This paper analyzes a method to approximate the first passage time probability density function which turns to be particularly useful if only sample data are available. The method relies on a ...Laguerre-Gamma polynomial approximation and iteratively looks for the best degree of the polynomial such that a normalization condition is preserved. The proposed iterative algorithm relies on simple and new recursion formulae involving first passage time moments. These moments can be computed recursively from cumulants, if they are known. In such a case, the approximated density can be used also for the maximum likelihood estimates of the parameters of the underlying stochastic process. If cumulants are not known, suitable unbiased estimators relying on κ-statistics might be employed. To check the feasibility of the method both in fitting the density and in estimating the parameters, the first passage time problem of a geometric Brownian motion is considered.
•An approximation of the first passage time probability density function is proposed•The proposed approximation is of Laguerre-Gamma polynomial type•The resulting recursive nested algorithm involves FPT moments.•A suitable normalization condition is used as stopping criterion.•Estimation of the parameters is proposed through a likelihood function.•Approximations are computable even if only FPT sample data are available.•The special case of Geometric Brownian Motion is analyzed.
An improved recursive Levenberg–Marquardt algorithm (RLM) is proposed to more efficiently train neural networks. The error criterion of the RLM algorithm was modified to reduce the impact of the ...forgetting factor on the convergence of the algorithm. The remedy to apply the matrix inversion lemma in the RLM algorithm was extended from one row to multiple rows to improve the success rate of the convergence; after that, the adjustment strategy was modified based on the extended remedy. Finally, the performance of this algorithm was tested on two chaotic systems. The results show improved convergence.
We propose a distributed recursive Gaussian process (drGP) regression framework for building received-signal-strength (RSS) map. The proposed framework adopts independent mobile devices in prescribed ...local areas to construct local RSS maps through recursive computation of the posterior distribution of the RSS on a fixed set of grids as training data gradually become available. The training input positions can be either precise or subject to errors of known distribution. All the local RSS maps are then fused to give a global map in the second step. The proposed framework is of significantly reduced computational complexity and scalable to big data generated from large-scale sensor networks. We further demonstrate its use in both static fingerprinting and mobile target tracking. The experimental results show that with our distributed framework satisfactory positioning accuracy can be achieved with much less complexity and storage than the standard framework.
•A new model of phased-mission systems with common bus is proposed.•Common bus performance sharing and common cause failures are considered in the model.•A recursive algorithm is provided for the ...system reliability evaluation.•Optimal element allocation problem is formulated and solved by genetic algorithm.
Phased-mission common bus (PMCB) systems are systems with a common bus structure, performing missions with consecutive and non-overlapping phases of operations. PMCB systems are found throughout industry, e.g., power generating systems, parallel computing systems, transportation systems, and are sometimes characterized by their common cause failures. Reliability evaluation of PMCB systems plays an important role in system design, operation, and maintenance. However, current studies have focused on either phased-mission systems or common bus systems because of their complexity. The challenge in practice is to consider phased-mission systems together with common bus structures and common cause failures. To solve this problem, we propose an evaluation algorithm for PMCB systems with common cause failures by coupling the structure function of a common bus performance sharing system and an existing recursive algorithm. To weigh the efficiency of the proposed algorithm, its complexity is discussed. To improve the reliability of PMCB systems, we adopt the genetic algorithm method to search for the optimal allocation strategies of the service elements. We use both analytical and numerical examples to illustrate the application of the proposed algorithm.
In this paper, we propose an optimized GO-FLOW algorithm for time-dependent system reliability analysis. The optimized GO-FLOW algorithm is implemented based on recursive calculation of the complete ...set of minimum path sets. The algorithm is augmented with a cut-off criterion for probabilistic models to offer a much more flexible approach to achieve the trade-off between computational complexity and accuracy. The optimization method and algorithm are tested with an example case study of reliability analysis of auxiliary feedwater system in nuclear power plants. The verification results show that the retrofitting GO-FLOW method is capable of efficient processing of the shared signals and providing accuracy solutions at high speed.
In this article, we consider the problem of estimating diffraction attenuation from the approximation of terrain using a multiple bridged knife-edge model. This model can be considered as a ...generalization of the well-known multiple knife-edge (MKE) one where spaces between knife-edges are bridged by reflecting surfaces. A series-based-standard solution is presented in the literature but suffers from its very high computational complexity. We, thus, propose to generalize the recursive Vogler algorithm developed for the MKE model to tackle this problem. To reduce complexity, the proposed algorithm exploits the recursive form to avoid repeated calculations of the existing solution. Moreover, we provide a complexity analysis of both the standard algorithm and the proposed algorithm based on the number of computed integrals. Both theoretical and numerical results show that our proposed algorithm is faster than the original one while having identical accuracy, hence proving the effectiveness of our solution.
The integer order differentiation by integration method based on the Jacobi orthogonal polynomials for noisy signals was originally introduced by Mboup, Join and Fliess. We propose to extend this ...method from the integer order to the fractional order to estimate the fractional order derivatives of noisy signals. Firstly, two fractional order differentiators are deduced from the Jacobi orthogonal polynomial filter, using the Riemann-Liouville and the Caputo fractional order derivative definitions respectively. Exact and simple formulae for these differentiators are given by integral expressions. Hence, they can be used for both continuous-time and discrete-time models in on-line or off-line applications. Secondly, some error bounds are provided for the corresponding estimation errors. These bounds allow to study the design parameters' influence. The noise error contribution due to a large class of stochastic processes is studied in discrete case. The latter shows that the differentiator based on the Caputo fractional order derivative can cope with a class of noises, whose mean value and variance functions are polynomial time-varying. Thanks to the design parameters analysis, the proposed fractional order differentiators are significantly improved by admitting a time-delay. Thirdly, in order to reduce the calculation time for on-line applications, a recursive algorithm is proposed. Finally, the proposed differentiator based on the Riemann-Liouville fractional order derivative is used to estimate the state of a fractional order system and numerical simulations illustrate the accuracy and the robustness with respect to corrupting noises.
•Impact between two non-uniform elastic rods with piecewise constant characteristic impedance is considered.•By use of 1D theory and a recursive algorithm, the distribution of characteristic ...impedance of the impacting rod is determined so that a desired piecewise constant impact force is realized up to a certain time.•Examples of desired exponentially decreasing and linearly increasing impact forces are presented.•The impact force realized by use of the recursive algorithm is compared with the impact force obtained by use of 3D FE simulation.
Axial impact between two elastic rods with piecewise constant characteristic impedance is considered. The distribution of characteristic impedance of the impacted rod and the impact velocity are given. By use of a 1D recursive algorithm, the characteristic impedances of the impacting rod are determined as long as they are all positive so that a prescribed impact force is realized. A condition for positivity of the characteristic impedance is derived in terms of transmission coefficients for wave energy. At the time from which positivity of all characteristic impedances cannot be maintained, or earlier, the characteristic impedance of the impacting body is continued, e.g., at the level of the last positive characteristic impedance or at level zero corresponding to cutting off the impacting rod. Examples of prescribed exponentially decreasing and linearly increasing impact forces are presented for a uniform impacted rod with constant characteristic impedance. In these examples, there is good agreement between the prescribed impact force and the impact force obtained from 3D FE simulation with a piecewise linear diameter of the impacting body that approximates the piecewise constant diameter obtained by use of the 1D recursive algorithm.
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