Extreme Values Method Research Articles

Effect of Ruhrstahl Heraeus Refining Time on Inclusions and Rolling Contact Fatigue Life of a High‐Carbon Chromium Bearing Steel

According to the variation in the average composition, the average size, the number density, and the area fraction of large‐size inclusions during Ruhrstahl Heraeus (RH) refining process, large‐size inclusions in the high‐carbon chromium‐bearing steel reach the lowest level when the vacuum cycle time is 25 min. When the soft blowing time reaches over 25 min, the number density and area fraction of large‐size inclusions increase. The rolling contact fatigue (RCF) life of the forged steel samples is measured using a thrust RCF tester, indicating that the fatigue life of no. 1 steel (vacuum cycle 40 min, soft blowing 20 min) is 12% higher than that of no. 2 steel (vacuum cycle 20 min, soft blowing 40 min). Based on the estimation of the characteristic size of inclusions in the forged steel by the statistics of extreme values (SEV) method, it is concluded that when the characteristic size and the chemical composition of inclusions in steels are similar, the RCF life is increased by 12% when the number density of large‐size inclusions decreases from 0.63 to 0.44 mm−2.

Evaluation of maximum non-metallic inclusion sizes in steel by statistics of extreme values method based on Micro-CT imaging

Non-metallic inclusions have become a matter of concern for several properties of steel. The effective evaluation of inclusions in steel would provide critical information to evaluate the steel quality. In this study, an evaluation method based on X-ray Micro-Computed Tomography (Micro-CT) experiments was proposed. First, Micro-CT experiments were carried out to characterize the inclusions. Then, the characterizations of the inclusions were collected based on the 2D slices and their 3D features. The extreme values were evaluated by statistics of extreme values method with these data. The evaluation results were compared with those obtained by international standard ASTM E2283-08. The results demonstrated that the evaluation method based on inclusion sizes collected from 3D inclusion information provided a stable result. It means that the extreme value evaluation method with the 3D data based on Micro-CT was an effective method.

Minor seismic hazard changes in the broader area of Pournari artificial lake after the first filling (W. Greece)

The broader area of Pournari dam (Western Greece) is investigated regarding the potential seismic hazard change after its impoundment in the early 1980’s. During this impoundment, an increase in local earthquake activity with certain features of induced seismicity was observed. Within the third and fourth month after the first filling, two moderate seismic events occurred, on March 10, 1981 (ML=5.6) and on April 10, 1981 (ML=4.7), with focal depths 13 km and 10 km, respectively, indicating migration of seismicity to shallower depths. The latter is considered as mechanical response change of background from undrained to the drained response (flysch formation).We investigate the potential local seismic hazard and the induced seismicity changes due to the establishment of the reservoir using three time-windows. The first one covers the period up to 1980, before the impoundment, the second starts immediately after the impoundment (1981-2009), while the third is focused on the whole instrumental period 1900-2009. For these time-windows, seismic hazard was initially assessed using the extreme values method. The traditional Cornell-McGuire approach was following applied for the whole instrumental period as a validation test, regarding the reliability of the results obtained by the extreme values method. The results reveal a small decrease of the estimated values of Peak Ground Acceleration (PGA), Peak Ground Velocity (PGV) and maximum expected magnitude (Mmax). The results are compared to the seismic hazard study case of Polyphyto dam (NW Greece), located on a different seismotectonic regime.

Computing Methods in the Analysis of Road Accident Reconstruction Uncertainty

The study is dedicated to the problem of uncertainty in the analysis of accident situations in road traffic. The term “uncertainty” is generally known when used with reference to measurement techniques, but its application to the analyses of accident situations in road traffic, including accident reconstruction, is a relatively new field of knowledge. The objectives of this work include the presentation and examination of selected aspects related to the taking of uncertainty into account when analysing the course of an accident and making the necessary calculations. Apart from the scientific objectives, an important utilitarian goal may also be pointed out. The data and methods presented may be used by automotive technology experts in their accident reconstruction work. The paper shows seven methods that enable the taking into account of the uncertainty of the data used for calculations, i.e. extreme values method, total differential method, higher-order total differential method, finite-difference method, Gauss method, method based on the description of stochastic processes, and Monte-Carlo method. Apart from formal (mathematical) descriptions of the methods, an example of their use for the estimation of uncertainty of selected quantities that describe an accident situation has been demonstrated. The bad and good points of individual methods have been shown in the context of the application considered.

Prediction of maximum carbon element content in continuous casting billets of 82B cord steel based on statistics of extreme values method

The research of carbon content along the casting direction of 82B cord steel billets is of great significance for improving the quality of cord products from subsequent processing. However, the traditional segregation and billets quality evaluation methods have certain limitations, such as sampling length and analysis area, which affect the accuracy of quality judgment. Thus, the statistics of extreme values (SEV) was introduced to predict the maximum value of carbon element content along the casting direction, which can quantitatively characterize the segregation degree. The size of the selected billet is 150 mm × 150 mm, and the sampling location is the centerline of the billet. The experiment was conducted by considering the effect of cooling intensity and casting speed on the maximum value of carbon element content. Firstly, the calculation results show that the SEV method can predict the maximum value of carbon element content along the casting direction of 82B cord steel, and the SEV method is proved to be effective by analyzing the carbon distribution and fluctuation in billets. To some extent, the SEV method can break the limitations of the sampling length and analysis area by predicting the maximum value of carbon element on a larger range of continuous casting billets with few samples. During the continuous casting process, the increase in cooling intensity makes the surface shrinking rate increase, which can slow down the flow of solute-enriched liquid to the center, and the center segregation can be reduced. On the other hand, the function area of the final electromagnetic stirring can be expanded with the increase in the casting speed, which can reduce the concentration of carbon element in the center of the billets and reduce the maximum value of carbon element content. It can provide a new theoretical reference for the quantitative calculation of carbon content in continuous casting billets and the quality evaluation of continuous casting billets.

Atlantic Oscillation indices in meridional distribution

The goal of this study was to define new oscillation indices of the Atlantic Ocean covering latitudes of both hemispheres, for the period from 1900 until 2014. Indices described sea level atmospheric pressure (SLP) oscillations between neighbouring cells of global atmospheric circulation (northern and southern Hadley, Ferrel and polar cells) and were calculated using two methods: conventional (based on SLP values in selected stations) and extreme values method (counted using maximum or minimum SLP from adequate areas). Twelve time series of new Atlantic Oscillation indices have been obtained—six conventional and six extreme, which have been presented in continuous form and through selection data by seasons: December–February (DJF), and June–August (JJA). The indices’ time series showed similarities in shared maxima and minima moments and long-lasting increasing tendency of five extreme and three conventional indices. There were strong correlations between oscillation indices describing variability in Hadley cells on both hemispheres (conventional 0.593–0.907, extreme 0.088–0.908). A strong correlation occurred between Southern Atlantic and Antarctic South Atlantic Extreme indices (0.668 to 0.979). Overall, stronger connections were found between extreme indices than the conventional ones, and most regularities were found in the Southern Hemisphere oscillations and wintertime indices (DJF for Northern and JJA for Southern Hemisphere). Power spectrum analysis showed major impact of 6- and 12-month periods, as well as less distinct significance of approximately 5.5-year-long interval and its multiples.

Estimation of maximum inclusion by statistics of extreme values method in bearing steel

A statistic method, statistics of extreme values (SEV), was described in detail, which can estimate the size of maximum inclusion in steel. The characteristic size of the maximum inclusion in a high clean bearing steel (GCr15) was evaluated by this method, and the morphology and composition of large inclusions found were analyzed by scanning electron microscopy (SEM). When standard inspection area (S0) is 280 mm2 the characteristic size of the biggest inclusion found in 30 standard inspection area is 23.93 µm, and it has a 99.9% probability of the characteristic size of maximum inclusion predicted being no larger than 36.85 pm in the experimental steel. SEM result shows that large inclusions found are mainly composed of CaS, calcium-aluminate and MgO. Compositing widely exists in large inclusions in high clean bearing steel. Compared with traditional evaluation method, SEV method mainly focuses on inclusion size, and the estimation result is not affected by inclusion types. SEV method is suitable for the inclusion evaluation of high clean bearing steel.

High cycle fatigue property and fracture behavior of high-strength austempered ductile iron

The high cycle fatigue tests of high-strength austempered ductile iron of grade 1200/850/04 (ASTM 897 M-06) were conducted by the high frequency fatigue machine. The results show that the S–N curve decreases continuously and there is no conventional fatigue limit at 107 cycles. According to the fracture surface observations, at short fatigue life region the specimens fail from defects at specimen surface and at long fatigue life region the specimens fail from internal defects with fish-eye area around it. According to the defect sizes measured in the standard inspection areas of the material, the maximum defect size evaluated by the statistics of extreme values method is in accordance with that of the fatigue test results. Meanwhile, it is obvious that the fatigue strength of austempered ductile iron is influenced by the original defect size and the fatigue limit can be well evaluated by the Murakami equation.

Effect of micro-inclusions on subsurface-initiated rolling contact fatigue of a railway wheel

The objectives of this paper are to investigate the size of the maximum micro-inclusion in a railway wheel using ultrasonic fatigue testing and to evaluate the effect of the micro-inclusion on subsurface-initiated rolling contact fatigue of the railway wheel. Fatigue specimens with a large risk volume were quenched, tempered and oxynitrocarburized to increase both the strength of the matrix and the resistance to surface corrosion, which ensured that all of the specimens fractured from the internal inclusion under water cooling. The test results show that the size of the micro-inclusion obtained using the fatigue method are much larger than those obtained by a traditional surface analysis method, which means that the accuracy of the fatigue method is higher than that of the traditional method. The maximum square root of the micro-inclusion area and the maximum length of the major axis of the elliptical micro-inclusion for a full-sized railway wheel are estimated using the statistics of extreme values method to be 296 µm and 736 µm, respectively. Based on the estimated maximum micro-inclusion sizes and principles of fracture mechanics, the critical loading of the railway wheel for both subsurface-initiated fatigue and fatigue initiated at a deep-lying material defect are obtained.

Assessment of the statistical earthquake hazard parameters for the Central Anatolia region, Turkey

The aim of this study is to evaluate the Central Anatolia region of Turkey with regard to seismicity and earthquake hazard using available data on Mw ≥ 4.0 earthquakes that occurred between 1900 and 2011 and the Gumbel Extreme Values method. Additionally, the study also aimed to determine the parameters associated with earthquake hazards. The seismicity analysis for the Central Anatolia region was performed by evaluating past earthquakes in six source regions located within the area falling within 38–41° N latitude and 30–35° E longitude. For each region, the researcher determined the occurrence probability and the return period for earthquakes strong enough to cause material damage and the possible maximum magnitudes for earthquakes that might occur in the future within a certain time period. Based on the study results, the researcher determined that the North Anatolian fault zone (zone 1) in Central Anatolia is the region characterized by the highest probability (89 %) than an Mw ≥ 7.0 magnitude earthquake will occur within the next 100 years and that the return period in this zone for such an earthquake is 50 years.

Seismic hazard assessment in Polyphyto Dam area (NW Greece) and its relation with the "unexpected" earthquake of 13 May 1995 (<i>M</i><sub>s</sub> = 6.5, NW Greece)

Abstract. Seismic hazard assessment and seismicity changes are investigated in the Kozani–Grevena area, at the western margin of internal Hellenides in NW Greece. The region is of great interest, since it was characterized by very low seismic activity until 1995, when the "unexpected" Kozani–Grevena earthquake (Ms = 6.5) occurred. This event is of significant importance for Greece, since it, along with the 1999 Athens earthquake, initiated the modification of the Greek Building Code. In order to detect any seismicity changes, the seismicity of the region was divided into three time windows: the first up to 1973, the second from 1900 to 1994 and the third covering the entire instrumental period. For the above mentioned time windows, seismic hazard assessment was performed using the extreme values method. The results indicate an increase of the peak ground acceleration (PGA) values after the impoundment, with the exception of the area in the vicinity of the NE edge of the Dam. Before the occurrence of the 1995 event, the epicentral region also exhibited higher PGA values than before the impoundment. The most significant increase in PGA values is observed SE of the Polyphyto artificial lake, where the largest values are observed for the second and the third period. The coincident increase in the number of earthquakes and in the PGA values may be attributed to the impoundment of the Polyphyto Dam. The maximum expected magnitude is calculated by the extreme values method and Gumbel's third asymptotic distribution. The results reveal similar values of maximum expected magnitudes (Mmax = 6.5), independent of the seismicity rate, indicating that the 13 May 1995 earthquake was not an "unexpected" event, since the magnitude of an oncoming earthquake depends mainly on the tectonics of the region and the characteristics of the active faults.

Inclusion size evaluation and fatigue strength analysis of 35CrMo alloy railway axle steel

The axial loading fatigue tests of 35CrMo alloy railway axle steel were carried out with the untreated specimens and those treated by nitrocarburization. It is found that the untreated 35CrMo steel specimens fracture from surface, while those of the treated specimens fracture from internal inclusions. In order to investigate the inclusion size in the material, the ultrasonic fatigue tests were conducted for the 35CrMo steel by applying large risk volume specimens with straight section after nitrocarburization. The results show that the cracks of all the specimens initiate from the internal inclusion. The statistics of extreme values (SEV) method was applied to evaluate the maximum inclusion size in the large volume material and the full-scale axle. Based on the evaluated maximum inclusion sizes and the fracture mechanics, different fracture behaviors of axial loading specimens and full-scale axle as well as the effect of inclusion size on fatigue strength of full-scale axles were analyzed based on the fracture mechanics.

Evaluation of Maximum Inclusion Size and Fatigue Limit for High Strength Steel in Rotating Rending

Based on the observation of fracture surfaces for a low-alloy high strength steel under rotating bending in very high cycle regime, a newly defined method about inspection plane under rotating bending was developed in this paper. By using the statistics of extreme values (SEV) method, the maximum sizes of inclusion and FGA corresponding to the control volume of specimen are evaluated to be about 41.38 μm and 58.51 μm on the basis of this newly defined inspection plane, and the corresponding values of fatigue limit are evaluated to be 690 MPa and 654 MPa, respectively. It should be noted that fatigue design based on former involves a certain amount of risk in very high cycle regime.

Quantitative Study on Nonmetallic Inclusion Particles in Steels by Automatic Image Analysis With Extreme Values Method

The presence of nonmetallic inclusion particles which appear during steelmaking process is harmful to the properties of steels, which is mainly as a function of some aspects such as size, volume fraction, shape, and distribution of these particles. The automatic image analysis technique is one of the most important tools for the quantitative determination of these parameters. The classical Student approach and the Extreme Values Method (EVM) were used for the inclusion size and shape determination and the evaluation of distance between the inclusion particles. The results thus obtained indicated that there were significant differences in the characteristics of the inclusion particles in the analyzed products. Both methods achieved results with some differences, indicating that EVM could be used as a faster and more reliable statistical methodology.

Estimating inclusion size in WE43-T6 magnesium alloys based on Gumbel extreme values

Estimating the maximum inclusion size in a large volume of clean metal from observations on a small volume is an important problem faced by the metallurgical industries. Static and fatigue behaviors and other mechanical properties of the material are influenced by the maximum inclusion sizes. This paper presents first application of the extreme values method for estimating the largest inclusion in WE43-T6 magnesium alloys. The actual dimensions of the largest pore and oxide in WE43-T6 magnesium alloys are found to be consistent with the dimensions predicted using the Gumbel extreme values (GEV) distribution obtained by both tomography and metallography. In this respect application of the Gumbel extreme values to describe clusters of intermetallic particles and predict the maximum intermetallic size in WE43 magnesium alloys may also be reasonably used.

Interrelationship between statistical methods for estimating the size of the maximum inclusion in clean steels

Two types of approach based on the statistics of extremes have been developed recently to estimate the sizes of large inclusions in clean steel. The first type (termed here “threshold” approaches) includes methods based on the Generalized Pareto distribution (GPD) and the Exponential distribution (EXPGPD). Both of these methods use measurements of the sizes of all inclusions larger than a certain threshold size in a sample. The second type of approach (termed here the “extreme values” type) includes the Statistics of Extreme Values (SEV) method and the Generalized Extreme Values (GEV) method. In these, only the size of the largest inclusion in each of a set of samples is measured. This paper compares the four methods and describes their inter-relationship. The distribution of large sizes depends on a shape parameter ξ. The influence of ξ on confidence intervals for the characteristic size of the maximum inclusion is studied by considering the shape of the likelihood function. The value of ξ is found to have a considerable effect on the precision of estimation. In the methods based on the GPD and GEV the value of ξ is not specified in advance. In such a case the GPD method gives more precise estimation of the characteristic size of the maximum inclusion than the GEV method. On the other hand in the EXPGPD and SEV methods ξ is assumed to be zero. In this case the EXPGPD method gives more precise estimation than the SEV method. The choice of a method of estimation of the characteristic size of the maximum inclusion is discussed in the light of these findings.

The precision of methods using the statistics of extremes for the estimation of the maximum size of inclusions in clean steels

The maximum inclusion size in clean steels influences fatigue behaviour and other mechanical properties. Hence, its estimation and the uncertainties associated with the estimation are important issues for steel makers and users. Here, two methods based on the statistics of extremes, one termed the Statistics of Extreme Values (SEV) method and the other the Generalized Pareto Distribution (GPD) method, are used for the estimation. Both methods use data on the size of inclusions revealed on the surface of sampled areas. The influence of the number of sample areas and the way the sample areas are grouped on the estimated result and its confidence limits is determined and compared. For both the SEV and the GPD methods, the estimated largest inclusion size is relatively insensitive to the number of sample areas but, as might be expected, the width of the confidence interval decreases steeply as the number of sample areas increases. A key point is that the SEV method has a narrower confidence interval than the GPD method for a given number of sample areas, because the SEV method makes an extra assumption about the form of the distribution of large inclusions. The particular assumption is difficult to justify on the basis of the data alone, and leads to a potentially over-optimistic estimate of precision. For practical application of the GPD estimation procedure, the number of sample areas needed for estimation depends on the confidence interval required and the volume of steel of interest. It is suggested on the basis of the GPD size distribution that fatigue failure initiation in a component is unlikely to be caused by the single largest inclusion, but rather by more frequently occurring inclusions near the top of the size range. This provides the conceptual basis for a statistically based design approach in which the estimated distribution of inclusion sizes is used in defect tolerance design of steel components and in control of steel production processes.

Estimating the upper tail of flood‐peak frequency distributions using hydrometeorological information

In its 1988 report, the National Research Council Committee on Estimating the Probabilities of Extreme Floods identified principles for improving the estimation of floods with annual exceedance probabilities of the order of 10−3 or smaller. This paper presents a methodology for estimating the probability of extreme floods which makes use of these principles. Its core is the “peak‐to‐volume” method [Bradley and Potter, 1992], which is based on separately estimating the probability distributions of flood volumes and flood peaks conditioned on volumes. In its original form it relies on extrapolating a conventionally estimated probability distribution, the distribution of flood volumes. To strengthen this step, we propose use of the gradient of extreme values (GRADEX) method [Guillot and Duband, 1967], in which the upper tail of the flood volume distribution is deduced from that Of precipitation. We enhance the GRADEX method by exploiting the work of Smith [1989], who developed a regional model for estimating the upper tail of a frequency distribution based on extreme order statistics. An example illustrates the proposed method.