4.3 Analytic Development of Availability and Maintainability in Engineering Design 483 Fig. 4.38 Example of defined computer automated complexity (Tang et al. 2001) An indicative example of defined computer automated complexity is given in Fig. 4.38 (Tang et al. 2001). b) Complicatedness as a Function of Complexity Complicatedness is the degree to which any control over the system is able to manage the level of complexity presented by the system. The means of control can be another system or a person. Complicatedness is a function of complexity, K = K(C). Clearly, at C = 0, K = 0, the properties of a complicatedness function are essentially the same as those of complexity but they are definitely not identi- cal. For example, consider K when C →∞. Inevitably, there is a level of complex- ity at which any means of system control simply cannot cope with the system as a whole. The system then becomes unmanageable through diminished or lack of control. It is relatively easy to visualise a graph for g = g(x,y) with C g = O(p 2 ) (i.e. two- dimensional), and less easy to visualise a graph for h = h(x,y, z) with C h = O(p 3 ) (i.e. three-dimensional). However, a surface with four variables is indeed difficult to visualise, although complexity has only reached O(p 4 ). Consider the incomprehen- sible systems A and B where C a = O(p 100 ) and C b = O(p 1,000 ). The complicated- ness functions are virtually the same in this case, K a ≈ K b , although O(p 1,000 ) O(p 100 ). Therefore, when C = 0,K = 0andC → ∞,thenK →K max . Systems are designed to operate and be controllable at an optimal point of com- plexity, i.e. C ∗ .WhereC < C ∗ , although complexity increases, it is well within the interval of controllability. Where C = C ∗ , the system complexity is optimal with re- spect to its ability to be co ntrolled and, where C > C ∗ , c omplexity is increasin g, and the system can be controlled only with decelerating (i.e. exponentially diminishing) 484 4 Availability and Maintainability in Engineering Design Fig. 4.39 Logistic function of complexity vs. complicatedness (Tang et al. 2001) effectiveness. This can be expressed mathematically as: dK dC = {0 , ∞} (i.e. in the open interval between 0,∞) . d 2 K d 2 C > 0atC < C ∗ where complexity is increasing faster than complicatedness. d 2 K d 2 C = 0atC = C ∗ where complicatedness has reached an inflection point. d 2 K d 2 C < 0atC > C ∗ where complicatedness has reached saturation. For C < C ∗ ,d 2 K/ d 2 C > 0, complexity is increasing faster than complicatedness. For C > C ∗ ,d 2 K/ d 2 C < 0, the ability to manage comp lexity has reached dimin- ishing returns. Because the logistic function is one of the simplest mathematical expressions that has all the properties considered previously, it is adopted to express complicat- edness as indicated in the following expression and illustrated in Fig. 4.39 (Tang et al. 2001): K(C)= K max (1+ e − α C ) (4.192) where: e is the transcendental number e = 3.27182818284 α is a constant specific to the measure of control C is the complexity of the system K max = 1 indicates absolute complicatedness. 4.3 Analytic Development of Availability and Maintainability in Engineering Design 485 There are other means of expressing complicatedness, such as using the Weibull distribution. The major differences, though, are the location of the inflection point, the growth pattern before and after the inflection point, and the symmetry around the inflection point. c) Designing for Complex but Uncomplicated Systems The complexity of engineering designs increases relative to the integration of their input vectors. The integration of system elements resulting in new interactions and changes in bandwidth (due to volume or capacity constraints) increases the initial design’s complexity. However, engineered complexity can reduce intractably com- plicated input vectors to a minimum number of output vectors that renders the sys- tem controllable—and system complexity manageable. The application of neural networks is increasingly being considered for process control of complex integrated systems, in situations where there are intractable numbers of data points to analyse. This approach has proven effective for engineering designs in which the process is controlled in real time by adaptive and distributed artificial n e ural networks (ANN) embedded in distributed control systems. The application of ANN is considered in detail in Sect. 5.3.3. Earlier, the vehicle transmission was presented as a complex system that is uncomplicated. The automatic transmission presents the system image of A = {P,R,N, D 1 ,D 2 ,D 3 }, λ ij = 24, the number of linkages between the transmission interactions (four per ratio), and the bandwidth of linkages (capacity) between the interactions β ij = 1; thus, C a =(6 2 )(24)(1)=864 (where P = park, R = reverse, N = neutral and D 1 to D 3 = drive transmission ratios). However, the manual trans- mission presents the system image of M = {P,R,N,D 1 ,D 2 ,D 3 ,C}whereC = clutch. This needs to be engaged and disengaged, so C’s interaction bandwidth is 2. Thus, λ ij = 10 (two per ratio) with β ij = 1, and λ mn = 14 with β mn = 2. The complexity of the manual transmission is: C m = 7 2 [10+(14)·2] 2 = 38,416 . Suppose, for a novicedriver,C ∗ ≈C a = 864and, atC ≈40,000, K max = 1,indicating absolute complicatedness. The analytic form of the complicatedness function for engineering design can now b e d eter mined for a system with complexity C and complicatedness K: • Determine optimal complexity, C ∗ , which can be optimally controlled. • At the optimal complexity C ∗ ,setK ∗ = 1/ 2. • Solve for α from K ∗ = 1/ (1 + e − α C ∗ ) where K max = 1. • Determine K(C)=1/(1 + e − α C ). 486 4 Availability and Maintainability in Engineering Design 4.4 Application Modelling of Availability and Maintainability in Engineering Design In Sect. 1.1, the five main objectives that need to be accomplished in pursuit of the goal of the research in this handbook are: • the development of appropriate theory on the integrity of engineering design for use in mathematical and computer models; • determination of the validity of the developed theory by evaluating several case studies of engineering designs that have been recently constructed, that are in the process of being constructed, or that have yet to be constructed; • application of mathematical an d computer modelling in engineering design veri- fication; • determination of the feasibility of a practical app lication of intelligent com puter automated methodology in engineering design reviews through the development of the appropriate industrial, simulation and mathematical models. The following models have been developed, each for a specific purpose and with specific expected results, in partly achieving these objectives: • RAMS analysis model, to validate the developed theory on the determination of the integrity of engineering design. • Process equipment models (PEMs), for application in dynamic systems simula- tion modelling to initially determine mass-flow balances for preliminary engi- neering designs of large integrated process systems, and to evaluate and verify process design integrity of complex integrations of systems. • Artificial intelligence-based (AIB) model, in which r elatively new artificial intel- ligence (AI) modelling techniques, such as inclusion of knowledge-based expert systems within a blackboard model, have been applied in the development of intelligent computer automated methodology for determining the integrity of en- gineering design. The process equipment models (PEMs) for a pplication in dynamic systems simula- tion modelling will now be looked at in detail. 4.4.1 Process Equipment Models (PEMs) As indicated previously, process equipment models (PEMs) have been developedfor application in dynamic systems simulation modelling to initially determine mass- flow balances for preliminary engineering designs of large integrated process sys- tems. The dynamic systems simulation modelling was developed using the propri- etary OOP simulation shell, Extend c (Diamond 1997). Extend c is a flexible simulation modelling system with a customisable interface where system blocks can be modified or created using a built-in compiled language. It combines the most powerful features of object oriented programming (OOP) for 4.4 Application Modelling of Availability and Maintainability in Engineering Design 487 advanced dynamic simulation with discrete event/continuoussystem/combined sim- ulation capability, top-down/bottom-up systems hierarchic reachability, animated graphics, advanced statistical and sensitivity analysis, and computer interface with drag-and-drop and point- a nd-click capabilities. The PEMs incorp orate all the essential preliminaries of process analysis to de- termine mass-flow balances for preliminary engineering designs of large integrated process systems. The simulation models also incorporate algorithms of process de- sign integrity for assessing reliability, availability, maintainability and safety re- quirements of process systems. These are incorporated in specific probability distri- bution modifiers within each PEM. The application of dynamic systems simulation modelling incorporating the PEMs is primarily intended to determine the applica- bility and capability of simulation modelling during the engineering design stage, in accurately assessing the effect of complex integrations of systems in large engi- neered installations. The dynamic systems simulation modelling is based on classic methodology of systems simulation, which is described in detail in the following presentation of the application of computer modelling in engineering design verification. The PEMs have been developed within the Extend c Performan ce Modelling program (Extend 2001), integrated into a dynamic systems simulation blackboard model for application in concurrent engineering design in an integrated collaborative de- sign environment in which automated continual design reviews may be conducted throughout the engineering design process b y remotely located design groups com- municating via the internet. Design methodology and dynamic systems simulation The integration of dy- namic systems simulationwith blackboarddesign methodologyallows forthe devel- opment and integration of the basic building blocks of systems engineering design that can be represented in a design knowledge base. Support systems in the form of general-purpose design knowledge sources are similarly developed to support the design knowledge base. The design knowledge base and design knowledge sources form the core of an integrated design support system. The design objects in the de- sign knowledge base can be synthesised to generate conceptual design solutions, as illustrated in Fig. 4.40. A dynamic systems simulation blackboard model (ICS 2002) is developedto con- trol the design knowledge sources and integrate the knowledge-based design appli- cations such as the PEM blocks. The designknowledgebase contains design objects, relations, constraints in terms of intended function and interfaces, as well as detailed information in terms of geometry and sizing. The blackboard model The blackboard model is a paradigm that enables the flex- ible integration of analytic methodology into a single problem-solving environ- ment. In terms of the type of problems that it can solve, there is only one major assumption—that the problem-solving activity generates a set of intermediate re- sults. This is evident throughout the dynamic systems simulation m odelling inte- grated into the blackboard model, with systems selection in hierarchical structures as illustrated in Fig. 4.41. 488 4 Availability and Maintainability in Engineering Design Fig. 4.40 Blackboard model and the process simulation model The blackboard model consists of a data structure (the blackboard) containing information (the context) that permits a set of modules (knowledge sources) to inter- act. The blackboard can be seen as a global database or working memory in which distinct representations of knowledge and intermediate results are integrated uni- formly. It is also a means of communication among design teams, and can be used as a common display for review and performance evaluation. Blackboard architecture consists of three major components: • The knowledge sources, which are software specialist modules. Each knowledge source provides specific expertise. The ability to support interaction and cooper- ation among diverse knowledge sources creates enormous flexibility in engineer- ing design. Flexibility in this context is the ability to change the blackboard database imple- mentation, the insertion/retrieval strategies, and the representation of blackboard objects withoutmodifyingknowledgesources orbase datasuch as design specifi- cations. Flexibility in blackboardarchitecture for engineeringd esign is important for two reasons. First, understanding of the insertion/retrieval characteristics and the representation of b lackboard objects m ay be uncertain and, therefore, sub- ject to change as the design is developed. Second, even after a schematic model prototype of the d esign has been completed, the number and placement of black- 4.4 Application Modelling of Availability and Maintainability in Engineering Design 489 Fig. 4.41 Systems selection in the blackboard model board objects may differ from those of the prototype. This requires changes to the blackboardrepresentationto achievethe desired levelof performance(Corkill et al. 1987). • The blackboard, which is a shared repository of problems, partial solutions, sug- gestions, and contributed information. The blackboard can be thought of as a dy- namic libr ary of solutions to the design problem that have been contributed by other knowledge sources. Thus, a blackboard in engineering design is an ap- proach that allows knowledge sources to cooperate in solving a design problem. This is analogous to a group of designers standing around a blackboard. The blackboard is a database that is used to hold shared information among the par- ticipants (or knowledge sources). It may be structured so as to represent different levels of abstraction as well as distinct and possibly overlapping concepts in the design solution. The division of the blackboard into systems hierarchy levels (as with the PEMs) parallels the process of abstraction of the knowledge, allowing elements at each level to be described approximately as abstractions of elements at the next lower level. This par tition of the kn owledge is usefu l, in that a partial solution (i.e. group of hypotheses relating to design optimisation) at one level can be used to constrain the design at lower system levels. 490 4 Availability and Maintainability in Engineering Design Fig. 4.42 Design equipment list data in the blackboard model • The control shell, which controls the flow of problem-solving activity in the sys- tem. Knowledge sources need a mechanism to organise their application in the most effective and coherent fashion. In a blackboard system, this is provided by the control shell. Knowledge sources Each knowledgesource is data-directed,in that the blackboard is monitored for data matching-specific design preconditions. Knowledge sources may be classified in a number of different ways depending on the characteristic that is used to discriminate these. For example, a generic knowledge source may b e use- ful in a whole set of knowledge-based systems (e. g. design equipment list data for application in dynamicsystems simulation modelling of a particular design solution, as illustrated in Fig. 4.42), or sp ecific to one applicatio n (e. g. specific probability distribution modifiers within each PEM for assessing reliability, availability, main- tainability and safety requirements of process systems in a desig n). The generic knowledge source in Fig. 4.42 of design equipment list data, for application in dynamic systems simulation models of specific alumina processing stages, gives relevant data of the equipment such as equipment code, flow volumes, mass-flow volumes, liquid volumes and solids volumes. 4.4 Application Modelling of Availability and Maintainability in Engineering Design 491 Fig. 4.43 Systems hierarchy in the blackboard model context The context The context is a set of entries or context elements in the blackboard that contain the information representing the state o f the solution process. For ex- ample, in the dynamic systems simulation blackboard model, PEMs are selected ac- cording to a systems hierarchy,as illustrated in Fig. 4.43. Those entries may inc lude perceptions, observations, hypotheses, decisions, goals, interpretations, judgements or expectations. Also, they may have relationships to one another. In particular, one such organisation may combine a set of entries as the representation of a single ob- ject viewed from different levels of abstraction. There can be objects that represent goals, questions and information, knowledge sources, and other general concepts in the blackboard, as well as domain-specific objects. Figure 4.43 illustrates the selection of information representing the state of the alumina process by plant/facility (third train), operation/area (b auxite grinding) and section/building (also bauxite grinding). The user interface The user interface permits the interaction of the user (designer) with events inside the blackboard and indirectly with the rest of the knowledge sources comprising the system. This interaction may occur in both directions—by the users modifyingthe flow of controlof the system by means of commandsand an- swers to questions, or by the system informingthe user of important events, prompt- ing for answers, or explaining decisions. The user interface manages the question 492 4 Availability and Maintainability in Engineering Design Fig. 4.44 User interface in the blackboard model and answer protocols, and informs the user of importantevents during the program’s execution. Among its most importan t capabilities are the following: it check s if an answer is valid, (based on pre-specified o r dynamic menus or constraints), advises the user o n valid or desirable answers, manages default values, and automatically completes queried answers. Figure 4.44 illustrates a process pre-commissioning user interface in the black- board model for information relating to a specific alumina p rocess equipment: the bauxite grinding system, and ball mill assembly. Dynamic system simulation in engineering design Dynamic system simulation in engineering design provides for typical virtual prototyping of engineering pro- cesses, rather than experiments on the physical prototype. Not only does virtual prototyping make design verification faster and less expensive but it also provides various design teams in a collaborative design environment with immediate feed- back on design decisions. This, in turn, promises a more comprehensive exploration of design alternatives and a better performing final design. To fully exploit the ad- vantages of virtual prototyping, dynamic system simulation is the most efficient and effective. However, these simulation models have to be easy to create. Creating dy- namic simulation models is a complex activity that can be quite time-consuming. . 1. • Determine K(C)=1/(1 + e − α C ). 486 4 Availability and Maintainability in Engineering Design 4.4 Application Modelling of Availability and Maintainability in Engineering Design In Sect. 1.1,. with drag -and- drop and point- a nd-click capabilities. The PEMs incorp orate all the essential preliminaries of process analysis to de- termine mass-flow balances for preliminary engineering designs of. grinding system, and ball mill assembly. Dynamic system simulation in engineering design Dynamic system simulation in engineering design provides for typical virtual prototyping of engineering