2.4. Statistical information for risk analysis and safety

The safety and risk analysis is carried out using statistical information on dangerous events and damages. The systematization of data on major natural disasters and man-made disasters is carried out at the international and national levels [2, 3, 17]. Statistical studies show that modern global, national, sectoral and object security problems are the result of centuries-old quantitative and qualitative transformations both in social development and in the system "nature-machine-human." The uneven growth of damage from major disasters creates a real threat to the economy not only of individual regions but also for the planet as a whole. The scale and consequences of natural disasters and man-made disasters today are very tangible not only for developing countries but also for technologically advanced countries. The total losses currently for developed countries are 5–10% of GDP or more. In value terms, the total losses exceed 350 billion dollars (Figure 5).

Extreme losses are also attributed to individual catastrophic events. The losses from the hurricane Katrina (USA, 2005) amounted to 140 billion dollars. The accident at the Sayano-Shushenskaya hydroelectric power station resulted in the death of 75 people and damaged over 7.5 billion Roubles. Tsunami and the accident at the nuclear power plant "Fukushima" (Japan, 2011) led to the death of 20,000 people and damage of over \$ 300 billion.

Based on the analysis of statistical data and estimates, modern man-caused hazards are characterized by the following values [2]:


The given statistical data can serve as a basis for categorizing man-made hazards according to the levels of risks of accidents and catastrophes. Risk diagrams can be represented by a power law of the following type:

$$R(\tau) = \mathbb{C}\_{\mathfrak{u}}\{\mathcal{U}(\tau)\}^m \tag{17}$$

For natural disasters, natural-technogenic, and technogenic accidents and disasters, the value of m is in the range 0.3–1.0. For technogenic accidents and disasters, m = 0.55–0.60. The principal feature of distribution of losses according to the probabilities is that for critical and strategically important objects, large losses occur, leading to "heavy tails" of distributions.

Probabilistic Modelling in Solving Analytical Problems of System Engineering

http://dx.doi.org/10.5772/intechopen.75686

13

The development and implementation of large infrastructure projects based on the achievements of science and technology not only dramatically increased opportunities in all areas of the world community but also created high risks of man-caused and natural-technogenic catastrophes at a global level. Modern engineering systems have destructive energy potential comparable to those of natural disasters. At the same time, the possibilities of parrying and localizing technogenic catastrophes are limited, despite the achievements of scientific and

3. Solving engineering problems using probabilistic modelling

3.1. Probabilistic modelling of safe crack growth and estimation of the durability of

Crack growth up to a critical size under cyclic and long-term static loading is a rather complex process, which can be described by various crack growth equations. Methods for estimation of the lifetime of structures containing defects can be developed on the basis these equations. However, there are insufficient studies of the probabilistic aspects of crack growth, which greatly limit the opportunity for practical applications of these methods. To overcome this restriction, probabilistic models of the crack growth have been developed. This part presents

technological progress.

Figure 5. Losses from catastrophes of recent decades [3].

structures

where CU is a coefficient that depends on the dimension of the coordinates; m is an indicator that depends on the type of object.

Figure 5. Losses from catastrophes of recent decades [3].

methods of fracture mechanics, and for the level of construction, by the methods of structural mechanics. It should be noted that if fracture of individual elements, caused by MCD, can be considered as independent events, then at structure level there is an agreed redistribution of loads, and formation of the focus of MSD should be considered as a cooperated process.

The safety and risk analysis is carried out using statistical information on dangerous events and damages. The systematization of data on major natural disasters and man-made disasters is carried out at the international and national levels [2, 3, 17]. Statistical studies show that modern global, national, sectoral and object security problems are the result of centuries-old quantitative and qualitative transformations both in social development and in the system "nature-machine-human." The uneven growth of damage from major disasters creates a real threat to the economy not only of individual regions but also for the planet as a whole. The scale and consequences of natural disasters and man-made disasters today are very tangible not only for developing countries but also for technologically advanced countries. The total losses currently for developed countries are 5–10% of GDP or more. In value terms, the total

Extreme losses are also attributed to individual catastrophic events. The losses from the hurricane Katrina (USA, 2005) amounted to 140 billion dollars. The accident at the Sayano-Shushenskaya hydroelectric power station resulted in the death of 75 people and damaged over 7.5 billion Roubles. Tsunami and the accident at the nuclear power plant "Fukushima" (Japan, 2011) led to

Based on the analysis of statistical data and estimates, modern man-caused hazards are

• in the frequency of occurrence of failures, accidents, and disasters (1/year): objects of

–109

–106

• in the risks of failures, accidents, and disasters: objects of technical regulation 10<sup>3</sup>

The given statistical data can serve as a basis for categorizing man-made hazards according to the levels of risks of accidents and catastrophes. Risk diagrams can be represented by a power

where CU is a coefficient that depends on the dimension of the coordinates; m is an indicator

; hazardous industrial facilities 100

; critical objects 104

–10�<sup>3</sup> ; –10�<sup>1</sup>

–105

; strategically important facilities 106–1011;

–107

<sup>R</sup>ð Þ¼ <sup>τ</sup> Cuf g <sup>U</sup>ð Þ<sup>τ</sup> <sup>m</sup> (17)

; critical objects 10�<sup>1</sup>

; hazardous industrial

; strategically important

–

–105 ;

2.4. Statistical information for risk analysis and safety

12 Probabilistic Modeling in System Engineering

losses exceed 350 billion dollars (Figure 5).

characterized by the following values [2]:

technical regulation 10<sup>1</sup>

–10<sup>7</sup>

hazardous industrial facilities 104

10�<sup>2</sup>

facilities 104

law of the following type:

that depends on the type of object.

objects.

the death of 20,000 people and damage of over \$ 300 billion.

–100

; critical objects 105

• in economic losses (dollars): objects of technical regulation 103

; strategically important objects 10�<sup>2</sup>

For natural disasters, natural-technogenic, and technogenic accidents and disasters, the value of m is in the range 0.3–1.0. For technogenic accidents and disasters, m = 0.55–0.60. The principal feature of distribution of losses according to the probabilities is that for critical and strategically important objects, large losses occur, leading to "heavy tails" of distributions.

The development and implementation of large infrastructure projects based on the achievements of science and technology not only dramatically increased opportunities in all areas of the world community but also created high risks of man-caused and natural-technogenic catastrophes at a global level. Modern engineering systems have destructive energy potential comparable to those of natural disasters. At the same time, the possibilities of parrying and localizing technogenic catastrophes are limited, despite the achievements of scientific and technological progress.
