Modeling nonlinear dynamical systems using support vector machine

The paper proposes a new method for identifying orders of input-output models for unknown nonlinear dynamic systems. The approach is based on the continuity property of the nonlinear functions which represent input-output models of continuous dynamic systems. The approach does not depend on any nonlinear function approximation methods and solely depends on the system's input-output data measured in experiments. By evaluating the modification of an index which is defined as Lipschitz number with the successive modification of model orders, the appropriate model orders can be determined simply and reliably. Theoretical background of the present approach is discussed. Several examples from chaotic dynamic systems, nonlinear plant models are presented to demonstrate the effectiveness of the present method.

The paper presents a review of the studies that were conducted at Energy Systems Institute (ESI) SB RAS in the field of mathematical modeling of nonlinear input-output dynamic systems with Volterra polynomials. The first part presents an original approach to identification of the Volterra kernels. The approach is based on setting special multi-parameter families of piecewise constant test input signals. It also includes a description of the respective software; presents illustrative calculations on the example of a reference dynamic system as well as results of computer modeling of real heat exchange processes. The second part of the review is devoted to the Volterra polynomial equations of the first kind. Studies of such equations were pioneered and have been carried out in the past decade by the laboratory of ill-posed problems at ESI SB RAS. A special focus in the paper is made on the importance of the Lambert function for the theory of these equations.

Multi-scale fuzzy modeling of multivariable discrete-time nonlinear dynamical systems is approached analytically in this paper. The underlying idea of this approach is to introduce the idea of multi-scale fuzzy quantization. More globally supported membership functions are used at coarser scales to capture global characteristics of the unknown system, whereas more locally supported membership functions are used at finer scales to fill in the local features. Starting from the coarsest scale down to finer ones, a projection method is used to extract a partial fuzzy-model (in terms of fuzzy membership functions and fuzzy rules) from the residual of the system at each scale until the residual drops below a prescribed modeling error bound. The multi-scale fuzzy model is then obtained by assembling the partial fuzzy models together. To reach a near optimal fuzzy model, a rule reduction technique has also been developed to delete some fuzzy rules. An illustrative example is used to demonstrate the effectiveness of the scheme.

In this paper, a model of nonlinear dynamic system with Lévy jumps based on cargo sorting DNA robot is studied. Firstly, nonlinear biochemical reaction system based on cargo sorting DNA robot model is established. Considering the influence of external disturbances on the system, nonlinear biochemical reaction system with Lévy jump is built and its dimensionality is reduced. Secondly, in order to prove that the built system conforms to the actual meaning, the existence and uniqueness of the system solution is verified. Next, the sufficient conditions for the completion of cargo pick-up of cargo sorting DNA robot and the continued sufficiency are introduced, and the progress of cargo sorting DNA robot under different noise intensities is analyzed. Then, it is proved that the positive recursion of the reaction can better describe and show the persistence of the system. Finally, numerical simulations verify the correctness of the theoretical results. The results show that the end of cargo pick-up with DNA robots for cargo sorting is closely related to the intensity of noise.KeywordsCargo sorting DNA robotNonlinear system modelLévy jumpLyapunov functionPositive recursion

Accurate estimation of river flow can have a significant importance in water resources management. In this study, Genetic programming (GP) and Support Vector Machine (SVM) methods were used to forecast daily discharge of Barandoozchay River. The daily discharge data of Barandoozchay River measured at the Dizaj hydrometric station during 2007 to 2011 was used for modeling, which 80% of the data used for training and remaining 20% used for testing of models. The results showed that in the both of considered methods, the models including discharges of one, two and three days ago had higher accuracy in verification step and the accuracy of models decreased with increasing discharge values. Comparing the performance of GP and SVM methods indicated that, however the accuracy of the GP method with the R=0.978 and RMSE=1.66 (m3/s) was slightly more than SVM method with R=0.976 and RMSE=1.80 (m3/s), but the SVM is easier than GP method. Thus, the SVM method can be used as an alternative method in forecasting daily river discharge.

The paper proposes a general framework for modelling non-linear dynamic systems based on a support vector machine (SVM): it first provides a short introduction to regression SVMs, then uses a standard SVM to model a non-linear auto-regressive and moving average (NARMAX) model, and contains a theoretical discussion about its robustness under low and high noise by its properties. The simulation results indicate that the SVM method can reduce the effect of samples and noise for modelling, and its performance is better than that of the neural network modelling method.

Flood susceptibility mapping using a novel ensemble weights-of-evidence and support vector machine models in GIS

Accuracy of data and information on various types of land use and land cover (LULC) is crucial in watershed management planning. The development of remote sensing technology in predicting LULC has been widely used, such as the Support Vector Machine (SVM) and Random Trees (RT) methods. Both methods are part of the model of machine learning and belong to the category of supervised learning. This method can predict, study, and recognize data patterns from the results of training data. The aim of this research is the use of SVM and RT methods for the identification of LULC. Based on the SVM method analysis results, the forest area is 211.61 km2, coffee plantations are 32.92 km2, shrubs are 16.85 km2, built-up/bare land is 3.40 km2, the water body is 3.17 km2, and cloud/shadow is 6.79 km2. While the RT method obtained a forest area of 215.51 km2, coffee plantations covering an area of 29.32 km2, shrubs are covering an area of 16.32 km2, built-up/bare land surrounding an area of 7.22 km2, water body covering an area of 2.62 km2, and cloud/shadow covering an area of 3.75 km2. Overall, the percentage accuracy of the SVM method of 87%, and the RT of 86%. The success rate of modeling SVM (AUC = 0.73) and RT (AUC = 0.75) based on the results of data validation using the area under the receiver operating characteristic curve (AUC) was considered fair good.

The specifications of the forests in Kalimantan are part of the vegetation type which is characteristic of dry lowland forests that are rich in biodiversity. The Kalimantan forest area is known as an area that has the highest vascular biodiversity in the world. Until 2014, the rate of forest loss as a source of biodiversity was always high every year. The National Polar-Orbiting Suomi Partnership (Suomi NPP) is a new generation of weather satellite imagery from NASA which currently continues to develop application algorithms for environmental monitoring. The support vector machine (SVM) method is a one-class learning machine method with artificial neural network methods that can recognize patterns from input or examples given and also include supervised learning. This study aims to analyze the effect of each parameter on the SVM method and the combination that can produce the highest accuracy, and analyze the ability of the SVM method for making hotspot maps based on the number of forest fire areas in East Kalimantan. The results of the study showed that the Support Vector Machine (SVM) method on the spectral data produced a total of 85%.

Fuzzy recurrent stochastic configuration networks (FRSCNs) are a class of randomized neurofuzzy models that have shown success in modeling nonlinear dynamic systems. However, the data generated from the real-world industry process often exhibits nonstationary characteristics, which could lead to the resulting model with poor generalization performance. This article presents an online self-learning FRSCN (OSL-FRSCN) for problem-resolving. OSL-FRSCNs integrate the self-organizing learning strategies into FRSCNs, maintaining the model's strong fuzzy inference capabilities while enhancing their continuous learning abilities for nonstationary data streams. The network parameters are updated online using the projection algorithm based on the newly arriving data streams. Moreover, the network structure can be dynamically adjusted in the light of the fuzzy recurrent stochastic configuration (FRSC) algorithm and an improved sensitivity analysis. Comprehensive comparisons over two nonlinear system identification tasks and two industrial applications are carried out. Numerical results clearly demonstrate that the proposed OSL-FRSCNs outperform other neurofuzzy and nonfuzzy models with sound generalization, verifying their effectiveness in modeling nonlinear systems with nonstationary dynamics.

This paper presents a new fuzzy inference system for modeling of nonlinear dynamic systems based on input and output data with measurement noise. The proposed fuzzy system has a number of fuzzy rules and parameter values of membership functions which are automatically generated using the extended relevance vector machine (RVM). The RVM has a probabilistic Bayesian learning framework and has good generalization capability. The RVM consists of the sum of product of weight and kernel function which projects input space into high dimensional feature space. The structure of proposed fuzzy system is same as that of the Takagi-Sugeno fuzzy model. However, in the proposed method, the number of fuzzy rules can be reduced under the process of optimizing a marginal likelihood by adjusting parameter values of kernel functions using the gradient ascent method. After a fuzzy system is determined, coefficients in consequent part are found by the least square method. Examples illustrate effectiveness of the proposed new fuzzy inference system.

Sirekap is a mobile application that was built to help the public monitor and oversee the development of the 2024 elections held in Indonesia. The research aims to apply the Support Vector Machine algorithm in analyzing sentiment about the use of the Sirekap application in 2024. The Support Vector Machine method is used to classify user sentiment into classes, namely positive, negative, and very negative. The amount of data used is 15,000 data sourced from Sirekap application reviews on Google PlayStore, with more detailed research stages including data collection, data preprocessing, data labeling, visualization, word weighting, and testing and analysis. The results show that the Support Vector Machine algorithm provides an accuracy of 88% for the Sirekap 2024 application. These results are expected to help developers to develop further the Sirekap 2024 application in improving the quality of the application and providing better user comfort Based on the results of the sentiment analysis of Sirekap 2024 application users on the Google Play store using the Support Vector Machine (SVM) method, an accuracy rate of 88% was obtained in classifying the sentiment of reviews into positive, negative, and very negative. This shows that the Support Vector Machine method is quite accurate for sentiment analysis of Indonesian text data. Overall, most reviews are very negative with a percentage reaching 76.9%, followed by negative reviews at 12.6%, and the least are positive reviews at 11%.

In this paper, we develop a low-cost portable spectrometer based on Support Vector Machines (SVM) method. The purpose of the spectrometer development is for halal food research project. The portable spectrometer uses various light-emitting diodes (LEDs), light sensor and Arduino microcontroller. The initial research of the spectrometer is testing various oil, such as palm oil, olive oil, sesame oil, soybean oil, and lard. The waveform analysis of each oil can be distinguished by spectroscopy method. But, by using Support Vector Machines (SVM) method the various oil can be distinguished and classified better. The data measurement, classification, and graphical interface result show on the interface of Raspberry Pi based on Python 2.7. Thus, the spectrometer can be used for lard detection.

The problem of creating mathematical models of nonlinear dynamical systems does not have an unambiguous solution and requires the creation of a separate synthesis method for each such object. To develop a method for synthesizing mathematical models of an extensive class of nonlinear dynamical systems with polynomial nonlinearities. The work uses a method based on the solution of the Volterra integral equation in the ideology set forth in Van Trees H.L., according to which the structure of a nonlinear dynamical object present47s a series connection of the linear part, characterizing the inertial properties of the system, and the nonlinear element, given by static characteristic. The difference of the suggested version of the method from the classical one, proposed in the works of Van Trees H.L., is an expansion of their input and output signals into Fourier series and a representation of the inertial part of these systems by their Bode plots, connected into one structure with input and output signals and non-linearity by Volterra integral equation. The algorithm of the proposed method is disclosed by the example of solving the problem of identifying a nonlinear dynamical system which impulse response of the inertial part satisfies the separability requirement, the order of the polynomial nonlinearity is three, and the model of the input signal has the form of a sinusoid "raised" over the time axis on a priori given constant level. A computational experiment was carried out on the example of nonlinear dynamical systems with the third order of the nonlinear characteristic and the first and second orders of the model of the inertial part of these systems with the specified algorithms of their parametric identification. The suggested method allows to synthesis the mathematical model of a nonlinear dynamical system with the polynomial static characteristic to the case when the input signal has an arbitrary number of harmonics, and the model of the inertial part and the nonlinear polynomial function have an arbitrary order.

Beras Miskin (Raskin) Program is a program of social protection, as supporters of other programs such as nutrition improvement, healthy increase, education and productivity improvement of Poor Households. According to Badan Pusat Statistika, there were 14 criteria to determine a household is classified as poor households. Based on these criteria it will be classified of recipient households and non-recipient households of Beras Miskin (Raskin) Program by Support Vector Machine (SVM) method using LibSVM. The concept of classification by SVM is search for the best hyperplane which serves as a separator of two classes of data in the input space. Kernel function is used to convert the data into a higher dimensional space to allow a separation. LibSVM is a package program created by Chih-Chung Chang and Chih-Jen Lin from Department of Computer Science at National Taiwan University. The method used by LibSVM to obtain global solution of duality lagrange problem is decomposition method. To determine the best parameters of kernel function, used k-vold cross validation method and grid search algorithm. In this classification by SVM method using LibSVM, obtain the best accuracy value as 83,1933%, which is the kernel function Radial Basis Function (RBF). Keywords : Beras Miskin (Raskin) Program, Classification, Support Vector Machine (SVM), LibSVM, Kernel Function