Ladder Network Research Articles

The locating number of hexagonal Möbius ladder network

Due to the immense applications of interconnection networks, various new networks are designed and extensively used in computer sciences and engineering fields. Networks can be expressed in the form of graphs, where node become vertex and links between nodes are called edges. To obtain the exact location of a specific node which is unique from all the nodes, several nodes are selected this is called locating/resolving set. Minimum number of nodes in the locating set is called locating number. In this article, we find the exact value of locating number of newly designed hexagonal Mobius ladder network.

Design of multiband matching ladders without mutual coupling using parametric representation of Brune functions

In this study, a semianalytical method for the design of mutual coupling free multiband matching networks is introduced. A new parametric representation of Brune functions is used for the construction of multiband ladder network topologies without mutual induction. The method involves the use of Fujisawa's constraints for low pass ladders having finite transmission zeros, in a parametric representation of driving point impedance function resulting in mutual inductance free Brune sections. The developed parametric representation is incorporated with Real Frequency Techniques to design matching networks with a plurality of pass bands. Several illustrative design examples are presented to validate the method.

Analysis of lightning impulse voltage distribution for a dry-type transformer using three different winding types

In this study, simulation and test results for lightning impulse voltage distribution in a dry-type transformer were compared for three different winding methods by using round, flat, and strip conductors. Distribution of the voltage inside the transformer windings at high frequencies had a different behavior than that of at low frequencies. The transformer had non-linear voltage distributions at high frequencies due to the inner capacitance and inductance of its windings. The ladder network model was used for the analysis of high frequency signals for voltage distribution. The parameters of the model were calculated analytically and numerically using a finite element analysis (FEA) software. The analytical solution method of a matrix obtained from the ladder network model was presented. Finally, simulation and test results were given and compared.

Reconnection–less reconfigurable low–pass filtering topology suitable for higher–order fractional–order design

The paper discusses a new design of a current–mode reconnection–less reconfigurable fractional–order (FO) low–pass filter of various orders. The filtering structure is based on a 4th–order leap–frog topology using operational transconductance amplifiers as basic building blocks. The resulting order of the filter is given by the setting of current gains (allowing the reconnection–less reconfiguration) alongside with the values of the fractional–order capacitors realized by the RC ladder networks. For this purpose, RC ladder networks of orders 0.3, 0.4, 0.5, 0.6 and 0.7 have been designed. The fractional–order form of the filter contains from one up to four FO capacitors (remaining capacitors (if there are any) are of integer–order) allowing to obtain low–pass functions of order of 3 + α, 2 + α, 1 + α, 2 + α + β, 1 + α + β, α + β, 1 + α + β + γ, α + β + γ and α + β + γ + δ. The proposed filter offers a wide variety of possible order combinations with an increasing degree of freedom as the number of fractional–order capacitors within the structure increases. The proposal is supported by the PSpice simulations of magnitude and phase characteristics, pole frequency adjustment and stability analysis. Moreover, the experimental measurements of the implemented filter were carried out and compared with the simulation results. The possibility of the electronic control of the fractional order is also discussed and presented.

Semi‐supervised long short‐term memory for human action recognition

In real human action recognition task, it is a common phenomenon that there are many unlabelled samples and few labelled samples. How to make good use of unlabelled samples to improve the generalisation ability of models is the focus of semi-supervised learning research. In this study, the authors present two semi-supervised methods based on long short-term memory (LSTM) to learn discriminative hidden features. One is the LSTM ladder network, the other is the Symmetrical LSTM network. By them unlabelled samples can be used automatically to improve learning performance without relying on external interaction. Both on the NTU-RGB + D dataset and the Kinetics dataset, their methods achieve >10 and 5% improvements, separately.

Semi-supervised process fault classification based on convolutional ladder network with local and global feature fusion

Effective fault classification is of great significance to isolate and eliminate faults in the smart manufacturing process, especially for chemical industry. However, incipient faults and limited labeled samples make it hard to classify faults accurately. This motivates the formulation of a semi-supervised convolutional ladder network with local and global feature fusion. In the algorithm, a convolutional ladder network is developed to capture higher-order correlations from both labeled and unlabeled samples simultaneously to overcome the problem caused by limited labeled samples, skipped connections are embedded within which to make a balance between supervised and unsupervised feature learning for further identifying faults. To improve the classification performance on incipient faults, a local and global feature fusion strategy is proposed to enhance the representation of incipient faults. Furthermore, a semi-supervised dynamic data representation strategy is introduced to jointly deal with labeled and unlabeled process samples, which enables the proposed method to handle process dynamics by characterizing temporal information of process variables. Experiments on the Tennessee Eastman process show that the proposed method is effective for process fault classification when labeled samples are limited compared to the state-of-the-art algorithms.

A Global Maximum Error Controller Based Nonlinearity Aware TPWL Method for Reducing Nonlinear Systems

Model order reduction is a common practice to reduce large order systems so that their simulation and control become easy. Nonlinearity aware trajectory piecewise linear is a variation of trajectory piecewise linearization technique of order reduction that is used to reduce nonlinear systems. With this scheme, the reduced approximation of the system is generated by weighted sum of the linearized and reduced sub-models obtained at certain linearization points on the system trajectory. This scheme uses dynamically inspired weight assignment that makes the approximation nonlinearity aware. Just as weight assignment, the process of linearization points selection is also important for generating faithful approximations. This article uses a global maximum error controller based linearization points selection scheme according to which a state is chosen as a linearization point if the error between a current reduced model and the full order nonlinear system reaches a maximum value. A combination that not only selects linearization points based on an error controller but also assigns dynamic inspired weights is shown in this article. The proposed scheme generates approximations with higher accuracies. This is demonstrated by applying the proposed method to some benchmark nonlinear circuits including RC ladder network and inverter chain circuit and comparing the results with the conventional schemes.

Cost-Sensitive and Sparse Ladder Network for Software Defect Prediction

Cost-Sensitive and Sparse Ladder Network for Software Defect Prediction

Scalable compact modeling of trap generation near the EB spacer oxide interface in SiGe HBTs

This paper presents a physics-based scalable formulation for interface trap generation in the vicinity of the emitter-base spacer oxide interface in advanced SiGe HBTs. Aging tests were performed for various emitter dimensions to investigate the scalability of the dynamics of hot-carrier degradation. An improved formulation of the bond dissociation rate is also proposed incorporating a scaling rule depending on the avalanche current density. The hydrogen diffusion through the EB spacer has been modeled using an RC ladder network and has been scaled according to the hydrogen diffusion volume. Its accuracy has been validated over a wide range of aging tests and various geometry features.

Model Order Reduction of an Induction Motor Using a Cauer Ladder Network

In this article, a method for motor model order reduction is developed using the Cauer ladder network (CLN). The analyzed domain is decomposed into stator and mover domains, where the multiport CLN of each domain is constructed independently of the other. The two domains are connected through electromagnetic field modes at the boundary. The boundary condition is derived from the coordinate transformation. The reduced model accurately reconstructs the induction motor property affected by slot harmonics.

Projection based weight normalization: Efficient method for optimization on oblique manifold in DNNs

Optimizing deep neural networks (DNNs) often suffers from the ill-conditioned problem. We observe that the scaling based weight space symmetry (SBWSS) in rectified nonlinear network will cause this negative effect. Therefore, we propose to constrain the incoming weights of each neuron to be unit-norm, which is formulated as an optimization problem over the Oblique manifold. A simple yet efficient method referred to as projection based weight normalization (PBWN) is also developed to solve this problem. This proposed method has the property of regularization and collaborates well with the commonly used batch normalization technique. We conduct comprehensive experiments on several widely-used image datasets including CIFAR-10, CIFAR-100, SVHN and ImageNet for supervised learning over the state-of-the-art neural networks. The experimental results show that our method is able to improve the performance of different architectures consistently. We also apply our method to Ladder network for semi-supervised learning on permutation invariant MNIST dataset, and our method achievers the state-of-the-art methods: we obtain test errors as 2.52%, 1.06%, and 0.91% with only 20, 50, and 100 labeled samples, respectively.

Investigation on the generation of high voltage quasi-square pulses with a specific two-node PFN-Marx circuit.

A specific multi-stage two-node pulse forming network (PFN)-Marx topology circuit, which can produce high voltage quasi-square pulses, is investigated and designed in this paper. The specificity of this circuit is that the PFN-Marx is formed by several uniform ladder networks that have two sections of the LC unit and a ladder network formed by four-node capacitors. Compared with conventional PFN-Marx generators formed by equal-value capacitors and inductors with more than four nodes, the number of capacitors in the circuit designed here can be reduced significantly. A five-stage two-node PFN-Marx is assembled to verify the validity of the topology circuit. The experimental results show that the PFN-Marx can generate a quasi-square pulse with a pulse width of 105 ns, flat-top of 50 ns, and amplitude of 80 kV with ±3% voltage variation. The topology circuit design is promising to achieve higher voltage (more stages) and longer pulse width.

Modal Decomposition of 3-D Quasi-Static Maxwell Equations by Cauer Ladder Network Representation

Modal Decomposition of 3-D Quasi-Static Maxwell Equations by Cauer Ladder Network Representation

A Semi-Supervised and Incremental Modeling Framework for Wafer Map Classification

Wafer map analysis provides critical information for quality control and yield improvement tasks in semiconductor manufacturing. In particular, wafer patterns of gross failing areas (GFA) are important clues to identify the causes of relevant failures during the manufacturing process. In this work, a semi-supervised classification framework is proposed for wafer map analysis, and its application to wafer bin maps with GFA patterns classification is demonstrated. The Ladder network and the semi-supervised variational autoencoder are adopted to classify wafer bin maps in comparison with a standard convolutional neural network (CNN) model on two real-world datasets. The results have illustrated that two semi-supervised models are consistently and substantially better than the CNN model across various training data percentages by effective utilization of the unlabeled data. Active learning and pseudo labeling are also utilized to accelerate the learning curve.

Model Order Reduction for Linear Time-Invariant System With Symmetric Positive-Definite Matrices: Synthesis of Cauer-Equivalent Circuit

This article introduces a new model order reduction method for a linear time-invariant system with symmetric positive-definite matrices. The proposed method allows the construction of a reduced model, represented by a Cauer-equivalent circuit, from the original system. The method is developed by extending the Cauer ladder network method for the quasi-static Maxwell's equations, which is shown to be regarded as the Lanczos algorithm with respect to a self-adjoint matrix. As a numerical example, a Cauer-equivalent circuit is generated from a simple mathematical model as well as the finite-element (FE) model of a magnetic reactor that is driven by a pulsewidth modulation voltage wave. The instantaneous power obtained from the circuit analysis is shown to be in good agreement with that obtained from the original FE model.

Multi-Port Model Order Reduction Using a Matrix Cauer Ladder Network

To achieve efficient multi-port model order reduction, a multi-port Cauer ladder network (CLN) method is formulated that directly yields resistance and inductance matrices that constitute the network elements in the matrix Cauer form. The eddy-current field driven by multiple power sources is accurately reconstructed using a small number of network elements. The matrix Cauer form achieves faster convergence of the transfer function than a single-port CLN method and almost the same convergence as a block Pade via Lanczos (PVL) method.

Cauer Ladder Network Representation of a Nonlinear Eddy-Current Field Using a First-Order Approximation

An approximation approach is proposed for the analysis of nonlinear quasi-static eddy currents adopting a Cauer ladder network (CLN). When there are nonlinear magnetic materials in the analysis domain, the electric and magnetic modes and their corresponding values for resistors and inductors in the CLN may vary according to the level of saturation in the core. Considering the effects of the modes and their magnitudes on the saturation imposes a heavy computational burden, which brings the efficiency of the CLN method into question. This article studies a first-order approximation of the nonlinear CLN method to keep the nonlinearization procedure computationally effective, simple, and accurate. Numerical tests are carried out for a 2-D nonlinear inductor excited with rectangular and sinusoidal excitations to show the accuracy of the proposed nonlinear resolution method.

A new and reliable dual model- and data-driven TOC prediction concept: A TOC logging evaluation method using multiple overlapping methods integrated with semi-supervised deep learning

The total organic carbon content (TOC) is the most important parameter when determining the source rock quality. At present, there are two main types of TOC well logging calculation methods: model-driven and data-driven methods. However, research on the these two types of methods has slowed over the past ten years, and the ongoing research is very limited; thus, it is difficult to improve the TOC calculation accuracy. This paper analyses the advantages and disadvantages of current methods and proposes a new model- and data-driven TOC prediction concept to improve the TOC prediction accuracy. The proposed concept takes the curve obtained with the overlap method as an input instead of using a conventional log curve; we believe that deep learning is best suited to accomplish this task. We propose a new integrated semi-supervised deep learning network—the integrated deep semi-supervised ladder network (IDLN) algorithm—for small-sample well logging interpretation problems based on the proposed approach. A two-step method consisting of intelligent curve overlapping and automatic TOC prediction is employed to better interpret logging data and core data; this method can predict the TOC without manually overlapping curves. Testing the data from 12 wells in 3 blocks revealed that the proposed concept and IDLN algorithm greatly improve the TOC prediction accuracy, and the mean square error was reduced by more than 50%. The new method is also more reasonable for locating non-reservoir segments. Moreover, this novel approach can further enhance the TOC prediction accuracy and may even constitute a new research direction for improving the existing logging interpretation theory. These novel principles can ultimately help evaluate source rock reservoirs.

Graph Regularized Variational Ladder Networks for Semi-Supervised Learning

To tackle the problem of semi-supervised learning (SSL), we propose a new autoencoder-based deep model. Ladder networks (LN) is an autoencoder-based method for representation learning which has been successfully applied on unsupervised learning and semi-supervised learning. However, It ignores the manifold information of high-dimensional data and usually achieves unmeaning features which are very difficult to use in the subsequent tasks, such as prediction and recognition. To these issues, we proposed Graph Regularized Variational Ladder Networks (GRVLN), which explicitly and implicitly employs the manifold structure of data. Our contributions can be summarized as two folds: (1) Graph regularization is used to build all decoder layers, which explicitly promotes the manifold learning via graph laplacian matrixs; (2) Variational autoencoder is used as the backbone instead of traditional autoencoder in the encoder layers for implicitly learning the manifold structure of data distribution. Compared with ladder networks and other autoencoder-based methods, GRVLN achieves superior performance in semi-supervised classification tasks. Experimental results show that our method also has a comparable performance with state-of-the-art methods on several benchmark data sets.

Semi-Supervised Speech Emotion Recognition With Ladder Networks

Speech emotion recognition (SER) systems find applications in various fields such as healthcare, education, and security and defense. A major drawback of these systems is their lack of generalization across different conditions. For example, systems that show superior performance on certain databases show poor performance when tested on other corpora. This problem can be solved by training models on large amounts of labeled data from the target domain, which is expensive and time-consuming. Another approach is to increase the generalization of the models. An effective way to achieve this goal is by regularizing the models through multitask learning (MTL), where auxiliary tasks are learned along with the primary task. These methods often require the use of labeled data which is computationally expensive to collect for emotion recognition (gender, speaker identity, age or other emotional descriptors). This study proposes the use of ladder networks for emotion recognition, which utilizes an unsupervised auxiliary task. The primary task is a regression problem to predict emotional attributes. The auxiliary task is the reconstruction of intermediate feature representations using a denoising autoencoder. This auxiliary task does not require labels so it is possible to train the framework in a semi-supervised fashion with abundant unlabeled data from the target domain. This study shows that the proposed approach creates a powerful framework for SER, achieving superior performance than fully supervised single-task learning (STL) and MTL baselines. We implement the approach with sentence-level or frame-level features, demonstrating the flexibility of our approach. Additionally, the generalization of the ladder networks is evaluated in cross-corpus settings using sentence-level features, obtaining important improvements. Compared to the STL baselines, the proposed approach achieves relative gains in concordance correlation coefficient (CCC) between 3.0% and 3.5% for within corpus evaluations, and between 16.1% and 74.1% for cross corpus evaluations, highlighting the power of the architecture.