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A simple method combining Output‐Error (OE) model and Finite‐Difference Time‐Domain (FDTD) method is proposed to reconstruct lightning current in this paper. First, the FDTD method is adopted to calculate electromagnetic fields of any desired point, and the transfer function between the obtained fields and channel base current is built by using OE model. Then, the lightning current is reconstructed by putting the actual measured electromagnetic field into the corresponding transfer function. The validity of the proposed method is demonstrated through the measured data given in the literature. Moreover, three influence factors on the reconstruction performance of this method are analyzed as well, including the effect of distance from field observation point to lightning channel, ground conductivity and the velocity of return stroke. Key Points A simple method combining Output‐Error model and Finite‐Difference Time‐Domain method is proposed to reconstruct lightning current in this paper The validity of the proposed method is demonstrated through the measured data given in the literature The return stroke speed plays an important role in the reconstruction method

This study considers the output regulation problem of switched discrete-time linear systems via dual design of error feedback and a switching law. The authors consider the case that the states of both the controlled system and the exosystem are unavailable. Also, no solvability of the output regulation problem for each subsystem is required. They only use the available information provided by the measured output tracking error to design the switching law and controllers to solve the output regulation problem of the switched system. In addition, they adopt different coordinate transformations instead of common coordinate transformation and they study the case that the exosystem is a switched system which can make the tracked trajectories more sophisticated.

One-hot encoding is the prevalent method used in neural networks to represent multi-class categorical data. Its success stems from its ease of use and interpretability as a probability distribution when accompanied by a softmax activation function. However, one-hot encoding leads to very high dimensional vector representations when the categorical data’s cardinality is high. The Hamming distance in one-hot encoding is equal to two from the coding theory perspective, which does not allow detection or error-correcting capabilities. Binary coding provides more possibilities for encoding categorical data into the output codes, which mitigates the limitations of the one-hot encoding mentioned above. We propose a novel method based on Zadeh fuzzy logic to train binary output codes holistically. We study linear block codes for their possibility of separating class information from the checksum part of the codeword, showing their ability not only to detect recognition errors by calculating non-zero syndrome, but also to evaluate the truth-value of the decision. Experimental results show that the proposed approach achieves similar results as one-hot encoding with a softmax function in terms of accuracy, reliability, and out-of-distribution performance. It suggests a good foundation for future applications, mainly classification tasks with a high number of classes.

The bias compensation technique combined with the least-squares estimation algorithm with forgetting factors is applied to the parameter estimation of output error models with moving average noise. It is shown that the bias term induced by the noise is determined by the weighted average variance of the white noise and the parameters of the unknown noise model. Therefore, in order to give a recursive estimation of the bias term, an interactive estimation of the weighted average variance and noise parameters is constructed by using the principle of hierarchical identification. In addition, a recursive form is also established to estimate the so-called weighted average variance of the white noise. The estimation algorithm is finally established by combining the interactive estimation and the recursive estimation of weighted average variance. A simulation example is employed to show the effectiveness of the proposed bias compensation based least-squares estimation algorithm with two forgetting factors.

Thermal stress is one of the main sources of micro-electro-mechanical systems (MEMS) devices error. The Wheatstone bridge is the sensing structure of a typical piezoresistive MEMS pressure sensor. In this study, the thermal stress induced by potting adhesive in MEMS pressure sensor was investigated by experiments, calculated by analytics and analyzed by simulations. An experiment system was used to test the sensor at different air pressures and temperatures. The error becomes greater with the decrease in pressure. A set of novel formulas were proposed to calculate the stress–strain on Wheatstone bridge. The error increases with the temperature deviating from 25 °C. A full-scale geometric model was developed, and finite element simulations were performed, to analyze the effect of the stress on MEMS pressure sensor induced by different temperatures and thicknesses of potting adhesive. Simulation results agree well with the experiments, which indicated that there is a 3.48% to 6.50% output error in 0.35 mm potting adhesive at 150 °C. With the thickness of potting adhesive increasing, the variations of output error of the Wheatstone bridge present an N-shaped curve. The output error meets a maximum of 5.30% in the potting adhesive of 0.95 mm and can be reduced to 2.47%, by increasing the potting adhesive to 2.40 mm.

The hemispherical resonator gyroscope (HRG) is a typical capacitive Coriolis vibratory gyroscope whose performance is inevitably influenced by the uneven electrostatic forces caused by the uneven excitation capacitance gap between the resonator and outer base. First, the mechanism of uneven electrostatic forces due to the significantly uneven capacitance gap in that the non-uniformity of the electrostatic forces can cause irregular deformation of the resonator and further affect the performance and precision of the HRG, was analyzed. According to the analyzed influence mechanism, the dynamic output error model of the HRG was established. In this work, the effect of the first four harmonics of the uneven capacitance gap on the HRG was investigated. It turns out that the zero bias and output error, caused by the first harmonic that dominates mainly the amplitude of the uneven capacitance gap, increase approximately linearly with the increase of the amplitude, and periodically vary with the increase of the phase. The effect of the other three harmonics follows the same law, but their amplitudes are one order of magnitude smaller than that of the first one, thus their effects on the HRG can be neglected. The effect of uneven electrostatic forces caused by the first harmonic on the scale factor is that its nonlinearity increases approximately linearly with the increase of the harmonic amplitude, which was analyzed in depth. Considering comprehensively the zero bias, the modification rate of output error, and scale factor nonlinearity, the tolerance towards the uneven excitation capacitance gap was obtained.

Optimal input design for system identification is an area of intensive modern research. This paper considers the identification of output error (OE) model, for the case of constrained output variance. The constraint plays a very important role in the process industry, in the reduction of degradation of product quality. In this paper, it is shown, in the form of a theorem, that the optimal input signal, with constrained output, is achieved by a minimum variance controller together with a stochastic reference. The key problem is that the optimal input depends on the system parameters to be identified. In order to overcome this problem, a two-stage adaptive procedure is proposed: obtaining an initial model using PRBS as input signal; application of adaptive minimum variance controller together with the stochastic variable reference, in order to generate input signals for system identification. Theoretical results are illustrated by simulations.

In this paper, fractional Hammerstein system identification is considered, where the linear block is of fractional order. The original discrete Hammerstein system is first converted to a fractional polynomial nonlinear state-space model (PNLSS), which allows a better parameterization of the model. An output-error identification approach is developed based on the robust Levenberg–Marquardt algorithm, whose nevralgic point is the calculation of parametric sensitivity functions. These last are developed as a multivariable fractional PNLSS model which effectively reduces the computational effort. Various simulations are used to test the method’s efficiency and its statistical performance is analyzed using Monte Carlo simulation. Finally, the method is evaluated through a heating experimental benchmark. The obtained results show good agreement with the real system outputs.

This paper addresses a modified auxiliary model stochastic gradient recursive parameter identification algorithm (M-AM-SGRPIA) for a class of single input single output (SISO) linear output error models with multi-threshold quantized observations. It proves the convergence of the designed algorithm. A pattern-moving-based system dynamics description method with hybrid metrics is proposed for a kind of practical single input multiple output (SIMO) or SISO nonlinear systems, and a SISO linear output error model with multi-threshold quantized observations is adopted to approximate the unknown system. The system input design is accomplished using the measurement technology of random repeatability test, and the probabilistic characteristic of the explicit metric value is employed to estimate the implicit metric value of the pattern class variable. A modified auxiliary model stochastic gradient recursive algorithm (M-AM-SGRA) is designed to identify the model parameters, and the contraction mapping principle proves its convergence. Two numerical examples are given to demonstrate the feasibility and effectiveness of the achieved identification algorithm.

Based on the model-free adaptive control (MFAC) theory, the temperature tracking control problem of single-effect LiBr/H2O absorption chiller is explored. Due to the complex nonlinearity and strong coupling characteristics of the absorption refrigeration system, model-free adaptive control strategy is designed for its temperature tracking control. Nevertheless, the traditional model-free adaptive control has a slow tracking speed and poor denoising ability. In order to improve its control effect, output error rate is added to the objective function and new control laws of model-free adaptive control with output error rate (MFAC-OER) have been derived through an exhaustive convergence and stability analysis. The input information and output information of the absorption refrigeration system, namely the hot water pump frequency and chilled water outlet water temperature, are combined. The data model of the absorption refrigeration system is subsequently deduced using a compact format dynamic linearization method. Next, based on the single-effect absorption chiller experimental platform in our laboratory, its sixth-order dynamic model is built. Finally, the effectiveness and practicability of the improved control strategy are illustrated by numerical simulations and experimental operating data from our laboratory as well as by the dynamical model of the absorption chiller.