Industrial informatics (Bi, 2017) is a field that broadly consists of applying computing technologies to industrial environments (Lee et al., 2014). Its goal, within the context of Industry 4.0 (Lasi et al., 2014), is to move away from traditional, fully electro-mechanical systems toward cyber-components, that is, software-controlled industrial processes (Parri et al., 2021). This has several advantages over established practices, including safer and more secure environments, thanks to new monitoring technologies (Zhou and Peng, 2020); resilience and fault-tolerance (Gao et al., 2015); distributed and remote control and operation (Buse and Wu, 2004); and improved efficiency, thanks to the integration of optimization algorithms and artificial intelligence (Gaudio et al., 2021). The practice of developing industrial informatics is fairly codified in the literature, starting from industrial internet of things (Butun et al., 2020) to the broader umbrella of Industry 4.0 (Ghobakhloo, 2020).

However, one key aspect the literature lacks in the deployment of industrial informatics is a comprehensive theoretical framework (and associated tooling) for how to modernize extant industries—retrofitting state-of-the-art industrial informatics into legacy systems. In the industrial context, blank-slate designs are seldom, if ever, the case; rather, (costly) legacy equipment is augmented to meet the goals of upgrades, requiring practitioners to employ ad hoc approaches to the scenario at hand (Lins et al., 2017).

Examples of such challenges can be found in the literature, including Ben-Guang et al. (2000), Hills et al. (2016), Guerreiro et al. (2018), Lins and Oliveira (2020), and Tran et al. (2022). Unfortunately, almost all are confined in scope to the specific environment in which the authors were working, reflecting the lack of, and need for, a more holistic understanding of retrofitting practices in the discipline to help bring new technology to the industry (Fryer and Garcia, 2020).

Therefore, in alignment with the authors’ experience with retrofitting real-time systems (Tavares et al., 2012; Gomes et al., 2015), this paper presents a perspective on the problem regarding real-time operation which attempts to begin the scholarly development of such a comprehensive framework. We offer the following contributions:

• Formalizing the problem of retrofitting real-time (cyber-physical) industrial systems with computational intelligence as a minimization problem.

Once systems are retrofitted with computational intelligence, a central coordinating system can exploit this additional information and actuation power to perform global optimizations (which is, of course, the motivation behind retrofitting in the first place). Regardless of what precise optimization is performed, new system sum execution time e (total) can be modeled as follows: e t o t a l = α ∑ n = 0 i − 1 ∑ k = 0 f n − 1 e t n , k p t n , k + e t n , c + λ x p t n , c , α ∈ ] 0,1 ] , (5)

where α is the inverse of the optimization factor, assuming this is always positive (a negative optimization factor would correspond to performance degradation).

The overarching problem can be formally expressed as satisfying α ∑ n = 0 i − 1 ∑ k = 0 f n − 1 e t n , k p t n , k + e t n , c + λ x p t n , c < ∑ n = 0 i − 1 ∑ k = 0 f n − 1 e t n , k p t n , k , α ∈ ] 0,1 ] , (6)

which simplifies into α 1 − α ∑ n = 0 i − 1 e t n , c + λ x p t n , c < ∑ n = 0 i − 1 ∑ k = 0 f n − 1 e t n , k p t n , k , α ∈ ] 0,1 ] . (7)

The sum of execution times of computational tasks ∑ n = 0 i − 1 e ( t n , c ) p ( t n , c ) is approximately constant for a given value of α = α _a , such that we can re-formulate the aforementioned statement as α 1 − α a + i λ x < ∑ n = 0 i − 1 ∑ k = 0 f n − 1 e t n , k p t n , k , α = α a . (8)

Borrowing from scheduling theory (Sinnen and Sousa, 2005; Blagodurov et al., 2010; Johnson et al., 2010), it is safe to assume there is a lower bound (typically non-0 but sufficiently close to 0) for contention as a function of phase choices for the execution of computational tasks (minimizing alignment of periodic execution). An optimal formulation F for choosing these phases is predicated on knowledge of periods and execution times of all extant tasks across systems, formulated as K(S _i ), i ∈ [0, N [, K(S _i ) ∈ [0, 1], such that λ x = 1 F ◦ K S i , λ x ∈ [ λ min , ∞ [ , (9)

where F◦K(S _i ) denotes the function composition of F over K(S _i ) equivalent to F(K(S _i )) (note that contention is typically modeled as having an infinite upper bound to denote system deadlock). Replacing λ(x) in Eq. 8 and solving for K(S _i ), we obtain α 1 − α a + i F ◦ K S i < ∑ n = 0 i − 1 ∑ k = 0 f n − 1 e t n , k p t n , k , α = α a , (10) ≡ i F ◦ K S i < 1 − α α ∑ n = 0 i − 1 ∑ k = 0 f n − 1 e t n , k p t n , k − a , α = α a , (11) ≡ F ◦ K S i > i 1 − α α ∑ n = 0 i − 1 ∑ k = 0 f n − 1 e t n , k p t n , k − a , α = α a , (12) ≡ K S i > F − 1 i 1 − α α ∑ n = 0 i − 1 ∑ k = 0 f n − 1 e t n , k p t n , k − a , α = α a . (13)

Thus, showing that total knowledge about the tasks of extant systems required to optimize them when retrofitting computational intelligence is a function of a possible optimization factor (conversely, that optimization is a function of prior knowledge). Thus, it is important to develop methodologies, theories, and tools to determine system behavior (Section 5).

To illustrate the aspects considered in the model thus far, consider the example industrial system depicted in Figure 2. The two parallel systems produce items at different rates, depending on operational parameters. The robotic arm picks items from the intermediate item buffers and transfers them to subsequent stations (not depicted) for further processing.

Through modernization efforts, all systems have been connected to central intelligence through a communication medium, such as an industrial ethernet. New computational tasks have been added to each system; the goal is to communicate real-time production rates to central intelligence so that it can optimize robotic arm operation by moving it as little as possible (preserving power and potentially using it for other operations in the downtime) as long as item buffer rates are not exceeded.

Figure 3 depicts timing behavior before modernization (top); parallel systems produce items at different rates, depicted in blue and red, respectively, where a hyper-period corresponds to three executions of the first system and two executions of the second. In this example, assuming buffer capacity is greater than 1, and executing a robotic arm operation as frequently as the production rate of the first system is wasteful.

An incorrect approach to computational task execution is shown in the middle of Figure 3, where the computational task is depicted in green. Here, periods in both systems are chosen the same as production tasks, resulting in both systems attempting to access the shared medium at the same time, resulting in contention. Total execution time is thus extended, delaying production. On the other hand, a better chosen set of periods results in the behavior depicted in Figure 3 (bottom), where no contention is exhibited, resulting in non-decreased performance, whilst preserving the advantages of optimized robotic arm operation. Formally, systems 1 and 2 contain a single task, with periods 1 p ( t i , j ) equal to 1 p ( t 1,0 ) = 3 and 1 p ( t 2,0 ) = 2 , respectively, and execution times e (t _i,j ) equal to e (t _1,0) = 1 and e (t _2,1) = 2, respectively. From Figure 3, λ(2) = 1 for the poorly selected case; thus, we can replace variables in Eq 4 with: min p t n , c , ∀ n ∈ [ 0,2 [ ∑ n = 0 0 ∑ k = 0 0 e t n , k p t n , k + e t n , c + λ x p t n , c = 1 × 3 + 2 × 2 + min p t n , c , ∀ n ∈ [ 0,2 [ 1 * 2 + 1 * 1 , 1 + λ x 3 × 3 + 1 + λ x 2 × 2 = 7 + 3 = 10 . (14)

This shows that selecting periods for the computational tasks equal to half the rate of the original tasks (and out of phase with each other) results in no performance degradation. Critically, the values in this case study can be verified experimentally and fairly simply; in more complex systems, it would be difficult to estimate λ(x) and 1 p ( t i , j ) without significant profiling.

Our simulated example, despite its simplicity, already clearly illustrates the pitfalls of poor retrofitting of legacy systems. With stochastically generated execution times and periods of computational tasks, total sum execution time increases exponentially as the number of concurrent systems grows (Figure 1). Per system, we can see that average execution time increases (Table 1).

The negative impact of poor retrofitting decisions has several impacts on practitioners. It greatly complicates the design effort, adding to engineers' cognitive load. It constitutes several additional variables that constrain the optimization problem; critically, it poses a discovery and estimation challenge for both known and unknown “unknowns”. Whilst our focus in this paper was on the real-time performance aspects of cyber-physical systems, that is merely illustrative, the broader challenge encompasses not only this but also includes throughput, communication, monitoring, security, and safety.

We identify a few directions that research must pursue to solving these challenges.

• Estimation methodology. With so many unknowns that affect the problem and the infamous lack of reliable legacy design documentation, a comprehensive methodology for estimating required parameters is required. Practitioners cannot rely on ad hoc approaches; know-how from the disciplines of diagnostics and reverse engineering must be formalized within the context of industrial informatics.