Neural network based method for compensating model error

Two traditional methods for compensating function model errors, the method of adding systematic parameters and the least-squares collection method, are introduced. A proposed method based on a BP neural network （called the H-BP algorithm） for compensating function model errors is put forward. The function model is assumed as y =f（x1, x2,… ,xn）, and the special structure of the H-BP algorithm is determined as （ n ＋ 1） ×p × 1, where （n ＋ 1） is the element number of the input layer, and the elements are xl, x2,…, xn and y＇ （ y＇ is the value calculated by the function model）; p is the element number of the hidden layer, and it is usually determined after many tests; 1 is the dement number of the output layer, and the element is △y = y0-y＇（y0 is the known value of the sample）. The calculation steps of the H-BP algorithm are introduced in detail. And then, the results of three methods for compensating function model errors from one engineering project are compared with each other. After being compensated, the accuracy of the traditional methods is about ± 19 mm, and the accuracy of the H-BP algorithm is ± 4. 3 mm. It shows that the proposed method based on a neural network is more effective than traditional methods for compensating function model errors.

Wavelet Neural Network Based on NARMA-L2 Model for Prediction of Thermal Characteristics in a Feed System

Research of thermal characteristics has been a key issue in the development of high-speed feed system. Most of the work carried out thus far is based on the principle of directly mapping the thermal error against the temperature of critical machine elements irrespective of the operating conditions. But recent researches show that different sets of operating parameters generated significantly different error values even though the temperature of the machine elements generated was similar. As such, it is important to develop a generic thermal error model which is capable of evaluating the positioning error induced by different operating parameters. This paper ultimately aims at the development of a comprehensive prediction model that can predict the thermal characteristics under different operating conditions （feeding speed, load and preload of ballscrew） in a feed system. A novel wavelet neural network based on feedback linearization autoregressive moving averaging （NARMA-L2） model is introduced to predict the temperature rise of sensitive points and thermal positioning errors considering the different operating conditions as the model inputs. Particle swarm optimization（PSO） algorithm is brought in as the training method. According to ISO230-2 Positioning Accuracy Measurement and ISO230-3 Thermal Effect Evaluation standards, experiments under different operating conditions were carried out on a self-made quasi high-speed feed system experimental bench HUST-FS-001 by using Pt100 as temperature sensor, and the positioning errors were measured by Heidenhain linear grating scale. The experiment results show that the recommended method can be used to predict temperature rise of sensitive points and thermal positioning errors with good accuracy. The work described in this paper lays a solid foundation of thermal error prediction and compensation in a feed system based on varying operating conditions and machine tool characteristics.

Simple model based on artificial neural network for early prediction and simulation winter rapeseed yield

The aim of the research was to create a prediction model for winter rapeseed yield.The constructed model enabled to perform simulation on 30 June,in the current year,immediately before harvesting.An artificial neural network with multilayer perceptron(MLP) topology was used to build the predictive model.The model was created on the basis of meteorological data(air temperature and atmospheric precipitation) and mineral fertilization data.The data were collected in the period 2008–2017 from 291 productive fields located in Poland,in the southern part of the Opole region.The assessment of the forecast quality created on the basis of the neural model has been verified by defining forecast errors using relative approximation error(RAE),root mean square error(RMS),mean absolute error(MAE),and mean absolute percentage error(MAPE) metrics.An important feature of the created predictive model is the ability to forecast the current agrotechnical year based on current weather and fertilizing data.The lowest value of the MAPE error was obtained for a neural network model based on the MLP network of 21:21-13-6-1:1 structure,which was 9.43%.The performed sensitivity analysis of the network examined the factors that have the greatest impact on the yield of winter rape.The highest rank 1 was obtained by an independent variable with the average air temperature from 1 January to 15 April of 2017(designation by the T1-4_CY model).

Prediction of constrained modulus for granular soil using 3D discrete element method and convolutional neural networks

To efficiently predict the mechanical parameters of granular soil based on its random micro-structure,this study proposed a novel approach combining numerical simulation and machine learning algorithms.Initially,3500 simulations of one-dimensional compression tests on coarse-grained sand using the three-dimensional(3D)discrete element method(DEM)were conducted to construct a database.In this process,the positions of the particles were randomly altered,and the particle assemblages changed.Interestingly,besides confirming the influence of particle size distribution parameters,the stress-strain curves differed despite an identical gradation size statistic when the particle position varied.Subsequently,the obtained data were partitioned into training,validation,and testing datasets at a 7:2:1 ratio.To convert the DEM model into a multi-dimensional matrix that computers can recognize,the 3D DEM models were first sliced to extract multi-layer two-dimensional(2D)cross-sectional data.Redundant information was then eliminated via gray processing,and the data were stacked to form a new 3D matrix representing the granular soil’s fabric.Subsequently,utilizing the Python language and Pytorch framework,a 3D convolutional neural networks(CNNs)model was developed to establish the relationship between the constrained modulus obtained from DEM simulations and the soil’s fabric.The mean squared error(MSE)function was utilized to assess the loss value during the training process.When the learning rate(LR)fell within the range of 10-5e10-1,and the batch sizes(BSs)were 4,8,16,32,and 64,the loss value stabilized after 100 training epochs in the training and validation dataset.For BS?32 and LR?10-3,the loss reached a minimum.In the testing set,a comparative evaluation of the predicted constrained modulus from the 3D CNNs versus the simulated modulus obtained via DEM reveals a minimum mean absolute percentage error(MAPE)of 4.43%under the optimized condition,demonstrating the accuracy of this approach.Thus,by combining DEM and CNNs,the variation of soil’s mechanical characteristics related to its random fabric would be efficiently evaluated by directly tracking the particle assemblages.

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.

NONLINEAR MODELING AND CONTROLLING OF ARTIFICIAL MUSCLE SYSTEM USING NEURAL NETWORKS

The pneumatic artificial muscles are widely used in the fields of medicalrobots, etc. Neural networks are applied to modeling and controlling of artificial muscle system. Asingle-joint artificial muscle test system is designed. The recursive prediction error (RPE)algorithm which yields faster convergence than back propagation (BP) algorithm is applied to trainthe neural networks. The realization of RPE algorithm is given. The difference of modeling ofartificial muscles using neural networks with different input nodes and different hidden layer nodesis discussed. On this basis the nonlinear control scheme using neural networks for artificialmuscle system has been introduced. The experimental results show that the nonlinear control schemeyields faster response and higher control accuracy than the traditional linear control scheme.

A New Selective Neural Network Ensemble Method Based on Error Vectorization and Its Application in High-density Polyethylene (HDPE) Cascade Reaction Process

Chemical processes are complex, for which traditional neural network models usually can not lead to satisfactory accuracy. Selective neural network ensemble is an effective way to enhance the generalization accuracy of networks, but there are some problems, e.g., lacking of unified definition of diversity among component neural networks and difficult to improve the accuracy by selecting if the diversities of available networks are small. In this study, the output errors of networks are vectorized, the diversity of networks is defined based on the error vectors, and the size of ensemble is analyzed. Then an error vectorization based selective neural network ensemble (EVSNE) is proposed, in which the error vector of each network can offset that of the other networks by training the component networks orderly. Thus the component networks have large diversity. Experiments and comparisons over standard data sets and actual chemical process data set for production of high-density polyethylene demonstrate that EVSNE performs better in generalization ability.

Estimating Average Reservoir Pressure： A Neural Network Approach with Limited Data

Insight into average oil pressure in gas reservoirs and changes in production （time）, play a critical role in reservoir and production performance, economic evaluation and reservoir management. In all practicality, average reservoir pressure can be conducted only when producing wells are shut in. This is regarded as a pressure build-up test. During the test, the wellbore pressure is recorded as a function of time. Currently, the only available method with which to obtain average reservoir pressure is to conduct an extended build-up test. It must then be evaluated using Homer or MDH （Miller, Dyes and Huchinson） valuation procedures. During production, average reservoir pressure declines due to fluid withdrawal from the wells and therefore, the average reservoirpressure is updated, periodically. A significant economic loss occurs during the entire pressure build-up test when producing wells are shut in. In this study, a neural network model has been established to map a nonlinear time-varying relationship which controls reservoir production history in order to predict and interpolate average reservoir pressure without closing the producing wells. This technique is suitable for constant and variable flow rates.

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.

Novel Neural Network Inspired by Neuro-Endocrine-Immune System with Its Application to Beam Pumping Unit

Inspired by the modulation mechanism of neuroendocrine-immune system(NEIs),a novel structure of artificial neural network(ANN) named NEI-NN and its learning method are presented.The NEI-NN includes two parts,i.e.,positive subnetwork(PSN) and negative sub-network(NSN).The neuron functions of PSN and NSN are designed according to the increased and decreased secretion functions of hormone,respectively.In order to make the novel neural network learn quickly,the novel neuron based on some characteristics of NEIs is also redesigned.Besides the normal input signals,two control signals are considered in the proposed solution.One is the enable/disable signal,and the other is the slope control signal.The former can modify the structure of NEI-NN,and the later can regulate the evolutionary speed of NEINN.The NEI-NN can obtain the optimized network structure by using error back-propagation(BP) learning algorithm.Since the modeling of the beam pumping unit is very difficult by using the conventional method,the modeling of bean bump unit is chosen to examine the performance of the NEI-NN.The experiment results show that the optimized structure and learning speed of NEI-NN are better than those of the conventional neural network.

Spindle Thermal Error Optimization Modeling of a Five-axis Machine Tool

Aiming at the problem of low machining accu- racy and uncontrollable thermal errors of NC machine tools, spindle thermal error measurement, modeling and compensation of a two turntable five-axis machine tool are researched. Measurement experiment of heat sources and thermal errors are carried out, and GRA（grey relational analysis） method is introduced into the selection of tem- perature variables used for thermal error modeling. In order to analyze the influence of different heat sources on spindle thermal errors, an ANN （artificial neural network） model is presented, and ABC（artificial bee colony） algorithm is introduced to train the link weights of ANN, a new ABC- NN（Artificial bee colony-based neural network） modeling method is proposed and used in the prediction of spindle thermal errors. In order to test the prediction performance of ABC-NN model, an experiment system is developed, the prediction results of LSR （least squares regression）, ANN and ABC-NN are compared with the measurement results of spindle thermal errors. Experiment results show that the prediction accuracy of ABC-NN model is higher than LSR and ANN, and the residual error is smaller than 3 pm, the new modeling method is feasible. The proposed research provides instruction to compensate thermal errors and improve machining accuracy of NC machine tools.

Synchronization of chaos using radial basis functions neural networks

The Radial Basis Functions Neural Network （RBFNN） is used to establish the model of a response system through the input and output data of the system. The synchronization between a drive system and the response system can be implemented by employing the RBFNN model and state feedback control. In this case, the exact mathematical model, which is the precondition for the conventional method, is unnecessary for implementing synchronization. The effect of the model error is investigated and a corresponding theorem is developed. The effect of the parameter perturbations and the measurement noise is investigated through simulations. The simulation results under different conditions show the effectiveness of the method.

A neural network method for estimating weighted mean temperature over China and adjacent areas

To improve the applicability of the global pressure and temperature 2 wet(GPT2w)model in estimating the weighted mean temperature in China and adjacent areas,the error compensation technology based on the neural network was proposed,and a total of 374800 meteorological profiles measured from 2006 to 2015 of 100 radiosonde stations distributed in China and adjacent areas were used to establish an enhanced empirical model for estimating the weighted mean temperature in this region.The data from 2016 to 2018 of the remaining 92 stations in this region was used to test the performance of the proposed model.Results show that the proposed model is about 14.9%better than the GPT2w model and about 7.6%better than the Bevis model with measured surface temperature in accuracy.The performance of the proposed model is significantly improved compared with the GPT2w model not only at different height ranges,but also in different months throughout the year.Moreover,the accuracy of the weighted mean temperature estimation is greatly improved in the northwestern region of China where the radiosonde stations are very rarely distributed.The proposed model shows a great application potential in the nationwide real-time ground-based global navigation satellite system(GNSS)water vapor remote sensing.

Dynamic Coordination of Uncalibrated Hand/Eye Robotic System Based on Neural Network

A nonlinear visual mapping model is presented to replace the image Jacobian relation for uncalibrated hand/eye coordination. A new visual tracking controller based on artificial neural network is designed. Simulation results show that this method can drive the static tracking error to zero quickly and keep good robustness and adaptability at the same time. In addition, the algorithm is very easy to be implemented with low computational complexity.

ANN model of subdivision error based on genetic algorithm

According to the test data of subdivision errors in the measuring cycle of angular measuring system, the characteristics of subdivision errors generated by this system are analyzed. It is found that the subdivision errors are mainly due to the rotary-type inductosyn itself. For the characteristic of cyclical change, the subdivision errors in other measuring cycles can be compensated by the subdivision error model in one measuring cycle. Using the measured error data as training samples, combining GA and BP algorithm, an ANN model of subdivision error is designed. Simulation results indicate that GA reduces the uncertainty in the training process of the ANN model, and enhances the generalization of the model. Compared with the error model based on the least-mean-squared method, the designed ANN model of subdivision errors can achieve higher compensating precision.

Investigating the Synthesis of RBF Networks

The approximation capability of RBF networks is investigated using a test function and a fixed finite number of training data. The test function used allows to confirm the recently introducedconcept of second derivative dependent placement of RBF centers. Different Gaussian RBF networksare trained varying the width and the number of centers (number of hidden units). The dependenceof the approximation error on these network parameters is studied experimentally.

Support vector regression-based internal model control

This paper proposes a design of internal model control systems for process with delay by using support vector regression(SVR).The proposed system fully uses the excellent nonlinear estimation performance of SVR with the structural risk minimization principle.Closed-system stability and steady error are analyzed for the existence of modeling errors.The simulations show that the proposed control systems have the better control performance than that by neural networks in the cases of the training samples with small size and noises.

Laser Interferometer Based Measurement for Positioning Error Compensation in Cartesian Multi-Axis Systems

Accuracy is one of the most important key indices to evaluate multi-axis systems’ (MAS’s) characteristics and performances. The accuracy of MAS’s such as machine tools, measuring machines and robots is adversely affected by various error sources, including geometric imperfections, thermal deformations, load effects, and dynamic disturbances. The increasing demand for higher dimensional accuracy in various industrial applications has created the need to develop cost-effective methods for enhancing the overall performance of these mechanisms. Improving the accuracy of a MAS by upgrading the physical structure would lead to an exponential increase in manufacturing costs without totally eliminating geometrical deviations and thermal deformations of MAS components. Hence, the idea of reducing MAS’s error by a software-based alternative approach to provide real-time prediction and correction of geometric and thermally induced errors is considered a strategic step toward achieving the full potential of the MAS. This paper presents a structured approach designed to improve the accuracy of Cartesian MAS’s through software error compensation. Four steps are required to develop and implement this approach: (i) measurement of error components using a multidimensional laser interferometer system, (ii) tridimensional volumetric error mapping using rigid body kinematics, (iii) volumetric error prediction via an artificial neural network model, and finally (iv) implementation of the on-line error compensation. An illustrative example using a bridge type coordinate measuring machine is presented.

Backlash Error Measurement and Compensation on the Vertical Machining Center

The position errors in the axis direction of a vertical machine center have been measured by means of the VM101 linear encored measurement system. The character of the backlash error is discussed;results show that the backlash error has great influence on the position error. The position accuracy is enhanced after the backlash errors are compensated.

基于PSO-BP神经网络的分拣机器人视觉反馈跟踪

针对分拣机器人视觉反馈跟踪精度差、耗时较长的问题,研究基于粒子群算法-反向传播(particle swarm optimization-back propagation,PSO-BP)神经网络的分拣机器人视觉反馈跟踪方法,以提升视觉反馈跟踪效果。依据分拣机器人的视觉反馈信息,建立分拣机器人运动学模型,并求解分拣机器人机械臂输出位置和输入位置的误差函数;利用PSO算法优化BP神经网络的权值与偏置;在权值与偏置优化后的BP神经网络内,输入误差函数,预测分拣机器人视觉反馈跟踪控制量;利用预测视觉反馈跟踪控制量,在线调整增量式比例-积分-微分(proportional-integral-derivative,PID)的参数,输出高精度的分拣机器人视觉反馈跟踪控制量,实现分拣机器人视觉反馈跟踪。实验结果表明,该方法可有效视觉反馈跟踪分拣机器人机械臂的关节角;存在干扰情况下,在运行时间为10 s左右时,阶跃响应趋于稳定;有干扰情况下,视觉反馈跟踪的平均误差为0.09 cm,耗时平均值为0.10 ms;无干扰情况下,平均误差为0.03 cm,耗时平均值为0.04 ms。