Information uncertainty in engineering systems

2.4.2.1 Abstraction and modeling of engineering systems

Uncertainty modeling and analysis in engineering started with the employ- ment of safety factors using deterministic analysis, then was followed by probabilistic analysis with reliability-based safety factors. Uncertainty in engineering was traditionally classified into objective and subjective types. The objective types included the physical, statistical, and modeling sources of uncertainty. The subjective types were based on lack of knowledge and expert-based assessment of engineering variables and parameters. This clas- sification was still deficient in completely covering the entire nature of uncer- tainty. The difficulty in completely modeling and analyzing uncertainty stems from its complex nature and its invasion of almost all epistemological levels of a system by varying degrees, as discussed in Chapter 1.

Table 2.10 Theories to Model and Analyze Ignorance Types

Theory

Confusion &

Conflict Inaccuracy Ambiguity

Randomness

& Sampling Vagueness Coarseness Simplification

Classical sets Probability Statistics Bayesian Fuzzy sets Rough sets Evidence Possibility Monotone measure Interval probabilities Interval analysis © 2001 by CRC Press LLC

Engineers can deal with information for the purpose of system analysis and design. Information in this case is classified, sorted, analyzed, and used to predict system attributes, variables, parameters, and performances. How- ever, it can be more difficult to classify, sort, and analyze the uncertainty in this information and use it to assess uncertainties in our predictions.

Uncertainties in engineering systems can be mainly attributed to ambi- guity, likelihood, approximations, and inconsistency in defining the archi- tecture, variables, parameters and governing prediction models for the sys- tems. The ambiguity component comes from either not fully identifying possible outcomes or incorrectly identifying possible outcomes. Likelihood builds on the ambiguity of defining all the possible outcomes by introducing probabilities to represent randomness and sampling. Therefore, likelihood includes the sources (1) physical randomness and (2) statistical uncertainty due to the use of sampled information to estimate the characteristics of the population parameters. Simplifications and assumptions, as components of approximations, are common in engineering due to the lack of knowledge and the use of analytical and prediction models, simplified methods, and idealized representations of real performances. Approximations also include vagueness and coarseness. The vagueness-related uncertainty is due to sources that include (1) the definition of some parameters, e.g., structural performance (failure or survival), quality, deterioration, skill and experience of construction workers and engineers, environmental impact of projects, conditions of existing structures using linguistic measures; (2) human factors; and (3) defining the interrelationships among the parameters of the prob- lems, especially for complex systems. The coarseness uncertainty can be noted in simplification models and behavior of systems. Other sources of ignorance include inconsistency with its components of conflict and confu- sion of information and inaccuracies due to, for example, human and orga- nizational errors.

Analysis of engineering systems commonly starts with a definition of a system that can be viewed as an abstraction of the real system. The abstrac- tion is performed at different epistemological levels (Ayyub, 1992 and 1994). The process of abstraction can be graphically represented as shown in Figure 2.27. A resulting model from this abstraction depends largely on the engineer (or analyst) who performed the abstraction, hence on the subjective nature of this process. During the process of abstraction, the engineer needs to make decisions regarding what aspects should or should not be included in the model. These aspects are shown in the Figure 2.27. Aspects that are abstracted and not abstracted include the previously identified uncertainty types. In addition to the abstracted and nonabstracted aspects, unknown aspects of the system can exist due to blind ignorance, and they are more difficult to deal with because of their unknown nature, sources, extents, and impact on the system.

In engineering, it is common to perform uncertainty modeling and anal- ysis of the abstracted aspects of the system with a proper consideration of the nonabstracted aspects of a system. The division between abstracted and

nonabstracted aspects can be a division of convenience that is driven by the objectives of the system modeling, or simplification of the model. However, the unknown aspects of the systems are due to blind ignorance that depends on the knowledge of the analyst and the state of knowledge about the system in general. The effects of the unknown aspects on the ability of the system model to predict the behavior of the real system can range from none to significant.

2.4.2.2 Ignorance and uncertainty in abstracted aspects of a system

Engineers and researchers dealt with the ambiguity and likelihood types of uncertainty in predicting the behavior and designing engineering systems using the theories of probability and statistics and Bayesian methods. Prob- ability distributions were used to model system parameters that are uncer- tain. Probabilistic methods that include reliability methods, probabilistic engineering mechanics, stochastic finite element methods, reliability-based design formats, and other methods were developed and used for this pur- pose. In this treatment, however, a realization was established of the presence

Figure 2.27 Abstraction and ignorance for engineering systems. Real System Abstr action at se v er al epistemological le v els . Engineer or Analyst

A model of the real system Abstracted Aspects

of the System

Non-abstracted Aspects of the System

Unknown Aspects of the System: Blind

Ignorance

Ambiguity Likelihood Approximation Inconsistency

Vagueness Coarseness Simplifications Randomness Sampling Confusion Conflict Inaccuracy Unknowns Irrelevance Fallacy Unspecificity Non- specificity

of the approximations type of uncertainty. Subjective probabilities were used to deal with this type that are based on mathematics used for the frequency- type of probability. Uniform and triangular probability distributions were used to model this type of uncertainty for some parameters. The Bayesian techniques were also used, for example, to deal with combining empirical and subjective information about these parameters. The underlying distri- butions and probabilities were, therefore, updated. Regardless of the nature of uncertainty in the gained information, similar mathematical assumptions and tools were used that are based on probability theory.

Approximations arise from human cognition and intelligence. They result in uncertainty in mind-based abstractions of reality. These abstractions are, therefore, subjective and can lack crispness, they can be coarse in nature, or they might be based on simplifications. The lack of crispness, called vagueness, is distinct from ambiguity and likelihood in source and natural properties. The axioms of probability and statistics are limiting for the proper modeling and analysis of this uncertainty type and are not completely rele- vant, nor completely applicable. The vagueness type of uncertainty in engi- neering systems can be dealt with using appropriately fuzzy set theory (Zadeh, 1965). Fuzzy set theory has been developed by Zadeh (1965, 1968, 1973, 1975, 1978) and used by scientists, researchers, and engineers in many fields. Example applications are provided elsewhere (Kaufmann and Gupta, 1985; Kaufmann, 1975). In engineering, the theory was proven to be a useful tool in solving problems that involve the vagueness type of uncertainty. For example, civil engineers and researchers started using fuzzy sets and systems in the early 1970s (Brown, 1979 and 1980; Brown and Yao, 1983). To date, many applications of the theory in engineering were developed. The theory has been successfully used in, for example (Ayyub, 1991; Blockley, 1975, 1979a, 1979b, 1980; Blockley et al., 1983; Shiraishi and Furuta, 1983; Shiraishi et al., 1985; Yao, 1979, 1980; Yao and Furuta, 1986; Blockley et al., 1975 to 1983; Furuta et al., 1985 and 1986; Ishizuka et al., 1981 and 1983; Itoh and Itagaki, 1989; Kaneyoshi, 1990; Shiraishi et al., 1983 and 1985; Yao et al. 1979, 1980, 1986),

• strength assessment of existing structures and other structural engi- neering applications;

• risk analysis and assessment in engineering;

• analysis of construction failures, scheduling of construction activities, safety assessment of construction activities, decisions during con- struction and tender evaluation;

• the impact assessment of engineering projects on the quality of wild- life habitat;

• planning of river basins; • control of engineering systems; • computer vision; and

Coarseness in information can arise from approximating an unknown relationship or set by partitioning the universal space with associated belief levels for the partitioning subsets in representing the unknown relationship or set (Pawlak, 1991). Such an approximation is based on rough sets as described in Chapter 4. Pal and Skowron (1999) provide background and detailed information on rough set theory, its applications, and hybrid fuzzy- rough set modeling. Simplifying assumptions are common in developing engineering models. Errors resulting from these simplifications are com- monly dealt with in engineering using bias random variables that are assessed empirically. A system can also be simplified by using knowledge- based if-then rules to represent its behavior based on fuzzy logic and approx- imate reasoning.

2.4.2.3 Ignorance and uncertainty in nonabstracted aspects of a system

In developing a model, an analyst or engineer needs to decide, at the different levels of modeling a system, upon the aspects of the system that need to be abstracted and the aspects that need not to be abstracted. The division between abstracted and nonabstracted aspects can be for convenience or to simplify the model. The resulting division can depend on the analyst or engineer, as a result of his or her background, and the general state of knowledge about the system.

The abstracted aspects of a system and their uncertainty models can be developed to account for the nonabstracted aspects of the system to some extent. Generally, this accounting process is incomplete. Therefore, a source of uncertainty exists due to the nonabstracted aspects of the system. The ignorance categories and uncertainty types in this case are similar to the previous case of abstracted aspects of the system. These categories and types are shown in Figure 2.27.

The ignorance categories and uncertainty types due to the nonabstracted aspects of a system are more difficult to deal with than the uncertainty types due to the abstracted aspects of the system. The difficulty can stem from a lack of knowledge or understanding of the effects of the nonabstracted aspects on the resulting model in terms of its ability to mimic the real system. Poor judgment or human errors about the importance of the nonabstracted aspects of the system can partly contribute to these uncertainty types, in addition to contributing to the next category, uncertainty due to the unknown aspects of a system.

2.4.2.4 Ignorance due to unknown aspects of a system

Some engineering failures have occurred because of failure modes that were not accounted for in the design stages of these systems. The nonaccounting for the failure modes can be due to (1) blind ignorance, negligence, using irrelevant information or knowledge, human errors, or organizational errors; or (2) a general state of knowledge about a system that is incomplete. These

unknown system aspects depend on the nature of the system under consid- eration, the knowledge of the analyst, and the state of knowledge about the system in general. The nonaccounting of these aspects in the models for the system can result in varying levels of impact on the ability of these models in mimicking the behavior of the systems. The effects of the unknown aspects on these models can range from none to significant. In this case, the ignorance categories include wrong information and fallacy, irrelevant information,

and unknowns as shown in Figure 2.27.

Engineers dealt with nonabstracted and unknown aspects of a system by assessing what is commonly called the modeling uncertainty, defined as the ratio of a predicted system’s variables or parameters (based on the model) to the value of the parameter in the real system. This empirical ratio, which is called the bias, is commonly treated as a random variable that can consist of objective and subjective components. Factors of safety are intended to safeguard against failures. This approach of bias assessment is based on two implicit assumptions: (1) the value of the variable or parameter for the real system is known or can be accurately assessed from historical information or expert judgment; and (2) the state of knowledge about the real system is complete or bounded, and reliable. For some systems, the first assumption can be approximately examined through verification and validation, whereas the second assumption generally cannot be validated.