the feasibility of the application of the nonlinear model in the experimental advanced superconducting tokamak (EAST), the voltage balance equation is checked for the different scenarios and applied to calculate and analyze the noninductive current in shots #73999 and #66740, respectively. Calculation results indicate that the #73999 shot H-mode plasma discharge is full noninductive current drive and occupies approximately 99% of plasma current. It is a good agreement with the simulation result (98%) by the integrated modeling under the framework OMFIT with equilibrium code EAST equilibrium fitting (EFIT), and transport codes TGYRO and ONETWO in EAST. For the #66740 shot, it is nearly full noninductive current drive.

The Role of Beach Morphology and Mid-Century Climate Change Effects on Wave Runup and Storm Impact on the Northern Yucatan Coast

Wave runup is a relevant parameter to determine the storm impact on barrier islands. Here, the role of the beach morphology on wave runup and storm impact was investigated at four coastal communities located on the northern Yucatan coast. Current wave conditions based on regional wind simulations, topo-bathymetric transects measured at each location, and a nonlinear wave transformation model were employed to reconstruct multi-year runup time series. Dune morphology features and extreme water levels (excluding storm surge contributions) were further employed to determine the storm impact at each site for different return periods. Despite the similar offshore conditions along the coast, extreme water levels (i.e., runup and setup) showed intersite differences that were mainly ascribed to subaerial and submerged morphological features. Numerical results showed that the average surf zone beach slope, sandbars, berm, and dune elevation played an important role in controlling extreme water levels and storm impact at the study sites under the present climate. Moreover, in order to assess the potential effect of climate change on coastal flooding, we analyzed wave runup and storm impact in the best-preserved site by considering wave conditions and sea level rise (SLR) projections under the RCP 8.5 scenario. Modelling results suggest no significant increase in the storm impact regime between the present and future conditions in the study area unless SLR is considered. It was found that to accurately estimate SLR contribution, it should be incorporated into mean sea level prior to performing numerical wave runup simulations, rather than simply adding it to the resulting wave-induced water levels.

An Extensive Study on Deep Learning: Techniques, Applications

Deep learning is associate degree future field of machine learning (ML) analysis. It consists of variety of numerous concealed layers of artificial neural networks ANN). Deep learning methods applies nonlinear transformation and high-level model abstraction to giant databases. Recent advances in deep learning design among several fields have already contributed considerably to computer science. This text present class study on commitments and novel uses of escalated instruction of intensive education. The subsequent examination presents however and during which key application intensive algorithms for learning are used. Additionally, deep learning methodology is given with enhancements and its hierarchy in linear and non-linear functions and compared with a lot of ancient algorithms in widespread applications. The status of the survey of art provides a common rundown on the novel thought and therefore rising learning and deep learning quality.

The nonlinear characteristics of transformer broadband

At present, the modeling of the transformer broadband nonlinear characters is based on the nonlinear features of 50Hz, so there are still some questions. In this paper, the magnetic hysteresis loop of the silicon steel in the the range of 50Hz to 100kHz is measured by using a measuring system composed of a 25cm Epstein square coil and an amh-1m magnetometer. The J-A parameters of the silicon steel core in the frequency wide range of the range of the optimized by using the hybrid means on the oneran fish swarm and L-M. Then, the nonlinear core model of transformer based on J-A parameters is set in PSPICE. Based on the model, the transformer simulation circuit is built. By applying sinusoidal voltage signal of the specific frequency to the nonlinear transformer model with the specific frequency, the non-linear characters of the transformer in wide frequency range areed. It is found the nonlinear characters of the transformer core change dramatically with the change of the frequency. Therefore, in the broadband nonlinear modeling of the transformer, using the nonlinear characters at 50Hz to nonlinear the broadband model will lead to large error. In the follow-up modeling research, scholars should consider the nonlinear characters of the transformer to the set the model, and try to use the nonlinear characters of the transformer under the frequencies for the broadbandlinear modeling.

Power Transformer Model in Railway Applications Based on Bond Graph and Parameter Identification

Validation and verification are the most important issues in railway applications due to cost and security reasons. Therefore, having a model of the system would be necessary in this case. Due to nonideal test conditions in industrial applications, an accurate parameter identification process has to be defined. In this article, the bond graph method is used to model energy exchanges within the components of a traction chain. More precisely, the nonlinear transformer model and its parameter identification are studied. In the case of nonideal test conditions, the usual Jiles–Atherton (JA) parameter identification procedure cannot be performed. Regarding the state of the art, the JA parameter identification is discussed. It is highlighted that an incomplete hysteresis cycle, including the extremum point and coercive field, is mandatory for accurate parameter identification. The proposed identification process is applied to a real-application case. The obtained parameters are then inserted into the overall system model. The consecutive simulations are compared with experimental data obtained through the traction chain test bench.

Improved Piecewise Linear Transformation for Precise Warping of Very-High-Resolution Remote Sensing Images

A large number of evenly distributed conjugate points (CPs) in entirely overlapping regions of the images are required to achieve successful co-registration between very-high-resolution (VHR) remote sensing images. The CPs are then used to construct a non-linear transformation model that locally warps a sensed image to a reference image’s coordinates. Piecewise linear (PL) transformation is largely exploited for warping VHR images because of its superior performance as compared to the other methods. The PL transformation constructs triangular regions on a sensed image from the CPs by applying the Delaunay algorithm, after which the corresponding triangular regions in a reference image are constructed using the same CPs on the image. Each corresponding region in the sensed image is then locally warped to the regions of the reference image through an affine transformation estimated from the CPs on the triangle vertices. The warping performance of the PL transformation shows reliable results, particularly in regions inside the triangles, i.e., within the convex hulls. However, the regions outside the triangles, which are warped when the extrapolated boundary planes are extended using CPs located close to the regions, incur severe geometric distortion. In this study, we propose an effective approach that focuses on the improvement of the warping performance of the PL transformation over the external area of the triangles. Accordingly, the proposed improved piecewise linear (IPL) transformation uses additional pseudo-CPs intentionally extracted from positions on the boundary of the sensed image. The corresponding pseudo-CPs on the reference image are determined by estimating the affine transformation from CPs located close to the pseudo-CPs. The latter are simultaneously used with the former to construct the triangular regions, which are enlarged accordingly. Experiments on both simulated and real datasets, constructed from Worldview-3 and Kompsat-3A satellite images, were conducted to validate the effectiveness of the proposed IPL transformation. That transformation was shown to outperform the existing linear/non-linear transformation models such as an affine, third and fourth polynomials, local weighted mean, and PL. Moreover, we demonstrated that the IPL transformation improved the warping performance over the PL transformation outside the triangular regions by increasing the correlation coefficient values from 0.259 to 0.304, 0.603 to 0.657, and 0.180 to 0.338 in the first, second, and third real datasets, respectively.

Kernel-Based Mixture Mapping for Image and Text Association

Modeling the relationship between multimodal media, including images, videos, and text, can reduce the gap between the modalities and promote cross-media retrieval, image annotation, etc. In this paper, we propose a new approach called kernel-based mixture mapping (KMM) to model the semantic correlations between web images and text. With this approach, we first construct latent high-dimensional feature spaces based on kernel theory to address the nonlinearity of both the data distributions in the input spaces and the cross-model correlation. Second, we present a probabilistic neighborhood model to describe the spatial locality of semantics by assuming that proximate examples in feature spaces generally have the same semantics and a conditional model to describe cross-modal conditional dependency. Finally, we build a probabilistic mixture model to jointly model the spatial locality of semantics and the conditional dependency between different modalities. By combining nonlinear transformation and probabilistic models, KMM can address the nonlinearity of cross-modal correlation, the complexity of semantic distributions at the global scale, and the continuity of semantic distributions at the local scale. We present a hybrid optimization algorithm to find the solution of KMM based on expectation-maximization and subgradient ascent; this algorithm avoids estimating the parameters of KMM in high-dimensional feature space and is proved to converge to an (local) optimal solution. We demonstrate the performance of KMM using four public datasets. The experimental results show that our approach outperforms the compared methods when modeling the relationships between images and text.

On the role of uncertainty for the study of wave–structure interaction

We present a methodology to quantify the breakwater failure by means of the partial coupling of a nonlinear wave transformation model and a structural dynamic model. Nonlinear wave transformation is simulated by a two-dimensional VOF-type model (Cornell Breaking Wave and Structures), which solves the Reynolds-averaged Navier–Stokes (RANS) equations with a turbulence closure and a free-surface tracking scheme. The numerical model is used to calculate wave-induced forces and overtopping volume on low mound breakwaters. This information is further employed as the boundary conditions in a structure dynamic model to quantify the structural failure. Simulations over a wide range of wave conditions allow us to investigate the role of both epistemic-type and aleatoric uncertainty on wave-induced sliding and overtopping. Monte Carlo simulations are employed to conduct several realizations for an assessment of the aleatoric uncertainty in the failure prediction. The latter approach allows us to obtain ensemble values and the corresponding (natural) variability of overtopping, lateral forces, and sliding for a given forcing. Moreover, numerical results show that the structure displacement is sensitive to frequency spread values (epistemic uncertainty), whereas wave overtopping is less sensitive to such parameter. This approach can be employed to develop parameterizations that include the aleatoric uncertainty in their prediction.

Building feature space of extreme learning machine with sparse denoising stacked-autoencoder

The random-hidden-node extreme learning machine (ELM) is a much more generalized cluster of single-hidden-layer feed-forward neural networks (SLFNs) which has three parts: random projection, non-linear transformation, and ridge regression (RR) model. Networks with deep architectures have demonstrated state-of-the-art performance in a variety of settings, especially with computer vision tasks. Deep learning algorithms such as stacked autoencoder (SAE) and deep belief network (DBN) are built on learning several levels of representation of the input. Beyond simply learning features by stacking autoencoders (AE), there is a need for increasing its robustness to noise and reinforcing the sparsity of weights to make it easier to discover interesting and prominent features. The sparse AE and denoising AE was hence developed for this purpose. This paper proposes an approach: SSDAE-RR (stacked sparse denoising autoencoder – ridge regression) that effectively integrates the advantages in SAE, sparse AE, denoising AE, and the RR implementation in ELM algorithm. We conducted experimental study on real-world classification (binary and multiclass) and regression problems with different scales among several relevant approaches: SSDAE-RR, ELM, DBN, neural network (NN), and SAE. The performance analysis shows that the SSDAE-RR tends to achieve a better generalization ability on relatively large datasets (large sample size and high dimension) that were not pre-processed for feature abstraction. For 16 out of 18 tested datasets, the performance of SSDAE-RR is more stable than other tested approaches. We also note that the sparsity regularization and denoising mechanism seem to be mandatory for constructing interpretable feature representations. The fact that a SSDAE-RR approach often has a comparable training time to ELM makes it useful in some real applications.

The Research on Establishing Method of the Broadband Nonlinear Transformer Model

The transformer model is one of the most needed to improving components of the modern transient simulation software. A new nonlinear broadband frequency (50Hz-10MHz) model of power transformer is proposed in this paper. The model is divided into a linear block and a nonlinear block by a reasonable equivalent transformation. The linear block is set up through measuring and synthesizing. And the nonlinear block is derived by the impendence of iron core. The final circuit model is built in Simulink, and the comparisons between the simulation and measurement results verify the feasibility and validity of the model.

Experimental and Lagrangian modeling of nonlinear water waves propagation on a sloping bottom

This paper presents an experimental and theoretical investigation of nonlinear water wave propagation over a sloping bed. Firstly, a series of monochromatic wave laboratory experiments were performed in order to measure the particle trajectories, evolution of wave profile, and wave phase velocity as wave propagates on a sloping bottom. The particle trajectories are quantified by means of images from a high speed camera, whereas the evolution of wave profile and variation of wave phase velocity are measured by a wave gauge array. Subsequently, the free-surface elevation, phase velocity, particle trajectories, and breaking wave height are estimated using a Lagrangian nonlinear wave transformation model. Model predictions show a reasonable agreement with experimental data.

Numerical experiments on transverse oscillations induced by normal-incident waves in a rectangular harbor of constant slope

In a rectangular harbor with a constant bottom slope, transverse oscillation may occur. This kind of wave has a maximum amplitude at the dead end of the harbor and decays exponentially in the offshore direction. This numerical investigation, using the nonlinear wave transformation model FUNWAVE 2.0, demonstrates the generation of subharmonic and synchronous transverse oscillations within a harbor induced by waves impacting normally on. The subharmonic transverse oscillations are trivial if the bottom slope is small, while the synchronous transverse oscillations are trivial and irrelevant for the bottom slopes. For checking the system responses, transverse oscillations within the harbor that also has a small bottom slope across the harbor were also examined. The generation of subharmonic oscillation seems not to be affected by a small transverse bottom slope; however, the synchronous transverse oscillations are enhanced significantly.

Generating data from improper distributions: application to Cox proportional hazards models with cure

Cure rate models are survival models characterized by improper survivor distributions which occur when the cumulative distribution function, say F, of the survival times does not sum up to 1 (i.e. F(+∞)<1). The first objective of this paper is to provide a general approach to generate data from any improper distribution. An application to times to event data randomly drawn from improper distributions with proportional hazards is investigated using the semi-parametric proportional hazards model with cure obtained as a special case of the nonlinear transformation models in [Tsodikov, Semiparametric models: A generalized self-consistency approach, J. R. Stat. Soc. Ser. B 65 (2003), pp. 759–774]. The second objective of this paper is to show by simulations that the bias, the standard error and the mean square error of the maximum partial likelihood (PL) estimator of the hazard ratio as well as the statistical power based on the PL estimator strongly depend on the proportion of subjects in the whole population who will never experience the event of interest.

The seamless model for three-dimensional datum transformation

With extensive applications of space geodesy, three-dimensional datum transformation model has been necessarily used to transform the coordinates in the different coordinate systems. Its essence is to predict the coordinates of non-common points in the second coordinate system based on their coordinates in the first coordinate system and the coordinates of common points in two coordinate systems. Traditionally, the computation of seven transformation parameters and the transformation of non-common points are individually implemented, in which the errors of coordinates are taken into account only in the second system although the coordinates in both two systems are inevitably contaminated by the random errors. Moreover, the coordinate errors of non-common points are disregarded when they are transformed using the solved transformation parameters. Here we propose the seamless (rigorous) datum transformation model to compute the transformation parameters and transform the non-common points integratively, considering the errors of all coordinates in both coordinate systems. As a result, a nonlinear coordinate transformation model is formulated. Based on the Gauss-Newton algorithm and the numerical characteristics of transformation parameters, two linear versions of the established nonlinear model are individually derived. Then the least-squares collocation (prediction) method is employed to trivially solve these linear models. Finally, the simulation experiment is carried out to demonstrate the performance and benefits of the presented method. The results show that the presented method can significantly improve the precision of the coordinate transformation, especially when the non-common points are strongly correlated with the common points used to compute the transformation parameters.

Development of a nonlinear geometric transformer model based on an incremental circuit of its magnetic core

In this paper, the investigation is focused on the topology-based geometric models of power transformers. These models take into account any type of core design, the geometrical characteristics of the magnetic core, and the nonlinear characteristics of the core material. These models differ from each other in the way in which the magnetic part is described. The methods, which have been proposed for the description of the magnetic part of a power transformer, are based on the conventional magnetic circuit of the core and present disadvantages. In this paper, a new method for the derivation of the differential equations of the magnetic core of the transformer is proposed by introducing a new auxiliary incremental circuit, more easily handled mathematically in antithesis to the conventional magnetic circuit that is used in the literature until now. Specifically, using the proposed circuit one can directly write the differential equations of the magnetic part of the transformer, the coupling between the windings of the transformer is easily calculated, the equations of the electric and the magnetic part are decoupled as well as the state equations of the electrical part can be written in standard form. The proposed method can be combined with any methodology presented in the literature on the core losses modeling without any restriction. The simulation results show forth that the proposed method of transformer modeling is suitable for transients and power quality studies. Moreover, the proposed method can be a useful tool on sensitivity analysis during the design stage of small and large power transformers as well.

Symmetric diffeomorphic registration of fibre orientation distributions

Registration of diffusion-weighted images is an important step in comparing white matter fibre bundles across subjects, or in the same subject at different time points. Using diffusion-weighted imaging, Spherical Deconvolution enables multiple fibre populations within a voxel to be resolved by computing the fibre orientation distribution (FOD). In this paper, we present a novel method that employs FODs for the registration of diffusion-weighted images. Registration was performed by optimising a symmetric diffeomorphic non-linear transformation model, using image metrics based on the mean squared difference, and cross-correlation of the FOD spherical harmonic coefficients. The proposed method was validated by recovering known displacement fields using FODs represented with maximum harmonic degrees (lmax) of 2, 4 and 6. Results demonstrate a benefit in using FODs at lmax=4 compared to lmax=2. However, a decrease in registration accuracy was observed when lmax=6 was used; this was likely caused by noise in higher harmonic degrees. We compared our proposed method to fractional anisotropy driven registration using an identical code base and parameters. FOD registration was observed to perform significantly better than FA in all experiments. The cross-correlation metric performed significantly better than the mean squared difference. Finally, we demonstrated the utility of this method by computing an unbiased group average FOD template that was used for probabilistic fibre tractography. This work suggests that using crossing fibre information aids in the alignment of white matter and could therefore benefit several methods for investigating population differences in white matter, including voxel based analysis, tensor based morphometry, atlas based segmentation and labelling, and group average fibre tractography.

Based on time series and RBF network plant disease forecasting

The RBF network is one novel effective forward neural network, it realizes through the nonlinear primary function's linear combination from space RN to the space RM nonlinear transformation, BFm and GM (1,1) combined model,especially qualify in nonlinear time series plant disease forecast. Model GM(1,1) was built for plant disease collected during simulative occurrence experiments. At the same time, the data of disease index and disease incidence were analyzed as reference.The results of experiments reveal that the co-deviation of Model GM(1,1) parameter a and b, cov(a,b), coincides with the standard deviation of disease index and disease incidence. This indicates that Grey system theory is effective for disease incidence analysis and the parameters of GM(1,1) can well reflect the change of plant disease occurrence.This article takes the forecast object by the wheat banded sclerotial blight, proposed that based on the RBF network's plant disease forecasting model, the simulation experiment showed that this model to the plant disease short and medium term forecast is possible effective.

A phase-averaged non-linear wave transformation model

Long-term predictive morphological models are essential for planning and management of coastlines. However, to have widespread applicability such models must be computationally efficient. To achieve this aim, an approximate method was developed to depict the non-linear wave parameters as a wave is propagated across the nearshore zone, where the wave is considered to be transformed by the processes of shoaling, refraction and breaking. Non-linear approximations for the parameters of wave height, wave length, wave orbital velocities and velocity moments are described by this method and the results compared primarily with experimental data from both planar beaches and barred profiles. The results of this validation exercise demonstrated that the new method can adequately describe the relevant non-linear wave parameters. Nonetheless, in order to achieve an undemanding approach, the proposed method involved the use of specially defined constants that are fitted empirically. The sensitivity of the approximate wave parameters to these empirical constants are also investigated and discussed.

A Corrected Likelihood Approach for the Nonlinear Transformation Model with Application to Fluorescence Lifetime Measurements Using Exponential Mixtures

A fast and efficient estimation method is proposed that compensates the distortion in nonlinear transformation models. A likelihood-based estimator is developed that can be computed by an EM-type algorithm. The consistency of the estimator is shown and its limit distribution is provided. The new estimator is particularly well suited for fluorescence lifetime measurements, where only the shortest arrival time of a random number of emitted fluorescence photons can be detected and where arrival times are often modeled by a mixture of exponential distributions. The method is evaluated on real and synthetic data. Compared to currently used methods in fluorescence, the new estimator should allow a reduction of the acquisition time of an order of magnitude.