Niels C. Lind

Fast probability integration by three-parameter normal tail approximation

Abstract A new method of fast probability integration is presented, based on a three-parameter normal tail approximation to a non-normal distribution function. Values of the distribution function, the probability density function and its derivative are matched at the approximation point with the approximating function. The approximation point is the known “design point”, used within the framework of second moment reliability theory. The proposed method is as fast as the available two-parameter algorithm, but is apparently more accurate.

CITATION LIFE CYCLES OF TEN CITATION CLASSICS

Not all highly cited papers have the same citation life cycle curves, i.e. curves of frequency of citations received vs. time. The citation life of ten randomly selected Citation Classics, five in medicine and five in biochemistry, are studied longitudinally in time and compared with a random sample of ten non-classics of the same cohort. There are pronounced differences in the life cycle curves; two distinct types are suggested. Type A, comprised of both high and low cited papers in both fields, has an early peak of citation rate and may be approximated by a bilinear cumulative citation curve with a break at six years of age, when three quarters of the total number of citations have occurred. Type B, in this study comprised of extremely highly cited methodological Citation Classics, exhibit a constant or slowly accelerating growth rate with a vigorous citation life extending over the entire period studied and typically one third or less of the total citations accumulated at six years of age.

Some thoughts on the human development index

The Human Development Index (HDI) of a nation, proposed by UNDP (1990), is the average of its score, relative to all other nations, on three basic indicators: GDP per person, life expectancy and literacy. The HDI and its components are examined critically with respect to accuracy, sensitivity, and discriminant power. Differential implications for evaluating a particular project or regulation are derived, suggesting some ways to improve the HDI. It is concluded that the HDI is potentially a powerful instrument for world social development and bears examination for validity and consistency with public objectives.

Approximate reliability analysis using normal polynomial and simulation results

Approximate solutions are presented to evaluate the probability of failure of a structural system using simulation results. The solutions are based on a family of normal polynomial models fitted to the simulated data points with fractile constraints. The normal polynomial approximates well to some of the well-known distribution types. A simple model with a third-order normal polynomial appears appropriate for practical reliability analysis. The approximation reduces the required number of simulation trials.

Modelling of uncertainty in discrete dynamical systems

Abstract Dynamic systems that are not Gaussian, stationary and linear are difficult to model by full probabilistic analysis. Sufficient information for practical application can often be obtained by second moment analysis, described in the paper. Alternatively, second moment analysis can be performed using point distributions. Two new methods in this class, one exact for linear systems and one approximate, are described. Examples show the application and illustrate the accuracy.

Models of human error in structural reliability

Abstract Among the many human factors that have importance for structural reliability, human error is dominant. With many alternative error mechanisms operative, many mathematical models must be studied and compared with observation to select a best strategy for maximum reliability. Three types are presented here: a simple discrete model, a filter model of error elimination, and an error combination model. Results are calculated for examples with parameter values common in Civil Engineering structural practice.

Social and economic criteria of acceptable risk

Abstract A simple normative theory is proposed for the responsible management of risks to the public. A ‘lifesaving’ alternative, if it is truly to save lives, should return to the community more years of life expectancy in good health than the years of work consumed to pay for its cost. This common-sense time principle of risk management provides a criterion for acceptable risk that is applicable in connection with cost-utility analysis. The principle is a benchmark, providing a unified rationale for the assessment of risks in health care and technology. Integration of acceptable risk criteria with criteria for national performance can be achieved via applicable compound social indices such as the Life Quality Index or the Human Development Index.

A compound index of national development

The Life Product Index (LPI) is a combination of life expectancy and gross domestic product. It is structured to the notion of ‘quality-adjusted life’ and calibrated to conform with the value of economic activity reflected in the national time budget. The LPI can serve as a guide in national policy planning. It can also be used as an indicator of sensible regulation of hazardous technology and as a guide in the assessment of individual projects. An LPI criterion for net benefit assessment of a project, policy or proposed regulation is derived from first principles. Application is illustrated by an example.

A cross entropy method for flood frequency analysis

The cross-entropy method with fractile constraints has been developed to estimate a random variable when the data are a set of independent observations of the variable. The method can claim several advantages over existing methods. It uses a reference distribution like the prior distribution in Bayesian analysis and likewise generates a posterior distribution.The method is of interest, in particular, because it satisfies two fundamental requirements for selfconsistency in the analysis of a probabilistic system based on data: a principle of invariance and a principle of data monotonicity.The method is applied to flood analysis. Robustness of the minimum cross-entropy method is compared with other methods: the methods of moments and the maximum likehood.

Simplified theories of cyclic plasticity

SummarySimple theories of plasticity such as flow rules associated with a single yield surface are sufficiently accurate in predicting plastic behaviour for monotonic loading. However, for alternating or cyclic loads, such theories cannot describe complex plastic behaviour with sufficient accuracy. The concept of multiple loading surfaces or internal state parameters may then be introduced and respective plasticity theories become considerably complicated, requiring step by step integration of incremental relations for both strain and internal parameters.The present paper is aimed at elaborating relatively simple models of cyclic behaviour that could be expressed in terms of generalized stresses and strains and could be applied in treating boundary-value problems for beams, plates and shells. Finite stress-strain relations are derived in several subdomains of the stress space, both for loading, unloading and subsequent loading conditions. It is assumed that a set of discrete points from the past history affects the actual state. Some particular cases of cyclic loading of a tube and circular plates are considered in detail in order to illustrate applicability of proposed description.ZusammenfassungEinfache Theorien, wie einer einzigen Fließfläche zugeordnete Fließgesetze, beschreiben das plastische Verhalten hinreichend genau bei monotoner Belastung. Ihre Genauigkeit ist jedoch unzureichend um das komplexe plastische Verhalten bei wechselnder oder zyklischer Belastung zu beschreiben. Das Konzept veränderlicher Fließflächen oder innerer Zustandsvariablen kann dann benützt werden. Die entsperchenden Theorien werden beträchtlich komplizierter, schrittweise Integration der Zuwachsbeziehungen für Verzerrungen und die inneren Zustandsvariablen wird erforderlich.Das Ziel vorliegender Arbeit ist die Ermittlung relativ einfacher Modelle des zyklischen Verhaltens, ausdrückbar in verallgemeinerten Spannungen und Verzerrungen und anwendbar bei der Behandlung von Randwertproblemen von Stäben, Platten und Schalen. Endliche Spannungs-Verzerrungs-Bedingungen werden in verschiedenen Teilgebieten des Spannungsraumes hergeleitet, für Belastung, Entlastung und für Wiederbelastung. Es wird dabei angenommen, daß eine diskrete Menge von Punkten der Geschichte den augenblicklichen Zu-stand beeinflußt. Im Detail werden einige Spezialfälle der zyklischen Belastung von Rohren und Kreisplatten zur Illustration der Anwendbarkeit der vorgeschlagenen Beschreibung betrachtet.