J Intell Manuf DOI 10.1007/s10845-017-1366-7 An approach for composing predictive models from disparate knowledge sources in smart manufacturing environments Duck Bong Kim1 Received: 2 March 2017 / Accepted: 6 September 2017 © Springer Science+Business Media, LLC 2017 Abstract This paper describes an approach that can compose predictive models from disparate knowledge sources in smart manufacturing environments. The capability to compose disparate models of individual manufacturing components with disparate knowledge sources is necessary in manufacturing industry, because this capability enables us to understand, monitor, analyze, optimize, and control the performance of the system made up of those components. It is based on the assumption that the component models and component sources used in any particular composition can be represented using the same collection of system ‘viewpoints’. With this assumption, creating this integrated collection is much easier than it would be. This composition capability provides the foundation for the ability to predict the performance of the system from the performances of its components—called compositionality. Compositionality is the key to solve decision-making/optimization problems related to that system-level prediction. For those problems, compositionality can be achieved using a three-tiered, abstraction architecture. The feasibility of this approach is demonstrated in an example in which a multi-criteria decision making method is used to determine the optimal process parameters in an additive manufacturing process. Keywords Smart manufacturing · Data analytics · Compositionality · Decision making · Additive manufacturing B 1 Duck Bong Kim firstname.lastname@example.org Manufacturing and Engineering Technology, College of Engineering, Tennessee Technological University, Cookeville, TN, USA Introduction In order to survive in a severe market competition, manufacturing companies should be agile while addressing their business processes, ranging from the system design to the maintenance. Thus, manufacturing companies are under pressure to become more innovative and to develop new strategies to increase (1) the productivity and efficiency of their manufacturing processes and (2) the quality and reliability of their products. In addition, the waste should be minimized as much as possible and the resources should be effectively allocated while they achieve the desired profitability. To address these issues, recently, a number of information-based technologies including smart manufacturing (SM), cloud services (CS), and internet of things (IoT) have been proposed (Gallaher et al. 2016; Anderson 2016; Davis et al. 2012; Shrouf et al. 2014). In one way or another, all of these technologies enable new types of modeling and analysis methods that have the potential to provide the necessary foundation for these new strategies (Lee et al. 2013; SMLC 2011). Especially, analytical modeling and analysis methodologies provide the possibility to address SM-related tasks and problems for satisfying different stakeholders’ desires. Realizing this potential, however, requires researchers to overcome significant hurdles: (1) featuring high uncertainty, conflicting objectives, heterogeneous forms of data and information, multi-interests, and perspectives, and (2) accounting for complex and dynamically evolving manufacturing systems. These have led to consistent research efforts on the use of modeling and analysis methodologies to enhance the SMrelated tasks and problems. The multi-criteria decision making (MCDM) method (Wang et al. 2009) is considered as one of the possible solutions to reduce the complexity and difficulty when 123 J Intell Manuf requirements are conflicting. An operational evaluation and decision-support approach is suitable for addressing multicriteria-related problems. However, there are still several issues in using the MCDM methods in the SM environments. Mainly, it is the “how to compose disparate analytical problems into a unified analytical problem?” Composing analytical problems is not a simple task with specific reasons. First, it relates to (1) the use of different unit of measure and (2) complexity due to its evolving manufacturing system and dynamically changing environment. Second, it should trace the rationale (e.g., motivation, reason, background, constraints) of the design and manufacturing for the improvements, but these results in burden on composing analytical problems from disparate knowledge sources with irrelevant technical details. Third, the aggregated model from multiple local predictive model, called here global predictive model, should be verified and validated although each local predictive model satisfies the confidence level required. It should quantify the uncertainty and its propagation of the global predictive model, since it relates to multiple criteria with subjective normalization and weighting factors. In addition, it has interoperability issues. Most of current approaches for performing the MCDM problems are stand-alone, which means users typically model and analyze the manufacturing processes using customized methods for their specific application tools or modeling environments. This causes interoperability problems, information duplication or even inefficient implementation. Moreover, to analyze process performance, comprehensive background knowledge about SM and operations research (OR) are required. To resolve these issues, a systematic and comprehensive methodology with contributions from multiple experts should be investigated, developed, and provided. However, it is still difficult for manufacturers and decisionmakers to get the full advantages of SM paradigm and modeling and analysis techniques, particularly the small and medium enterprises (SMEs), due to the complexity and lack of resources. Among these hurdles, we focus on the composition of analytical models and MCDM methods. We propose an approach to compose predictive models of manufacturing components them into an aggregated, systemlevel, predictive model. The novelty of this research lies in firstly introducing the concept of viewpoints for the model composition from disparate, analytical, experimental, and informational sources in SM environments. The aggregated model is then used to create the different objective functions and constraints that make up a MCDM problem. Individual objective-function weights are specified using an interactive environment for scientific computing, such as IPython notebook. For a case study, we show how this composition process works and demonstrate its effectiveness in the case of an additive manufacturing (AM) process, which involves finding optimal process parameters. “Related work” section reviews 123 the related work and “The proposed approach” section introduces the three-tier approach. “Domains-of-discourse tier”, “Problem-domain tier”, and “Analytical-technology domain” sections include detailed descriptions of those tiers, i.e., domain of discourse, problem domain, and analytical technology domain, respectively. Then, the AM case study is described in “A case study” section. “Discussion and conclusion” section discusses the advantage/disadvantage of this approach and provides a conclusion of this work. Related work The related work falls into three categories: life cycle assessment (LCA) frameworks for managing manufacturingprocesses knowledge, single-criteria optimization methods, and multi-criteria optimization methods, respectively. Each paragraph explains the current state-of-the-art and the main limitations of these categories with respect to composability. LCA frameworks (ISO 2006) provide systematic and logical procedures that help assess environmental impacts of products and manufacturing processes. These impacts can analyze the sustainability-related performance of those products and processes (Jacquemin et al. 2012). To date, the applications of LCA frameworks have been primarily for products because they have several limitations when applied to manufacturing processes. For an instance, most LCA frameworks do not support all of dynamic and diverse characteristics of those processes. In addition, they do not fully support the analytical capabilities needed to model the mathematical details needed for process optimization. To address these limitations, an approach that can generate and compose mathematical models is needed. Because of this, process optimization is typically still done manually by process planners based on his/her knowledge and experience. As a result, process optimization, in general,—and sustainability optimization, in particular—is often time-consuming and highly inconsistent. In addition, efforts to collect the historical data needed to improve the process planner’s sustainability-related knowledge and decisions have been limited. To address this limitation, several different types of data-collection and knowledgemanagement systems have been proposed. Their advantages and disadvantages are discussed in Yusof and Latif (2014). One major disadvantage is the lack of companion analytical capabilities that can transform this knowledge into optimal process decisions. Recently, researchers have begun to address this disadvantage for both single and multi-criteria optimization problems. Examples of the single criteria optimization problem include Kim et al. (2015), Campatelli et al. (2014), and Rajemi et al. (2010). Kim et al. (2015) proposed a modelbased approach that provides a systematic procedure to J Intell Manuf improve sustainability performances of SM processes. Campatelli et al. (2014) used an experimental approach combined with the response surface method (RSM) to determine the optimal process settings for minimizing the power consumption in a milling process. Rajemi et al. (2010) established a new methodology for optimizing the energy footprint for a machined part and derived an economic tool-life formula for minimizing the total energy footprint. These single criteria decision making methods are straight forward and easy to develop, but this single objective function is limited in when satisfying multiple stakeholders’ desires. It means this traditional single criteria approach is not suitable for solving the complexity and the multi-interests/criteria/objectives in dynamically evolving SM processes and environments. Multi-criteria decision-making (MCDM) methods have been applied in both assessment and optimization problems. Vinodh et al. (2014) developed a decision support system (DSS) that can assess the sustainability of manufacturing organizations by taking into consideration various factors needed for maintaining sustainability. Arslan et al. (2004) also developed a DSS for machine-tool selection by using a weighted average of several criteria including productivity, flexibility, space, adaptability, precision, cost, reliability, safety, environment, maintenance, and service. Zhao et al. (2012) proposed an LCA-supported, environmentally conscious, process-planning methodology with a set of ranking/weighting schemes for impact aggregation. Madic et al. (2016) proposed a weighted aggregated sum product assessment (WASPAS) method for determination of manufacturing process parameters (e.g., laser power, cutting speed, and gas pressure) in the case of laser cutting, based on Taguchi’s L9 method. Sen et al. (2017) developed a hybrid framework consisting of three MCDM methods, such as decision-making trail and evaluation laboratory (DEMATEL), analytical network process (ANP), and restricted multiplier data envelopment analysis (RMDEA). Rudnik and Kacprzak (2017) presented a fuzzy technique for order preference by comparing it to ideal solution (FTOPSIS) for a practical solution in the case of discrete flow control in a manufacturing system. However, these methods do not provide the cost-effective solutions for composing the various optimization problems. Moreover, it has an interoperability issue. These methods are stand-alone, meaning that specific application tools or modeling environments are necessary or information can be unnecessarily duplicated. The proposed approach Conventional MCDM methods manage the complexities associated with decision-support by resolving the conflicting interests and preferences. Methods differ in exactly how the “resolving” get done. However, as we noted earlier, these methods do not provide cost-effective solutions to two problems: (1) creating and (2) composing the various constraints associated with the different criteria. In this paper, we provide an approach that can provide cost-effective solutions to those two problems. The proposed approach uses an integrated set of tools to perform, validate, and reuse the composition of different, analytic-analysis results of various manufacturing processes. The integration is based on the 3-tiered architecture depicted in Fig. 1. The three tiers are denoted as “domains of discourse”, “problem domain”, and “analyticaltechnology domain”. Each tier addresses a different level of abstraction, creates tools consistent with that abstraction, and contributes those tools to the approach. These tiers are discussed in turn below. The Domains-of-discourse tier includes representations of all static and dynamic information related to the production resources and processes. Static information includes any database schema, conceptual models, or ontologies. Examples include the quality information framework (QIF) (Zhao et al. 2012), business-to-manufacturing markup language (B2MML) (B2MML 2003), MTConnect schema (Vijayaraghavan and Dornfeld 2010), and property ontologies (Denno and Kim 2015). Dynamic information describes the current state of production processes and equipment. For example, results of the inspection processes are in the form of QIF Results; results of sensor data would in the MTConnect format. An important point to note about this tier is that actual information structures are not optimized for the solution of any particular optimization problem. Rather, the tier simply accepts the information in whatever forms were generated by processes that created them. The Problem-domain tier represents all of the viewpoints relevant to the particular optimization problem being solved. Each such viewpoint can be captured in a problemformulation metamodel (PFM), which describes the schema or pattern of the mathematical modeling method underlying the problem. For example, supposed the particular optimization problem is generating a production schedule for a job shop. The PFM might describe that job shop as a configuration of its queues and a collection of its resources. The information needed to create that configuration comes from the domains-of-discourse tier. In this production-scheduling example, the PFM would need information from several different viewpoints including process plans, production resources, product demand, and inventory status. Figure 1 depicts the viewpoints related to another problem: the additive manufacturing (AM), parameter-optimization problem. The associated viewpoints for that problem are part requirements, tensile strength, processing time, surface roughness, and equipment characteristics. The actual optimization problem is formulated as the specification of a set of constraints and an objective function as described in “Problem-domain tier” section. 123 J Intell Manuf Fig. 1 Conceptual view of three-tier analytical approach and its usage in an example problem The Analytical-technology-domain tier includes a metamodel of the analytical tools available to solve different kinds of optimization problems. Figure 1 depicts the use of an optimization metamodel for a class of such tools. It might include optimization programming language (OPL) (Hentenryck 1999), a mathematical programming language (AMPL) (Fourer et al. 1990), and general algebraic modeling systems (GAMS) (Bussieck and Meeraus 2004). That metamodel is defined as a meta-object facility (MOF) (OMG 2014) conforming model. Such models include specifications of classes and their relationships. Each instance of the model (1) consists of a collection of instances of the classes and relationships and (2) represents the formulation of each particular analytical problem in the terms of the specific analytical tool that will be used to solve it. This collection of instances and relationships can be serialized and used as inputs to the analytical tool. For example, a collection of instances representing the example problem could be serialized as OPL code and executed by an optimization tool that is capable of processing OPL. Domains-of-discourse tier Figure 2 shows the first tier, domain of discourse, including five main steps: define decision goals, identify relevant manufacturing viewpoints, collect data for those viewpoints, develop predictive models, and check model fidelity. The following subsections explain the details of each step. 123 Define decision goals Decision goals need to be understood clearly to avoid incorrect results and wrong decisions. The understanding must include both the scope of, and the reason for, those decisions. For example, one decision goal might involve (1) selecting process parameters for an AM machine, which is the scope, and (2) minimizing energy consumption and manufacturing cost, which is the reason. Identify manufacturing viewpoints Achieving the defined decision goals requires information from several different manufacturing viewpoints. That information can be represented digitally in different ways including domain-specific languages, semantic-web technologies, and ontology techniques, among others. Four principles are proposed to select and represent these viewpoints. 1. Systematic principle: viewpoints should reflect all of the essential characteristics of, and cover the performance of, the entire SM system under consideration. 2. Independency principle: viewpoints should not have inclusion relationships at the same level of abstraction and should reflect the performance of alternatives from different aspects. 3. Measurability principle: performance-related viewpoints should be quantitatively measurable. 4. Analytical principle: viewpoints related to any analytical analysis should be abstracted as predictive models. In J Intell Manuf Fig. 2 Example of procedures in the domain of discourse addition, the predictive models should be normalized to compare or operate directly when multi-criteria decisionmaking is involved. Develop predictive models In general, predictive models fall into three categories: empirical models, analytical models, and hybrid models. The procedure for developing or refining predictive models is different in each of these categories and can vary depending on the details of the particular model. The following describes a typical procedure for empirical models. Developing empirical models involves four steps: (1) determine the experimental design, (2) choose the type of model (choices include regression, response surface model, neural networks, and inductive learning), (3) run the experiment and collect the data, and (4) fit the data to the chosen model. This four-step process is illustrated in the first column in Fig. 2. The analytical and hybrid models are shown in second and third columns, respectively. If there is high confidence in the analytical model, it is used to develop predictive model. In contrast, if the confidence level of the analytical model is low, the model can be updated by incorporating the local empirical model into the analytical model (hybrid model). Supposed that Y is a vector Yˆ1 , Yˆ2 , . . . , Ŷn of performance-criteria responses and x1 , x2 , . . . xn are vectors of decision variables. The functional relationships for these criteria are described as (1) Y1 = Yˆ1 + ε1 = f 1 x1,1 , x1,2 , . . . , x1,i + ε1 (2) Y2 = Yˆ2 + ε2 = f 2 x2,1 , x2,2 , . . . , x2, j + ε2 ... Yn = Ŷn + εn = f n xn,1 , xn,2 , . . . , xn,k + εn , (3) where f 1 , f 2 , . . . , f n can be regression functions and ε1 , ε2 , . . ., and εn are the error terms. Check model fidelity After the functional forms of the predictive models have been developed, they should be examined by checking the model’s fidelity—for regression models the fidelity can be measured by the correlation coefficient R. Model fidelity includes model accuracy, model reliability, and model robust- 123 J Intell Manuf ness (Eddy et al. 2014). Model accuracy indicates “how close sample points that are included in the model are to the model itself”. Model reliability denotes “how close any points that are not included in the model are to the model itself”. Model robustness takes into account “the resolution between rank adjacent alternatives identified by the model and the effect of all variability due to the accuracy and reliability measures”. Problem-domain tier Figure 3 represents the second tier, problem domain, containing five steps (1) normalize the predictive model, (2) determine the weighting factors of the criteria, (3) check reliability, (4) develop a global predictive model, and (5) check confidence level. The following subsections explain the details of each step. Normalize predictive models Aggregating different performance criteria directly to obtain the overall objective function or to develop an aggregated predictive model is difficult because each criterion may have a different unit of measure. If this happens, a normalization step is necessary to make each response dimensionless, comparable, and additive. As described in Wang et al. (2009), there are several different normalization methods. Popular methods include linear min–max normalization, target-based normalization, balance of opinions, and distance-to-reference country. Note, since the method choice can significantly affect the decision, each method should be carefully considered with respect to the decision goals. Normalization transforms response values by dividing them by a selected reference value. For example, in linear min–max normalization, that value is the difference between the min and max values. The resulting normalized predictive model can be represented formally a Normalize Ŷ1 = Normalize Ŷ2 = Ŷ¯ 1 = f¯1 x1,1 , x1,2 , . . . , x1,k Ŷ¯ 2 = f¯2 x2,1 , x2,2 , . . . , x2,k (4) (5) ... Normalize Ŷn = Ŷ¯ n = f¯n xn,1 , xn,2 , . . . , xn,k (6) Determine weighting factors After normalization, determining the weighting factors is next because the weights needs to prioritize the relative importance between responses (indicators/criteria). As we saw with normalization, weighting factors also can affect the results significantly; consequently, the choice of weighting factors should be selected carefully with respect to the decision goals. Frequently, weights are determined in consultation with manufacturing experts who use one of two approaches: an equal-weighting approach or a rankorder-weighting approach (Wang et al. 2009). If all criteria are deemed of equal importance, then the equal-weights approach is used. Otherwise, a rank-order-weighting method, which considers the relative importance among responses as its main criterion, is used. Three approaches are in common use today (Wang et al. 2009); they are (1) subjective, pairwise weighting such as the one used in AHP, (2) objective weighting method such as the Entropy method and the TOPSIS method, and (3) a hybrid method such multiplication synthesis and additive synthesis. Check reliability Fig. 3 Procedures in the problem domain 123 Since weighting factors can significantly affect the final result, they are sometimes checked to see whether they are reliable or not. For example, to check the reliability of the weighting factors used in AHP, the consistency ratio (CR) can be used (Saaty 2008). When the CR is low, that indicates “not consistent”. When this happens, more experts and decision makers need to update the weighting factors and decrease the CR. This process repeats until a satisfactory CR is achieved. Once that happens, the normalized predictive models and their weighting factors are known. J Intell Manuf Develop a global predictive model After checking the reliability, the individual, normalized, predictive models with the weighting factors are composed to develop a global predictive model (Kim et al. 2015; Denno and Kim 2015) or it can be multi-objective decision-making problem. It can consist of three types of model: empirical, analytical, and hybrid. Also, there are several methods (Wang et al. 2009) for composing this global predictive model (e.g., weighted sum, weighted geometric mean, and AHP). Check confidence level The composed global predictive model needs to be evaluated whether it satisfies the required confidence level or not. The accuracy, reliability, and robustness of the model need to be considered, as well (Eddy et al. 2014). Even though each local predictive model already satisfies the required confidence level, there is no guarantee that the global predictive model will satisfy its own confidence level. In other words, it is not easy to quantify the uncertainty of the global predictive model as a simple function of the uncertainties of the individual models. The difficulty lies in the fact that the global uncertainty is impacted by multiple, interacting criteria with subjective normalization methods and weighting factors. If that global uncertainty is too high, the global predictive model can be updated with a robustness model (see Fig. 3). Analytical-technology domain Figure 4 shows the third tier, analytical technology domain, including three steps: (1) translate the global predictive model into optimization problem, (2) execute optimization problem using an analytical solver, and (3) check feasibility and optimality. The following subsections explain the details of each step. Translate a global predictive model into an optimization problem As noted above, the global predictive model is used to develop the multi-criteria objective function. To complete the creation of the optimization problem, we need to formulate all of the constraints. Constraints can be generated from the various viewpoints. For example, the process-plan viewpoint provides information need to formulate both the necessary precedence constraints and resource constrains. The order viewpoint provides the information needed to formulate due date constraints. To provide this information, all manufacturing viewpoints can be translated into a neutral representation and stored in the manufacturing viewpoint database for reusability. Fig. 4 Procedures in the analytical technology domain Execute optimization problem After generating the required optimization formulation, we generate a predictive metamodel using the approaches described in Kim et al. (2015) and Denno and Kim (2015). The metamodel code must then be serialized to generate the exact input for each specific, analytical-optimization tool. Each such tool consists of a solver and a modeling environment. A solver (e.g., CPLEX OMG 2014) is a generic term indicating a piece of software that solves a mathematical optimization problem formulated as a linear program, a nonlinear program, and, a mixed integer linear program, among others. Each solver typically can solve many such “programs” using a number of well-known solution methods. A modeling environment (e.g., AMPL Fourer et al. 1990 and GAMS Bussieck and Meeraus 2004) provides general and intuitive ways to express mathematical optimization problems, generates problem instances, offers features for importing data, invokes solvers, analyzes results, scripts extended algorithmic schemes, and interfaces to other applications. Check feasibility and optimality The generated results from the solver need to be checked for both feasibility and optimality. If the problem has been formulated correctly, this is generally not a problem. If the check fails, tracing the reason of the infeasibility and the incorrectness back to the detailed information in multiple manufacturing viewpoints is required. The new formulation will go through the same steps as before. A case study To illustrate use of this approach for composing predictive models from disparate knowledge sources, we used the previous case study described in Kim et al. (2015). It is to 123 J Intell Manuf define and refine process and material parameters in the metal laser-sintering AM process. The previous case study used six equation-based models to predict how process performance and part quality will respond to changes in the smart manufacturing environment. Consequently, the results from the previous case study provide actionable recommendations to a decision-maker for the control purpose. However, the original work involved only a single optimization criterion, which means the previous approach and case study cannot manage the multiple criteria at the same time. In this case, based on the previous example, we extend the single optimization problem to a multi-criteria one. Specifically, we focus on how the various predictive models are integrated into a single, multi-criteria objective function. Domain of discourse Define decision goals (Y1 −Y5 ) are utilized from the previous research in Kim et al. (2015), as shown below: Y1 = (αtime × L) + x y x=1 y=1 z z=1 βtime 5 V Pi × x3 V Ai Y2 = x1 /(x2 × x3 × x4 ) × Vol. × 52 × Y3 = (9) 841.6 + 0.175x2 −2.375x 3 + 5.5x5 − 16.6x22 − 19.9x32 −22.45x 25 + 0.2x2 x3 − 3.85x2 x5 + 0.55x3 x5 Y5 = (8) 3.0 + 0.05x1 +1.9625x 3 +0.0125x4 + 0.95x12 + 0.025x32 +1.525x 24 + 0.025x1 x3 + 0.075x1 x4 + 0.05x3 x4 Y4 = (7) (10) 55.0 + 0.5875x1 +19.975x 3 +0.0375x 4 + 4.55x12 + 0.125x32 + 9.85x42 − 0.175x1 x3 + 0.6x1 x4 + 0.125x 3 x4 . (11) The decision goal is to find the optimal process and material parameters for manufacturing a (54 × 54 × 28 mm) turbine blade with a volume of 20,618 mm3 using a laser-sintering process. This process was performed by an EOS M270 directmetal, laser-sintering machine (DMLS) using Raymor Ti– 6Al–4V powder with an apparent density of 2.55 g/cm3 . where αtime is 10.82 s, L is the number of layers, and βtime is 0.0125 s. The average occupancy rate in each voxel (VPi /VAi ) is assumed to be 0.3. To verify the predictive model (Y3 −Y5 ), R 2 error (the coefficient of determination) was performed. Identify relevant manufacturing viewpoints Problem domain From the six manufacturing viewpoints (Kim et al. 2015), we only selected five optimization criteria: manufacturing time (Y1 ), energy consumption (Y2 ), volumetric error (Y3 ), tensile strength (Y4 ), and surface roughness (Y5 ). It is considered that the manufacturing time violates the first principle “independency” in “Identify manufacturing viewpoints” section. Since the manufacturing cost can be considered as a higher level, compared to other Y1 –Y5 , we did not include it in this case study. In addition, we selected five, bounded, decision variables: laser power X 1 (80–160) W, scanning speed X 2 (360–840) mm/s, layer thickness X 3 (20–50) µm, hatch distance X 4 (100–160) µm, and Oxygen X 5 (0.13–0.17)%. Normalize the predictive models Develop predictive models In this step, predictive models for manufacturing time (Y1 ) and energy consumption (Y2 ) are represented using analytical model—Eqs. (7) and (8), respectively. The remaining criteria, volumetric error (Y3 ), tensile strength (Y4 ), and surface roughness (Y5 ) are represented using empirical (regression) models—Eq. (9) through Eq. (11). Taguchi design is used to determine the key process parameters with an analysis of variance (ANOVA) test. Then, predictive models are developed by using the Box–Behnken experimental design and response surface method (RSM). The five predictive models 123 Since the criteria have different units, a normalization step for the five predictive models is required to make each response dimensionless and comparable. We used the linear min–max normalization method (Wang et al. 2009) and the following rules to achieve that normalization. The first rule is, if a target value of a response is “the-larger-the-better” as tensile such strength, the normalized predictive model Ŷ¯ n is estimated by: Ŷn − min Ŷn (12) Ŷ¯ n = max Ŷn − max Ŷn where Ŷ¯ n is 0 ≤ Ŷ¯ n ≤ 1. If a target value of a response is “the-smaller-the-better” such as manufacturing time, energy consumption, volumetric error, and surface roughness, the normalized predictive model (Ŷ¯ n ) is estimated by: max Ŷn − Ŷn Ŷ¯ n = max Ŷn − min Ŷn (13) J Intell Manuf Table 1 Min and max values for the five responses Responses min Ŷn Unit Manufacturing time Ŷ1 Energy consumption Ŷ2 Volumetric error Ŷ3 Tensile strength Ŷ4 Surface roughness Ŷ5 max Ŷn max Ŷn − min Ŷn s 6871.17 17,080.54 10,209.37 kJ 245.45 4581.78 4336.33 % 1.06 7.68 6.62 MPa 770.00 841.99 71.99 µm 35.12 90.67 55.55 Table 2 Results of determined weights according to the manufacturing viewpoints considered and its validation Cases Manufacturing viewpoints Y1 Weights Validation Y2 Y3 Y4 Y5 W1 W2 W3 × × × 0.125 0.088 0.363 × × 0.194 0.125 Case 1 × × Case 2 × × Case 3 × × × 0.164 0.539 Each minimum and maximum value of each response (Y1 −Y5 ) is calculated by minimizing and maximizing each response without constraint. Table 1 shows the min/max values and its difference values for the five responses. Determine weighting factors From several methods (e.g., TOPSIS and Entropy) for weighting factor determination, the analytical hierarchy process (AHP) is used to determine the relative weights of each criterion as an example and due to its simplicity and efficiency (Saaty 2008). A square and reciprocal pairwise comparison matrix A of order 5 is formulated, based on the relative weights of criteria. In this case study, this matrix will be as an example in Eq. (14): Y1 Y2 A = Y3 Y4 Y5 ⎡ ⎢ ⎢ ⎢ ⎣ Y1 1 1/2 3 2 2 Y2 2 1 3 3 2 Y3 1/3 1/3 1 1/2 1/2 Y4 1/2 1/3 2 1 1 Y5 1/2⎤ 1/2⎥ ⎥ 2 ⎥ ⎦ 1 1 (14) CI (λmax − n) = /R I RI (n − 1) W5 Nanda max Random index CR 0.221 0.203 5.072 1.12 0.016 0.356 0.325 4.044 0.9 0.016 3.009 0.58 0.008 0.297 Random index (RI) is 1.12 when the number of criteria (n) is 5. Then, the CR is 0.016, which means the estimated weights are consistent (Saaty 2008). Table 2 shows the considered manufacturing viewpoints and its results of weights and validation with respect to three cases. Just as in Case 1, this can be extended to Cases 2 and 3. From the table, it is easy to see that the weights are consistent. Develop a global predictive model After determining the weights, the final, global predictive model can be one of two approaches: single-objective decision-making or multi-objective decision-making. In this step, we use a simple weighted sum method (Saaty 2008) for generating the single-objective function, called a global predictive model. The summation is constructed based on the normalized predictive models and the subjective weight assigned to them. The formula is as follows: Y = f (x1 , x2 , . . . , xn ) = n w j Ŷ¯ j (16) j=1 where ω j = 1. Each weight for each indicator is calculated as 0.125, 0.088, 0.363, 0.221, and 0.203, respectively. For the reliability check for the weights, the consistency ratio (CR) is calculated by: CR = W4 The final, global, predictive model for Case 1 is shown in Eq. (17). In a similar way, the global predictive models for Cases 2 and 3 can be formulated. Y = w1 × max Ŷ1 − Ŷ1 max Ŷ1 − minŶ1 (15) + w3 × The consistency index (CI) is estimated by (λmax −n)/(n−1). The maximum value of lambda (λmax ) is calculated as 5.072. +w5 × + w2 × max Ŷ3 − Ŷ3 max Ŷ3 − minŶ3 max Ŷ5 − Y5 max Ŷ5 − minŶ5 max Ŷ2 − Ŷ2 max Ŷ2 − minŶ2 + w4 × Ŷ4 − minŶ4 max Ŷ4 − minŶ4 (17) 123 J Intell Manuf Fig. 5 Example of optimization programming language (OPL) source code Analytical technology domain Translate it to the OPL metamodel for a MCDM problem The Analytical-technology-domain tier includes a metamodel of the analytical tools available to solve different kinds of optimization problems. Figure 1 depicts the use of an optimization metamodel for a class of such tools that might include optimization programming language (OPL) (Hentenryck 1999), A mathematical programming language (AMPL) (Fourer et al. 1990), and general algebraic modeling systems (GAMS) (Bussieck and Meeraus 2004). That metamodel is defined as a meta-object facility (MOF) (OMG 2014) conforming model. Such models include specifications of classes and their relationships. Each instance of the model (1) consists of a collection of instances of the classes and relationships and (2) represents the formulation of each particular analytical problem in the terms of the specific analytical tool that will be used to solve it. This collection of instances and relationships can be serialized and used as input to the analytical tool. For example, a collection of instances representing the example problem could be serialized as OPL code and executed by an optimization tool that is capable of processing OPL. This multi-criteria function is a weighted composition of the generated predictive models of each response. In our approach, these predictive models are treated as information objects that must be organized into a template for optimization. The template directs the mapping of these mathematical predictive models, and similarly constructed constraints, into such objects. The resulting information objects are then used to populate a metamodel that serves as an interface for the particular tool that is used to solve that optimization problem.1 Analytical models, such as Eq. (17), and the bounds for each decision variable, become the objective function and the constraints, respectively, in the multi-criteria optimization formulation problem. They are assigned as the same roles of information objects in the metamodel, which was created using the optimization programming language (OPL) (Hentenryck 1999). Figure 5 shows the window snapshot containing some portions of the OPL source codes for case study 3 in IBM ILOG CPLEX optimization studio (version 12.4), which denotes the minimum and maximum values, its predictive models, the integrated single objective function, and its constraints. 1 123 Note, each such tool will require its own metamodel. J Intell Manuf It considers three manufacturing viewpoints: manufacturing time (Y1 ), volumetric error (Y3 ), and tensile strength (Y4 ). Actionable recommendations We used the methods described in our previous research (Kim et al. 2015; Denno and Kim 2015), to serialize these objects so that they can be used as inputs into the optimization solver in IPython notebook environment (Pérez and Granger 2007). Figure 6 shows the window snapshot containing example code and its result of case study 3 in the IPython notebook environment. The results denote the optimal results, the optimal manufacturing parameters, and its results of responses, respectively. Table 3 shows the objective function and constraints, optimal results, optimal manufacturing parameters, and the results of the responses. In Case 1, the objective function is to maximize Y with constraints (Y1 ≤ 8572.7 s, Y2 ≤ 1518 kJ, Y3 ≤ 4.68%, Y4 ≥ 800 MPa, and Y5 ≤ 70.67 µm). The optimal manufacturing parameters (X 1 : 116.50 W, X 2 : 503.49 mm/s, X 3 : 28.32 µm, X 4 : 131.37 µm, andX 5 : 0.153%) are determined. In addition, the maximized value of Y is 0.799. Other responses include Y1 = 12,081.00 s, Y2 = 1282.22 kJ, Y3 = 2.14%, Y4 = 836.51 MPa, and Y5 = 46.12 µm. Just as in Case 1, this can be extended to Cases 2 and 3. This case study demonstrates that the optimal process parameters can be determined with respect to the different stakeholders’ needs. This approach can provide products and services at a better quality, and resources should be allocated efficiently while they achieve the desired profitability and minimize wastes (e.g., air pollutants) in SM environments. Discussion and conclusion Discussion One of the benefits of our approach is reusability. As shown in “Analytical technology domain” section, each individual predictive model can be created in a modular way, independent of the other predictive models. To provide an actionable recommendation in certain manufacturing/design conditions, the individual predictive models can be composed to create the required multi-criteria objective function and constraints. In other words, individual predictive models can be reused in different optimization formulations according to the defined objective and constraints, as shown in Table 3. This leads to a Fig. 6 Example code and its result of case study 3 in the IPython notebook environment 123 J Intell Manuf Table 3 Input and outputs of Cases 1, 2, and 3 Case 1 Case 2 Case 3 Objective: max (Y) constraints Objective: max (Y ) constraints Objective: max (Y ) constraints Input Objective/constraints Y1 ≤ 12,081 s Y1 ≤ 10,081 s Y1 ≤ 15,000 s Y2 ≤ 1518 kJ Y2 ≤ 1218 kJ Y3 ≤ 3.65% Y3 ≤ 4.68% Y4 ≥ 810.0 MPa Y4 ≥ 820.0 MPa Y4 ≥ 800 MPa Y5 ≤ 65.34 µm Y5 ≤ 70.67 µm Output Optimal results Y = 0.799 Optimal manufacturing parameters X 1 = 116.50 W X 1 = 100.91 W X 1 = 119.51 W X 2 = 503.49 mm/s X 2 = 500.96 mm/s X 2 = 502.94 mm/s X 3 = 28.32 µm X 3 = 33.98 µm X 3 = 28.74 µm X 4 = 131.37 µm X 4 = 130.67 µm X 4 = 130.51 µm X 5 = 0.153% X 5 = 0.154% X 5 = 0.153% Y1 = 12,081.00 s Y1 = 10,081.00 s Y1 = 11,907.10 s Y2 = 1282.22 kJ Y2 = 935.42 kJ Y3 = 2.19 kJ Y3 = 2.14% Y4 = 839.32 MPa Y4 = 836.89 MPa Y4 = 836.51 MPa Y5 = 54.39 µm Results of responses Y = 0.793 Y = 0.807 Y5 = 46.12 µm reduction of time and effort compared to how these activities might be performed in traditional quality processes. Another benefit is that our approach is compatible with a number of production-information standards. We believe it would not be difficult to superimpose the approach on manufacturing systems that apply open standards for machine monitoring, manufacturing execution, and quality reporting, such as MTConnect (Vijayaraghavan and Dornfeld 2010), quality information framework (QIF) (Zhao et al. 2012), and ISA-95 (Scholten 2007). The third benefit is that our approach is flexible and yet enables automation. It can be implemented with assorted optimization approaches and solver tools. Our use of IPython notebook (Pérez and Granger 2007) provides great freedom in problem formulation. We use web services to communicate between the notebook and supporting information and tools. This means that routine analysis can be automated, while less common activities can be performed as manual steps inside the notebook. Choosing weights that accurately capture the interests and preferences of the various stakeholders is still more of an art than a science. The reasons include the uncertainty of information, the vagueness of human feelings, and the recognition that terms like “equal”, “moderate”, “essential”, “very strong”, and “absolute” are qualitative. Consequently, converting these qualitative terms into quantitative weights for the criteria can be a time-consuming, iterative process. Yet, this process is necessary because the results from the 123 optimization can be affected significantly by the choices of methods for scaling, normalization, weighting, and aggregation (Bohringer and Jochem 2007). The composition of the global predictive model from multiple local predictive models generates uncertainty propagation issues. Although each local predictive model may satisfy the confidence level required, their composition may not. This can happen because of the way the uncertainty in each local model propagates when it is composed with other local predictive models. Since each local predictive model has its own uncertainties as shown in Eqs. (1)–(3), uncertainties in local predictive models are also scaled, normalized, weighted, and aggregated (SNWAed) during the procedure for the global predictive model generation. Thus, the SNWAed uncertainty is not the simple summation of uncertainties of each local predictive model. We did not take care of these SNWAed uncertainties, since it is the out scope in this paper. The uncertainties in local predictive models can be categorized as either aleatory, epistemic, or a mixture of two (Roy and Oberkampf 2011). There are four main sources of uncertainty: model inputs, model assumptions, model form, and numerical approximations. As a result, epistemic uncertainties can be reduced with a more accurate model, more detailed knowledge, or better quality data. These uncertainties exist in input/output data and a local predictive model itself. Thus, the global predictive model needs to be investigated to determine whether it satisfies the required confidence J Intell Manuf level or not. For this task, quantifying uncertainty and its propagation regarding different local predictive models will be performed in the near future. Conclusion This paper proposes a comprehensive and systematic approach to composing predictive models of manufacturing processes from disparate analytical, experimental, and informational sources. This approach is based on a three-tier architecture consisting of domain of discourse, problem domain, and analytical technology domain. The main benefit of this architecture is that it facilitates complex decision-making based on multiple decision criteria. To demonstrate the proposed approach, we described a case study related to an additive manufacturing process. The decision was to determine the optimal manufacturing process parameters using an optimization formulation with (1) an objective function based on five, different, weighted criteria and (2) interval constraints that bound five different process variables. It aims to provide the cost-effective solutions to compose the various optimization problems without being burdens from irrelevant technical details. In addition, it provides traces (e.g., motivation, constraints, and background) of the decision-making and its verifiability for the results. In the near future, we will investigate and quantify the uncertainties in local predictive models and its propagated uncertainties in a global predictive model. Acknowledgements This research work has been done with the main author’s previous colleagues: Peter Denno (National Institute of Standards and Technology, NIST) and Dr. Albert Jones (NIST). 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