A Neural-network-based Alternative Scheme to Include Nonhydrostatic Processes in an Atmospheric Dynamical Core

Here,a nonhydrostatic alternative scheme(NAS)is proposed for the grey zone where the nonhydrostatic impact on the atmosphere is evident but not large enough to justify the necessity to include an implicit nonhydrostatic solver in an atmospheric dynamical core.The NAS is designed to replace this solver,which can be incorporated into any hydrostatic models so that existing well-developed hydrostatic models can effectively serve for a longer time.Recent advances in machine learning(ML)provide a potential tool for capturing the main complicated nonlinear-nonhydrostatic relationship.In this study,an ML approach called a neural network(NN)was adopted to select leading input features and develop the NAS.The NNs were trained and evaluated with 12-day simulation results of dry baroclinic-wave tests by the Weather Research and Forecasting(WRF)model.The forward time difference of the nonhydrostatic tendency was used as the target variable,and the five selected features were the nonhydrostatic tendency at the last time step,and four hydrostatic variables at the current step including geopotential height,pressure in two different forms,and potential temperature,respectively.Finally,a practical NAS was developed with these features and trained layer by layer at a 20-km horizontal resolution,which can accurately reproduce the temporal variation and vertical distribution of the nonhydrostatic tendency.Corrected by the NN-based NAS,the improved hydrostatic solver at different horizontal resolutions can run stably for at least one month and effectively reduce most of the nonhydrostatic errors in terms of system bias,anomaly root-mean-square error,and the error of the wave spatial pattern,which proves the feasibility and superiority of this scheme.

THE MODEL VALIDATION OF DYNAMIC NEURAL NETWORKS

This paper investigates the problem of the model validation in identifying discrete-time-nonlinear dynamic systems by using neural networks with a single hidden layer.Based on the estimation theory,a synthetic error-index(SEI)criterion for the neural network models has been developed.By using the powerful training algorithm of recursive prediction error (RPE),two simulated non-linear systems are studied,and the results show that the synthetic error-index criterion can be used to verify the dynamic neural network models.Furthermore,the proposed technique is much simple in calculation than that of the effective correlation tests.Finally,some problems required by further study are discussed.

Dynamics Modeling and Robust Trajectory Tracking Control for a Class of Hybrid Humanoid Arm Based on Neural Network

In order to solve the problem of trajectory tracking for a class of novel serial-parallel hybrid humanoid arm（HHA）, which has parameters uncertainty, frictions, disturbance, abrasion and pulse forces derived from motors, a multistep dynamics modeling strategy is proposed and a robust controller based on neural network（NN）-adaptive algorithm is designed. At the first step of dynamics modeling, the dynamics model of the reduced HHA is established by Lagrange method. At the second step of dynamics modeling, the parameter uncertain part resulting mainly from the idealization of the HHA is learned by adaptive algorithm. In the trajectory tracking controller, the radial basis function（RBF） NN, whose optimal weights are learned online by adaptive algorithm, is used to learn the upper limit function of the total uncertainties including frictions, disturbances, abrasion and pulse forces. To a great extent, the conservatism of this robust trajectory tracking controller is reduced, and by this controller the HHA can impersonate mostly human actions. The proof and simulation results testify the validity of the adaptive strategy for parameter learning and the neural network-adaptive strategy for the trajectory tracking control.

Predicting Model for Complex Production Process Based on Dynamic Neural Network

Based on the comparison of several methods of time series predicting, this paper points out that it is necessary to use dynamic neural network in modeling of complex production process. Because self feedback and mutual feedback are adopted among nodes at the same layer in Elman network, it has stronger ability of dynamic approximation, and can describe any non linear dynamic system. After the structure and mathematical description being given, dynamic back propagation (BP) algorithm of training weights of Elman neural network is deduced. At last, the network is used to predict ash content of black amber in jigging production process. The results show that this neural network is powerful in predicting and suitable for modeling, predicting, and controling of complex production process.

Neural Network Modeling and System Simulating for the Dynamic Process of Varied Gap Pulsed GTAW with Wire Filler

As the base of the research work on the weld shape control during pulsed gas tungsten arc welding （GTAW） with wire filler, this paper addressed the modeling of the dynamic welding process. Topside length Lt, maximum width Wt and half-length ratio Rh1 were selected to depict topside weld pool shape, and were measured on-line by vision sensing. A dynamic neural network model was constructed to predict the usually unmeasured backside width and topside height of the weld through topside shape parameters and welding parameters. The inputs of the model were the welding parameters （peak current, pulse duty ratio, welding speed, filler rate）, the joint gap, the topside pool shape parameters （Lt, Wt, and Rh1）, and their history values at two former pulse, a total of 24 numbers. The validating experiment results proved that the artificial neural network （ANN） model had high precision and could be used in process control. At last, with the developed dynamic model, steady and dynamic behavior was analyzed by simulation experiments, which discovered the variation rules of weld pool shape parameters under different welding parameters, and further knew well the characteristic of the welding process.

Neural network modeling for dynamic pulsed GTAW process with wire filler based on MATLAB

Double-sided weld pool shapes were determined by multiple welding parameters and wire feed parameters during pulsed GTAW with wire filler. Aiming at such a system with multiple inputs and outputs, an effective modeling method, consisting of the impulse signal design, model structure and parameter identification and verification, was developed based on MATLAB software. Then, dynamic neural network models, TDNNM (Topside dynamic neural network model) and BHDNNM (Backside width and topside height dynamic neural network model), were established to predict double-sided shape parameters of the weld pool. The characteristic relationship of the welding process was simulated and analyzed with the models.

Hybrid dynamic model of polymer electrolyte membrane fuel cell stack using variable neural network

The polymer electrolyte membrane（PEM） fuel cell has been regarded as a potential alternative power source,and a model is necessary for its design,control and power management.A hybrid dynamic model of PEM fuel cell,which combines the advantages of mechanism model and black-box model,is proposed in this paper.To improve the performance,the static neural network and variable neural network are used to build the black-box model.The static neural network can significantly improve the static performance of the hybrid model,and the variable neural network makes the hybrid dynamic model predict the real PEM fuel cell behavior with required accuracy.Finally,the hybrid dynamic model is validated with a 500 W PEM fuel cell.The static and transient experiment results show that the hybrid dynamic model can predict the behavior of the fuel cell stack accurately and therefore can be effectively utilized in practical application.

Identification of Artificial Neural Network Models for Three-Dimensional Simulation of a Vibration-Acoustic Dynamic System

Industrial noise can be successfully mitigated with the combined use of passive and Active Noise Control (ANC) strategies. In a noisy area, a practical solution for noise attenuation may include both the use of baffles and ANC. When the operator is required to stay in movement in a delimited spatial area, conventional ANC is usually not able to adequately cancel the noise over the whole area. New control strategies need to be devised to achieve acceptable spatial coverage. A three-dimensional actuator model is proposed in this paper. Active Noise Control (ANC) usually requires a feedback noise measurement for the proper response of the loop controller. In some situations, especially where the real-time tridimensional positioning of a feedback transducer is unfeasible, the availability of a 3D precise noise level estimator is indispensable. In our previous works [1,2], using a vibrating signal of the primary source of noise as an input reference for spatial noise level prediction proved to be a very good choice. Another interesting aspect observed in those previous works was the need for a variable-structure linear model, which is equivalent to a sort of a nonlinear model, with unknown analytical equivalence until now. To overcome this in this paper we propose a model structure based on an Artificial Neural Network (ANN) as a nonlinear black-box model to capture the dynamic nonlinear behaveior of the investigated process. This can be used in a future closed loop noise cancelling strategy. We devise an ANN architecture and a corresponding training methodology to cope with the problem, and a MISO (Multi-Input Single-Output) model structure is used in the identification of the system dynamics. A metric is established to compare the obtained results with other works elsewhere. The results show that the obtained model is consistent and it adequately describes the main dynamics of the studied phenomenon, showing that the MISO approach using an ANN is appropriate for the simulation of the investigated process. A clear conclusion is reached highlighting the promising results obtained using this kind of modeling for ANC.

Dynamic prediction of gas emission based on wavelet neural network toolbox

This paper presents a method for dynamically predicting gas emission quantity based on the wavelet neural network （WNN） toolbox. Such a method is able to predict the gas emission quantity in adjacent subsequent time intervals through training the WNN with even time-interval samples. The method builds successive new model with the width of sliding window remaining invariable so as to obtain a dynamic prediction method for gas emission quantity. Furthermore, the method performs prediction by a self-developed WNN toolbox. Experiments indicate that such a model can overcome the deficiencies of the traditional static prediction model and can fully make use of the feature extraction capability of wavelet base function to reflect the geological feature of gas emission quantity dynamically. The method is characterized by simplicity, flexibility, small data scale, fast convergence rate and high prediction precision. In addition, the method is also characterized by certainty and repeatability of the predicted results. The effectiveness of this method is confirmed by simulation results. Therefore, this method will exert practical significance on promoting the application of WNN.

Development of an integrated dynamic model for supply security and resilience analysis of natural gas pipeline network systems

An integrated dynamic model of natural gas pipeline networks is developed in this paper.Components for gas supply,e.g.,pipelines,junctions,compressor stations,LNG terminals,regulation stations and gas storage facilities are included in the model.These components are firstly modeled with respect to their properties and functions and,then,integrated at the system level by Graph Theory.The model can be used for simulating the system response in different scenarios of operation,and evaluate the consequences from the perspectives of supply security and resilience.A case study is considered to evaluate the accuracy of the model by benchmarking its results against those from literature and the software Pipeline Studio.Finally,the model is applied on a relatively complex natural gas pipeline network and the results are analyzed in detail from the supply security and resilience points of view.The main contributions of the paper are:firstly,a novel model of a complex gas pipeline network is proposed as a dynamic state-space model at system level;a method,based on the dynamic model,is proposed to analyze the security and resilience of supply from a system perspective.

Dynamic modeling and RBF neural network compensation control for space flexible manipulator with an underactuated hand

In space operation,flexible manipulators and gripper mechanisms have been widely used because of light weight and flexibility.However,the vibration caused by slender structures in manipulators and the parameter perturbation caused by the uncertainty derived from grasping mass variation cannot be ignored.The existence of vibration and parameter perturbation makes the rotation control of flexible manipulators difficult,which seriously affects the operation accuracy of manipulators.What’s more,the complex dynamic coupling brings great challenges to the dynamics modeling and vibration analysis.To solve this problem,this paper takes the space flexible manipulator with an underactuated hand(SFMUH)as the research object.The dynamics model considering flexibility,multiple nonlinear elements and disturbance torque is established by the assumed modal method(AMM)and Hamilton’s principle.A dynamic modeling simplification method is proposed by analyzing the nonlinear terms.What’s more,a sliding mode control(SMC)method combined with the radial basis function(RBF)neural network compensation is proposed.Besides,the control law is designed using a saturation function in the control method to weaken the chatter phenomenon.With the help of neural networks to identify the uncertainty composition in the SFMUH,the tracking accuracy is improved.The results of ground control experiments verify the advantages of the control method for vibration suppression of the SFMUH.

Neural-Network-Based Nonlinear Model Predictive Tracking Control of a Pneumatic Muscle Actuator-Driven Exoskeleton

Pneumatic muscle actuators(PMAs)are compliant and suitable for robotic devices that have been shown to be effective in assisting patients with neurologic injuries,such as strokes,spinal cord injuries,etc.,to accomplish rehabilitation tasks.However,because PMAs have nonlinearities,hysteresis,and uncertainties,etc.,complex mechanisms are rarely involved in the study of PMA-driven robotic systems.In this paper,we use nonlinear model predictive control(NMPC)and an extension of the echo state network called an echo state Gaussian process(ESGP)to design a tracking controller for a PMA-driven lower limb exoskeleton.The dynamics of the system include the PMA actuation and mechanism of the leg orthoses;thus,the system is represented by two nonlinear uncertain subsystems.To facilitate the design of the controller,joint angles of leg orthoses are forecasted based on the universal approximation ability of the ESGP.A gradient descent algorithm is employed to solve the optimization problem and generate the control signal.The stability of the closed-loop system is guaranteed when the ESGP is capable of approximating system dynamics.Simulations and experiments are conducted to verify the approximation ability of the ESGP and achieve gait pattern training with four healthy subjects.

Dale’s Principle Is Necessary for an Optimal Neuronal Network’s Dynamics

We study a mathematical model of biological neuronal networks composed by any finite number N ≥ 2 of non-necessarily identical cells. The model is a deterministic dynamical system governed by finite-dimensional impulsive differential equations. The statical structure of the network is described by a directed and weighted graph whose nodes are certain subsets of neurons, and whose edges are the groups of synaptical connections among those subsets. First, we prove that among all the possible networks such as their respective graphs are mutually isomorphic, there exists a dynamical optimum. This optimal network exhibits the richest dynamics: namely, it is capable to show the most diverse set of responses (i.e. orbits in the future) under external stimulus or signals. Second, we prove that all the neurons of a dynamically optimal neuronal network necessarily satisfy Dale’s Principle, i.e. each neuron must be either excitatory or inhibitory, but not mixed. So, Dale’s Principle is a mathematical necessary consequence of a theoretic optimization process of the dynamics of the network. Finally, we prove that Dale’s Principle is not sufficient for the dynamical optimization of the network.

DOWNSCALING FORECAST OF MONTHLY PRECIPITATION OVER GUANGXI BASED ON BP NEURAL NETWORK MODEL

Variables fields such as enstrophy, meridional-wind and zonal-wind variables are derived from monthly 500 hPa geopotential height anomalous fields. In this work, we select original predictors from monthly 500-hPa geopotential height anomalous fields and their variables in June of 1958 - 2001, and determine comprehensive predictors by conducting empirical orthogonal function (EOF) respectively with the original predictors. A downscaling forecast model based on the back propagation (BP) neural network is built by use of the comprehensive predictors to predict the monthly precipitation in June over Guangxi with the monthly dynamic extended range forecast products. For comparison, we also build another BP neural network model with the same predictands by using the former comprehensive predictors selected from 500-hPa geopotential height anomalous fields in May to December of 1957 - 2000 and January to April of 1958 - 2001. The two models are tested and results show that the precision of superposition of the downscaling model is better than that of the one based on former comprehensive predictors, but the prediction accuracy of the downscaling model depends on the output of monthly dynamic extended range forecast.

Estimation of Battery State of Health Using Back Propagation Neural Network

100 pieces of 26650-type Lithium iron phosphate（LiFePO4） batteries cycled with a fixed charge and discharge rate are tested, and the influence of the battery internal resistance and the instantaneous voltage drop at the start of discharge on the state of health（SOH） is discussed. A back propagation（BP） neural network model using additional momentum is built up to estimate the state of health of Li-ion batteries. The additional 10 pieces are used to verify the feasibility of the proposed method. The results show that the neural network prediction model have a higher accuracy and can be embedded into battery management system（BMS） to estimate SOH of LiFePO4 Li-ion batteries.

A REALISTIC MODEL OF NEURAL NETWORKS

A realistic model of neural networks was proposed in this paper.The dynamicprocess of neural impulse discharging was considered.The equations of the model correspondto postsynaptic potentials,receptor potentials,initial segment graded potentials and the impulsetrain along the axon respectively.To solve the equations numerically,a recurrent algorithm and itscorresponding flow chart was also developed.The simulation results can imitate adaptation,post-excitation inhibition,and phase locking of sensory receptors;they can also imitate the transientresponses of lateral inhibitory network and Mach band phenomenon when they trended to besteady.The simulation results also showed that the lateral inhibitory network was sensitive tomoving objects.

Constructing reduced model for complex physical systems via interpolation and neural networks

The work studies model reduction method for nonlinear systems based on proper orthogonal decomposition (POD)and discrete empirical interpolation method (DEIM). Instead of using the classical DEIM to directly approximate thenonlinear term of a system, our approach extracts the main part of the nonlinear term with a linear approximation beforeapproximating the residual with the DEIM. We construct the linear term by Taylor series expansion and dynamic modedecomposition (DMD), respectively, so as to obtain a more accurate reconstruction of the nonlinear term. In addition, anovel error prediction model is devised for the POD-DEIM reduced systems by employing neural networks with the aid oferror data. The error model is cheaply computable and can be adopted as a remedy model to enhance the reduction accuracy.Finally, numerical experiments are performed on two nonlinear problems to show the performance of the proposed method.

Self-Constructing Neural Network Modeling and Control of an AGV

Tracking precision of pre-planned trajectories is essential for an auto-guided vehicle (AGV). The purpose of this paper is to design a self-constructing wavelet neural network (SCWNN) method for dynamical modeling and control of a 2-DOF AGV. In control systems of AGVs, kinematical models have been preferred in recent research documents. However, in this paper, to enhance the trajectory tracking performance through including the AGV’s inertial effects in the control system, a learned dynamical model is replaced to the kinematical kind. As the base of a control system, the mathematical models are not preferred due to modeling uncertainties and exogenous inputs. Therefore, adaptive dynamic and control models of AGV are proposed using a four-layer SCWNN system comprising of the input, wavelet, product, and output layers. By use of the SCWNN, a robust controller against uncertainties is developed, which yields the perfect convergence of AGV to reference trajectories. Owing to the adaptive structure, the number of nodes in the layers is adjusted in online and thus the computational burden of the neural network methods is decreased. Using software simulations, the tracking performance of the proposed control system is assessed.

Nonlinear Systems Identification via an Input-Output Model Based on a Feedforward Neural Network

This paper develops a feedforward neural network based input output model for a general unknown nonlinear dynamic system identification when only the inputs and outputs are accessible observations. In the developed model, the size of the input space is directly related to the system order. By monitoring the identification error characteristic curve, we are able to determine the system order and subsequently an appropriate network structure for systems identification. Simulation results are promising and show that generic nonlinear systems can be identified, different cases of the same system can also be discriminated by our model.

Dynamic Equivalent Modeling for Black-box Microgrids Under Multi-operating-point by Using LSTM

Since the high penetration of distributed energy sources complicates the dynamics of electrical power systems,accurate dynamic models are indispensable for study on the transient behavior of the microgrid(MG).In some practices,the lack of full detailed information results in failure of dif-ferential equation based dynamic modeling,which leads to a demand for a black-box MG modeling method.It is a critical challenge to maintain the effectiveness of the black-box model under a wide operating range and various fault conditions.In this paper,inspired by the mathematical equivalence between the recurrent neural network(RNN)and differential-algebraic equations(DAEs),a dynamic equivalent modeling method,using long short-term memory(LSTM),is presented to tackle this challenge.At first,the modeling equivalence and advantages of our basic idea are explained.Then,modeling procedures,including data preparation and design guidelines,are presented.Finally,the proposed method is applied to a multi-microgrid testing system for performance evaluation.The results,under various scenarios,reveal that the proposed modeling method has an adequate capability for representing the dynamic behaviors of a black-box MG under grid fault and operating point changing conditions.Index Terms-Deep learning,dynamic behavior,dynamic equivalent model,microgrid,neural network.