*3.4. Uncertainty Quantification*

The procedure outlined in the previous subsection quantifies uncertainty in fatigue damage accumulation. However, the probabilistic model (1) requires uncertainty in stress ranges rather than in the fatigue damage. Therefore, it is now described how uncertainty in fatigue damage can be transformed into uncertainty in stress ranges, as indicated in step four in Figure 2.

The fatigue damage accumulation, *D*, is proportional to the stress ranges, Δ*s*, according to *D* ∝ Δ*sm* (assuming a linear SN curve), from which it follows Δ*s* ∝ *D*1/*m*. The stress range distribution parameters can be computed from Monte Carlo simulations. Alternatively, assuming the damage distribution function is normal, the stress range distribution's mean, *μ*Δ*s*, and coefficient of variation (CoV), *c*Δ*s*, can be approximated as

$$
\mu\_{\Lambda s} = \mu\_i^{1/m} \tag{5}
$$

and

$$
\omega\_{\Lambda s} = \frac{c\_i}{m'} \tag{6}
$$

where *μi* and *ci* are the mean and CoV of the fatigue damage distribution due to the uncertainty associated with *αj*.


2.2 Measuring system

Before starting those practical experiments, we had been developing the measuring system for individual traits [12], regarding human information processing. This system is simulated interactive communication between an instructor (A) and a learner (B) with using ICT (a) ! (b) ! (c) ! (d) (Figure 4). In the field of educational technology studies, they call this interaction as learning process. When the learner responses to the instructor (A) after the information or instruction for assignments from the instructor (A) conveyed to her or him, the one session of activity has been considered as coming into effect of learning (Figure 5).

From this theory of learning processing, we predicted that language information processing might be the same as each other (Figure 5, ①). Then, instead of the instruction or assignment, we decided to use questionnaires of YGPI (Yatabe-Guilford Personality Inventory), which is consisted of 120 short sentences and 12 factors (10 of 120 each), and more, they are composed of two main factors, emotional and non-emotional factors. Subjects are required to choose responses to questionnaires among "yes," "no," or "either," comparing with their daily activities or behavior. The system also measures their response time from the start of presenting the questionnaire to subjects' replies (Figure 5, ② and ③). Card has

Figure 4. Learning processing.

Figure 5. Human information processing.

introduced the theory that the perceptional system (τp), cognitive system (τc), and motor system (τM) are involved in simple reaction time [17, 18].


*6.3.5 AVF/AVG assessment*

Using the eyes, ears and fingertips, AVF/AVG are assessed for complications. Inspection (observe and look for):

Palpation (touch and feel):

Auscultation (listen to the fistula):

• Listen for bruit: listen to entire access every treatment and note changes in sound characteristics.

AVF/AVG physical examination is crucial to evaluate the proper function and to detect possible signs of complications. If any sign of complication is present, the VA should not be used and the patients should be evaluated by the nephrologist [43].


6. Soot concentration from (TDI) compression ignition engine

Figure 7 illustrates the soot concentration in the exhaust gas at 1500 and 3000 rpm. In a directinjection diesel engine, the fuel-air distribution is not homogeneous. Therefore, in addition to the excess-air ratio, soot formation is also controlled by the mixing of air and fuel [19]. The formation of soot depends upon the condition of the engine, the type of the combustion chamber and differences in the physical and chemical properties of the fuel [19]. The soot emission is reduced when a shared volume of n-butanol is added to DF. This is because the oxygen atoms attached to the hydroxyl group of n-butanol hinder (through moderation) the production of the precursors responsible for the formation of soot [21]. The low C/H ratio of nbutanol also reduces soot formation. In Study P, as well as in the author's study, the soot concentration was substantially reduced. The soot concentration reduced when n-butanol/DF

Figure 7. Soot emissions against varying BMEP (a) at 1500 rpm (b) at 3000 rpm [21].

blends were used as indicated in Figure 7. The soot concentration for the blends was always lower than that of DF in both the speeds: 1500 and 3000 rpm, when measured against BMEP. The soot emission reduction with increasing the shared volume of n-butanol to DF was 55.5, 77.8, and 85.1% for B5, B10, and B20, respectively in the 75% load with 1500 rpm. The reduction of soot emission for all the test fuels was higher in the engine tests with 3000 rpm than with 1500 rpm. The reduction of soot emission was highest in the 75% load. The small deviation exhibited by the blends from the trend in the 25 and 50% load with 3000 rpm is not well known: it might be caused by the temperature distribution during the combustion process, as temperature also plays an important role in the formation and oxidation of soot.