Deterministic design approach

Figure 4.2 Comparison of the probabilistic and deterministic design approaches...

It should be noted that, for the selected example, the design stress determined by probabilistic means corresponds - in a deterministic design approach - to a safety factor of about 844 MPa/348 M Pa = 2.4. The advantage in the probabilistic approach is that a realistic reliability can be determined, and that total safety - which does not exist in reality - is not implied. 

In some structural dynamics problems, a widely used simplified approach consists in the assumption that loads are considered to be the only source of uncertainty. For example, earthquake or wind actions are modelled as stochastic processes and the standard random vibration theory is used assuming that all other parameters are deterministically defined. Structural response is a stochastic process whose parameters are deterministic (Lutes Sarkani, 2002). In such a case it is possible to define the conventional (with reference to deterministic optimization) OF and restraints concerning the structural response processes or related quantities. This structural design approach... 

Deterministic design values may be given as the mean value plus one standard deviation, which in general gives a safer approach, and takes into account that model uncertainty for wave overtopping is always significant. 

In the probabilistic approach for hazard evaluation, this information is complemented by a selected probability limit (value), but it is not to be used in a deterministic design (structural and functional). In the deterministic approach for hazard evaluation, the reference load case may be identified without explicit reference to an aircraft type or to a probability of occurrence. 

In conclusion, the engineering practice for research reactor design suggests that neither approach may be completely rehable nor effective, and therefore the following mixed approach is proposed, in agreement with Ref. [1]. This proposal is more in line with current practice in Member States, where a simplified risk informed probabilistic approach is used to clarify the use of a more code oriented deterministic design. 

The probabilistic approach considers the flaw distribution and stress distribution in the material. This approach will be useful when high stresses and their complex distributions are present. In these situations, both empirical and deterministic designs have limitations. The flaw distribution can be characterized by the Weibull approach [1]. This approach is based on the weakest link theory. This theory says that a given volume of a ceramic under a uniform stress will fail at the most severe flaw. Thus, the probability of failure F is given by the following equation ... 

An important aspect of the simple probabilistic approach used above was that it provided a transparent means of explaining to the company the reasons behind the design decisions. It gave a degree of clarity not provided by a deterministic approach and ultimately gave the engineers more confidence in their designs. 

Wet-weather processes are subject to high variability. A simple deterministic model result in terms of the impacts on the water quality is out of scope. From a modeling point of view, a stochastic description is a realistic solution for producing relevant results. Furthermore, an approach based on a historical rainfall series as model input is needed to establish extreme event statistics for a critical CSO impact that can be compared to a water quality criterion. In terms of CSO design including water quality, this approach is a key point. 

Such a design procedure is clearly a far cry from the linear quadratic Gaussian techniques in which robustness is obtained in an indirect manner by inventing measurement noise and introducing stochastic processes into an essentially deterministic problem. Nevertheless, the two approaches have amazing mathematical parallels [16]. 

Deterministic catalyst design is slowly supplementing the traditional heuristic approaches, comprising ... 

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