Establishing formal state space models via quantization forquantum control systems

Formal state space models of quantum control systems are deduced and a scheme to establish formal state space models via quantization could been obtained for quantum control systems is proposed. State evolution of quantum control systems must accord with Schrdinger equations, so it is foremost to obtain Hamiltonian operators of systems. There are corresponding relations between operators of quantum systems and corresponding physical quantities of classical systems, such as momentum, energy and Hamiltonian, so Schrdinger equation models of corresponding quantum control systems via quantization could been obtained from classical control systems, and then establish formal state space models through the suitable transformation from Schrdinger equations for these quantum control systems. This method provides a new kind of path for modeling in quantum control.

Network-Based Predictions and Simulations by Biological State Space Models: Search for Drug Mode of Action

Since time-course microarrav data are short but contain a large number of genes, most of statistical models should be extended so that they can handle such statistically irregular situations. We introduce biological state space models that are established as suitable computational models for constructing gene networks from microarray gene expression data. This chapter elucidates theory and methodology of our biological state space models together with some representative analyses including discovery of drug mode of action. Through the applications we show the whole strategy of biological state space model analysis involving experimental design of time-course data, model building and analysis of the estimated networks.

Monte Carlo Likelihood Estimation of Mixed-Effects State Space Models with Application to HIV Dynamics

The statistical inference for generalized mixed-effects state space models （MESSM） are investigated when the random effects are unknown. Two filtering algorithms are designed both of which are based on mixture Kalman filter. These algorithms are particularly useful when the longitudinal ts are sparse. The authors also propose a globally convergent algorithm for parameter estimation of MESSM which can be used to locate the initial value of parameters for local while more efficient algorithms. Simulation examples are carried out which validate the efficacy of the proposed approaches. A data set from the clinical trial is investigated and a smaller mean square error is achieved compared to the existing results in literatures.

Design Criterion for Fixture Layout Based on the State Space Model in M ultistation Assembly Processes

The fixture layout is crucial to assure the product quality in a multistation assembly process （MAP）. A well-designed fixture layout will make the final product＇s variability be insensitive to the fixture variation inputs. As the basis of the fixture layout design, the design criterion plays an important role in the effectiveness of a solution and the optimization efficiency. In this paper, an effective and efficient design criterion is proposed for the fixture layout with a fixed reference point （FRP） in an MAP. First of all, a state space model for the individual port＇s variation propagation and accumulation is developed, which is the mathematical foundation of the proposed criterion. Then, based on this model, a novel design criterion used to evaluate the performance of the fixture layout is proposed for the fixture layout with an FRP. Finally, a method extracted from the proposed design criterion is developed for quick fixture layout design. A four-station assembly process is used to validate the effectiveness and efficiency of the proposed models and methods.

Application of the state space model to the system of wave energy conversion Analytical method for wave forces on singleoscillating rectangular buoy

A new analytical method is proposed to analyze the force acting on a rectangular oscillating buoy due to linear waves.In the method a new analytical expression for the diffraction velocity potential is obtained first by use of theeigenfunction expansion method and then the wave excitation force is calculated by use of the known incident wavepotential and the diffraction potential. Compared with the classical analytical method, it can be seen that the presentmethod is simpler for a two-dimensional problem due to the comparable effort needed for the computation ofdiffraction potential and for that of radiated potential. To verify the correctness of the method, a classical example inthe reference is recomputed and the obtained results are in good accordance with those by use of other methods,which shows that the present method is correct.

Quantum-dot Semiconductor Optical Amplifiers in State Space Model

A state space model(SSM) is derived for quantum-dot semiconductor optical amplifiers(QD-SOAs).Rate equations of QD-SOA are formulated in the form of state update equations,where average occupation probabilities along QD-SOA cavity are considered as state variables of the system.Simulations show that SSM calculates QD-SOA′s static and dynamic characteristics with high accuracy.

A Generalized State Space Average Model for Parallel DC-to-DC Converters

The high potentiality of integrating renewable energies,such as photovoltaic,into a modern electrical microgrid system,using DC-to-DC converters,raises some issues associated with controller loop design and system stability.The generalized state space average model(GSSAM)concept was consequently introduced to design a DC-to-DC converter controller in order to evaluate DC-to-DC converter performance and to conduct stability studies.This paper presents a GSSAM for parallel DC-to-DC converters,namely:buck,boost,and buck-boost converters.The rationale of this study is that modern electrical systems,such as DC networks,hybrid microgrids,and electric ships,are formed by parallel DC-to-DC converters with separate DC input sources.Therefore,this paper proposes a GSSAM for any number of parallel DC-to-DC converters.The proposed GSSAM is validated and investigated in a time-domain simulation environment,namely a MATLAB/SIMULINK.The study compares the steady-state,transient,and oscillatory performance of the state-space average model with a fully detailed switching model.

Deviation Diagnosis and Analysis of Hull Flat Block Assembly Based on a State Space Model

Dimensional control is one of the most important challenges in the shipbuilding industry. In order to predict assembly dimensional variation in hull flat block construction, a variation stream model based on state space was presented in this paper which can be further applied to accuracy control in shipbuilding. Part accumulative error, locating error, and welding deformation were taken into consideration in this model, and variation propagation mechanisms and the accumulative rule in the assembly process were analyzed. Then, a model was developed to describe the variation propagation throughout the assembly process. Finally, an example of fiat block construction from an actual shipyard was given. The result shows that this method is effective and useful.

State Estimation Moving Window Gradient Iterative Algorithm for Bilinear Systems Using the Continuous Mixed p-norm Technique

This paper studies the parameter estimation problems of the nonlinear systems described by the bilinear state space models in the presence of disturbances.A bilinear state observer is designed for deriving identification algorithms to estimate the state variables using the input-output data.Based on the bilinear state observer,a novel gradient iterative algorithm is derived for estimating the parameters of the bilinear systems by means of the continuous mixed p-norm cost function.The gain at each iterative step adapts to the data quality so that the algorithm has good robustness to the noise disturbance.Furthermore,to improve the performance of the proposed algorithm,a dynamicmoving window is designed which can update the dynamical data by removing the oldest data and adding the newestmeasurement data.A numerical example of identification of bilinear systems is presented to validate the theoretical analysis.

State Space Modeling and Implementation of a New Transformer Based Multilevel Inverter Topology with Reduced Switch Count

This paper presents a new transformer based multilevel inverter, with a novel pulse width modulation scheme to achieve seven-level inverter output voltage. The proposed inverter switching pattern consists of three fundamental frequency sinusoidal reference signals with an offset value, and one high frequency triangular carrier signal. This switching scheme has been implemented using an 8-bit Xilinx SPARTAN-3E field programmable gate array based controller. In addition, the state space model of the proposed inverter is developed. The significant features of the proposed topology are: reduction of the power switch count and the gate drive power supply unit, the provision of a galvanic isolation between load and sources by a centre tap transformer. An exhaustive comparison has been made of the existing multilevel inverter topologies and the proposed topology. The performances of the proposed topology with resistive, resistive-inductive loads are simulated in a MATLAB environment and validated experimentally on a laboratory prototype.

Retraction control of motorized seat belt system with linear state observer

A design and verification of linear state observers which estimate state information such as angular velocity and load torque for retraction control of the motorized seat belt (MSB) system were described. The motorized seat belt system provides functions to protect passengers and improve passenger's convenience. Each MSB function has its own required belt tension which is determined by the function's purpose. To realize the MSB functions, state information, such as seat belt winding velocity and seat belt tension are required. Using a linear state observer, the state information for MSB operations can be estimated without sensors. To design the linear state observer, the motorized seat belt system is analyzed and represented as a state space model which contains load torque as an augmented state. Based on the state space model, a linear state observer was designed and verified by experiments. Also, the retraction control of the MSB algorithm using linear state observer was designed and verified on the test bench. With the designed retraction control algorithm using the linear state observer, it is possible to realize various types of MSB functions.

Accuracy comparison of short-term oil price forecasting models

A forecasting model of the monthly crude oil price is investigated using the data between 1988 and 2009 from U. S. Energy Information Administration. First generalized auto-regressive condi- tional beteroskedasticity （GARCH） is applied to a state space model, a hybrid model （SS-GARCH） is proposed. Afterwards by computing a special likelihood function with two weak assumptions, model parameters are estimated by means of a faster algorithm. Based on the SS-GARCH model with the identified parameters, oil prices of next three months are forecasted by applying a Kalman filter. Through comparing the results between the SS-GARCH model and an econometric structure model, the SS-GARCH method is shown that it improves the forecasting accuracy by decreasing the index of mean absolute error （ RMSE ） from 7. 09 to 2.99, and also decreasing the index of MAE from 3. 83 to 1.69. The results indicate that the SS-GARCH model can play a useful role in forecasting short-term crude oil prices.

Using Pipeline Instructions by Parallel Simulation of Mathematical Models

Simulation is an important and useful technique helping users understand and model real life systems. Once built, the models can run proving realistic results. This supports making decisions on a more logical and scientific basis. The paper introduces method of simulation, and describes various types of its application. The authors used the method of analysis of the creation and implementation of the programme code. The authors compared parallel instruction of computing defined to pipelined instructions. The power of simulation is that a common model can be used to design a large variety of systems. An important aspect of the simulation method is that a simulation model is designed to be repeated in actual computer systems, especially in multicore processors. For this reason, it is important to minimize average waiting time for fetch and decode stage instructions. The objective of the research is to prove that the parallel operation of programme code is faster than sequential operation code on the multi processor architecture. The system modeling uses methods and simulation on the parallel computer systems is very precise. The time benefit gained in simulation of mathematical model on the pipeline processor is higher than the one in simulation of mathematical model on the multi processors computer system.

A new online modelling method for aircraft engine state space model

To overcome the drawbacks of current modelling method for aircraft engine state space model,a new method is introduced.The form of state space model is derived by using Talyor series to expand the nonlinear model that is implicit equations and involves many iterations.A partial derivative calculation method for iterations is developed to handle the influence of iterations on parameters.The derivative calculation and the aerothermodynamics calculations are combined in the component level model with fixed number Newton-Raphson(N-R)iterations.Mathematical derivation and simulations show the convergence ability of proposed method.Simulations show that comparing with the linear parameter varying model and centered difference based state space model,much higher accuracy of proposed online modelling method is achieved.The accuracy of the state space model built by proposed method can be maintained when the step amplitudes of inputs are within 2%,and the responses of the state space model can match those of the component level model when each input steps larger amplitudes.In addition,an online verification was carried out to show the capability of modelling at any operating point and that state space model can predict future outputs accurately.Thus,the effectiveness of the proposed method is demonstrated.

Applied RCM^2 Algorithms Based on Statistical Methods

The main purpose of this paper is to implement a system capable of detecting faults in railway point mechanisms. This is achieved by developing an algorithm that takes advantage of three empirical criteria simultaneously capable of detecting faults from records of measurements of force against time. The system is dynamic in several respects： the base reference data is computed using all the curves free from faults as they are encountered in the experimental data; the algorithm that uses the three criteria simultaneously may be applied in on-line situations as each new data point becomes available; and recursive algorithms are applied to filter noise from the raw data in an automatic way. Encouraging results are found in practice when the system is applied to a number of experiments carried out by an industrial sponsor.

Locating Error Considering Dimensional Errors Modeling for Multistation Manufacturing System

Multistation machining process is widely applied in contemporary manufacturing environment. Modeling of variation propagation in multistation machining process is one of the most important research scenarios. Due to the existence of multiple variation streams, it is challenging to model and analyze variation propagation in a multi-station system. Current approaches to error modeling for multistation machining process are not explicit enough for error control and ensuring final product quality. In this paper, a mathematic model to depict the part dimensional variation of the complex multistation manufacturing process is formulated. A linear state space dimensional error propagation equation is established through kinematics analysis of the influence of locating parameter variations and locating datum variations on dimensional errors, so the dimensional error accumulation and transformation within the multistation process are quantitatively described. A systematic procedure to build the model is presented, which enhances the way to determine the variation sources in complex machining systems. A simple two-dimensional example is used to illustrate the proposed procedures. Finally, an industrial case of multistation machining part in a manufacturing shop is given to testify the validation and practicability of the method. The proposed analytical model is essential to quality control and improvement for multistation systems in machining quality forecasting and design optimization.

Development of an integrated dynamic model for supply security and resilience analysis of natural gas pipeline network systems

An integrated dynamic model of natural gas pipeline networks is developed in this paper.Components for gas supply,e.g.,pipelines,junctions,compressor stations,LNG terminals,regulation stations and gas storage facilities are included in the model.These components are firstly modeled with respect to their properties and functions and,then,integrated at the system level by Graph Theory.The model can be used for simulating the system response in different scenarios of operation,and evaluate the consequences from the perspectives of supply security and resilience.A case study is considered to evaluate the accuracy of the model by benchmarking its results against those from literature and the software Pipeline Studio.Finally,the model is applied on a relatively complex natural gas pipeline network and the results are analyzed in detail from the supply security and resilience points of view.The main contributions of the paper are:firstly,a novel model of a complex gas pipeline network is proposed as a dynamic state-space model at system level;a method,based on the dynamic model,is proposed to analyze the security and resilience of supply from a system perspective.

Robust Remaining Useful Life Estimation Based on an Improved Unscented Kalman Filtering Method

In the Prognostics and Health Management(PHM),remaining useful life(RUL)is very important and utilized to ensure the reliability and safety of the operation of complex mechanical systems.Recently,unscented Kalman filtering(UKF)has been applied widely in the RUL estimation.For a degradation system,the relationship between its monitored measurements and its degradation states is assumed to be nonlinear in the conventional UKF.However,in some special degradation systems,their monitored measurements have a linear relation with their degradation states.For these special problems,it may bring estimation errors to use the UKF method directly.Besides,many uncertain factors can result in the fluctuations of the estimated results,which may have a bad influence on the RUL estimation method.As a result,a robust RUL estimation approach is proposed in this paper to reduce the errors and randomness of estimation results for this kind of degradation problems.Firstly,an improved unscented Kalman filtering is established utilizing the Kalman filtering(KF)method and a linear adaptive strategy.The linear adaptive strategy is used to adjust its noise term adaptively.Then,the robust RUL estimation is realized by the improved UKF.At last,three problems are investigated to demonstrate the effectiveness of the proposed method.

Reliability Prediction Method Based on State Space Model for Rolling Element Bearing

Reliability analysis based on equipment's performance degradation characteristics is one of the significant research areas in reliability research. Nowadays, many researches are carried on multi-sample analysis. But it is limited for a single equipment reliability prediction. Therefore, the method of reliability prediction based on state space model(SSM) is proposed in this research. Feature energy of the monitored signals is extracted with the wavelet packet analysis and the associated frequency band energy with online monitored data. Then,degradation feature is improved by moving average filtering processing taken as input pair model parameter of SSM to be estimated. In the end, state space predicting model of degradation index is established. The probability density distribution of the degradation index is predicted, and the degree of reliability is calculated. A real testing example of bearing is used to demonstrate the rationality and effectiveness of this method. It is a useful method for single sample reliability prediction.

Predictive Functional Controller with a Similar Proportional Integral Optimal Regulator Structure:Comparison with Traditional Predic-tive Functional Controller and Application to Heavy Oil Coking Equipment

By extending the system's state variables,a novel predictive functional controller has been developed.The structure of this controller is similar to that of classical proportional integral(PI)optimal controller and in-cludes a control block that can perform a feed-forward control of future P-step set points.It considers both the state variables and the output errors in its cost function,which results in enhanced control performance compared with traditional state space predictive functional control(TSSPFC)methods that consider only the predictive output er-rors.The predictive functional controller(PFC)has been compared with TSSPFC in terms of tracking ability,dis-turbance rejection,and also based on its application to heavy oil coking equipment.The results obtained show the effectiveness of the controller.