Research Into Modeling And Prediction Of Nonlinear Time Series Based On Napofics (Alternate Positive Negative Feedbackics) And Multi-Dimensional Taylor Network

There is inherent relationship between adjacent data of time series, which is an essential feature of the time series. The modeling and forecasting based on time series is to according to the observed value of the system establish a mathematical model to reflect the dynamic relationship between time series, and to reveal the motion law of the systems in order to predict the future changes and the trend of development. It is an important part of the prediction method system. Through the integrated use of input and output data, rather than the mechanism, to set up analytical model for nonlinear time series, especially to build an analytical model of the system having the phenomenon of quantitative change to qualitative change is particularly important. Therefore, the research of time series modeling and forecasting methods is of great significance either at the level of scientific study such as disclosing the movement of the system and further development of existing theory to enhance the movement of exploration and cognitive systems, or at the level of scientific applications such as collapse and other destructive disaster forecasting of major engineering structures and vital infrastructure and environmental pollution monitoring. To this end, the new modeling method of nonlinear time series and its application in prediction is studied in this dissertation especially aiming at the time series whose state changes from stabilization to revulsion and then re-stabilization to re-revulsion due to quantitative and qualitative changes. Firstly, aiming at the nonlinear time series, a novel can be used for network time series forecasting model the multi-dimensional Taylor network is proposed and a new method of nonlinear time series prediction combined with this model is presented; Secondly, based on the one-step prediction with the multi-dimensional Taylor network, the network is applied to multi-step prediction of chaotic systems, and an self-adaptation multi-step prediction method based on the multi-dimensional Taylor network by sliding the data window to realize the multi-step prediction of chaotic time series is presented; Then, aiming at the evolution that the state of some systems varies from stabilization to revulsion, and then turns to stabilization again, a novel dynamic model to describe the evolution by Napofics (Alternate positive negative feedbackics) which was proposed by the supervisor of this dissertation& Professor Yan Hong-sen after years of methodology study and a method based on the model for nonlinear time series prediction are put forward; Finally, combining with the material systems variation of the state varying from steady to severe, and then turning to steady again causing by changes from quantity to quality, the judgment scale of the equivalent positive and negative feedback extends to multiple and take the speed of state change as the first scale and the acceleration of state change as the second scale. The state stability is divided according to state change severity and trends. The multi-scale alternate positive negative feedback model based on multi-dimensional Taylor network is proposed and applied forecasting simulation.The main contents of this dissertation are introduced in detail as follows:1. Aiming at the nonlinear time series, a novel and unlike previous network models of commonly used research methods- the multi-dimensional Taylor network is proposed. The network is a new network model with outstanding advantages in building systems analytical model. Firstly, the structure and operation principle of the model are introduced in detail. The feasibility of constructing the form of multi-dimensional Taylor network is proved. The expressions of weighted terms are defined. And on the basis of it, a novel time series prediction method based on the multi-dimensional Taylor network is put forward. The characteristics of this method is that based on the observed data of the nonlinear time series, n-variables first order polynomial difference equations of the system are obtained by the multi-dimensional Taylor network and the dynamic characteristics can be described without prior knowledge and mechanism of the system, thus realizing the prediction of the nonlinear time series. Finally, examples of typical Lorenz chaotic time series and monitoring data of a large construction project demonstrate the effectiveness and feasibility of the proposed method.2. For the widespread phenomena of chaos in the real system, a new self-adaptation multi-step prediction method based on the multi-dimensional Taylor network is proposed to realize the multi-step prediction of chaotic time series, which is a typical nonlinear time series. The polynomial of multi-dimensional Taylor network is defined and it is demonstrated that this polynomial can approximate the multivariate function which is defined on bounded closed set. The correctness of the expression of n-order differential input of multi-dimensional Taylor network is proved. Based on these, the proposed self-adaptation multi-step prediction method differs from the chaotic time series prediction method with phase space reconstruction. It is unnecessary to choose the embedding dimension and delay times which are the two key parameters in the process of phase-space reconstruction. Without prior knowledge and mechanism of the system, the multi-dimensional Taylor Network model is set up according to time series data with chaotic. The adaptive model is achived by sliding the data window to realize the multi-step prediction of chaotic time series. Finally, examples results indicate the validity and the better predictive accuracy of this method.3. Aiming at the evolution that the state of some systems changes from stabilization to revulsion, and then re-stabilization to re-revulsion, the ideas of equivalent positive and negative feedbacks are introduced and according to the combination of this ideas and the above evolution, the dynamic model to describe the evolution by Napofics (Alternate positive negative feedbackics) and a method based on the model for nonlinear time series prediction are presented. The feasibility of using the model of Napofics to describe the evolution that the state of some systems changes from stabilization to revulsion and then re-stabilization to re-revulsion is demonstrated. The state stability is separated according to the severity extent of the sequence data change. The superposition of multiple dead zone functions is used to reflect the positive feedback effect caused by the outbreak of energy in different periods of rapid change. The general dynamics equation reflecting the changes of the system can be established without needing the internal mechanism of the system, which can realize the prediction of future data. And describe the variation of the system state varying from stabilization to revulsion, and then re-stabilization to re-revulsion by dynamic mathematical model. The simulation results show the effectiveness of the model. Finally, an example simulation verifies the effectiveness and feasibility of this method.4. Combining with the material systems whose state changes from stabilization to revulsion and then re-stabilization to re-revulsion due to quantitative and qualitative changes, and according to the multi-dimensional Taylor network and the introduction of the concept of multi-scale, the multi-scale alternate positive negative feedback model based on the multi-dimensional Taylor network is proposed. The correctness of the description of the system evolution with multiple scales and the establishment of the multi-scale model is demonstrated. The equivalent positive and negative feedback are introduced into the model and they are discriminated by the speed of state change as the first scale and the acceleration of state change as the second scale. The state stability is separated according to the change intensity of the state and the trend of changes, and the above variation is expressed in the form of dynamic equations. The model can express the change intensity of the state and the trend of changes in the upheaval of the data as specific functions and the model is a general model based on observation data. Finally, the model is applied in time series forecast and the model is established and is used to forecast based on the actual measured data of the system which has the typical phenomenon of quantitative change to qualitative change. The results show the model can reflect the variation of the system accurately, and it can effectively applied in forecast and it has high precision. The model provides a novel and effective means for complex system modeling and forecasting which has this kind of the variation.