Abstract: Higher ground-level ozone (GLO) concentration adversely affects human health, vegetations as well as activities in the ecosystem. In Malaysia, most of the analysis on GLO concentration are carried out using the average value of GLO concentration, which refers to the centre of distribution to make a prediction or estimation. However, analysis which focuses on the higher value or extreme value in GLO concentration is rarely explored. Hence, the objective of this study is to classify the tail behaviour of GLO using generalized extreme value (GEV) distribution estimation the return level using the corresponding modelling (Gumbel, Weibull, and Frechet) of GEV distribution. The results show that Weibull distribution which is also known as short tail distribution and considered as having less extreme behaviour is the best-fitted distribution for four selected air monitoring stations in Peninsular Malaysia, namely Larkin, Pelabuhan Kelang, Shah Alam, and Tanjung Malim; while Gumbel distribution which is considered as a medium tail distribution is the best-fitted distribution for Nilai station. The return level of GLO concentration in Shah Alam station is comparatively higher than other stations. Overall, return levels increase with increasing return periods but the increment depends on the type of the tail of GEV distribution’s tail. We conduct this study by using maximum likelihood estimation (MLE) method to estimate the parameters at four selected stations in Peninsular Malaysia. Next, the validation for the fitted block maxima series to GEV distribution is performed using probability plot, quantile plot and likelihood ratio test. Profile likelihood confidence interval is tested to verify the type of GEV distribution. These results are important as a guide for early notification on future extreme ozone events.
Abstract: The statistical modelling of precipitation data for a
given portion of territory is fundamental for the monitoring of
climatic conditions and for Hydrogeological Management Plans
(HMP). This modelling is rendered particularly complex by the
changes taking place in the frequency and intensity of precipitation,
presumably to be attributed to the global climate change. This paper
applies the Wakeby distribution (with 5 parameters) as a theoretical
reference model. The number and the quality of the parameters
indicate that this distribution may be the appropriate choice for
the interpolations of the hydrological variables and, moreover, the
Wakeby is particularly suitable for describing phenomena producing
heavy tails. The proposed estimation methods for determining the
value of the Wakeby parameters are the same as those used for
density functions with heavy tails. The commonly used procedure
is the classic method of moments weighed with probabilities
(probability weighted moments, PWM) although this has often shown
difficulty of convergence, or rather, convergence to a configuration
of inappropriate parameters. In this paper, we analyze the problem of
the likelihood estimation of a random variable expressed through its
quantile function. The method of maximum likelihood, in this case,
is more demanding than in the situations of more usual estimation.
The reasons for this lie, in the sampling and asymptotic properties of
the estimators of maximum likelihood which improve the estimates
obtained with indications of their variability and, therefore, their
accuracy and reliability. These features are highly appreciated in
contexts where poor decisions, attributable to an inefficient or
incomplete information base, can cause serious damages.
Abstract: Reducing energy consumption became the major concern for all countries of the world during the recent decades. In general, power saving is currently the nominal goal of most industrial countries. It is well known that fossil fuels are the main pillar of development of world countries. Unfortunately, the increased rate of fossil fuel consumption will lead to serious problems caused by an expected depletion of fuels. Moreover, dangerous gases and vapors emission lead to severe environmental problems during fuel burning. Consequently, most engineering sectors especially the mechanical sectors are looking for improving any machine accompanied by reducing its energy consumption. Crank-Rocker planar mechanism is the most applied in mechanical systems. Besides, it is one of the most significant parts of the machines for obtaining the oscillatory motion. The transmission angle of this mechanism can be considered as an optimum value when its extreme values are equally varied around 90°. In addition, the transmission angle plays an important role in decreasing the required driving power and improving the dynamic properties of the mechanism. Hence, appropriate selection of mechanism links lengthens, which assures optimum transmission angle leads to decreasing the driving power. Moreover, mechanism's links manufactured from composite materials afford link's lightweight, which decreases the required driving torque. Furthermore, wear and corrosion problems can be treated through using composite links instead of using metal ones. This paper is dealing with improving the performance of crank-rocker mechanism using composite links due to their flexural elastic modulus values and stiffness in addition to high damping of composite materials.
Abstract: Uncertainties related to fatigue damage estimation of
non-linear systems are highly dependent on the tail behaviour
and extreme values of the stress range distribution. By using
a combination of the First Order Reliability Method (FORM)
and Monte Carlo simulations (MCS), the accuracy of the fatigue
estimations may be improved for the same computational efforts.
The method is applied to a bottom-fixed, monopile-supported large
offshore wind turbine, which is a non-linear and dynamically sensitive
system. Different curve fitting techniques to the fatigue damage
distribution have been used depending on the sea-state dependent
response characteristics, and the effect of a bi-linear S-N curve is
discussed. Finally, analyses are performed on several environmental
conditions to investigate the long-term applicability of this multistep
method. Wave loads are calculated using state-of-the-art theory, while
wind loads are applied with a simplified model based on rotor thrust
coefficients.
Abstract: The construction of Intensity-Duration-Frequency (IDF) curves is one of the most common and useful tools in order to design hydraulic structures and to provide a mathematical relationship between rainfall characteristics. IDF curves, especially those in Peninsular Malaysia, are often built using moving windows of rainfalls. However, these windows do not represent the actual rainfall events since the duration of rainfalls is usually prefixed. Hence, instead of using moving windows, this study aims to find regionalized distributions for IDF curves of extreme rainfalls based on storm events. Homogeneity test is performed on annual maximum of storm intensities to identify homogeneous regions of storms in Peninsular Malaysia. The L-moment method is then used to regionalized Generalized Extreme Value (GEV) distribution of these annual maximums and subsequently. IDF curves are constructed using the regional distributions. The differences between the IDF curves obtained and IDF curves found using at-site GEV distributions are observed through the computation of the coefficient of variation of root mean square error, mean percentage difference and the coefficient of determination. The small differences implied that the construction of IDF curves could be simplified by finding a general probability distribution of each region. This will also help in constructing IDF curves for sites with no rainfall station.
Abstract: In this paper, temperature extremes are forecast by
employing the block maxima method of the Generalized extreme
value(GEV) distribution to analyse temperature data from the
Cameroon Development Corporation (C.D.C). By considering two sets
of data (Raw data and simulated data) and two (stationary and
non-stationary) models of the GEV distribution, return levels analysis
is carried out and it was found that in the stationary model, the
return values are constant over time with the raw data while in the
simulated data, the return values show an increasing trend but with
an upper bound. In the non-stationary model, the return levels of
both the raw data and simulated data show an increasing trend but
with an upper bound. This clearly shows that temperatures in the
tropics even-though show a sign of increasing in the future, there
is a maximum temperature at which there is no exceedence. The
results of this paper are very vital in Agricultural and Environmental
research.
Abstract: Modeling and forecasting dynamics of rainfall
occurrences constitute one of the major topics, which have been
largely treated by statisticians, hydrologists, climatologists and many
other groups of scientists. In the same issue, we propose, in the
present paper, a new hybrid method, which combines Extreme
Values and fractal theories. We illustrate the use of our methodology
for transformed Emberger Index series, constructed basing on data
recorded in Oujda (Morocco).
The index is treated at first by Peaks Over Threshold (POT)
approach, to identify excess observations over an optimal threshold u.
In the second step, we consider the resulting excess as a fractal object
included in one dimensional space of time. We identify fractal
dimension by the box counting. We discuss the prospect descriptions
of rainfall data sets under Generalized Pareto Distribution, assured by
Extreme Values Theory (EVT). We show that, despite of the
appropriateness of return periods given by POT approach, the
introduction of fractal dimension provides accurate interpretation
results, which can ameliorate apprehension of rainfall occurrences.
Abstract: At-site flood frequency analysis is used to estimate
flood quantiles when at-site record length is reasonably long. In
Australia, FLIKE software has been introduced for at-site flood
frequency analysis. The advantage of FLIKE is that, for a given
application, the user can compare a number of most commonly
adopted probability distributions and parameter estimation methods
relatively quickly using a windows interface. The new version of
FLIKE has been incorporated with the multiple Grubbs and Beck test
which can identify multiple numbers of potentially influential low
flows. This paper presents a case study considering six catchments in
eastern Australia which compares two outlier identification tests
(original Grubbs and Beck test and multiple Grubbs and Beck test)
and two commonly applied probability distributions (Generalized
Extreme Value (GEV) and Log Pearson type 3 (LP3)) using FLIKE
software. It has been found that the multiple Grubbs and Beck test
when used with LP3 distribution provides more accurate flood
quantile estimates than when LP3 distribution is used with the
original Grubbs and Beck test. Between these two methods, the
differences in flood quantile estimates have been found to be up to
61% for the six study catchments. It has also been found that GEV
distribution (with L moments) and LP3 distribution with the multiple
Grubbs and Beck test provide quite similar results in most of the
cases; however, a difference up to 38% has been noted for flood
quantiles for annual exceedance probability (AEP) of 1 in 100 for one
catchment. This finding needs to be confirmed with a greater number
of stations across other Australian states.
Abstract: The global solved problem is the calculation of the
parameters of ceramic material from a set of destruction tests of
ceramic heads of total hip joint endoprosthesis. The standard way of
calculation of the material parameters consists in carrying out a set of
3 or 4 point bending tests of specimens cut out from parts of the
ceramic material to be analysed. In case of ceramic heads, it is not
possible to cut out specimens of required dimensions because the
heads are too small (if the cut out specimens were smaller than the
normalised ones, the material parameters derived from them would
exhibit higher strength values than those which the given ceramic
material really has). A special destruction device for heads
destruction was designed and the solved local problem is the
modification of this destructive device based on the analysis of
tensile stress in the head for two different values of the depth of the
conical hole in the head. The goal of device modification is a shift of
the location with extreme value of σ1max from the region of head’s
hole bottom to its opening. This modification will increase the
credibility of the obtained material properties of bioceramics, which
will be determined from a set of head destructions using the Weibull
weakest link theory.
Abstract: Today, the need for water sources is swiftly increasing due to population growth. At the same time, it is known that some regions will face with shortage of water and drought because of the global warming and climate change. In this context, evaluation and analysis of hydrological data such as the observed trends, drought and flood prediction of short term flow has great deal of importance. The most accurate selection probability distribution is important to describe the low flow statistics for the studies related to drought analysis. As in many basins In Turkey, Gediz River basin will be affected enough by the drought and will decrease the amount of used water. The aim of this study is to derive appropriate probability distributions for frequency analysis of annual minimum flows at 6 gauging stations of the Gediz Basin. After applying 10 different probability distributions, six different parameter estimation methods and 3 fitness test, the Pearson 3 distribution and general extreme values distributions were found to give optimal results.
Abstract: In this paper, we consider the application of Extreme
Value Theory as a risk measurement tool. The Value at Risk, for a set
of indices, from six Stock Exchanges of Frontier markets is
calculated using the Peaks over Threshold method and the
performance of the model index-wise is evaluated using coverage
tests and loss functions. Our results show that “fattailedness” alone of
the data is not enough to justify the use of EVT as a VaR approach.
The structure of the returns dynamics is also a determining factor.
This approach works fine in markets which have had extremes
occurring in the past thus making the model capable of coping with
extremes coming up (Colombo, Tunisia and Zagreb Stock
Exchanges). On the other hand, we find that indices with lower past
than present volatility fail to adequately deal with future extremes
(Mauritius and Kazakhstan). We also conclude that using EVT alone
produces quite static VaR figures not reflecting the actual dynamics
of the data.
Abstract: Extreme rainfall frequency analysis for Meteorological Sub-Division 4 of India was analyzed using L-moments approach. Serial Correlation and Mann Kendall tests were conducted for checking serially independent and stationarity of the observations. The discordancy measure for the sites was conducted to detect the discordant sites. The regional homogeneity was tested by comparing with 500 generated homogeneous regions using a 4 parameter Kappa distribution. The best fit distribution was selected based on ZDIST statistics and L-moments ratio diagram from the five extreme value distributions GPD, GLO, GEV, P3 and LP3. The LN3 distribution was selected and regional rainfall frequency relationship was established using index-rainfall procedure. A regional mean rainfall relationship was developed using multiple linear regression with latitude and longitude of the sites as variables.
Abstract: In this study, a field testing has been carried out to assess the power characteristics of some small scale wind turbines fabricated by one native technician from Tanzania. Two Horizontal Axis Wind Turbines (HAWTs), one with five and other with sixteen blades were installed at a height of 2.4m above the ground. The rotation speed of the rotor blade and wind speed approaching the turbines were measured simultaneously. The data obtained were used to determine how the power coefficient varies as a function of tip speed ratio and also the way in which the output power compares with available power in the wind for each turbine. For the sixteen-bladed wind turbine the maximum value of power coefficient of about 0.14 was found to occur at a tip speed ratio of around 0.65 while for the five bladed, these extreme values were respectively attained at approximately 0.2 and 1.7. The five bladed-wind turbine was found to have a higher power efficiency of about 37.5% which is higher compared to the sixteen bladed wind turbine whose corresponding value was 14.37%. This is what would be expected, as the smaller the number of blades of a wind turbine, the higher the electric power efficiency and vice versa. Some of the main reasons for the low efficiency of these machines may be due to the low aerodynamic efficiency of the turbine or low efficiency of the transmission mechanisms such as gearbox and generator which were not examined in this study. It is recommended that some other researches be done to investigate the power efficiency of such machines from different manufacturers in the country. The manufacturers should also be encouraged to use fewer blades in their designs so as to improve the efficiency and at the same time reduce materials used to fabricate the blades. The power efficiency of the electric generators used in the locally fabricated wind turbines should also be examined.
Abstract: This paper discusses the application of extreme events distribution taking the Limpopo River Basin at Xai-Xai station, in Mozambique, as a case analysis. We analyze the extreme value concepts, namely Gumbel, Fréchet, Weibull and Generalized Extreme Value Distributions and then extrapolate the original data to 1000, 5000 and 10000 figures for further simulations and we compare their outcomes based on these three main distributions.
Abstract: This paper focuses on operational risk measurement
techniques and on economic capital estimation methods. A data
sample of operational losses provided by an anonymous Central
European bank is analyzed using several approaches. Loss
Distribution Approach and scenario analysis method are considered.
Custom plausible loss events defined in a particular scenario are
merged with the original data sample and their impact on capital
estimates and on the financial institution is evaluated. Two main
questions are assessed – What is the most appropriate statistical
method to measure and model operational loss data distribution? and
What is the impact of hypothetical plausible events on the financial
institution? The g&h distribution was evaluated to be the most
suitable one for operational risk modeling. The method based on the
combination of historical loss events modeling and scenario analysis
provides reasonable capital estimates and allows for the measurement
of the impact of extreme events on banking operations.
Abstract: Extreme temperature of several stations in Malaysia is
modelled by fitting the monthly maximum to the Generalized
Extreme Value (GEV) distribution. The Mann-Kendall (MK) test
suggests a non-stationary model. Two models are considered for
stations with trend and the Likelihood Ratio test is used to determine
the best-fitting model. Results show that half of the stations favour a
model which is linear for the location parameters. The return level is
the level of events (maximum temperature) which is expected to be
exceeded once, on average, in a given number of years, is obtained.
Abstract: In this paper an algorithm for fast wavelength calibration of Optical Spectrum Analyzers (OSAs) using low power reference gas spectra is proposed. In existing OSAs a reference spectrum with low noise for precise detection of the reference extreme values is needed. To generate this spectrum costly hardware with high optical power is necessary. With this new wavelength calibration algorithm it is possible to use a noisy reference spectrum and therefore hardware costs can be cut. With this algorithm the reference spectrum is filtered and the key information is extracted by segmenting and finding the local minima and maxima. Afterwards slope and offset of a linear correction function for best matching the measured and theoretical spectra are found by correlating the measured with the stored minima. With this algorithm a reliable wavelength referencing of an OSA can be implemented on a microcontroller with a calculation time of less than one second.
Abstract: A measurement system for pH array sensors is
introduced to increase accuracy, and decrease non-ideal effects
successfully. An array readout circuit reads eight potentiometric
signals at the same time, and obtains an average value. The deviation
value or the extreme value is counteracted and the output voltage is a
relatively stable value. The errors of measuring pH buffer solutions are
decreased obviously with this measurement system, and the non-ideal
effects, drift and hysteresis, are lowered to 1.638mV/hr and 1.118mV,
respectively. The efficiency and stability are better than single sensor.
The whole sensing characteristics are improved.
Abstract: This paper tries to represent a new method for
computing the reliability of a system which is arranged in series or
parallel model. In this method we estimate life distribution function
of whole structure using the asymptotic Extreme Value (EV)
distribution of Type I, or Gumbel theory. We use EV distribution in
minimal mode, for estimate the life distribution function of series
structure and maximal mode for parallel system. All parameters also
are estimated by Moments method. Reliability function and failure
(hazard) rate and p-th percentile point of each function are
determined. Other important indexes such as Mean Time to Failure
(MTTF), Mean Time to repair (MTTR), for non-repairable and
renewal systems in both of series and parallel structure will be
computed.
Abstract: Data of wave height and wind speed were collected
from three existing oil fields in South China Sea – offshore
Peninsular Malaysia, Sarawak and Sabah regions. Extreme values
and other significant data were employed for analysis. The data were
recorded from 1999 until 2008. The results show that offshore
structures are susceptible to unacceptable motions initiated by wind
and waves with worst structural impacts caused by extreme wave
heights. To protect offshore structures from damage, there is a need
to quantify descriptive statistics and determine spectra envelope of
wind speed and wave height, and to ascertain the frequency content
of each spectrum for offshore structures in the South China Sea
shallow waters using measured time series. The results indicate that
the process is nonstationary; it is converted to stationary process by
first differencing the time series. For descriptive statistical analysis,
both wind speed and wave height have significant influence on the
offshore structure during the northeast monsoon with high mean wind
speed of 13.5195 knots ( = 6.3566 knots) and the high mean wave
height of 2.3597 m ( = 0.8690 m). Through observation of the
spectra, there is no clear dominant peak and the peaks fluctuate
randomly. Each wind speed spectrum and wave height spectrum has
its individual identifiable pattern. The wind speed spectrum tends to
grow gradually at the lower frequency range and increasing till it
doubles at the higher frequency range with the mean peak frequency
range of 0.4104 Hz to 0.4721 Hz, while the wave height tends to
grow drastically at the low frequency range, which then fluctuates
and decreases slightly at the high frequency range with the mean
peak frequency range of 0.2911 Hz to 0.3425 Hz.