Igor Rychlik

A new definition of the rainflow cycle counting method

Abstract A new equivalent definition of the rainflow cycle counting method is presented, which expresses the rainflow cycle amplitudes in explicit analytical formulae. The method attaches to each maximum of the strain function the amplitude of a corresponding cycle or two half cycles, which are evaluated independently from each other. This definition is more convenient for the statistical analysis of rainflow cycle amplitudes for a random loading process.

On the 'narrow-band' approximation for expected fatigue damage

The common hypothesis in the literature is that the expected damage due to stationary Gaussian loads can be conservatively estimated by approximating the load by a Gaussian narrow-band process. We prove the hypothesis for rainflow, peak-valley and zero-crossings amplitude counts. We present a general upper bound for the fatigue damage determined using the Miner-Palmgren rule and the rainflow counting method for any load with finite expected crossing intensity.

Rainflow analysis: Markov method

Abstract In this paper we discuss rainflow cycle counting methods and linear fatigue damage accumulation for stationary loads. The expected damage is computed by approximating the sequence of local extremes by a Markov chain. The algorithm is implemented as part of a ‘fatigue toolbox’. Several examples illustrate the results.

Wave characteristic distributions for Gaussian waves—Wave-length, amplitude and steepness

In as tationary stochastic process the wave-length and amplitude are defined as the difference in time and height between a crest and the following trough. The distributions of these quantities are of great practical importance, but no closed form expressions are known at present. In previous papers we have presented an approximation which gives correct upper and lower bounds, regardless of the covariance structure under Gaussian assumptions. In this paper the suggested approximations are compared to two simpler approximations, one due to Cavanie et al. (1976) based on a cosine process and a new one, derived by replacing the model process by its regression curve.

Modelling and statistical analysis of ocean-wave data using transformed Gaussian processes

In this paper we present a statistical analysis of wave characteristics in oceanographic data, using a transformed Gaussian random process for modelling, and to compare theoretical distributions of wave period and amplitude with observations. A natural transform (estimable from the data) is used throughout, the model compared with that based on purely (untransformed) Gaussian assumptions. The data are measurements of a sea state in deep and shallow water, at different geographical locations. One of the purposes of the paper is to use an appropriately sophisticated method to test the correctness of a Gaussian hypothesis in modelling wave data for ew!luation of extreme values and for fatigue analysis. Copyright

Models for road surface roughness

This study focuses on the statistical description and analysis of road surface irregularities that are essential for heavy-vehicle fatigue assessment. Three new road profile models are proposed: a homogenous Laplace moving average process, a non-homogenous Laplace process and a hybrid model that combines Gaussian and Laplace modelling. These are compared with the classical homogenous Gaussian process as well as with the non-homogenous Gaussian model that represents the road surface as a homogenous Gaussian process with Motor Industry Research Association spectrum enhanced by randomly placed and shaped irregularities. The five models are fitted to eight measured road surfaces and their accuracy and efficiency are discussed.

Simulation of load sequences from rainflow matrices: Markov method

For loads modeled as Markov chains there is a non-linear relation between rainflow and Markov matrices. The relation was proved by Rychlik and used to compute a rainflow matrix when the Markov matrix is known. In this paper the relation is inverted to find a Markov matrix when the rainflow matrix is given. The Markov matrix is then used to simulate a random load. Examples illustrating the method are given.

Velocities for moving random surfaces

For a stationary two-dimensional random field evolving in time, we derive statistical distributions of appropriately defined velocities. The results are based on a generalization of the Rice formula. We discuss importance of identifying the correct form of the distribution which accounts for the sampling bias. The theory can be applied to practical problems where evolving random fields are considered to be adequate models. Examples include changes of atmospheric pressure, variation of air pollution, or dynamical models of the sea surface elevation. We study the last application in more detail by applying the derived results to Gaussian fields representing irregular sea surfaces. In particular, we study statistical properties of velocities both for the sea surface and for the envelope field based on this surface. The latter is better fitted to study wave group velocities and is of particular interest for engineering applications. For wave and wave group velocities, numerical computations of distributions are presented and illustrated graphically.

Exact distributions for apparent waves in irregular seas

We discuss the long-run distributions of several characteristics for the apparent waves in a Gaussian sea. Three types of one-dimensional wave records are considered: 1) the seaway in time at a fixed position; 2) the instantaneous profile along a horizontal line; 3) the encountered seaway. Exact integral forms of the joint long run distributions are derived for the apparent periods, lengths, and heights. Results of numerical approximations of these distributions are presented in examples. For the computations we considered, as the input spectra, empirical estimates of the frequency spectra as well as JONSWAP type spectra. Effective algorithms are discussed and utilized in the form of a comprehensive computer package of numerical routines.

Rain-Flow-Cycle Distribution for Ergodic Load Processes

The Rain-Flow-Cycle (RFC) amplitude in an ergodic load process is studied. The ergodic distribution of the RFC-amplitude is defined using the sequence of extremes in the load process. In the special case when the sequence of extremes is an n-step Markov chain, the RFC-distribution is obtained as the solution of a certain functional equation. For a Gaussian load, approximations of the RFC-distribution are proposed, and the transition densities of extremes are approximated using the regression method.