Volume 11, Number 3, 2014
Special Issue on Recent Advances on Complex Systems Control, Modelling and Prediction (pp.231-287)
column
Display Method:
2014, vol. 11, no. 3, pp. 231-240, doi: 10.1007/s11633-014-0785-6
Abstract:
The goal of this paper is to analyze the Finnish gross domestic product (GDP) and to find chaos in the Finnish GDP. We chose Finland where data has been available since 1975, because we needed the longest time series possible. At first we estimated the time delay and the embedding dimension, which is needed for the Lyapunov exponent estimation and for the phase space reconstruction. Subsequently, we computed the largest Lyapunov exponent, which is one of the important indicators of chaos. Then we calculated the 0-1 test for chaos. Finally we computed the Hurst exponent by rescaled range analysis and by dispersional analysis. The Hurst exponent is a numerical estimate of the predictability of a time series. In the end, we executed a recurrent analysis and displayed recurrence plots of detrended GDP time series. The results indicated that chaotic behaviors obviously exist in GDP.
The goal of this paper is to analyze the Finnish gross domestic product (GDP) and to find chaos in the Finnish GDP. We chose Finland where data has been available since 1975, because we needed the longest time series possible. At first we estimated the time delay and the embedding dimension, which is needed for the Lyapunov exponent estimation and for the phase space reconstruction. Subsequently, we computed the largest Lyapunov exponent, which is one of the important indicators of chaos. Then we calculated the 0-1 test for chaos. Finally we computed the Hurst exponent by rescaled range analysis and by dispersional analysis. The Hurst exponent is a numerical estimate of the predictability of a time series. In the end, we executed a recurrent analysis and displayed recurrence plots of detrended GDP time series. The results indicated that chaotic behaviors obviously exist in GDP.
2014, vol. 11, no. 3, pp. 241-248, doi: 10.1007/s11633-014-0786-5
Abstract:
Most of the processes in the industry have nonlinear behavior. Control of such processes with conventional control methods could lead to unstable, suboptimal, etc., results. On the other hand, the adaptive control is a technique widely used for controlling of nonlinear systems. The approach here is based on the recursive identification of the external linear model as a linear representation of the originally nonlinear system. The controller then reacts to the change of the working point or disturbances which could occur by the change of the parameters, structure, etc. The polynomial synthesis together with the linear quadratic (LQ) approach is employed here for the controller synthesis. These techniques satisfy basic control requirements such as the stability, the reference signal tracking and the disturbance attenuation. Resulted controller could be tuned with the choice of weighting factors in LQ approach. This work investigates the effect of these factors on control results. Proposed methods are tested on the mathematical model of the isothermal continuous stirred-tank reactor and simulated results are also verified on the real model of the continuous stirred tank reactor.
Most of the processes in the industry have nonlinear behavior. Control of such processes with conventional control methods could lead to unstable, suboptimal, etc., results. On the other hand, the adaptive control is a technique widely used for controlling of nonlinear systems. The approach here is based on the recursive identification of the external linear model as a linear representation of the originally nonlinear system. The controller then reacts to the change of the working point or disturbances which could occur by the change of the parameters, structure, etc. The polynomial synthesis together with the linear quadratic (LQ) approach is employed here for the controller synthesis. These techniques satisfy basic control requirements such as the stability, the reference signal tracking and the disturbance attenuation. Resulted controller could be tuned with the choice of weighting factors in LQ approach. This work investigates the effect of these factors on control results. Proposed methods are tested on the mathematical model of the isothermal continuous stirred-tank reactor and simulated results are also verified on the real model of the continuous stirred tank reactor.
2014, vol. 11, no. 3, pp. 249-255, doi: 10.1007/s11633-014-0787-4
Abstract:
The purpose of this paper is to develop an implementable strategy of brake energy recovery for a parallel hydraulic hybrid bus. Based on brake process analysis, a dynamic programming algorithm of brake energy recovery is established. And then an implementable strategy of brake energy recovery is proposed by the constraint variable trajectories analysis of the dynamic programming algorithm in the typical urban bus cycle. The simulation results indicate the brake energy recovery efficiency of the accumulator can reach 60% in the dynamic programming algorithm. And the hydraulic hybrid system can output braking torque as much as possible. Moreover, the accumulator has almost equal efficiency of brake energy recovery between the implementable strategy and the dynamic programming algorithm. Therefore, the implementable strategy is very effective in improving the efficiency of brake energy recovery. The road tests show the fuel economy of the hydraulic hybrid bus improves by 22.6% compared with the conventional bus.
The purpose of this paper is to develop an implementable strategy of brake energy recovery for a parallel hydraulic hybrid bus. Based on brake process analysis, a dynamic programming algorithm of brake energy recovery is established. And then an implementable strategy of brake energy recovery is proposed by the constraint variable trajectories analysis of the dynamic programming algorithm in the typical urban bus cycle. The simulation results indicate the brake energy recovery efficiency of the accumulator can reach 60% in the dynamic programming algorithm. And the hydraulic hybrid system can output braking torque as much as possible. Moreover, the accumulator has almost equal efficiency of brake energy recovery between the implementable strategy and the dynamic programming algorithm. Therefore, the implementable strategy is very effective in improving the efficiency of brake energy recovery. The road tests show the fuel economy of the hydraulic hybrid bus improves by 22.6% compared with the conventional bus.
2014, vol. 11, no. 3, pp. 256-264, doi: 10.1007/s11633-014-0788-3
Abstract:
The growth of small errors in weather prediction is exponential on average. As an error becomes larger, its growth slows down and then stops with the magnitude of the error saturating at about the average distance between two states chosen randomly. This paper studies the error growth in a low-dimensional atmospheric model before, during and after the initial exponential divergence occurs. We test cubic, quartic and logarithmic hypotheses by ensemble prediction method. Furthermore, the quadratic hypothesis suggested by Lorenz in 1969 is compared with the ensemble prediction method. The study shows that a small error growth is best modeled by the quadratic hypothesis. After the error exceeds about a half of the average value of variables, logarithmic approximation becomes superior. It is also shown that the time length of the exponential growth in the model data is a function of the size of small initial error and the largest Lyapunov exponent. We conclude that the size of the error at the least upper bound (supremum) of time length is equal to 1 and it is invariant to these variables. Predictability, as a time interval, where the model error is growing, is for small initial error, the sum of the least upper bound of time interval of exponential growth and predictability for the size of initial error equal to 1.
The growth of small errors in weather prediction is exponential on average. As an error becomes larger, its growth slows down and then stops with the magnitude of the error saturating at about the average distance between two states chosen randomly. This paper studies the error growth in a low-dimensional atmospheric model before, during and after the initial exponential divergence occurs. We test cubic, quartic and logarithmic hypotheses by ensemble prediction method. Furthermore, the quadratic hypothesis suggested by Lorenz in 1969 is compared with the ensemble prediction method. The study shows that a small error growth is best modeled by the quadratic hypothesis. After the error exceeds about a half of the average value of variables, logarithmic approximation becomes superior. It is also shown that the time length of the exponential growth in the model data is a function of the size of small initial error and the largest Lyapunov exponent. We conclude that the size of the error at the least upper bound (supremum) of time length is equal to 1 and it is invariant to these variables. Predictability, as a time interval, where the model error is growing, is for small initial error, the sum of the least upper bound of time interval of exponential growth and predictability for the size of initial error equal to 1.
2014, vol. 11, no. 3, pp. 265-273, doi: 10.1007/s11633-014-0789-2
Abstract:
Advances in the technology of astronomical spectra acquisition have resulted in an enormous amount of data available in world-wide telescope archives. It is no longer feasible to analyze them using classical approaches, so a new astronomical discipline, astroinformatics, has emerged. We describe the initial experiments in the investigation of spectral line profiles of emission line stars using machine learning with attempt to automatically identify Be and B[e] stars spectra in large archives and classify their types in an automatic manner. Due to the size of spectra collections, the dimension reduction techniques based on wavelet transformation are studied as well. The result clearly justifies that machine learning is able to distinguish different shapes of line profiles even after drastic dimension reduction.
Advances in the technology of astronomical spectra acquisition have resulted in an enormous amount of data available in world-wide telescope archives. It is no longer feasible to analyze them using classical approaches, so a new astronomical discipline, astroinformatics, has emerged. We describe the initial experiments in the investigation of spectral line profiles of emission line stars using machine learning with attempt to automatically identify Be and B[e] stars spectra in large archives and classify their types in an automatic manner. Due to the size of spectra collections, the dimension reduction techniques based on wavelet transformation are studied as well. The result clearly justifies that machine learning is able to distinguish different shapes of line profiles even after drastic dimension reduction.
Combination of Model-based Observer and Support Vector Machines for Fault Detection of Wind Turbines
2014, vol. 11, no. 3, pp. 274-287, doi: 10.1007/s11633-014-0790-9
Abstract:
Support vector machines and a Kalman-like observer are used for fault detection and isolation in a variable speed horizontal-axis wind turbine composed of three blades and a full converter. The support vector approach is data-based and is therefore robust to process knowledge. It is based on structural risk minimization which enhances generalization even with small training data set and it allows for process nonlinearity by using flexible kernels. In this work, a radial basis function is used as the kernel. Different parts of the process are investigated including actuators and sensors faults. With duplicated sensors, sensor faults in blade pitch positions, generator and rotor speeds can be detected. Faults of type stuck measurements can be detected in 2 sampling periods. The detection time of offset/scaled measurements depends on the severity of the fault and on the process dynamics when the fault occurs. The converter torque actuator fault can be detected within 2 sampling periods. Faults in the actuators of the pitch systems represents a higher difficulty for fault detection which is due to the fact that such faults only affect the transitory state (which is very fast) but not the final stationary state. Therefore, two methods are considered and compared for fault detection and isolation of this fault: support vector machines and a Kalman-like observer. Advantages and disadvantages of each method are discussed. On one hand, support vector machines training of transitory states would require a big amount of data in different situations, but the fault detection and isolation results are robust to variations in the input/operating point. On the other hand, the observer is model-based, and therefore does not require training, and it allows identification of the fault level, which is interesting for fault reconfiguration. But the observability of the system is ensured under specific conditions, related to the dynamics of the inputs and outputs. The whole fault detection and isolation scheme is evaluated using a wind turbine benchmark with a real sequence of wind speed.
Support vector machines and a Kalman-like observer are used for fault detection and isolation in a variable speed horizontal-axis wind turbine composed of three blades and a full converter. The support vector approach is data-based and is therefore robust to process knowledge. It is based on structural risk minimization which enhances generalization even with small training data set and it allows for process nonlinearity by using flexible kernels. In this work, a radial basis function is used as the kernel. Different parts of the process are investigated including actuators and sensors faults. With duplicated sensors, sensor faults in blade pitch positions, generator and rotor speeds can be detected. Faults of type stuck measurements can be detected in 2 sampling periods. The detection time of offset/scaled measurements depends on the severity of the fault and on the process dynamics when the fault occurs. The converter torque actuator fault can be detected within 2 sampling periods. Faults in the actuators of the pitch systems represents a higher difficulty for fault detection which is due to the fact that such faults only affect the transitory state (which is very fast) but not the final stationary state. Therefore, two methods are considered and compared for fault detection and isolation of this fault: support vector machines and a Kalman-like observer. Advantages and disadvantages of each method are discussed. On one hand, support vector machines training of transitory states would require a big amount of data in different situations, but the fault detection and isolation results are robust to variations in the input/operating point. On the other hand, the observer is model-based, and therefore does not require training, and it allows identification of the fault level, which is interesting for fault reconfiguration. But the observability of the system is ensured under specific conditions, related to the dynamics of the inputs and outputs. The whole fault detection and isolation scheme is evaluated using a wind turbine benchmark with a real sequence of wind speed.
2014, vol. 11, no. 3, pp. 288-298, doi: 10.1007/s11633-014-0791-8
Abstract:
Online automatic fault diagnosis in industrial systems is essential for guaranteeing safe, reliable and efficient operations. However, difficulties associated with computational overload, ubiquitous uncertainties and insufficient fault samples hamper the engi-neering application of intelligent fault diagnosis technology. Geared towards the settlement of these problems, this paper introduces the method of dynamic uncertain causality graph, which is a new attempt to model complex behaviors of real-world systems under uncertainties. The visual representation to causality pathways and self-relied "chaining" inference mechanisms are analyzed. In particular, some solutions are investigated for the diagnostic reasoning algorithm to aim at reducing its computational complexity and improving the robustness to potential losses and imprecisions in observations. To evaluate the effectiveness and performance of this method, experiments are conducted using both synthetic calculation cases and generator faults of a nuclear power plant. The results manifest the high diagnostic accuracy and efficiency, suggesting its practical significance in large-scale industrial applications.
Online automatic fault diagnosis in industrial systems is essential for guaranteeing safe, reliable and efficient operations. However, difficulties associated with computational overload, ubiquitous uncertainties and insufficient fault samples hamper the engi-neering application of intelligent fault diagnosis technology. Geared towards the settlement of these problems, this paper introduces the method of dynamic uncertain causality graph, which is a new attempt to model complex behaviors of real-world systems under uncertainties. The visual representation to causality pathways and self-relied "chaining" inference mechanisms are analyzed. In particular, some solutions are investigated for the diagnostic reasoning algorithm to aim at reducing its computational complexity and improving the robustness to potential losses and imprecisions in observations. To evaluate the effectiveness and performance of this method, experiments are conducted using both synthetic calculation cases and generator faults of a nuclear power plant. The results manifest the high diagnostic accuracy and efficiency, suggesting its practical significance in large-scale industrial applications.
2014, vol. 11, no. 3, pp. 299-307, doi: 10.1007/s11633-014-0792-7
Abstract:
This paper presents the trajectory tracking control of an autonomous underwater vehicle (AUV). To cope with parametric uncertainties owing to the hydrodynamic effect, an adaptive control law is developed for the AUV to track the desired trajectory. This desired state-dependent regressor matrix-based controller provides consistent results under hydrodynamic parametric uncertainties. Stability of the developed controller is verified using the Lyapunov's direct method. Numerical simulations are carried out to study the efficacy of the proposed adaptive controller.
This paper presents the trajectory tracking control of an autonomous underwater vehicle (AUV). To cope with parametric uncertainties owing to the hydrodynamic effect, an adaptive control law is developed for the AUV to track the desired trajectory. This desired state-dependent regressor matrix-based controller provides consistent results under hydrodynamic parametric uncertainties. Stability of the developed controller is verified using the Lyapunov's direct method. Numerical simulations are carried out to study the efficacy of the proposed adaptive controller.
2014, vol. 11, no. 3, pp. 308-312, doi: 10.1007/s11633-014-0793-6
Abstract:
The tracking problem for a class of differential inclusion systems is investigated. Using global sliding mode control approach, a tracking control is proposed such that the output of a differential inclusion system tracks the desired trajectory asymptotically. An extensive reaching law is proposed to achieve the chattering reduction. Finally, an example is given to illustrate the validity of the proposed design.
The tracking problem for a class of differential inclusion systems is investigated. Using global sliding mode control approach, a tracking control is proposed such that the output of a differential inclusion system tracks the desired trajectory asymptotically. An extensive reaching law is proposed to achieve the chattering reduction. Finally, an example is given to illustrate the validity of the proposed design.
2014, vol. 11, no. 3, pp. 313-319, doi: 10.1007/s11633-014-0794-5
Abstract:
Airdrop is the most important approach for crisis transaction and unexpected events, it is necessary to investigate the flight characteristics of transport aircraft during the dropping process. This paper mainly focuses on the stability, controllability and model simplification of large aircraft with heavy cargo airdrop. In this process, the primary elements which have impact on force and moment are studied theoretically, the role of cargo mass, moving parameters and other factors on dynamical characteristics have been assessed by simulation and analysis. And then the aircraft model simplification is completed for control system designing in future. All the work above shows that the parameters of cargo moving play a dominant role in flight characteristics and the flight equations can be simplified to reduce the design complexity.
Airdrop is the most important approach for crisis transaction and unexpected events, it is necessary to investigate the flight characteristics of transport aircraft during the dropping process. This paper mainly focuses on the stability, controllability and model simplification of large aircraft with heavy cargo airdrop. In this process, the primary elements which have impact on force and moment are studied theoretically, the role of cargo mass, moving parameters and other factors on dynamical characteristics have been assessed by simulation and analysis. And then the aircraft model simplification is completed for control system designing in future. All the work above shows that the parameters of cargo moving play a dominant role in flight characteristics and the flight equations can be simplified to reduce the design complexity.
2014, vol. 11, no. 3, pp. 320-327, doi: 10.1007/s11633-014-0795-4
Abstract:
When calculating the sampled-date representation of nonlinear systems second-order hold (SOH) assumption can be applied to improving the precision of the discretization results. This paper proposes a discretization method based on Taylor series and the SOH assumption for the nonlinear systems with the time delayed non-affine input. The mathematical structure of the proposed discretization method is explored. This proposed discretization method can provide a precise and finite dimensional discretization model for the nonlinear time-delayed non-affine system by keeping the truncation order of the Taylor series. The performance of the proposed discretization method is evaluated by doing the simulation using a nonlinear system with the time-delayed non-affine input. Different input signals, time-delay values and sampling periods are considered in the simulation to investigate the proposed method. The simulation results demonstrate that the proposed method is practical and easy for time-delayed nonlinear non-affine systems. The comparison between SOH assumption with first-order hold (FOH) and zero-order hold (ZOH) assumptions is given to show the advantages of the proposed method.
When calculating the sampled-date representation of nonlinear systems second-order hold (SOH) assumption can be applied to improving the precision of the discretization results. This paper proposes a discretization method based on Taylor series and the SOH assumption for the nonlinear systems with the time delayed non-affine input. The mathematical structure of the proposed discretization method is explored. This proposed discretization method can provide a precise and finite dimensional discretization model for the nonlinear time-delayed non-affine system by keeping the truncation order of the Taylor series. The performance of the proposed discretization method is evaluated by doing the simulation using a nonlinear system with the time-delayed non-affine input. Different input signals, time-delay values and sampling periods are considered in the simulation to investigate the proposed method. The simulation results demonstrate that the proposed method is practical and easy for time-delayed nonlinear non-affine systems. The comparison between SOH assumption with first-order hold (FOH) and zero-order hold (ZOH) assumptions is given to show the advantages of the proposed method.
2014, vol. 11, no. 3, pp. 328-333, doi: 10.1007/s11633-014-0796-3
Abstract:
The trajectory tracking control is considered for nonholonomic mechanical systems with affine constraints and dynamic friction. A new state transformation is proposed to deal with affine constraints, and then an integral feedback compensation strategy is used to identify the dynamic friction. The proposed controller ensures that the output tracking errors converge to zero as t→∞. As an application, a detailed example is presented to illustrate the effectiveness of the control scheme.
The trajectory tracking control is considered for nonholonomic mechanical systems with affine constraints and dynamic friction. A new state transformation is proposed to deal with affine constraints, and then an integral feedback compensation strategy is used to identify the dynamic friction. The proposed controller ensures that the output tracking errors converge to zero as t→∞. As an application, a detailed example is presented to illustrate the effectiveness of the control scheme.
2014, vol. 11, no. 3, pp. 334-339, doi: 10.1007/s11633-014-0797-2
Abstract:
In view of single machine to infinite bus system with static synchronous compensator, which is affected by internal and external disturbances, a nonlinear adaptive robust controller is constructed based on the improved dynamic surface control method (IDSC). Compared with the conventional DSC, the sliding mode control is introduced to the dynamic surface design procedure, and the parameter update laws are designed using the uncertainty equivalence criterions. The IDSC method not only reduces the complexity of the controller but also greatly improves the system robustness, speed and accuracy. The derived controller cannot only attenuate the influences of external disturbances against system output, but also has strong robustness to system parameters variance because the damping coefficient is considered in the internal parameter uncertainty. Simulation result reveals that the designed controller can effectively improve the dynamic performances of the power system.
In view of single machine to infinite bus system with static synchronous compensator, which is affected by internal and external disturbances, a nonlinear adaptive robust controller is constructed based on the improved dynamic surface control method (IDSC). Compared with the conventional DSC, the sliding mode control is introduced to the dynamic surface design procedure, and the parameter update laws are designed using the uncertainty equivalence criterions. The IDSC method not only reduces the complexity of the controller but also greatly improves the system robustness, speed and accuracy. The derived controller cannot only attenuate the influences of external disturbances against system output, but also has strong robustness to system parameters variance because the damping coefficient is considered in the internal parameter uncertainty. Simulation result reveals that the designed controller can effectively improve the dynamic performances of the power system.
2014, vol. 11, no. 3, pp. 340-346, doi: 10.1007/s11633-014-0798-1
Abstract:
Consensus problem is investigated for heterogeneous multi-agent systems composed of first-order agents and second-order agents in this paper. Leader-following consensus protocol is adopted to solve consensus problem of heterogeneous multi-agent systems with time-varying communication and input delays. By constructing Lyapunov-Krasovkii functional, sufficient consensus conditions in linear matrix inequality (LMI) form are obtained for the system under fixed interconnection topology. Moreover, consensus conditions are also obtained for the heterogeneous systems under switching topologies with time delays. Simulation examples are given to illustrate effectiveness of the results.
Consensus problem is investigated for heterogeneous multi-agent systems composed of first-order agents and second-order agents in this paper. Leader-following consensus protocol is adopted to solve consensus problem of heterogeneous multi-agent systems with time-varying communication and input delays. By constructing Lyapunov-Krasovkii functional, sufficient consensus conditions in linear matrix inequality (LMI) form are obtained for the system under fixed interconnection topology. Moreover, consensus conditions are also obtained for the heterogeneous systems under switching topologies with time delays. Simulation examples are given to illustrate effectiveness of the results.
_00.jpg)
