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This paper presents the development of an optimization and modeling method for the objective functions of output power, efficiency and weight of an outer rotor permanent magnet brushless DC (BLDC) motor based on radial basis function (RBF) approximation technique. The proposed RBF‐based Pareto optimization method requires less knowledge about electric/magnetic formulas and can replace conventional optimizations based on these equations with higher accuracy. To apply the proposed optimization method, the initial design should be developed using such equations. Therefore, RBFs are used to model and predict engine behavior. To optimize the objective functions, we used a genetic algorithm optimization technique with nonlinear electric and magnetic constraints to find the Pareto front set. The design obtained by the proposed radial basis function Pareto optimization (RBFPO) method was finally verified by Ansoft Maxwell. The results of optimal design using the RBFPO method have higher output power and efficiency. Also, in addition to the advantage of a favorable accuracy, RBF‐based models are significantly faster than models available in simulation tools. [ABSTRACT FROM AUTHOR]

Summary: In this paper, a novel method is presented for dynamic behavioral modeling of nonlinear circuits. The proposed adjoint recurrent neural network (ARNN) model is an extension of the existing recurrent neural network (RNN) technique which adds derivative information to the training data set. This addition makes training more efficient while using fewer data in comparison with the conventional RNN method with the same accuracy. Also, formulation of proposed ARNN model makes it suitable for parallel computation. Therefore, the proposed technique makes the training process much more efficient than RNN by using derivative information and parallelization. Additionally, the proposed model is much faster compared to conventional models present in existing simulation tools. The validity and accuracy of the proposed model is illustrated through macromodeling of a commercial NXP's 74LVC04A device and a five‐stage complementary metal‐oxide semiconductor (CMOS) receiver device. [ABSTRACT FROM AUTHOR]

In this study, a framework for statistical design of a brushless DC (BLDC) motor is proposed in order to maximise yield while keeping efficiency as high as possible and the non‐linear constraints, that is, limitations of flux density, current density and physical dimensions, satisfied. The proposed yield maximisation method has two major steps: polyhedral approximation of the constraint region and yield maximisation. By implementing the proposed method, the optimum design parameters, that is, embrace, thickness and length of magnet, are obtained with maximum immunity to variations in magnet dimensions. Also, highly accurate artificial neural network‐based models are used to estimate the objective function and constraints. It is also shown that by adjusting performance constraints (efficiency and flux density), different design goals can be achieved which help to choose the appropriate design according to the designer's goals. [ABSTRACT FROM AUTHOR]

Here, the authors present a new constrained multi‐objective optimization method for maximizing output power and efficiency of switched reluctance motor (SRM). The constraints play a significant role in this process. Artificial neural network‐based models are created to represent the SRM behaviour which is a difficult task. For this reason, a single neural network for each objective is built and the number of training data has been increased to reach a good accuracy. The authors propose a neural network‐based adjoint Lp metric technique to combine several objective functions and constraints with different weight factors to a single function which should be minimized. To apply the constraints, an adjoint term is added to the original Lp function including only objective functions. The flux densities of the magnetic materials are selected as the optimization constraints. When approaching as close as possible to the saturation level, the SRM has a better performance. Adding an adjoint term to the original Lp leads to better optimization results which were proved by comparing with a conventional optimization. Also, all obtained results were finally validated by the Ansoft Maxwell software. [ABSTRACT FROM AUTHOR]

This article presents a new macromodeling approach for nonlinear electronic components and circuits based on long short-term memory (LSTM) neural network. LSTM proposes a more efficient training process in comparison with the conventional recurrent neural network (RNN) training. Conventional structures such as RNN suffer from the gradient vanishing problem during the training process. LSTM addresses this issue and solves this problem in an efficient way. In order to train the proposed structure, some input and output waveforms of the original circuit, called training waveforms, should be obtained from simulation tools or measurements. Model creation using proposed method does not require information on details inside the components and input–output training waveforms are sufficient to construct the model. The provided numerical results in this article show that the proposed method is more efficient than RNN techniques for modeling components and packages in terms of both speed and accuracy. The findings suggest that the proposed method significantly reduces the training time in comparison with conventional state-of-art modeling techniques. Furthermore, simulation time of the obtained model from the proposed technique is less than both conventional models (such as SPICE models) used in circuit simulation tools and models obtained from conventional RNN method. Three practical examples, namely, an audio amplifier, Texas Instruments (TIs) SN74AHCT540 device, and MOS inverter, are utilized to manifest the validity of the proposed macromodeling approach. [ABSTRACT FROM AUTHOR]

This study presents a new method for parametric modelling and optimisation of a permanent‐magnet brushless DC (BLDC) motor. We proposed an artificial neural network (ANN)‐based LP metric technique to combine and optimise different objective functions of a BLDC motor using ANN‐based models and compared with conventional optimisation methods with analytical models. To proceed with this optimisation problem, the LP function should be minimised. For applying constraints to this problem, a simple method called penalty factor is proposed, in which a penalty term was added to the LP function when the constraints are violated. We considered three goals in this optimisation: efficiency maximisation, speed maximisation and material cost minimisation. Since the load is constant torque in our case, more speed means more powerful motor, and to achieve the minimum material cost goal the volume of the magnet is set as an objective function. To find the optimum geometric parameters, we used gradient‐based method subject to non‐linear magnetic constraints. All the obtained results were validated by Ansoft Maxwell. Optimising using the proposed method including ANN‐based models does not require knowledge about complicated electric/magnetic equations. Also, ANN‐based BLDC motor model is more accurate than analytical models and faster than existing models in simulation tools. [ABSTRACT FROM AUTHOR]

Summary: In this paper, a new method called local‐global feedback recurrent neural network (LGFRNN) is proposed for dynamic behavioral modeling of nonlinear circuits. The structure of the proposed method is based on recurrent neural network and constructed by time‐delayed local and global feedbacks. Adding time‐delayed feedbacks has a great impact on the learning capability of previous neural network‐based methods. Moreover, time‐delayed local feedbacks alleviate the problem of slow convergency of the conventional neural network‐based methods in the training phase. The proposed LGFRNN can be trained only by having sampled input‐output waveforms of the original circuit without knowing the internal details of the circuit. A training algorithm based on real‐time recurrent learning (RTRL) is used to train LGFRNN. After the training phase, the proposed LGFRNN provides accurate macromodel of a nonlinear circuit. The proposed method is more accurate compared with the conventional neural‐based models (which do not benefit from time‐delayed local‐global feedbacks) and also significantly reduces the training time of the conventional models. Moreover, proposed LGFRNN is faster than the existing models in simulation tools. The validity of the proposed method is verified by time‐domain modeling of three nonlinear devices including commercial TI's SN74AHCT540 device, five‐stage complementary metal‐oxide‐semiconductor (CMOS) receiver, and commercial TI's LM324 power amplifier. [ABSTRACT FROM AUTHOR]

Abstract This paper introduces Deep Recurrent Neural Network (DRNN) structure for time-domain modeling of nonlinear circuits. DRNN can be directly trained by sampled input-output waveforms of the original nonlinear circuit without knowing the internal details of the circuit. A training algorithm based on Real-Time Recurrent Learning (RTRL) is developed to train the proposed DRNN. After the training phase, DRNN provides accurate and fast macromodel of the nonlinear circuit. Our experimental results show that DRNN extends the ability of conventional neural-based models to express the dynamic behavior of a nonlinear circuit, and also significantly enhances the accuracy of the conventional neural circuit modeling. Moreover, DRNN is considerately faster than the existing models in simulation tools. The validity and advantages of the proposed deep learning-based method are verified by time-domain modeling of three nonlinear devices including 5-stage CMOS receiver, commercial TI's LM324 power amplifier, and TI's SN74AHCT540 device. [ABSTRACT FROM AUTHOR]

In this paper, an adjoint state-space dynamic neural network method for modeling nonlinear circuits and components is presented. This method is used for modeling the transient behavior of the nonlinear electronic and photonic components. The proposed technique is an extension of the existing state-space dynamic neural network (SSDNN) technique. The new method simultaneously adds the derivative information to the training patterns of nonlinear components, allowing the training to be done with less data without sacrificing model accuracy, and, consequently, makes training faster and more efficient. In addition, this method has been formulated such that it can be suitable for the parallel computation. The use of derivative information and parallelization makes training using the proposed technique much faster than the SSDNN. In addition, the models created using the proposed method are much faster to evaluate compared with the conventional models present in traditional circuit simulation tools. The validity of the proposed technique is demonstrated through the transient modeling of the physics-based CMOS driver, commercial NXP’s 74LVC04A inverting buffer, and nonlinear photonic components. [ABSTRACT FROM PUBLISHER]

Summary: Recurrent neural networks (RNN) emerged as powerful tools to model and analyze the nonlinear behavior of electronic circuits accurately and quickly. Efforts to improve the accuracy of RNN will lead to the design of better‐quality products, which is essential in various fields such as the design of energy harvesting (EH) systems. EH techniques can provide the electrical energy needed for low‐power electronics without the need for a battery or with minimal dependency. Due to the importance of the active voltage balancing circuit in EH systems, we have proposed a new macromodeling method called dropout local‐feedback deep recurrent neural network (Dropout‐LFDRNN) to model and analyze this circuit along with two other nonlinear circuits as examples. This technique is an advance over the LFDRNN macromodeling method, and based on the obtained results from the measurements, we were able to build a fast macromodel for the active balancing circuit, which outperforms conventional deep recurrent neural network modeling method in terms of accuracy without sacrificing speed. It is worth mentioning that this proposed technique in this paper can be considered a viable approach for modeling and analysis of nonlinear electronic components and circuits. In addition to the advantage of generating a more accurate model, the model based on the Dropout‐LFDRNN approach is much faster than the existing transistor‐level models. [ABSTRACT FROM AUTHOR]

This paper presents a novel sensitivity-analysis-based adjoint neural-network (SAANN) technique to develop parametric models of microwave passive components. This technique allows robust parametric model development by learning not only the input–output behavior of the modeling problem, but also derivatives obtained from electromagnetic (EM) sensitivity analysis. A novel derivation is introduced to allow complicated high-order derivatives to be computed by a simple artificial neural-network (ANN) forward-back propagation procedure. New formulations are deduced for exact second-order sensitivity analysis of general multilayer neural-network structures with any numbers of layers and hidden neurons. Compared to our previous work on adjoint neural networks, the proposed SAANN is easier to implement into an existing ANN structure. The proposed technique allows us to obtain accurate and parametric models with less training data. Another benefit of this technique is that the trained model can accurately predict derivatives to geometrical or material parameters, regardless of whether or not these parameters are accommodated as sensitivity variables in EM simulators. Once trained, the SAANN models provide accurate and fast prediction of EM responses and derivatives used for high-level optimization with geometrical or material parameters as design variables. Three examples including parametric modeling of coupled-line filters, cavity filters, and junctions are presented to demonstrate the validity of this technique. [ABSTRACT FROM AUTHOR]

In order to model high-speed nonlinear circuits, recurrent neural network (RNN) has been widely used in computer-aided design (CAD) area to achieve high performance and fast models compared with the existing models. Despite their advantages, they still have challenges such as large training time and limited test accuracy. In this article, the batch normalization (BN) method is applied to deep RNN leading to a much shorter training time and more accurate models compared with the conventional RNN. The proposed BN-RNN method works by modifying the distribution of the internal nodes of a deep network in the training course as an internal auxiliary shift yielding a much faster training. Indeed, the internal covariance shift will be reduced and the training of deep neural networks will be accelerated via a normalization step applied to the layers of RNN. BN-RNN, moreover, has a beneficial effect on gradient flow through the grid by reducing the dependence of gradients on the scale of network parameters or their initial values. This provides a much better learning process without the risk of divergence. For verifying the proposed method, time-domain modeling of three high-speed nonlinear circuits operating at the GHz region is provided. Comparisons of the training and test errors between RNN and BN-RNN, and evaluation time comparisons between transistor level and the BN-RNN-based models for these circuits prove the higher speed of the models obtained from the BN-RNN method. In addition, it is shown that training using the proposed method requires much less CPU time and number of epochs. [ABSTRACT FROM AUTHOR]

In this paper, a framework for the statistical design of the flip-flops circuits is proposed to achieve a high yield, while meeting the performance, leakage power, switching power, and layout area design specifications. The proposed design solution provides the nominal design parameters, i.e., the widths and lengths of the flip-flop transistors, which provide maximum immunity to the process variations in the transistor dimensions and threshold voltage. The proposed framework shows that for a given flip-flop design specifications, a certain yield can be achieved. To further increase this yield, the proposed framework shows which design specifications should be relaxed. The transmission gate-based master-slave flip-flop is selected as a design case study in this paper, however, the proposed framework is applicable to any other flip-flop circuit in the nanometer regime. [ABSTRACT FROM AUTHOR]

Balancing the voltage of series connected supercapacitors is a necessity. Various passive and active balancing techniques are reported for alleviating the problems of leakage and overvoltage. In this paper, a novel active balancing approach based on boost converter is presented leading to the implementation of a piezoelectric energy harvesting (EH) system. Besides, this nonlinear boost converter is designed, implemented, and modeled using a new macromodeling approach. In this regard, data measured by the implemented boost converter passed through local feedback deep recurrent neural networks (LFDRNNs), in order to model the nonlinear behavior of this converter, and this model can be used to design the EH system. LFDRNN can be trained directly using the input–output waveform samples of the main circuit without knowing its internal details, and the obtained model has similar accuracy compared to the original circuit. The main focus of this paper is the new LFDRNN macromodeling method which is associated with the boost converter‐based active balancing technique. Our experimental results show that LFDRNN extends the ability of conventional neural network‐based models to express the dynamic behavior of nonlinear circuits while increasing the accuracy. Additionally, LFDRNN‐based models are much faster than existing models in simulation tools. [ABSTRACT FROM AUTHOR]