Ove Ditlevsen

Technical University of Denmark | DTU · Department of Mechanical Engineering

This book consists of the author’s two reports from 1988 on statistical analysis of seismic boulder reflection data read from recorded graphical deep soil profiles obtained along the planned tunnel line across the east channel of the Great Belt in Denmark (Storebælt).

This book is a collection of the author's scientific reports from 1987-1988 on statistical analysis of positions and geometric proportions of the visible boulders on the cliff shores in the vicinity of the planned tunnel line under the east channel of the Great Belt in Denmark (Storebaelt). The analysis was ordered by A/S Storebaeltsforbindelsen (T...

Tests data of bending strengths of a large number of timber beams of different spans made at the Swedish Institute for Wood Technology Research reveal a statistical structure that can be very well represented in a simple probabilistic model of series system type. The strength of each defect cross-section (e.g. a cross-section with a knot or a clust...

Subtitle: With Applications to Multidimensional Civil Engineering Systems. Category: An untraditional textbook on Uncertainty Mathematics that avoids advanced set theory except for the final Chapter 13: Appendix. Contents: 1.Uncertain Quantities, 2.The Expectation Model, 3.The Conditional Mean Model, 4.Matrix Formulations, 5.The Linearization...

The classical statistical uncertainty problem of estimation of upper tail probabilities on the basis of a small sample of observations of a Gaussian random variable is considered. Predictive posterior estimation is discussed, adopting the standard statistical model with diffuse priors of the two normal distribution parameters. Rarely the uncertaint...

The sources and characters of uncertainties in engineering modeling for risk and reliability analyses are discussed. While many sources of uncertainty may exist, they are generally categorized as either aleatory or epistemic. Uncertainties are characterized as epistemic, if the modeler sees a possibility to reduce them by gathering more data or by...

Key elements of the authors’ work on money equivalent time allocation to costs and benefits in risk analysis are put together as an entity. This includes the data supported dimensionless analysis of an equilibrium relation between total population work time and gross domestic product leading to the definition of the life quality time allocation ind...

The rapid climate shifts observed in the glacial climate are analysed. The transitions into the warm interstadial states, the onsets, are easy identifiable in the record. The distribution of waiting times between consecutive onsets is well fitted assuming the remaining residence time in each state to be independent on the past. That implies that it...

A balance differential equation between free time and money-producing work time on the national economy level is formulated in a previous paper in terms of two dimensionless quantities, the fraction of work time and the total productivity factor defined as the ratio of the Gross Domestic Product to the total salary paid in return for work. Among th...

Renewal point processes show up in many different fields of science and engineering. In some cases the renewal points become the only observable parts of an anticipated hidden random variation of some physical quantity. The hypothesis might be that a hidden random process originating from zero or some other low value only becomes visible at the tim...

The model correction factor method (MCFM) is used in conjunction with the first-order reliability method (FORM) to solve structural reliability problems involving integrals of non-Gaussian random fields. The approach replaces the limit-state function with an idealized one, in which the integrals are considered to be Gaussian. Conventional FORM anal...

Closed-form expressions are derived for the steady-state availability, mean rate of failure, mean duration of downtime and lower bound reliability of a general system with randomly and independently failing repairable components. Component failures are assumed to be homogeneous Poisson events in time and repair durations are assumed to be exponenti...

The LQI by Nathwani et al. (1997) is a social indicator that kept constant allocates a part of a country's GDP to life saving initiatives. Is the LQI built on empirical evidence of a social behaviour that implies a desired balance between free time and work time? It is shown herein that a time balancing principle leads to an explicit mathematical f...

The topic concerns the density of occurrence of boulders and the joint distribution of the primary boulder dimensions in the till deposits of the Great Belt region in Denmark. The investigation was made in 1987-88 on the initiative of A/S Storebaeltsforbindelsen in order to prepare the tendering for mak-ing a bored tunnel through the till deposit....

The old hierarchical stochastic load combination model of Ferry Borges and Cas-tanheta and the corresponding problem of determining the distribution of the extreme random load effect is the inspiration to this paper. The evaluation of the distribution function of the extreme value by use of a particular first order reliability method (FORM) was fir...

This paper reports on the statistical interpretation of seismic diffraction measurements of boulder locations. The measurements are made in a corridor along the planned tunnel line for the later realized bored tunnel through the till deposits under the East Channel of the Great Belt in Denmark. The investigation was made in 1987–1988 on the initiat...

The definition the life quality index for a country as originally suggested by Nathwani, Lind and Pandey is based on the gross domestic product (GDP), the expected life in good health at birth, and the fraction of life time the anonymous citizen of the country is occupied with money making work. The LQI is invented to serve as a mean to evaluate ho...

The object of this study is a stationary Gaussian white noise excited plane multistory shear frame with a large number of rigid traverses. All the traverse-connecting columns have finite symmetrical yield limits except the columns in one or more of the bottom floors. The columns behave linearly elastic within the yield limits and ideally plastic ou...

Tests data of bending strengths of a large number of timber beams of different spans obtained at the Swedish Institute for Wood Technology Research reveal a statistical structure that can be represented in a simple probabilistic model of series system type. A particular feature of the data from one of the large test series is that unintentionally t...

The old stochastic load combination model of Ferry Borges and Castanheta and the corresponding extreme random load effect value is considered. The evaluation of the distribution function of the extreme value by use of a particular first order reliability method was first described in a celebrated paper by Rackwitz and Fiessler. The method has becom...

The derivation of the life quality index (LQI) is revisited for a revision. This revision takes into account the unpaid but necessary work time needed to stay alive in clean and healthy conditions to be fit for effective wealth producing work and to enjoyable free time. Dimension analysis consistency problems with the standard power function expres...

To find the exact probability distribution of the global maximum or minimum of a random field within a bounded domain is a pending problem even for Gaussian fields. Except for very special examples of fields, recourse must be taken to approximate reasoning or asymptotic considerations to be judged with respect to accuracy by simulations. In this pa...

The standard Langevin equation is a first order stochastic differential equation where the driving noise term is a Brownian motion. The marginal probability density is a solution to a linear partial differential equation called the Fokker–Planck equation. If the Brownian motion is replaced by so-called α-stable noise (or Lévy noise) the Fokker–Plan...

The object of study is a stationary Gaussian white noise excited multi-degree-of-freedom (MDOF) linear elastic, ideal plastic, linearly damped, statically determinate oscillator with several potential elements of ideal plastic yielding. Specifically the study is exemplified for a plane multistory shear frame with rigid traverses where all the conne...

axj¨ o University, Sweden. ABSTRACT: Tests data of bending strengths of a large number of timber beams of different spans made at the Swedish Institute for Wood Technology Research reveal a statistical structure that can be represented in a simple probabilistic model of series system type. The strength of each defect cross-section (e.g. a cross-sec...

Simple stochastic differential equation models have been applied by several researchers to describe the dispersion of tracer particles in the planetary atmospheric boundary layer and to form the basis for computer simulations of particle paths. To obtain the drift coefficient, empirical vertical velocity distributions that depend on height above th...

This paper is partly tutorial by presenting well known classical decision theory in a slightly untraditional form, but it does also present thinking and results that have not been published in the engineering literature before. The paper introduces the mathematical modeling basis for rational formulation of decision criteria and public acceptance c...

A class of stationary non-Gaussian processes, referred to as the class of mixtures of translation processes, is defined by their finite dimensional distributions consisting of mixtures of finite dimensional distributions of translation processes. The class of mixtures of translation processes includes translation processes and is useful for both Mo...

This paper emphazises the adverse event categorization principle in risk acceptance analysis, and suggests the use of a standard type risk profile of lognormal type for each category of adverse events. The risk profile for a specified category of adverse events and corresponding to a given operation time is defined as the complementary probability...

Application of the Slepian model process concept to obtain approximate plastic displacement distributions of elasto-plastic shear frame oscillators of one or more degrees of freedom has in previous works been for white noise force excitation acting directly on the first floor mass of the shear frame. A suitable number of the lower floors has been c...

The stochastic wave load environment of offshore structures is of such a complicated nature that any engineering analysis requires extensive simplifications. This concerns both the transformation of the wave field velocities and accelerations to forces on the structure and the probabilistic description of the wave field itself. In this paper the la...

In this study a stochastic field model for the stillwater loading is formulated where the statistics (mean value, standard deviation, and correlation) of the sectional forces are obtained by integration of the load field over the relevant part of the ship structure. The objective of the model is to establish the stochastic load field conditional on...

: The model correction factor method (MCFM) is used in conjunction with the first-order reliability method (FORM) to solve structural reliability problems involving integrals of non-Gaussian random fields. The approach replaces the limit-state function with an idealized one, in which the integrals are considered to be Gaussian. Conventional FORM an...

Taking geometric non-linearity into account, an oscillator inthe form of a portal frame with a rigid traverse and withideal-elastic-ideal-plastic clamped-in columns behaves under horizontalexcitation as an ideal-elastic-hardening/softening-plastic oscillatorgiven that the columns carry a tension/compression axial force. Assumingthat the horizontal...

In thisstudy a stochastic field model for the still water loading is formulated where the statistics (mean value, standard deviation, and correlation) of the sectional forces are obtained by integration of the load field over the relevant part of the ship structure. The objective of the model is to establish the stochastic load field conditional on...

: A one degree of freedom elasto-plastic oscillator subject to stationary Gaussian white noise has a plastic displacement response process of intermittent character. During shorter or longer time intervals the oscillator vibrates within the elastic domain without undergoing any plastic displacements. These pieces of elastic response cannot be disti...

Probabilities of excursions of random processes and fields into critical domains are of fundamental interest in many civil engineering decision problems. Examples are reliability evaluations of structures subject to random load processes, the influence of the size of a structural element on the carrying capacity of the element when the local materi...

. A two-dimensional silo pressure model-problem is investigated by molecular dynamics simulations. A plane silo container is filled by a granular matter consisting of congruent elliptic particles dropped one by one into the silo. A suitable energy absorbing contact force mechanism is activated during particle collisions and collisions against the w...

: The Model Correction Factor Method is an intelligent response surface method based on simplified modeling. MCFM is aimed for reliability analysis in case of a limit state defined by an elaborate model. Herein it is demonstrated that the method is applicable for elaborate limit state surfaces on which several locally most central points exist with...

Measurements show that silo wall pressures exhibit large fluctuations in time and space during discharge of the silo. This observation is important for the design of the silo wall because spatial pressure variations may impose substantial bending moments in the silo wall that otherwise may be small or vanishing due to the carrying ability of the me...

Plastic displacements of a Gaussian white noise excited three degrees of freedom non-ideal elasto-plastic oscillator are measured in laboratory experiments and the plastic displacements are compared to computer simulated results for the corresponding ideal elasto-plastic oscillator. The comparative analysis leads to an equivalent ideal plastic yiel...

The problem of the arbitrary choice of variables for random field modelling in structural mechanics or in soil mechanics is treated. For example, it is relevant to ask the question of whether it is best to choose a stiffness field along a beam element or to choose its reciprocal field, the flexibility field, as the input to the stochastic finite el...

. Measurements show that silo wall pressures exhibit large fluctuations in time and space during discharge of the silo. This observation is important for the design of the silo wall because spatial pressure variations may impose substantial bending moments that otherwise may be small or vanishing due to the carrying ability of the membrane forces i...

. The geotechnical engineer is often faced with the problem of how to assess the statistical properties of a soil parameter on the basis of a sample measured in-situ or in the laboratory with the defect that some values have been replaced by interval bounds because the corresponding soil parameter values have turned out to exceed the capacity of th...

Introduction and abstract. It has almost become a standard in stochastic mechanics applications of stochastic di#erential equations that the driving forces are modeled as Gaussian white noises, that is, as scalar or vector Brownian motion increments. However, this modeling may not always lead to responses that comply well with observed data. In par...

: Taking geometric non-linearity into account an oscillator of the form as a portal frame with a rigid traverse and with ideal-elastic-ideal-plastic clamped-in columns behaves under horizontal excitation as an ideal-elastic-hardening#softening-plastic oscillator given that the columns carry a tension #compression axial force. Assuming that the hori...

. The paper reports on wind tunnel experiments with an elastically suspended circular cylinder vibrating under the excitation of natural wind of high turbulence degree. The natural wind turbulence was simulated by superposing the low frequency part of the natural wind turbulence on the background high frequency turbulence of the wind tunnel flow. T...

This paper recapitulates the acceptance criteria formalisms as they seem to appear most frequently in present practice of risk analysis. A definition is given of a practicable and conceptually simple mathematical modelling tool suited for accounting the benefit loss accumulation due to the random occurrence of adverse events. The elementary buildin...

. A stochastic model of hierarchical series system type for the bending strength of spruce beams is defined from the anticipation that the bending failure takes place at a cross-section with a defect cluster formed by knots or grain irregularities. The parameters of the model are estimated from measurements of the strengths of a large number of sho...

Previously published silo wall pressure measurements during plug flow of barley in a large concrete silo are re-analysed under the hypothesis that the wall pressures are gamma-distributed. The fits of the gamma distribution type to the local pressure data from each measuring cell are satisfactory. However, the estimated parameters of the gamma dist...

For the practical applications of probabilistic reliability methods it is important to make decisions about the target reliability level. Presently calibration to existing design practice seems to be the only practicable and politically reasonable solution to this decision problem. However, several difficulties of ambiguity and definition show up w...

Two sets of 50 samples of the displacement response of the top traverse relative to the second traverse of an experimental shear frame with three traverses subject to white noise base shaking of two different intensities have been recorded at Institut für Allgemeine Mechanik in 1995, and are in file available for analysis. The column connection bet...

The Slepian model process method has turned out to be a powerful tool to obtain accurate approximations to the probability distributions of the plastic displacements of a one degree of freedom linear elastic-ideal plastic oscillator subject to Gaussian white noise excitation. In the present paper the Slepian method is applied to obtain approximate...

The distribution of the sum of a finite number of identically distributed random variables is in many cases easily determined given that the variables are independent. The moments of any order of the sum can always be expressed by the moments of the single term without computational problems. However, in the case of dependency between the terms eve...

The limitations of the validity of the central limit theorem argument as applied to definite integrals of non-Gaussian random fields are empirically explored by way of examples. The purpose is to investigate in specific cases whether the asymptotic convergence to the Gaussian distribution is fast enough to justify that it is sufficiently accurate f...

The Slepian model process method has turned out to be a powerful tool to obtain accurate approximations to the long run probability distributions of the plastic displacements of a one degree of freedom linear elastic-ideal plastic oscillator (EPO) subject to stationary Gaussian white noise excitation. The paper extends the method to the simplest EP...

During the emptying phase silo wall pressures show large random fluctuations in time and space. The nonuniform variations of the pressure along the wall have a decisive influence on the bending moments in the silo wall. It seems difficult to formulate continuum mechanical models to explain these fluctuations that turn out very sensitive to the rand...

Pressure data obtained in experiments with an existing grain silo are used to estimate the parameters of a stochastic silo load model formulated by the first two authors in the first of three papers. The estimation procedure is based on the method of maximum likelihood as applied to point observations of a Gaussian random field with unknown distrib...

Pressure data obtained in experiments with an existing grain silo in the second paper were used to estimate the parameters of an empirical stochastic silo load model formulated in the first paper. The obtained silo load model is investigated in this paper with respect to its structural reliability implications. Before considering the silo wall as a...

For the practical applications of probabilistic reliability methods it is important to make decisions about the target reliability level. Presently calibration to existing design practice seems to be the only practicable and politically reasonable solution to this decision problem. However, several difficulties of ambiguity and definition show up w...

Consider structural elements with random strength that after a suitable transformation has normal distribution with unknown mean μ and known or unknown standard deviation σ. By proof testing of n of these structural elements to a given load level it is observed that none of the elements fail. Given solely this test information the problem is that i...

For long-Span bridges, the traffic load can be modeled as while-noise-load fields along the lanes. The mean and the intensity of the white-noise field depend on the traffic situation. Theoretical expressions in terms of the traffic parameters are available for these white-noise-field characteristics covering the entire range from free Poissonian tr...

The study of the plastic displacements of the response of the bilinear elasto-plastic oscillator (EPO) excited by a stationary wide-band Gaussian process motivates the problem of determining the long run fractions of differently characterized qualified envelope excursions of a stationary Gaussian process above given thresholds. An extension of a pr...

A load effect from the traffic load on a large bridge with a large interval of slowly varying nonzero influence on the load effect can be modeled as a Gaussian random process. The mean value function and the covariance function that completely determines the process can be obtained by modeling the traffic load along each lane as a translating white...

Structural series-system reliability analyses formulated solely by use of a finite number Of random variables can often be done with sufficient accuracy in terms of first- or second-order upper and lower bounds on the system failure probability. The bounds are of the first order if they are defined solely by the single-element-failure probabilities...

Under general conditions reliability analyses of elaborate structural models can be replaced by much simpler equivalent reliability analyses of corresponding idealized structural models such as those based on rigid-plastic theory. The equivalence is in the sense of being with respect to probability of failure and is obtained by applying a random fa...

A Gaussian stochastic silo load model for circular cells has been formulated and used for reliability analysis in two previous papers. In order to avoid negative stresses orthogonal to the wall the possibility of modeling the wall stresses by a non- Gaussian field such as the lognormal field is considered herein. Several fundamental problems by suc...

Slepian model process approximate reasoning is used to obtain representative net and absolute yield displacement processes for the symmetric elasto-plastic oscillator of one degree of freedom excited by stationary Gaussian white noise. Yieldings occur in clumps with yield increments of alternating sign. Distributions are obtained in closed analytic...

The reasoning that leads to the well-known second order bounds on the failure probability of a random variable series system reliability problem is applied to obtain similar formulae for upper and lower bounds on the mean outcrossing rate of a general vector process out of the safe set of a series system given that the stream of outcrossings satisf...

The self-contradiction in the title of this paper is only apparent because it concerns the application of a particular type of response surface method where the form of the response surface is generated by use of the simple rigid-plastic mechanical theory. The basis is the previously published 'model correction factor method'. Herein the method is...

On the basis of statistical analyses of populations of crack growth curves obtained by three independent experimental investigations (Virkler et al. growing central cracks in aluminium 2024-T3 alloy panels at a given stress ratio, Ghonem and Dore growing central cracks in aluminium 7075-T6 alloy panels at three different stress ratios, and Lassen g...

From a practical reliability analysis point of view ideal rigid-plastic yield hinge structural models are very attractive. This is due to their clear way of functioning. In fact, the most fundamental geometrical and statical conditions of the real structures are satisfied at least to the first order by such models. However, such models may not be s...

The probabilistic properties are modelled of the plastic displacement process component and the plastic work process of the response of a symmetric linear elasto-plastic oscillator excited by a stationary Gaussian process. Under the assumption of rare visits to the plastic domain these processes are taken to be homogeneous compound Poisson processe...

Computational practicability imposes strong restrictions on the choice of a random field model for stochastic interpolation (kriging) between measured values of a material property, say, at a large set of points in a material body. With background in an actual example of a large number of cone tip resistance measurements in clay till it is demonstr...

A method for upper bound approximations to the reliability with respect to rigid-ideal plastic structural collapse is presented. Usually only very few collapse mechanisms contribute significantly to the total probability of collapse. The problem is therefore to identify these few mechanisms. The method is illustrated for a spatial frame structure d...

n-Dimensional integration by Monte Carlo directional importance sampling using analytical or numerical integration for each simulated direction is discussed. A suitable general class of sampling distributions is considered. The class is denoted as the class of mixed ūgm-centred standard Gaussian and -truncated ūgm-centred standard Gaussian distribu...

An exact method for calculating the probability that a vector-valued Gaussian stationary process will cross out of a safe set in a given time, is presented. It is based on representing the process by a random trigonometric polynomial and then calculating the probability by directional simulation. Exact bounds for the error can be calculated, giving...

First-passage problems for compound Poisson processes appear in reliability investigations concerning damage accumulation in structures that are subject to random process excitations. Asymptotic first-passage time distributions are easily obtained. Their accuracies are studied by use of simulation. Surprisingly good accuracy is achieved.

The reliability with respect to plastic collapse of rigid frame and truss structures is estimated by directional simulation. This conditional expectation simulation method is especially attractive for this problem because the mechanical computation for each sample is the same as the computation required in a standard Monte Carlo simulation. For eac...

The paper aims at presenting an example (a model) of a code practice enabling reliability methods for design. The code text is given in parallel with an explanatory text. The latter does not have the status of a code. It is a fundamental requirement of this code that the reliability measure is relative in the sense that it induces an ordering of an...

The method of substitute polyhedral yield conditions is used iteratively in the method of invariant linear combinations of linearly associated lower bound safety margins. The purpose is to construct upper bound approximations to the reliability with respect to collapse of a finite element discretized rigid-ideal plastic wall. It is attempted to mak...

Aiming at reducing the sampling variance of the estimated probability on a given set, a generalization is given of the method of uniform mean centred directional sampling in the standardized Gaussian space. Two modifications of different nature are involved. The one consists in shifting the origin to a point different from the mean. The resulting o...

The difficulties are discussed concerning the definition of the safe set in random variable models of structural system reliability analysis. For frame structures the need for clarity and consistency motivates a continued interest in considering rigid-ideal plastic constitutive behavior assigned to discretized hinge models. General yield conditions...

Presentation d'une methode pour determiner la fonction de distribution des poids des camions susceptibles de passer sur un pont, a partir d'un echantillon aleatoire fini extrait d'une population infinie

The probability of the adverse event of upcrossing, within a given time interval, of some critical level by some structural random vibration response quantity is usually evaluated on the conservative side in terms of the mean upcrossing rate. Due to clumping of the upcrossings the evaluation may become overly conservative. This is remedied by only...

The unit volume weight of the material in a structural body is modeled as a random field, and the boundary of the body is modeled to be random. Both sources of randomness contribute in an interacting way to the variance of any considered self-weight load effect. A specific type of random vector-field modeling of the uncertain boundary is particular...

The author attempts to clarify and discuss the nature of the different sources of uncertainty relevant to structural reliability. In a mathematically unified model these should be taken into consideration when evaluating the reliability of a structure in probabilistic terms. The question is raised as to what empirical information is obtained about...

The topic is reliability analysis of frame structures with rigid-ideal plastic constitutive behavior assigned to discretized hinge models. General yield conditions with internal force interaction are considered. Adoption of the associated flow rule assures the validity of the static theorem. On this basis a theorem about linear combinations of so-c...