Comparison of nonlinear modeling methods for the composite rubber clamp

The cubic stiffness force model(CSFM)and Bouc-Wen model(BWM)are introduced and compared innovatively.The unknown coefficients of the nonlinear models are identified by the genetic algorithm combined with experiments.By fitting the identified nonlinear coefficients under different excitation amplitudes,the nonlinear vibration responses of the system are predicted.The results show that the accuracy of the BWM is higher than that of the CSFM,especially in the non-resonant region.However,the optimization time of the BWM is longer than that of the CSFM.

Mathematical Constraints in Multiscale Subgrid-Scale Modeling of Nonlinear Systems

To shed light on the subgrid-seale （SGS） modeling methodology of nonlinear systems such as the Navier-Stokes turbulence, we define the concepts of assumption and restriction in the modeling procedure, which are shown by generalized derivation of three general mathematical constraints for different combinations of restrictions. These constraints are verified numerically in a one-dimensional nonlinear advection equation. This study is expected to inspire future research on the SGS modeling methodology of nonlinear systems.

Extended Range(10–30 Days) Heavy Rain Forecasting Study Based on a Nonlinear Cross-Prediction Error Model

Extended range （10-30 d） heavy rain forecasting is difficult but performs an important function in disaster prevention and mitigation. In this paper, a nonlinear cross prediction error （NCPE） algorithm that combines nonlinear dynamics and statistical methods is proposed. The method is based on phase space reconstruction of chaotic single-variable time series of precipitable water and is tested in 100 global cases of heavy rain. First, nonlinear relative dynamic error for local attractor pairs is calculated at different stages of the heavy rain process, after which the local change characteristics of the attractors are analyzed. Second, the eigen-peak is defined as a prediction indicator based on an error threshold of about 1.5, and is then used to analyze the forecasting validity period. The results reveal that the prediction indicator features regarded as eigenpeaks for heavy rain extreme weather are all reflected consistently, without failure, based on the NCPE model; the prediction validity periods for 1-2 d, 3-9 d and 10-30 d are 4, 22 and 74 cases, respectively, without false alarm or omission. The NCPE model developed allows accurate forecasting of heavy rain over an extended range of 10-30 d and has the potential to be used to explore the mechanisms involved in the development of heavy rain according to a segmentation scale. This novel method provides new insights into extended range forecasting and atmospheric predictability, and also allows the creation of multi-variable chaotic extreme weather prediction models based on high spatiotemporal resolution data.

Determination of Melamine by Infrared Spectroscopy Based on Nonlinear Modeling

[Objective] The aim was to develop a nonlinear model of quantitative analysis of melamine content by infrared spectroscopy and provide theoretical basis for the nondestructive detection of melamine. [Method] According to dynamics,mathematical modeling and optimization theory,linear and nonlinear models were respectively set up by taking an absorption peak of 1 550 cm-1 as characteristic absorption peak. [Result] The correlation coefficient of nonlinear model was 0.922 7 and the recovery was 96%,which showed that the nonlinear model was more accurate than linearity model with correlation coefficient of 0.904 9 and recovery of 557%. [Conclusion] It is feasible to determine melamine content by using the nonlinear model quantitatively.

Hybrid LEAP modeling method for long-term energy demand forecasting of regions with limited statistical data

An accurate long-term energy demand forecasting is essential for energy planning and policy making. However, due to the immature energy data collecting and statistical methods, the available data are usually limited in many regions. In this paper, on the basis of comprehensive literature review, we proposed a hybrid model based on the long-range alternative energy planning (LEAP) model to improve the accuracy of energy demand forecasting in these regions. By taking Hunan province, China as a typical case, the proposed hybrid model was applied to estimating the possible future energy demand and energy-saving potentials in different sectors. The structure of LEAP model was estimated by Sankey energy flow, and Leslie matrix and autoregressive integrated moving average (ARIMA) models were used to predict the population, industrial structure and transportation turnover, respectively. Monte-Carlo method was employed to evaluate the uncertainty of forecasted results. The results showed that the hybrid model combined with scenario analysis provided a relatively accurate forecast for the long-term energy demand in regions with limited statistical data, and the average standard error of probabilistic distribution in 2030 energy demand was as low as 0.15. The prediction results could provide supportive references to identify energy-saving potentials and energy development pathways.

Modeling and Forecasting of Carbon Dioxide Emissions in Bangladesh Using Autoregressive Integrated Moving Average (ARIMA) Models

In the present paper, different Autoregressive Integrated Moving Average (ARIMA) models were developed to model the carbon dioxide emission by using time series data of forty-four years from 1972-2015. The performance of these developed models was assessed with the help of different selection measure criteria and the model having minimum value of these criteria considered as the best forecasting model. Based on findings, it has been observed that out of different ARIMA models, ARIMA (0, 2, 1) is the best fitted model in predicting the emission of carbon dioxide in Bangladesh. Using this best fitted model, the forecasted value of carbon dioxide emission in Bangladesh, for the year 2016, 2017 and 2018 as obtained from ARIMA (0, 2, 1) was obtained as 83.94657 Metric Tons, 89.90464 Metric Tons and 96.28557 Metric Tons respectively.

Support Vector Machine-Based Nonlinear System Modeling and Control

This paper provides an introduction to a support vector machine, a new kernel-based technique introduced in statistical learning theory and structural risk minimization, then presents a modeling-control framework based on SVM. At last a numerical experiment is taken to demonstrate the proposed approach's correctness and effectiveness.

Dynamic optimization oriented modeling and nonlinear model predictive control of the wet limestone FGD system

Nonlinear model predictive control(NMPC)scheme is an effective method of multi-objective optimization control in complex industrial systems.In this paper,a NMPC scheme for the wet limestone flue gas desulphurization(WFGD)system is proposed which provides a more flexible framework of optimal control and decision-making compared with PID scheme.At first,a mathematical model of the FGD process is deduced which is suitable for NMPC structure.To equipoise the model’s accuracy and conciseness,the wet limestone FGD system is separated into several modules.Based on the conservation laws,a model with reasonable simplification is developed to describe dynamics of different modules for the purpose of controller design.Then,by addressing economic objectives directly into the NMPC scheme,the NMPC controller can minimize economic cost and track the set-point simultaneously.The accuracy of model is validated by the field data of a 1000 MW thermal power plant in Henan Province,China.The simulation results show that the NMPC strategy improves the economic performance and ensures the emission requirement at the same time.In the meantime,the control scheme satisfies the multiobjective control requirements under complex operation conditions(e.g.,boiler load fluctuation and set point variation).The mathematical model and NMPC structure provides the basic work for the future development of advanced optimized control algorithms in the wet limestone FGD systems.

Selective ensemble modeling based on nonlinear frequency spectral feature extraction for predicting load parameter in ball mills

Strong mechanical vibration and acoustical signals of grinding process contain useful information related to load parameters in ball mills. It is a challenge to extract latent features and construct soft sensor model with high dimensional frequency spectra of these signals. This paper aims to develop a selective ensemble modeling approach based on nonlinear latent frequency spectral feature extraction for accurate measurement of material to ball volume ratio. Latent features are first extracted from different vibrations and acoustic spectral segments by kernel partial least squares. Algorithms of bootstrap and least squares support vector machines are employed to produce candidate sub-models using these latent features as inputs. Ensemble sub-models are selected based on genetic algorithm optimization toolbox. Partial least squares regression is used to combine these sub-models to eliminate collinearity among their prediction outputs. Results indicate that the proposed modeling approach has better prediction performance than previous ones.

Wavelet time series MPARIMA modeling for power system short term load forecasting

The wavelet power system short term load forecasting(STLF) uses a mulriple periodical autoregressive integrated moving average(MPARIMA) model to model the mulriple near periodicity, nonstationarity and nonlinearity existed in power system short term quarter hour load time series, and can therefore accurately forecast the quarter hour loads of weekdays and weekends, and provide more accurate results than the conventional techniques, such as artificial neural networks and autoregressive moving average(ARMA) models test results. Obtained with a power system networks in a city in Northeastern part of China confirm the validity of the approach proposed.

A nonlinear combination forecasting method based on the fuzzy inference system

It has been shown in recent economic and statistical studies that combining forecasts may produce more accurate forecasts than individual ones. However, the literature on combining forecasts has almost exclusively focused on linear combining forecasts. In this paper, a new nonlinear combination forecasting method based on fuzzy inference system is present to overcome the difficulties and drawbacks in linear combination modeling of non-stationary time series. Furthermore, the optimization algorithm based on a hierarchical structure of learning automata is used to identify the parameters of the fuzzy system. Experiment results related to numerical examples demonstrate that the new technique has excellent identification performances and forecasting accuracy superior to other existing linear combining forecasts.

Resolution of Relationship between Organizational Performance and Human Resource Management through Nonlinear Modeling

The relation between the HRM and the firm performance is analyzed statistically by many researchers in the literature. However, there are very few nonlinear approaches in literature for finding the relation between Human Resource Management (FIRM) and firm performance. This paper exposes the relationship between human resource management and organizational performance through the use of nonlinear modeling technique. The modeling is proposed based on Radial Basis Function (RBF) which is nonlinear modeling technique in literature. The relation between 12 input and 9 output parameters is investigated in this research that is collected between 54 companies in Turkey which indicated that the relationship between organizational management performance and relationship management can be modelled through nonlinearly.

Grey relationship analysis and grey forecasting modeling on thermal stability of synthetic single diamond

Through analyzing 7 Ib-type samples of synthetic single diamonds by their DTA and TG in air, we ascertained the extrapolated onset temperature on the curves of DTA as the characteristic temperature of their thermal stabilities. Based on the grey system theory, we analyzed 4 factors influential in the thermal stability by the grey relationship analysis, a quantitative method, and derived the grey relationship sequence, that is, the rank of the influence extent of 4 factors on the thermal stability. Furthermore, we established the grey forecasting model, namely GM(1,5), for predicting the thermal stability of single diamonds with their intrinsic properties, which was then examined by a deviation-probability examination. The results illustrate that it is reasonable to take the Extrapolated Onset Temperature in DTA as the characteristic temperature for thermal stability (TS) of Ib-type synthetic single diamonds. The nitrogen content and grain shape regularity of diamonds are dominating factors. Likewise, grain size and compressive strength are minor factors. In addition, GM(1,5) can be used to predict the thermal stability of Ib-type synthetic single diamonds available. The precision rank of GM(1,5) is ‘GOOD’.

Features of SAS Enterprise Guide for probabilistic Modeling System, Macroeconomic Analysis and Forecasting

This paper addresses to the problem of using SAS Enterprise Guide 6.1 as a means for building probabilistic models and as optimum method of modeling gross domestic product in terms of the economic crisis and social threats is proposed. Today in a complex socio-political and economic situation growing influence of external factors, presence of uncertainties and risks there exists a problem of anticipating potential threats in the humanitarian and social spheres and ways to overcome them aiming to provide food security and controllability of ecological situation. All these problems, as reported in the NATO program ＂Science for Peace and Security＂, are of high priority for the countries that need to take into account threats to security, including Ukraine. That is why in the framework of the project NUKR. SFPP G4877 ＂Modeling and Mitigation of Social Disasters Caused by Catastrophes and Terrorism＂ the problems of scientific prediction of national economy for the period to 2030 as one of the measures preventing growth of social tension in the country are disclosed.

Effect of Multipoint Heterogeneity on Nonlinear Transformations for Geological Modeling: Porosity-Permeability Relations Revisited

An analysis of statistical expected values for transformations is performed in this study to quantify the effect of heterogeneity on spatial geological modeling and evaluations. Algebraic transformations are frequently applied to data from logging to allow for the modeling of geological properties. Transformations may be powers, products, and exponential operations which are commonly used in well-known relations （e.g., porosity-permeability transforms）. The results of this study show that correct computations must account for residual transformation terms which arise due to lack of independence among heterogeneous geological properties. In the case of an exponential porosity-permeability transform, the values may be positive. This proves that a simple exponential model back-transformed from linear regression underestimates permeability. In the case of transformations involving two or more properties, residual terms may represent the contribution of heterogeneous components which occur when properties vary together, regardless of a pair-wise linear independence. A consequence of power- and product-transform models is that regression equations within those transformations need corrections via residual cumulants. A generalization of this result is that transformations of multivariate spatial attributes require multiple-point random variable relations. This analysis provides practical solutions leading to a methodology for nonlinear modeling using correct back transformations in geology.

Fuzzy modeling of multirate sampled nonlinear systems based on multi-model method

Based on the multi-model principle, the fuzzy identification for nonlinear systems with multirate sampled data is studied.Firstly, the nonlinear system with multirate sampled data can be shown as the nonlinear weighted combination of some linear models at multiple local working points. On this basis, the fuzzy model of the multirate sampled nonlinear system is built. The premise structure of the fuzzy model is confirmed by using fuzzy competitive learning, and the conclusion parameters of the fuzzy model are estimated by the random gradient descent algorithm. The convergence of the proposed identification algorithm is given by using the martingale theorem and lemmas. The fuzzy model of the PH neutralization process of acid-base titration for hair quality detection is constructed to demonstrate the effectiveness of the proposed method.

Study of Polluted Insulator Flashover Forecasting Based on Nonlinear Time Series Analysis

To solve the problem of the flashover forecasting of contaminated or polluted insulator,a flashover forecasting model of contaminated insulators based on nonlinear time series analysis is proposed in the paper.The ESDD is the key of flashover on polluted insulator.The ESDD value of insulator can be forecasted by the method of nonlinear time series analysis of the ESDD time series and a forecasting model of polluted insulator flashover is proposed in the paper.The forecasting model consists of two artificial neural networks that reflect relationship of environment,ESDD and flashover probability.The first is used to estimate the ESDD time series of insulator and the second is employed to calculate the probability of the flashover.A series of artificial pollution tests show that the results of the forecasting model is acceptable.

Research on modeling of nonlinear vibration isolation system based on Bouce Wen model

A feedforword neural network of multi-layer topologies for systems with hysteretic nonlinearity is constructed based on Bouce Wen differential model. It not only reflects the hysteresis force characteristics of the Bouce Wen model, but also determines its corresponding parameters. The simulation results show that restoring forceedisplacement curve hysteresis loop is very close to the real curve. The model trained can accurately predict the time response of system. The model is checked under the noise level. The result shows that the model has higher modeling precision, good generalization capability and a certain anti-interference ability.

End-to-end data-driven modeling framework for automated and trustworthy short-term building energy load forecasting

Conventional automated machine learning(AutoML)technologies fall short in preprocessing low-quality raw data and adapting to varying indoor and outdoor environments,leading to accuracy reduction in forecasting short-term building energy loads.Moreover,their predictions are not transparent because of their black box nature.Hence,the building field currently lacks an AutoML framework capable of data quality enhancement,environment self-adaptation,and model interpretation.To address this research gap,an improved AutoML-based end-to-end data-driven modeling framework is proposed.Bayesian optimization is applied by this framework to find an optimal data preprocessing process for quality improvement of raw data.It bridges the gap where conventional AutoML technologies cannot automatically handle missing data and outliers.A sliding window-based model retraining strategy is utilized to achieve environment self-adaptation,contributing to the accuracy enhancement of AutoML technologies.Moreover,a local interpretable model-agnostic explanations-based approach is developed to interpret predictions made by the improved framework.It overcomes the poor interpretability of conventional AutoML technologies.The performance of the improved framework in forecasting one-hour ahead cooling loads is evaluated using two-year operational data from a real building.It is discovered that the accuracy of the improved framework increases by 4.24%–8.79%compared with four conventional frameworks for buildings with not only high-quality but also low-quality operational data.Furthermore,it is demonstrated that the developed model interpretation approach can effectively explain the predictions of the improved framework.The improved framework offers a novel perspective on creating accurate and reliable AutoML frameworks tailored to building energy load prediction tasks and other similar tasks.

MODELING OF NONLINEAR SYSTEMS BY MULTIPLE LINEARIZED MODELS

In order to design linear controller for nonlinear systems,a simple but efficient method of modeling a nonlinear system was proposed by means of multiple linearized models at different operating points in the entire range of the expected changes of the operating points.The original nonlinear system was described by linear combination of these multiple linearized models,with the linear combination parameters being identified on line based on least squares method.Model Predictive Control,an optimization based technique,was used to design the linear controller.A sufficient condition for ensuring the existence of a linear controller for the original nonlinear system was also given.Good performance indicated by two simulated examples confirms the usefulness of the proposed method.