Remaining Useful Life Model and Assessment of Mechanical Products: A Brief Review and a Note on the State Space Model Method

The remaining useful life(RUL) prediction of mechanical products has been widely studied for online system performance reliability, device remanufacturing, and product safety(safety awareness and safety improvement). These studies incorporated many di erent models, algorithms, and techniques for modeling and assessment. In this paper, methods of RUL assessment are summarized and expounded upon using two major methods: physics model based and data driven based methods. The advantages and disadvantages of each of these methods are deliberated and compared as well. Due to the intricacy of failure mechanism in system, and di culty in physics degradation observation, RUL assessment based on observations of performance variables turns into a science in evaluating the degradation. A modeling method from control systems, the state space model(SSM), as a first order hidden Markov, is presented. In the context of non-linear and non-Gaussian systems, the SSM methodology is capable of performing remaining life assessment by using Bayesian estimation(sequential Monte Carlo). Being e ective for non-linear and non-Gaussian dynamics, the methodology can perform the assessment recursively online for applications in CBM(condition based maintenance), PHM(prognostics and health management), remanufacturing, and system performance reliability. Finally, the discussion raises concerns regarding online sensing data for SSM modeling and assessment of RUL.

THE STATE SPACE RECONSTRUCTION TECHNOLOGY OF DIFFERENT KINDS OF CHAOTIC DATA OBTAINED FROM DYNAMICAL SYSTEM

Certain deterministic nonlinear systems may show chaotic behavior. We consider the motion of qualitative information and the practicalities of extracting a part from chaotic experimental data. Our approach based on a theorem of Takens draws on the ideas from the generalized theory of information known as singular system analysis. We illustrate this technique by numerical data from the chaotic region of the chaotic experimental data. The method of the singular-value decomposition is used to calculate the eigenvalues of embedding space matrix. The corresponding concrete algorithm to calculate eigenvectors and to obtain the basis of embedding vector space is proposed in this paper. The projection on the orthogonal basis generated by eigenvectors of timeseries data and concrete paradigm are also provided here. Meanwhile the state space reconstruction technology of different kinds of chaotic data obtained from dynamical system has also been discussed in detail.

MLP training in a self-organizing state space model using unscented Kalman particle filter

Many Bayesian learning approaches to the multi-layer perceptron （MLP） parameter optimization have been proposed such as the extended Kalman filter （EKF）. This paper uses the unscented Kalman particle filter （UPF） to train the MLP in a self- organizing state space （SOSS） model. This involves forming augmented state vectors consisting of all parameters （the weights of the MLP） and outputs. The UPF is used to sequentially update the true system states and high dimensional parameters that are inherent to the SOSS moder for the MLP simultaneously. Simulation results show that the new method performs better than traditional optimization methods.

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.

Configuration Selection for Reconfigurable Manufacturing Systems by Means of Characteristic State Space

The configuration selection for reconfigurable manufacturing systems（RMS） have been tackled in a number of studies by using analytical or simulation models. The simulation models are usually based on fewer assumptions than the analytical models and therefore are more wildly used in modeling complex RMS. But in the absence of an efficient gradient analysis method of the objective function, it is time-consuming in solving large-scale problems by using a simulation model coupled with a meta-heuristics algorithm. In this paper, a new approach by means of characteristic state space is presented to improve the efficiency of the configuration selection for an RMS. First, a characteristic state equation is set up to represent the input and the output resources of each basic activity in an RMS. A production process model in terms of matrix equations is established by iterating the equations of basic activities according to the resource flows. This model introduces the production process into a characteristic state space for further analysis. Second, the properties of the characteristic state space are presented. On the basis of these properties, the configuration selection in an RMS is considered as a path-planning problem, and the gradient of the objective function is computed. Modified simulated annealing（SA） is also presented, in which neighborhood generation is guided by the gradient to accelerate convergence and reduce the run time of the optimization procedure. Finally, several case studies on the configuration selection for some actual reconfigurable assembly job-shops are presented and compared to the classical SA. The comparison shows relatively positive results. This study provides a more efficient configuration selection approach by using the gradient of the objective function and presents the relevant theories on which it is based.

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.

基于state-space-split法的滞回非线性系统随机动力响应分析

采用SSS(state-space-split)法,建立了引入Bouc-Wen滞回模型的杜芬非线性系统在高斯白噪声激励下的概率密度函数(PDF)的近似求解方法,分析了其随机动力响应变化规律。首先,将Bouc-Wen滞回模型引入杜芬非线性系统,分别考虑非线性系统中的几何非线性和材料非线性对动力响应的影响。随后,对该模型进行了等效线性化(EQL)处理,基于等效线性化法结果,介绍了SSS法的简化方法和计算原理,并通过该方法求解了三维FPK方程的近似联合概率密度函数。最后,将该方法应用于三个案例和一个工程实例,通过求解其概率密度函数分布及动力可靠度验证了提出方法的适用性、可行性和优越性。

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 Modal Identification Algorithm Combining Blind Source Separation and State Space Realization

A modal identification algorithm is developed, combining techniques from Second Order Blind Source Separation (SOBSS) and State Space Realization (SSR) theory. In this hybrid algorithm, a set of correlation matrices is generated using time-shifted, analytic data and assembled into several Hankel matrices. Dissimilar left and right matrices are found, which diagonalize the set of nonhermetian Hankel matrices. The complex-valued modal matrix is obtained from this decomposition. The modal responses, modal auto-correlation functions and discrete-time plant matrix (in state space modal form) are subsequently identified. System eigenvalues are computed from the plant matrix to obtain the natural frequencies and modal fractions of critical damping. Joint Approximate Diagonalization (JAD) of the Hankel matrices enables the under determined (more modes than sensors) problem to be effectively treated without restrictions on the number of sensors required. Because the analytic signal is used, the redundant complex conjugate pairs are eliminated, reducing the system order (number of modes) to be identified half. This enables smaller Hankel matrix sizes and reduced computational effort. The modal auto-correlation functions provide an expedient means of screening out spurious computational modes or modes corresponding to noise sources, eliminating the need for a consistency diagram. In addition, the reduction in the number of modes enables the modal responses to be identified when there are at least as many sensors as independent (not including conjugate pairs) modes. A further benefit of the algorithm is that identification of dissimilar left and right diagonalizers preclude the need for windowing of the analytic data. The effectiveness of the new modal identification method is demonstrated using vibration data from a 6 DOF simulation, 4-story building simulation and the Heritage court tower building.

STATIONARY DISTRIBUTIONS OF INFINITE PARTICLE SYSTEMS WITH NONCOMPACT STATE SPACE.

This paper deals with the preblem of existence and uniqueness of the stationary distributions (abbr., s. d.'s) for the processes constructed in [4] .The main results are stated in § 1. For the reader's convenience we first restate the existence theorems (Theorem 1 and 2) of the processes given in [4]. Then two existence theorems (Theorem 3 and 4) and a uniqueness theorem (Theorem 5) for the s. d.'s of the processes are presented. The last result (Theorem 6), as an application of the previous ones, is about the Schlgl model which comes from nonequilibrium statisticali physics. The details of the proofs of Theorem 3—6 are given in § 2—4.

Variable dimensional state space based global path planning for mobile robot

A variable dimensional state space（VDSS） has been proposed to improve the re-planning time when the robotic systems operate in large unknown environments.VDSS is constructed by uniforming lattice state space and grid state space.In VDSS,the lattice state space is only used to construct search space in the local area which is a small circle area near the robot,and grid state space elsewhere.We have tested VDSS with up to 80 indoor and outdoor maps in simulation and on segbot robot platform.Through the simulation and segbot robot experiments,it shows that exploring on VDSS is significantly faster than exploring on lattice state space by Anytime Dynamic A＊（AD＊） planner and VDSS is feasible to be used on robotic systems.

A Semantic Model of Multiple Space of Role and State ( I )

Language artificially classifies the varied phenomena of the chaotic world into four kinds of expressions: “real displacements”， “real shifts”， “virtual displacements” and “virtual shifts” This paper is mainly a semantic exploration of the “real displacements” and the achievement of the discussion is a foundation for the semantic study of the latter three kinds of expressions. Emphasis will be laid upon the verbs and their relationship with nouns. The “multiple space role-state-ring-chain” model designed in the paper is aimed at delving beneath the surface of a verb and studying its inner micro-world, so as to grasp the transformational rules among the surface, deep and underlying structures of a sentence and to promote the discovery for the mystery of human languages.

State Space Approach to Mass Exchange Network Synthesis

State space approach is an effective method to mass-exchange network (MEN) synthesis. By decomposing the network into two interactive parts, a distribution network and a process operator, the synthesis problem can be formulated into a mixed integer nonlinear programming (MINLP) model. In this article, a generalized state space model based on typical MEN is established and verified in two cases. A new asymmetrical operator and cost index are also adopted to speed up the solution process. The results demonstrate the efficiency of the proposed approach.

New coordination scheme for multi-robot systems based on state space models

A new coordination scheme for multi-robot systems is proposed. A state space model of the multi- robot system is defined and constructed in which the system＇s initial and goal states are included along with the task definition and the system＇s internal and external constraints. Task accomplishment is considered a transition of the system state in its state space （SS） under the system＇s constraints. Therefore, if there exists a connectable path within reachable area of the SS from the initial state to the goal state, the task is realizable. The optimal strategy for the task realization under constraints is investigated and reached by searching for the optimal state transition trajectory of the robot system in the SS. Moreover, if there is no connectable path, which means the task cannot be performed Successfully, the task could be transformed to be realizable by making the initial state and the goal state connectable and finding a path connecting them in the system＇s SS. This might be done via adjusting the system＇s configuration and/or task constraints. Experiments of multi-robot formation control with obstacles in the environment are conducted and simulation results show the validity of the proposed method.

STATE SPACE METHODS FOR DECENTRALIZED H_∞ CONTROL

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DIRECT SPECTURM ANALYSIS OF THE STATE SPACE FOR RANDOM VIBRATION OF MDOF LINEAR DAMPED SYSTEM

This paper proceeds from the general case of the unsymmetric linearized multi-degrees of free- dom(MDOF)systems.By adopting the general complex modal theory of the state space,the response analysis for a sys- tem subjected to random excitation of the same source is carried out using as a kind of direct spectrum analysis method in frequency domain.With the input of power spectral density function given,the explicit expression of the power spectral density function matrix of the output response can be obtained.By taking Fourier inverse transform,the integrated expres- sions of the correlation function matrix and of the spectrum moment matrix are obtained.Comparing with the time domain method,this method enjoys the merit of visualization and avoids the procedure of transformation from the obtained re- sponse correlation function to be solved for the output spectrum utilizing Fourier transform.This paper has extended the application range of the traditional frequency domain analysis method.The mean square values and variety of statistical val- ues can be obtained conveniently.This method and the time domain method are different in approach but equally satisfac- tory in their results.

Discrete state space method and modal extension method based impact sound synthesis model

The efficient and accurate synthesis of physical parameter-controllable impact sounds is essential for sound source identification. In this study, an impact sound synthesis model of a cylinder is proposed based on discrete state space（DSS） method and modal extension method（MEM）. This model is comprised of the whole three processes of the physical interaction, i.e., the Hertz contact process, the transient structural response process, and the sound radiation process. Firstly,the modal expanded DSS equations of the contact system are constructed and the transient structural response of the cylinder is obtained. Then the impact sound of the cylinder is acquired using improved discrete Raleigh integral. Finally, the proposed model is verified by comparing with existing models. The results show that the proposed impact sound synthesis model is more accurate and efficient than the existing methods and easy to be extended to the impact sound synthesis of other structures.

STATE SPACE TREE METHOD AND EXACT DECOMPOSITION ALGORITHM FOR FINDING NETWORK OVERALL RELIABILITY

First,the state space tree method for finding communication network overall re-liability is presented.It directly generates one disjoint tree multilevel polynomial of a networkgraph.Its advantages are smaller computational effort(its computing time complexity is O(en_l),where e is the number of edges and n_l is the number of leaves)and shorter resulting expression.Second,based on it an exact decomposition algorithm for finding communication network overallreliability is presented by applying the hypergraph theory.If we use it to carry out the m-timedecomposition of a network graph,the communication network scale which can be analyzed by acomputer can be extended to m-fold.

Amplitude-squared squeezing of the generalized odd-even coherent states of the anharmonic oscillator in a finite-dimensional Hilbert space

This paper discusses the properties of amplitude-squared squeezing of the generalized odd-even coherent states of anharmonic oscillator in finite-dimensional Hilbert space. It demonstrates that the generalized odd coherent states do exhibit strong amplitude-squared squeezing effects in comparison with the generalized even coherent states.