Properties and performance of orthogonal neural network in function approximation

This paper presents a new single-layer neural network which is based on orthogonal functions. This neural network is developed to avoid the problems of traditional feedforward neural networks such as the determination of initial weights and the numbers of layers and processing elements. The desired output accuracy determines the required number of processing elements. Because weights are unique, the training of the neural network converges rapidly. An experiment in approximating typical continuous and discrete functions is given. The results show that the neural network has excellent performance in convergence time and approximation error.

PDF HTML阅读 XML下载 导出引用 引用提醒 1988-2013年基于BP神经网络的植被叶面积指数遥感定量反演 DOI: 10.5846/stxb201703290547 作者: 作者单位: 南京林业大学,南京林业大学,南京林业大学,南京林业大学,南京林业大学,南京林业大学 作者简介: 通讯作者: 中图分类号: 基金项目: 国家重点研发计划资助项目（2017YFC0505505）；国家自然科学基金项目（31200534）；江苏高校优势学科建设工程资助项目；2014年江苏省普通高校学术学位研究生科研创新计划项目 Quantitative inversion of long sequential leaf area index using remote sensing based on BP neural network from 1988 to 2013 Author: Affiliation: Key Laboratory of Soil and Water Conservation and Ecological Restoration in Jiangsu Province,Collaborative Innovation Center of Sustainable Forestry in Southern China of Jiangsu Province,Nanjing Forestry University,Nanjing,Key Laboratory of Soil and Water Conservation and Ecological Restoration in Jiangsu Province,Collaborative Innovation Center of Sustainable Forestry in Southern China of Jiangsu Province,Nanjing Forestry University,Nanjing,Key Laboratory of Soil and Water Conservation and Ecological Restoration in Jiangsu Province,Collaborative Innovation Center of Sustainable Forestry in Southern China of Jiangsu Province,Nanjing Forestry University,Nanjing,Key Laboratory of Soil and Water Conservation and Ecological Restoration in Jiangsu Province,Collaborative Innovation Center of Sustainable Forestry in Southern China of Jiangsu Province,Nanjing Forestry University,Nanjing,Key Laboratory of Soil and Water Conservation and Ecological Restoration in Jiangsu Province,Collaborative Innovation Center of Sustainable Forestry in Southern China of Jiangsu Province,Nanjing Forestry University,Nanjing,Key Laboratory of Soil and Water Conservation and Ecological Restoration in Jiangsu Province,Collaborative Innovation Center of Sustainable Forestry in Southern China of Jiangsu Province,Nanjing Forestry University,Nanjing Fund Project: 摘要 | 图/表 | 访问统计 | 参考文献 | 相似文献 | 引证文献 | 资源附件 | 文章评论 摘要:叶面积指数（Leaf Area Index，LAI）高度综合了植被水平覆盖状况和垂直结构，以及枯枝落叶层厚薄和地下生物量多少，是植被影响土壤侵蚀的主要方面。区域尺度的时间序列叶面积指数揭示了区域土壤侵蚀的演化过程。因此，及时准确地掌握区域尺度上长时间序列的植被LAI，对研究土壤侵蚀动态变化与植被的关系至关重要。选择南京市1988-2013年10期遥感影像，基于反向传播（Back Propagation，BP）神经网络构建LAI反演模型，进行了长时间序列的叶面积指数反演。结合2009和2010年LAI实测值，验证与探讨了该模型的评价精度与适应性。结果表明：（1）该模型拟合度较高，2009和2010年平均相对误差、均方根误差、相关系数分别是0.2395和0.2174，0.2962和0.2581，0.7713和0.6844，各项精度评价指标均较好；（2）统计分析去除耕地后全市LAI变化，低植被覆盖（LAI<2）面积不断增加，高植被覆盖区（LAI>3）面积先减少后增加，耕地面积不断减少，符合南京市的发展变化规律；（3）主城区LAI年际变化与其他学者得到的南京市植被盖度变化趋势一致，反演结果的时序性较高。本文提出的基于反向传播神经网络模型反演长时间序列LAI是可行的，为区域尺度土壤侵蚀定量遥感监测提供新途径。 Abstract:Leaf Area Index(LAI) can reflect the horizontal coverage, vertical structure of vegetation, the thickness of the litter layer and the amount of underground biomass, which is the main aspect of vegetation affecting soil erosion. It is very important to monitor the changes in the amount of soil erosion, for useful information to guide the planning of soil and water conservation, protect the soil and water resources and control the soil erosion. Therefore, the method by which we obtain high quality and long sequential LAI at a regional scale is very important for analyzing the relationship between the dynamic changes in soil erosion and vegetation. Previous studies showed that the neural network had an incomparable superiority in terms of complex, nonlinear data fitting and pattern recognition, and had been successfully applied to inverse the LAI in Nanjing based on the multi-spectral remote sensing data derived from the Landsat 8 Operational Land Imager(OLI), four types of vegetation indices(Normalized Difference Vegetation Index, NDVI; Ratio Vegetation Index, RVI; Soil-adjusted Vegetation Index, SAVI; Modified Soil adjusted Vegetation Index, MSAVI), and measured LAI data. The results showed that the accuracy of retrieval was good. In this paper, we used the Back Propagation(BP) neural network model to inverse the LAI in Nanjing during 1988-2013 based on the data derived from Landsat 8 OLI and Landsat 5 Thematic Mapper(TM). Based on the measured values of LAI in 2009 and 2010, the evaluation accuracy and adaptability of the model were verified and discussed. The results showed that:(1) The model had a fitting of higher degree, and average relative errors(MAPE), root mean square errors(RMSE), and correlation coefficients(R) in 2009 and 2010 of 0.2395 and 0.2174, 0.2962 and 0.2581, and 0.7713 and 0.6844, respectively. Each accuracy evaluation index was good.(2) Following statistical analysis, we found that the low vegetation coverage area(LAI < 2) exhibited an increasing trend, the high vegetation coverage area(LAI > 3) presented a first decreasing and then increasing trend, while the cultivated land area decreased with the rapid development in Nanjing.(3) To analyze accurately the LAI, we extracted the LAI in the main urban area, and found that there was a relatively high inversion value, and the inter-annual change in LAI was consistent with the change in vegetation coverage in Nanjing reported by other studies. Therefore, we could see that the BP neural network model had a high accuracy for the time series LAI inversion. It provides a new way for quantitative remote sensing monitoring of regional soil erosion. Moreover, because of other potential limiting factors, such as the errors produced by the BP neural network model, the large area of the inversion area, the complexity of vegetation types and community structure, etc., the inversion accuracy of LAI through remote sensing still needs to be explored, and the inversion method improved. We will try to establish a multi-angle LAI inversion method to construct the coupling model of LAI and soil erosion or quantitative fusion of multi-source remote sensing images in the future study. 参考文献 相似文献 引证文献

This article discusses the application of orthogonal neural networks to detect collisions between multiple robot manipulators that work in an overlapped space. By applying an expansion/shrinkage algorithm, the problem of collision detection between arms is transformed into that among cylinders (or rectangular solids) and line segments. This mapping simplifies the collision detection problem and thus neural networks can be applied to solve it. The property of parallel processing enables neural networks to detect collisions rapidly. A single‐layer orthogonal neural network is developed to avert the problems of conventional multilayer feedforward neural networks such as initial weights and the number of layers and processing elements. This orthogonal neural network can approximate various functions and is used to calculate forward solution and to detect collisions. An efficient neural network system for collision detection is also developed. © 1995 John Wiley &amp; Sons, Inc.

In this paper, the effectiveness of the genetic algorithm-based back propagation (GABP) neural network model and its application to the breakout prediction in the continuous casting process are investigated. The formation of the sticking-type breakouts and the prediction principle of thermocouple thermometry method are analysed firstly. Then the genetic algorithm-based back propagation neural network model is proposed by fusing genetic algorithm (GA), and error back propagation neural network to offset the demerits of one paradigm by the merits of another. Finally, the GABP neural network model is applied to the breakout prediction in the continuous casting process; and the feasibility of the model is verified by the testing result with the accuracy rate of 97.56% and the prediction rate of 100%.

Aiming at the shortcomings of the low efficiency optimization algorithm and the tendency to fall into the local optimal solution in the existing shallow sea geoacoustic parameters inversion research, a shallow sea geoacoustic parameters inversion method based on the Back Propagation (BP) neural network model is proposed. First, the theoretical prediction value of the shallow sea sound pressure field is obtained through the Fast Field Method (FFM). Then the mapping relationship between the predicted sound pressure field and the geoacoustic parameters value to be inverted is established according to the BP neural network model. Finally, the measured sound pressure field data is brought into the neural network to obtain the inversion results. The experimental results show that, compared with the classic simulated annealing (Simulated Annealing, SA) algorithm, the BP neural network model converts the data matching process of the optimization algorithm into the construction of a relational model, avoiding multiple matching optimization processes for the inversion results, and the inversion results can be output directly, accurately, and efficiently. Under the premise of setting the same accuracy, the calculation time of the BP neural network model for the inversion result is shortened, and the number of iterations is reduced to 5% of the SA algorithm.

In view of emerging applications of alpha+beta titanium alloys in aerospace and defense, we have aimed to develop a Back propagation neural network (BPNN) model capable of predicting the properties of these alloys as functions of alloy composition and/or thermomechanical processing parameters. The optimized BPNN model architecture was based on the sigmoid transfer function and has one hidden layer with ten nodes. The BPNN model showed excellent predictability of five properties: Tensile strength (r: 0.96), yield strength (r: 0.93), beta transus (r: 0.96), specific heat capacity (r: 1.00) and density (r: 0.99). The developed BPNN model was in agreement with the experimental data in demonstrating the individual effects of alloying elements in modulating the above properties. This model can serve as the platform for the design and development of new alpha+beta titanium alloys in order to attain desired strength, density and specific heat capacity.

Catalysed diesel particulate filters (DPF) have been described as multifunctional reactor systems. Integration of selective catalytic reduction (SCR) functionality in the DPF creates an SCR-in-DPF system that achieves nitrous oxides (NOx) treatment along with particulate matter (PM) collection. The physical and chemical aspects of the integrated SCR-filter complicate system modelling. The goal of this work is to develop low-complexity model of the SCR-filter system which retains high fidelity. A high-fidelity model of the SCR-coated filter has been developed and validated. The performance of the model was described in a previous paper. Model complexity reduction is attempted in this paper. The objective is to achieve simulation times that can support the deployment of the model for online system control in an engine control unit. Two approaches were taken for the SCR-coated filter model order reduction (MOR): a “grey-box” approach via proper orthogonal decomposition (POD) and a “black box” approach via artificial neural network (ANN) function approximation. The POD method is shown to deliver a significant MOR while maintaining a high degree of fidelity but with less than 5% improvement in simulation time. The ANN method delivers a substantial MOR with reduction of three orders of magnitude in simulation time. The accuracy of the ANN model is satisfactory with good generalisation to new test data but noticeably inferior to the POD method.

Improving the resilience of enterprise safety production is one of the important ways to deal with the frequency of safety accidents. Based on the definition of enterprise safety production resilience, we fully consider the impacts of recovery resilience, self-organizing resilience, and learning resilience as the three dimensions of enterprise safety production resilience. We build a back propagation (BP) neural network model that analyzes the main factors of enterprise safety production resilience using the results of gray relational analysis as an input that can assess the resilience of enterprise safety production and provide a valuable reference for the improvement of an enterprise’s safety production level. The results show that the resilience of production safety obviously increased after the Chinese enterprises with low resilience (as predicted by the model) adopted the corresponding early warning methods. The gray relational degree analysis method can incorporate well the variables for the establishment of the BP neural network prediction model.

To study drivers’ driving behaviour in dilemma zones at signalized intersections, dilemma zones at signalized intersections are taken as the research objects. Based on analyzing the driving characteristics of motor vehicles. And collect the driving behavior parameters of video observations and road parameters of field observations, take these parameters as the factors which influence the drivers’ decision, conduct the significance analysis with SPSS(Statistical Product Service Solutions) for significant influencing factors, and then take these factors as the input value of BP(Back Propagation) neural network model, BP neural network model is set up and tested based on TensorFlow in Python. The prediction model of drivers’ decision-making in dilemma zone of signalized intersections under different speed limits is obtained, the research shows that the lower the speed limit, the better the accuracy of the intersection prediction. Further verified by comparison with the prediction model of drivers’ decision-making based on binary logistic, the accuracy of different prediction models is analyzed based on actual driver decisions.

The adaptive control method based on orthogonal function neural network is proposed for a class of chaotic nonlinear systems. The adaptive controller is constructed by using a single hidden layer Chebyshev orthogonal function neural network which has advantages such as simple calculation and fast convergence. The adaptive learning law of orthogonal neural network is derived to guarantee that the adaptive weight errors and the tracking error are bounded from Lyapunov stability theory. The uncertain nonlinear system with the external disturbances can track the desired reference trajectory with bounded errors by means of the adaptive feedback controller. Based on the orthogonal function neural network, the control of chaotic systems with uncertainties is studied. The results show that the approach proposed in this paper can overcome effectively the external disturbances.

Inadequate market segmentation and clustering problems could cause an enterprise to either miss a strategic marketing opportunity or not cash-in on a tactical campaign. The need for in-depth knowledge of customer segments and the need to overcome the limitations of using linear techniques to analyse non-linear problems requires a re-assessment of generally used approaches. The objectives of the research are (1) to consider the use of self-organising (SOM) neural networks for segmenting customer markets and (2) to analyse the predictive ability of backpropagation (BP) neural networks for classifying new customers by using the output provided by SOM neural networks. The nature and scope of neural networks are considered and the conceptual differences between Cluster Analysis and SOM neural networks as well as BP neural networks and multiple linear regression (MLR) static filter model are highlighted. The findings of the SOM neural network modelling indicate four natural clusters. In addition, the predictive ability of the BP neural network model was superior to that of MLR. Additional knowledge was also extracted from the BP neural network model by analysing the relationship between the input variables and each segment by means of input-output analysis. Sensitivity analysis was also used to identify important variables for each segment. Input-output analysis is also used to compile broad profiles of differences between the segments. The BP neural network model developed for this application is also suitable for deployment (i.e. classification of “new” customers) with a high level of confidence.

Sea surface temperature (SST) is one of the most important parameters in air–sea interaction, and its accurate prediction is of great significance in the study of global climate change. However, SST is affected by heat flux, ocean dynamic processes, cloud coverage, and other factors, which means it contains linear and nonlinear components. Existing prediction models, especially single prediction models, cannot effectively handle these linear and nonlinear components in the meantime, degrading their accuracy concerning the prediction of SST. To remedy this weakness, this paper proposes a novel prediction model by the Lagrange multiplier method to combine the auto-regressive integrated moving average (ARIMA) model and the back propagation (BP) neural network model, where these two models have superior prediction performance for linear and nonlinear components, respectively. Moreover, the genetic algorithm is exploited to construct the genetic algorithm BP (GABP) neural network to further improve the performance of the proposed model. To verify the effectiveness of the proposed model, experiments predicting the SST based on historic time-series data are performed. The experiment results indicate that the mean absolute error (MAE) of the ARIMA-GABP model is only 0.3033 °C and the root mean square error (RMSE) is 0.3970 °C, which is better than the ARIMA model, BP neural network model, long short-term memory (LSTM) model, GABP neural network model, and ensemble empirical model decomposition BP model among various datasets. Therefore, the proposed model has superior and robust performance concerning predicting SST.

Quantitative analysis of fatty acid value during rice storage based on olfactory visualization sensor technology

For the purpose of analyzing the application of back propagation (BP) neural network model in retinal vascular segmentation of color fundus images, in this study, the traditional BP neural network was first improved by adopting the additional momentum method. Second, adaptive histogram, morphological background subtraction, Gauss preprocessing matching filter and Heisen matrix were used to enhance the image and extract the features. Third, the retinal vascular segmentation algorithm for color fundus images was constructed based on optimized BP neural network. Finally, the DRIVE and MESSIDOR data sets of color fundus images were introduced to compare the proposed algorithm with the convolutional neural network (CNN) and pulse-coupled neural network (PCNN) algorithms in terms of performance. In addition, the three algorithms were also compared in terms of the sensitivity (Se), specificity (Sp), accuracy (Ac), average operation time for each image and F1 value. The results show that the BP neural network algorithm proposed in this study shows obvious advantage over the other two algorithms in the segmentation of color fundus images. In the DRIVE data set, the Se (81.37%), Sp (90.55%) and Ac (95.82%) of BP algorithm are the highest among the three; in the MESSIDOR data set, the Se (85.22%), Sp (91.08%) and Ac (96.16%) of BP algorithm are also highest; in the DRIVE and MESSIDOR data sets, the operation time of BP algorithm is (28.46 ± 3.19 ms; 24.73 ± 4.81 ms, respectively), which are significantly less than the other two algorithms. Besides, the F1 value of the proposed algorithm is obviously higher than that the other two algorithms. As a result, it is concluded that compared with the CNN algorithm and the PCNN algorithm, the proposed algorithm is more effective in the retinal vascular segmentation of color fundus images; the capillaries have better connectivity, and the proposed algorithm can improve the segmentation Ac while reducing the operation time.

Application of three-dimensional orthogonal neural network to craniomaxillary reconstruction