Identification of continuous-time model of hammerstein system using modified multi-verse optimizer

his thesis implements a novel nature-inspired metaheuristic optimization algorithm, namely the modified Multi-Verse Optimizer (mMVO) algorithm, to identify the continuous-time model of Hammerstein system. Multi-Verse Optimizer (MVO) is one of the most recent robust nature-inspired metaheuristic algorithm. It has been successfully implemented and used in various areas such as machine learning applications, engineering applications, network applications, parameter control, and other similar applications to solve optimization problems. However, such metaheuristics had some limitations, such as local optima problem, low searching capability and imbalance between exploration and exploitation. By considering these limitations, two modifications were made upon the conventional MVO in our proposed mMVO algorithm. Our first modification was an average design parameter updating mechanism to solve the local optima issue of the traditional MVO. The essential feature of the average design parameter updating mechanism is that it helps any trapped design parameter jump out from the local optima region and continue a new search track. The second modification is the hybridization of MVO with the Sine Cosine Algorithm (SCA) to improve the low searching capability of the conventional MVO. Hybridization aims to combine MVO and SCA algorithms advantages and minimize the disadvantages, such as low searching capability and imbalance between exploration and exploitation. In particular, the search capacity of the MVO algorithm has been improved using the sine and cosine functions of the Sine Cosine Algorithm (SCA) that will be able to balance the processes of exploration and exploitation. The mMVO based method is then used for identifying the parameters of linear and nonlinear subsystems in the Hammerstein model using the given input and output data. Note that the structure of the linear and nonlinear subsystems is assumed to be known. Moreover, a continuous-time linear subsystem is considered in this study, while there are a few methods that utilize such models. Two numerical examples and one real-world application, such as the Twin Rotor System (TRS) are used to illustrate the efficiency of the mMVO-based method. Various nonlinear subsystems such as quadratic and hyperbolic functions (sine and tangent) are used in those experiments. Numerical and experimental results are analyzed to focus on the convergence curve of the fitness function, the parameter variation index, frequency and time domain response and the Wilcoxon rank test. For the numerical identifications, three different levels of white noise variances were taken. The statistical analysis value (mean) was taken from the parameter deviation index to see how much our proposed algorithm has improved. For Example 1, the improvements are 29%, 33.15% and 36.68%, and for the noise variances, 0.01, 0.25, and 1.0 improvements can be found. For Example 2, the improvements are 39.36%, 39.61% and 66.18%, and for noise variances, the improvements are by 0.01, 0.25 and 1.0, respectively. Finally, for the real TRS application, the improvement is 7%. The numerical and experimental results also showed that both Hammerstein model subsystems are defined effectively using the mMVO-based method, particularly in quadratic output estimation error and a differentiation parameter index. The results further confirmed that the proposed mMVObased method provided better solutions than other optimization techniques, such as PSO, GWO, ALO, MVO and SCA

Least Squares Based and Two-Stage Least Squares Based Iterative Estimation Algorithms for H-FIR-MA Systems

This paper studies the identification of Hammerstein finite impulse response moving average (H-FIR-MA for short) systems. A new two-stage least squares iterative algorithm is developed to identify the parameters of the H-FIR-MA systems. The simulation cases indicate the efficiency of the proposed algorithms

Recursive search-based identification algorithms for the exponential autoregressive time series model with coloured noise

This study focuses on the recursive parameter estimation problems for the non-linear exponential autoregressive model with moving average noise (the ExpARMA model for short). By means of the gradient search, an extended stochastic gradient (ESG) algorithm is derived. Considering the difficulty of determining the step-size in the ESG algorithm, a numerical approach is proposed to obtain the optimal step-size. In order to improve the parameter estimation accuracy, the authors employ the multi-innovation identification theory to develop a multi-innovation ESG (MI-ESG) algorithm for the ExpARMA model. Introducing a forgetting factor into the MI-ESG algorithm, the parameter estimation accuracy can be further improved. With an appropriate innovation length and forgetting factor, the variant of the MI-ESG algorithm is effective to identify all the unknown parameters of the ExpARMA model. A simulation example is provided to test the proposed algorithms

Gradient-based iterative parameter estimation for bilinear-in-parameter systems using the model decomposition technique

The parameter estimation issues of a block-oriented non-linear system that is bilinear in the parameters are studied, i.e. the bilinear-in-parameter system. Using the model decomposition technique, the bilinear-in-parameter model is decomposed into two fictitious submodels: one containing the unknown parameters in the non-linear block and the other containing the unknown parameters in the linear dynamic one and the noise model. Then a gradient-based iterative algorithm is proposed to estimate all the unknown parameters by formulating and minimising two criterion functions. The stochastic gradient algorithms are provided for comparison. The simulation results indicate that the proposed iterative algorithm can give higher parameter estimation accuracy than the stochastic gradient algorithms

Least-Squares Based and Gradient Based Iterative Parameter Estimation Algorithms for a Class of Linear-in-Parameters Multiple-Input Single-Output Output Error Systems

The identification of a class of linear-in-parameters multiple-input single-output systems is considered. By using the iterative search, a least-squares based iterative algorithm and a gradient based iterative algorithm are proposed. A nonlinear example is used to verify the effectiveness of the algorithms, and the simulation results show that the least-squares based iterative algorithm can produce more accurate parameter estimates than the gradient based iterative algorithm

Least Squares Based Iterative Algorithm for the Coupled Sylvester Matrix Equations

By analyzing the eigenvalues of the related matrices, the convergence analysis of the least squares based iteration is given for solving the coupled Sylvester equations AX+YB=C and DX+YE=F in this paper. The analysis shows that the optimal convergence factor of this iterative algorithm is 1. In addition, the proposed iterative algorithm can solve the generalized Sylvester equation AXB+CXD=F. The analysis demonstrates that if the matrix equation has a unique solution then the least squares based iterative solution converges to the exact solution for any initial values. A numerical example illustrates the effectiveness of the proposed algorithm

Identification of the nonlinear systems based on the kernel functions

Constructing an appropriate membership function is significant in fuzzy logic control. Based on the multi-model control theory, this article constructs a novel kernel function which can implement the fuzzification and defuzzification processes and reflect the dynamic quality of the nonlinear systems accurately. Then we focus on the identification problems of the nonlinear systems based on the kernel functions. Applying the hierarchical identification principle, we present the hierarchical stochastic gradient algorithm for the nonlinear systems. Meanwhile, the one-dimensional search methods are proposed to solve the problem of determining the optimal step sizes. In order to improve the parameter estimation accuracy, we propose the hierarchical multi-innovation forgetting factor stochastic gradient algorithm by introducing the forgetting factor and using the multi-innovation identification theory. The simulation example is provided to test the proposed algorithms from the aspects of parameter estimation accuracy and prediction performance

Space-Time Continuous Models of Swarm Robotic Systems: Supporting Global-to-Local Programming

A generic model in as far as possible mathematical closed-form was developed that predicts the behavior of large self-organizing robot groups (robot swarms) based on their control algorithm. In addition, an extensive subsumption of the relatively young and distinctive interdisciplinary research field of swarm robotics is emphasized. The connection to many related fields is highlighted and the concepts and methods borrowed from these fields are described shortly

Mehrdimensionale Kanalschätzung für MIMO-OFDM

DIGITAL wireless communication started in the 1990s with the wide-spread deployment of GSM. Since then, wireless systems evolved dramatically. Current wireless standards approach the goal of an omnipresent communication system, which fulfils the wish to communicate with anyone, anywhere at anytime. Nowadays, the acceptance of smartphones and/or tablets is huge and the mobile internet is the core application. Given the current growth, the estimated data traffic in wireless networks in 2020 might be 1000 times higher than that of 2010, exceeding 127 exabyte. Unfortunately, the available radio spectrum is scarce and hence, needs to be utilized efficiently. Key technologies, such as multiple-input multiple-output (MIMO), orthogonal frequency-division multiplexing (OFDM) as well as various MIMO precoding techniques increase the theoretically achievable channel capacity considerably and are used in the majority of wireless standards. On the one hand, MIMO-OFDM promises substantial diversity and/or capacity gains. On the other hand, the complexity of optimum maximum-likelihood detection grows exponentially and is thus, not sustainable. Additionally, the required signaling overhead increases with the number of antennas and thereby reduces the bandwidth efficiency. Iterative receivers which jointly carry out channel estimation and data detection are a potential enabler to reduce the pilot overhead and approach optimum capacity at often reduced complexity. In this thesis, a graph-based receiver is developed, which iteratively performs joint data detection and channel estimation. The proposed multi-dimensional factor graph introduces transfer nodes that exploit correlation of adjacent channel coefficients in an arbitrary number of dimensions (e.g. time, frequency, and space). This establishes a simple and flexible receiver structure that facilitates soft channel estimation and data detection in multi-dimensional dispersive channels, and supports arbitrary modulation and channel coding schemes. However, the factor graph exhibits suboptimal cycles. In order to reach the maximum performance, the message exchange schedule, the process of combining messages, and the initialization are adapted. Unlike conventional approaches, which merge nodes of the factor graph to avoid cycles, the proposed message combining methods mitigate the impairing effects of short cycles and retain a low computational complexity. Furthermore, a novel detection algorithm is presented, which combines tree-based MIMO detection with a Gaussian detector. The resulting detector, termed Gaussian tree search detection, integrates well within the factor graph framework and reduces further the overall complexity of the receiver. Additionally, particle swarm optimization (PSO) is investigated for the purpose of initial channel estimation. The bio-inspired algorithm is particularly interesting because of its fast convergence to a reasonable MSE and its versatile adaptation to a variety of optimization problems. It is especially suited for initialization since no a priori information is required. A cooperative approach to PSO is proposed for large-scale antenna implementations as well as a multi-objective PSO for time-varying frequency-selective channels. The performance of the multi-dimensional graph-based soft iterative receiver is evaluated by means of Monte Carlo simulations. The achieved results are compared to the performance of an iterative state-of-the-art receiver. It is shown that a similar or better performance is achieved at a lower complexity. An appealing feature of iterative semi-blind channel estimation is that the supported pilot spacings may exceed the limits given the by Nyquist-Shannon sampling theorem. In this thesis, a relation between pilot spacing and channel code is formulated. Depending on the chosen channel code and code rate, the maximum spacing approaches the proposed “coded sampling bound”.Die digitale drahtlose Kommunikation begann in den 1990er Jahren mit der zunehmenden Verbreitung von GSM. Seitdem haben sich Mobilfunksysteme drastisch weiterentwickelt. Aktuelle Mobilfunkstandards nähern sich dem Ziel eines omnipräsenten Kommunikationssystems an und erfüllen damit den Wunsch mit jedem Menschen zu jeder Zeit an jedem Ort kommunizieren zu können. Heutzutage ist die Akzeptanz von Smartphones und Tablets immens und das mobile Internet ist die zentrale Anwendung. Ausgehend von dem momentanen Wachstum wird das Datenaufkommen in Mobilfunk-Netzwerken im Jahr 2020, im Vergleich zum Jahr 2010, um den Faktor 1000 gestiegen sein und 100 Exabyte überschreiten. Unglücklicherweise ist die verfügbare Bandbreite beschränkt und muss daher effizient genutzt werden. Schlüsseltechnologien, wie z.B. Mehrantennensysteme (multiple-input multiple-output, MIMO), orthogonale Frequenzmultiplexverfahren (orthogonal frequency-division multiplexing, OFDM) sowie weitere MIMO Codierverfahren, vergrößern die theoretisch erreichbare Kanalkapazität und kommen bereits in der Mehrheit der Mobil-funkstandards zum Einsatz. Auf der einen Seite verspricht MIMO-OFDM erhebliche Diversitäts- und/oder Kapazitätsgewinne. Auf der anderen Seite steigt die Komplexität der optimalen Maximum-Likelihood Detektion exponientiell und ist infolgedessen nicht haltbar. Zusätzlich wächst der benötigte Mehraufwand für die Kanalschätzung mit der Anzahl der verwendeten Antennen und reduziert dadurch die Bandbreiteneffizienz. Iterative Empfänger, die Datendetektion und Kanalschätzung im Verbund ausführen, sind potentielle Wegbereiter um den Mehraufwand des Trainings zu reduzieren und sich gleichzeitig der maximalen Kapazität mit geringerem Aufwand anzunähern. Im Rahmen dieser Arbeit wird ein graphenbasierter Empfänger für iterative Datendetektion und Kanalschätzung entwickelt. Der vorgeschlagene multidimensionale Faktor Graph führt sogenannte Transferknoten ein, die die Korrelation benachbarter Kanalkoeffizienten in beliebigen Dimensionen, z.B. Zeit, Frequenz und Raum, ausnutzen. Hierdurch wird eine einfache und flexible Empfängerstruktur realisiert mit deren Hilfe weiche Kanalschätzung und Datendetektion in mehrdimensionalen, dispersiven Kanälen mit beliebiger Modulation und Codierung durchgeführt werden kann. Allerdings weist der Faktorgraph suboptimale Schleifen auf. Um die maximale Performance zu erreichen, wurde neben dem Ablauf des Nachrichtenaustausches und des Vorgangs zur Kombination von Nachrichten auch die Initialisierung speziell angepasst. Im Gegensatz zu herkömmlichen Methoden, bei denen mehrere Knoten zur Vermeidung von Schleifen zusammengefasst werden, verringern die vorgeschlagenen Methoden die leistungsmindernde Effekte von Schleifen, erhalten aber zugleich die geringe Komplexität des Empfängers. Zusätzlich wird ein neuartiger Detektionsalgorithmus vorgestellt, der baumbasierte Detektionsalgorithmen mit dem sogenannten Gauss-Detektor verknüpft. Der resultierende baumbasierte Gauss-Detektor (Gaussian tree search detector) lässt sich ideal in das graphenbasierte Framework einbinden und verringert weiter die Gesamtkomplexität des Empfängers. Zusätzlich wird Particle Swarm Optimization (PSO) zum Zweck der initialen Kanalschätzung untersucht. Der biologisch inspirierte Algorithmus ist insbesonders wegen seiner schnellen Konvergenz zu einem akzeptablen MSE und seiner vielseitigen Abstimmungsmöglichkeiten auf eine Vielzahl von Optimierungsproblemen interessant. Da PSO keine a priori Informationen benötigt, ist er speziell für die Initialisierung geeignet. Sowohl ein kooperativer Ansatz für PSO für Antennensysteme mit extrem vielen Antennen als auch ein multi-objective PSO für Kanäle, die in Zeit und Frequenz dispersiv sind, werden evaluiert. Die Leistungsfähigkeit des multidimensionalen graphenbasierten iterativen Empfängers wird mit Hilfe von Monte Carlo Simulationen untersucht. Die Simulationsergebnisse werden mit denen eines dem Stand der Technik entsprechenden Empfängers verglichen. Es wird gezeigt, dass ähnliche oder bessere Ergebnisse mit geringerem Aufwand erreicht werden. Eine weitere ansprechende Eigenschaft von iterativen semi-blinden Kanalschätzern ist, dass der mögliche Abstand von Trainingssymbolen die Grenzen des Nyquist-Shannon Abtasttheorem überschreiten kann. Im Rahmen dieser Arbeit wird eine Beziehung zwischen dem Trainingsabstand und dem Kanalcode formuliert. In Abhängigkeit des gewählten Kanalcodes und der Coderate folgt der maximale Trainingsabstand der vorgeschlagenen “coded sampling bound”