A simple and efficient methodology to approximate a general non-Gaussian stationary stochastic process by a translation process

• Published in: Probabilistic engineering mechanics Vol. 26; no. 4; pp. 511 - 519
• Main Authors: Shields, M.D., Deodatis, G., Bocchini, P.
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01.10.2011; Elsevier
• Subjects: Computation; Exact sciences and technology; Iterative methods; Mathematical analysis; Mathematical models; Mathematics; Methodology; Non-Gaussian; Non-Gaussian stochastic fields and processes; Probability and statistics; Probability density functions; Probability theory and stochastic processes; Sciences and techniques of general use; Simulation; Spectral Representation Method; Stochastic processes; Translation fields and processes; Translations; Spectral Representation Method; Translation fields and processes; Non-Gaussian stochastic fields and processes; Simulation; Ergodic theory; Spectral method; processes; Non gaussian noise; Spectral energy distribution; Power spectral density; Ergodicity; Iterative method; Non stationary process; Stochastic process; Modeling; Optimization; Random field; Non-Gaussian stochastic fields and; Gaussian process; Probability density function; Stationary process; Compatibility
• ISSN: 0266-8920; 1878-4275
• DOI: 10.1016/j.probengmech.2011.04.003

Some widely used methodologies for simulation of non-Gaussian processes rely on translation process theory which imposes certain compatibility conditions between the non-Gaussian power spectral density function (PSDF) and the non-Gaussian probability density function (PDF) of the process. In many practical applications, the non-Gaussian PSDF and PDF are assigned arbitrarily; therefore, in general they can be incompatible. Several techniques to approximate such incompatible non-Gaussian PSDF/PDF pairs with a compatible pair have been proposed that involve either some iterative scheme on simulated sample functions or some general optimization approach. Although some of these techniques produce satisfactory results, they can be time consuming because of their nature. In this paper, a new iterative methodology is developed that estimates a non-Gaussian PSDF that: (a) is compatible with the prescribed non-Gaussian PDF, and (b) closely approximates the prescribed incompatible non-Gaussian PSDF. The corresponding underlying Gaussian PSDF is also determined. The basic idea is to iteratively upgrade the underlying Gaussian PSDF using the directly computed (through translation process theory) non-Gaussian PSDF at each iteration, rather than through expensive ensemble averaging of PSDFs computed from generated non-Gaussian sample functions. The proposed iterative scheme possesses two major advantages: it is conceptually very simple and it converges extremely fast with minimal computational effort. Once the underlying Gaussian PSDF is determined, generation of non-Gaussian sample functions is straightforward without any need for iterations. Numerical examples are provided demonstrating the capabilities of the methodology.