## Adaptable design of open architecture products with robust performanceAdaptable design of open architecture products with robust performance Jian Zhang
of China; (Received 17 July 2014; accepted 22 January 2015) Adaptable design is an approach to design adaptable products whose modules/configurations and parameter values can be changed during an operation stage to satisfy different customer requirements. An open architecture product is an adaptable product with open interfaces to allow the third-party vendors to develop new add-on modules and connect these add-on modules through the open interfaces. In this work, an open architecture adaptable product is modelled by a platform, alternative add-on modules, and open interfaces to connect the add-on modules with the platform. Both the specific add-on modules that need to be designed at the product development stage and the unknown add-on modules that could be added in the future are considered. In this research, a novel robust design approach is introduced to identify the optimal design of an open architecture adaptable product whose functional performance measures are the least sensitive to variations of the product and operating parameters due to uncertainties. First, characteristics of open architecture adaptable products are discussed. Methods for modelling of platform, add-on modules, and open interfaces are then introduced. A multi-level optimisation method is subsequently explained to identify the optimal design configuration and parameters considering product performance measures and their variations. Keywords: adaptable products; open architecture products; robust design; uncertainties ## 1.IntroductionIncreasing competition in the global marketplace demands products be adaptable to the changes of functional requirements, operation environments, and technology advancement. Adaptable product is the one that can be changed/adapted, such as reconfigured and upgraded, during a product operation stage to satisfy different requirements of customers (Gu, Hashemina, and Nee 2004). Compared with the traditional products whose functional performance and working conditions specified in the design stage cannot be changed after the products are manufactured, an adaptable product can be easily modified in the product operation stage to satisfy the changed requirements. Adaptable design is the design approach for developing adaptable products (Gu, Hashemina, and Nee 2004). Since introduction of the adaptable design concept, many adaptable design methods have been developed in the past decade (Gu, Xue, and Nee 2009). Li, Xue, and Gu (2008) introduced new adaptability evaluation measures considering the extendibility of functions, *Corresponding author. Email: peihuagu@stu.edu.cn © 2015 Taylor & Francis
upgradeability of modules, and customisability of components for identification of the optimal adaptable design based on evaluation to different design candidates. By comparing the actual structure of the product with its ideal structure that can be easily changed, Fletcher, Brennan, and Gu (2009) developed a method to evaluate adaptability of an adaptable product. Cheng et al. (2011) developed a structure-based approach to evaluate design by measuring essential adaptability and behavioural adaptability. Xue et al. (2012) extended the adaptable design method through modelling of the changeable requirements and product descriptions as numerical functions of the product life-cycle time parameter. The four key issues in research of adaptable design, including function modelling, design modelling, design evaluation and design process, requirements and methods in the key issues of adaptable design as well as applications of the adaptable design methods were summarised in a literature review by Gu, Xue, and Nee (2009). Product architecture also provides influence on an adaptable product. In general, both closed architecture and open architecture can be used in adaptable design (Koren et al. 2013; Peng et al. 2013). For an adaptable product with closed architecture, although interfaces among various changeable modules of the product are designed and these modules are connected through these interfaces to achieve different functions, these functional requirements are specified by the original equipment manufacturer (OEM). These modules are produced by the OEM and/or its suppliers according to specifications defined by the OEM. Most of the traditional reconfigurable products belong to this category. An open architecture product (OAP) can be considered as the product with a platform such that add-on modules developed by different vendors can be connected with the platform through interfaces of the platform (Koren et al. 2013). For an adaptable product with open architecture, specifications of the interfaces are open to the public to allow the third-party vendors to develop new modules with new functions as they like. A personal computer is a typical OAP that allows different devices developed by the third-party vendors to be connected with the motherboard through open USB interfaces. For the OAP, since different manufacturers/customers can participate the design of add-on modules, product variety can be easily achieved. Product sustainability, adaptability, upgradeability, and extendibility can also be achieved by designing an OAP (Koren et al. 2013). Despite the progress in research on adaptable design, the influence of uncertainties on performances of an OAP has never been investigated. Robustness is considered as the product’s capability to resist the influence of uncertainties on product performances. Product robustness is usually measured by the sensitivity of functional performance to parameter variations caused by uncertainties. Many robust design methods have been developed in the past decades. In this research area, Taguchi (1978, 1993) developed a robust design method by using the signalto-noise ratio (SNR) to measure the product robustness. Parkinson, Sorensen, and Pourhassan (1993) developed the robust design methods based on the analysis of the relations among product performance measures, product/operating parameters, and variations of these parameters. Du and Chen (2000) developed a robust design method to maintain the robustness of design feasibility by considering the influence of uncertainties on design constraints. Fonseca, Friswell, and Lees (2007) and Kumar et al. (2008) developed the randomised robust design methods by employing the Monte-Carlo method to simulate the influence of uncertainties on product functional performance. Samadiani et al. (2009) improved the robustness of a system considering different operation conditions. Zhang et al. (2010) and Hu, Azarm, and Almansoori (2013) developed the robust design methods considering multiple design objective functions. For the design of an adaptable product, robustness needs to be considered to improve the product quality (Zhang, Xue, and Gu 2012). Since modules/configurations and parameters of an adaptable product are changeable during the product operation stage, the existing robust design methods cannot be used directly for developing a robust adaptable product. Therefore, a robust adaptable design method is required to create an adaptable product whose functional performances are insensitive to uncertainties in parameters. In the research by Zhang et al. (2014), a robust adaptable design method considering changes of both configurations and parameter values was introduced. However, this robust adaptable design method cannot be used directly to design an OAP. The research presented in this paper aims at introducing a robust adaptable design approach for developing OAPs such that an OAP is adaptable to various changes in requirements during the product operation stage, meanwhile the functional performance measures are the least sensitive to parameter variations. ## 2.Open architecture productsIn this research, an OAP is considered as the one with a platform and open interfaces through which different add-on modules from different sources can be connected to satisfy the requirements of customers. Characteristics of OAPs include the following: An OAP is composed of a platform, add-on modules, and open interfaces to connect the platform and the add-on modules. Specifications and constraints of the open interface parameters are open to the public. The platform and add-on modules are connected by open interfaces through relationships defined by input and output parameters. Add-on modules can be specific ones that need to be designed during the product development stage and unknown ones that could be designed and added in the future. Add-on modules can be provided by both the OEM and the third-party vendors. OAPs provide variety and flexibilities to customers. At the product purchasing stage, customers can select the required add-on modules from all available ones based on their needs. At the product operation stage, customers can change, upgrade, and extend functions by using different add-on modules. Research on design of OAPs is based on the results achieved on design of mass produced products, mass customised products, reconfigurable products, and upgradeable products (Gu, Hashemina, and Nee 2004). Comparison between OAP with other types of products is provided in Table 1. For the mass produced products, functions are determined by the manufacturer and cannot be changed. For the mass customised products, different options are available for customers to select at the product purchasing stage. The mass customised products, however, usually cannot be changed in the product operation stage. Both reconfigurable products and upgradeable products enable customers to change product configurations during the product operation stage to satisfy different needs of customers. A reconfigurable product is usually used to replace multiple products with a single one. New components/modules are not added to the reconfigurable product during the product operation stage. For an upgradable product, new components/modules are usually used to replace the old ones for improving functions of the product. Table 1.Comparison among different types of products.
## 2.1.Platform and add-on modules in an OAPIn this research, an OAP as shown in Figure 1 is composed of a platform, different add-on modules, and interfaces to connect different add-on modules with the platform. Generally, the platform (M The specific add-on modules, M ## 2.2.Open interfaces in an OAPThe open interfaces in an OAP are used to connect the various add-on modules to the platform. Compared with a closed architecture product where interfaces are used to connect predefined modules, the open interfaces in an OAP allow new add-on modules developed by the third-party vendors to be connected with the platform to achieve additional functions. In this research, interactions between platform and add-on modules in an OAP are defined by input and output parameters of the open interfaces. Since both the specific add-on modules and the unknown add-on modules are considered in this work, the input/output parameters of interfaces for interactions between the platform and the add-on modules should be defined differently: Figure 1.Platform and add-on modules of an OAP. ## • Input/output parameters of interfaces for specific add-on modulesSince design configurations and parameters of the add-on modules are determined at the product development stage, the values of the input/output interface parameters can be calculated from the parameters of the platform and add-on modules. ## • Input/output parameters of interfaces for unknown add-on modulesSince design configurations and parameters of the add-on modules are not determined at the product development stage, the values of the input/output interface parameters have to be defined by constraints. In this research, constraints for discrete and continuous parameters are considered. ## 2.3.Robustness of an OAPAn adaptable design approach can be used for the design of OAPs. Generally, an OAP can be evaluated by different measures such as performance, product adaptability, cost, and so on. In this research, robustness is selected as the evaluation measure to identify the optimal design of OAP considering uncertainties in product/operating parameters. Adaptable products can be evaluated by their capabilities of change in the operation stage such as adaptabilities (or flexibilities) (de Neufville and Scholtes 2011; Inkermann, Stechert, and Vietor 2013). Adaptability is used to evaluate the capability of a product to be changed in the operation stage to satisfy different requirements (Gu, Hashemina, and Nee 2004; Olewnik and Lewis 2006). For an OAP, both the specific add-on modules with specific functions and the unknown add-on modules without specified functions are considered. Product adaptability measure can be achieved through connections of different add-on modules, including the specific add-on modules and the unknown add-on modules, with the platform of an OAP. In the research area of adaptable design, different methods have been developed for the evaluation of product adaptability (Suh, de Weck, and Chang 2007; Gu, Xue, and Nee 2009; Inkermann, Stechert, and Vietor 2013). Despite the progress, robustness, which can significantly influence the quality of an OAP, has never been considered in the past. Robustness is a measure to evaluate a design considering both the product performances and the variations of these performances. Generally, product robustness can be improved through minimising the sensitivity of product performance to parameter variations caused by uncertainties (Taguchi 1993). For an OAP, robustness is influenced by (1) add-on modules including specific and unknown add-on modules, (2) configurations of platform and add-on modules, and (3) parameter values associated with configurations. Since robustness of OAP has not been considered in adaptable design, the achieved OAPs based on the existing adaptable design methods are vulnerable to the variations of parameters due to uncertainties. In this research, robustness is selected as the evaluation measure by assuming the adaptabilities and costs of all feasible design candidates are comparable. ## 3.An adaptable design approach for developing robust OAPsAn OAP is one type of adaptable products. In this research, an adaptable design approach is introduced to identify the robust OAP whose functional performance measures are the least sensitive to the variation of parameters due to uncertainties. ## 3.1.Modelling of an OAPAn OAP is composed of a platform, add-on modules, and open interfaces. During the operation stage, different add-on modules are connected to the platform through the open interfaces to form different operation configuration states for achieving different functions. At the design stage, different design configuration candidates are provided such that the best one can be selected considering product robustness. Both the operation configuration states and the design configuration candidates are further modelled by parameters. The platform and add-on modules are connected through open interfaces. ## 3.1.1.Modelling of product operation configuration statesAn OAP usually has several open interfaces. For each interface, different add-on modules can be connected with the platform. For the OAP shown in Figure 1, the platform (M During the product operation stage, each interface of the platform can be used to connect with different add-on modules. In this work, each combination of the add-on modules and the platform for achieving a certain function is called an operation configuration state. When n operation configuration states of an OAP are considered, collection of these operation configuration states, S, is defined by S = {S Each operation configuration state is associated with a probability representing the percentage of time this operation configuration state is used considering all operation configuration states. Collection of the probabilities for the n operation configuration states, P, is defined by P = {P The i-th operation configuration state, S S where M ## 3.1.2.Modelling of product design configuration candidatesFor the design of an OAP, different feasible design configuration candidates can be created from the same design requirements. In this work, the different alternative configurations for selection in the design stage are called design configuration candidates. The platform and each of the specific add-on modules can be modelled by an AND–OR tree (Gu, Xue, and Nee 2009). In an AND–OR tree, when all the sub-nodes need to be selected to support a super-node, all these sub-nodes are associated with an AND relation. As shown in Figure 2(a), for example, a personal computer is composed of a motherboard, an internal data drive, a monitor, a mouse, etc. When the super-node is supported by one of its sub-nodes in the process of design configuration candidate selection, all these sub-nodes are associated with an OR relation. For example, either the DVD drive or the Blu-ray drive needs to be selected for the internal data drive. For each AND–OR tree, a configuration candidate with only AND relations can be created based on the following rules: The root node should be selected first. When the sub-nodes of a selected node are associated with an AND relation, all these subnodes should be selected. Figure 2.Modelling of design configuration candidates. (a) Modelling of feasible design configuration candidates. (b) A design configuration candidate generated from the AND–OR tree. When the sub-nodes of a selected node are associated with an OR relation, only one of these sub-nodes should be selected. Figure 2(a) shows an AND–OR tree and Figure 2(b) shows a created feasible design configuration candidate with only AND relations. A complete design configuration candidate is modelled by a design configuration candidate for the platform and the design configuration candidates for all the add-on modules. ## 3.1.3.Modelling of parametersA product operation configuration state or a product design configuration candidate is further modelled by parameters. In this work, the parameters of an OAP are classified into two categories: design parameters and non-design parameters (Zhang, Xue, and Gu 2012): Design parameters are those whose values need to be determined at the design stage. In this work, the design parameters are further classified into un-adaptable design parameters and adaptable design parameters. ◦ Un-adaptable design parameters are the parameters whose values are not changed in the product operation stage. For example, the width of an office chair is an un-adaptable design parameter. In this work, the values of un-adaptable design parameters are achieved through optimisation. ◦ Adaptable design parameters are the parameters whose values need to be adapted at the product operation stage when requirements are changed. For example, the height of an office chair is an adaptable design parameter which can be adjusted for different persons. In this work, the values of adaptable design parameters are calculated from requirements, working conditions and other product parameters based on design rules. Non-design parameters are those whose values are provided as given conditions in design. For example, the mechanical properties of materials selected for the office chair are non-design parameter. Design parameters (i.e. un-adaptable design parameters and adaptable design parameters) used in this research are different from the design parameters used in the axiomatic design. In the axiomatic design, functional requirements belong to functional domain and design parameters belong to physical domain. Functional requirements can be satisfied by the selection of physical design parameters (Suh 1999). Product performance is used to measure the degree that a functional requirement is satisfied by design parameters. In the axiomatic design, the physical design parameters can be used to represent all physical entities including modules, configurations, and parameters created in design (Suh 2001). The design parameters in our work are used to model parameters of product modules and configurations. For an OAP, the values of the input/output parameters of the open interfaces are calculated from the un-adaptable design parameters, adaptable design parameters, and non-design parameters of the platform and add-on modules. In addition, constraints can also be applied to these parameters. For an OAP, since both the specific add-on modules and the unknown add-on modules need to be considered, the values of the adaptable design parameters are changed in two different ways in the product operation stage. Change of adaptable design parameter values with specific add-on modules When all the add-on modules are specific add-on modules, the relation among product functional performance F, un-adaptable design parameters X Change of adaptable design parameter values with unknown add-on modules When some add-on modules are unknown add-on modules, since these unknown add-on modules are only defined by the constraints of interface parameters, the relation among product functional performance F, un-adaptable design parameters X ## 3.1.4.Modelling of interfaces for the interactions between platform and add-on modulesFor an OAP, the add-on modules are connected with the platform through the open interfaces. In this work, the interactions between the platform and the add-on modules are defined by the input and output parameters of the open interfaces. Figure 3 shows interactions between a platform and add-on modules through interfaces. The values of the input parameters of an interface for an addon module are determined by the values of the corresponding output parameters of the interface for the platform, while the values of the input parameters of an interface for the platform are determined by the values of the corresponding output parameters of the interface for the add-on module. When a specific add-on module is connected with the platform, such as the M When an unknown module is considered, such as the M Figure 3.Interactions between platform and add-on modules. When the interface input/output parameters are continuous parameters, they are defined by IjU ∈ [LIj,UjI]andOUj ∈ [LOj ,UjO],(4) where I [L When the interface input/output parameters are discrete parameters, they are defined by I where {A ## 3.2.Evaluation of robustness for an OAP## 3.2.1.Robustness with specific add-on modulesIn the product operation stage, an OAP is changed to different operation configuration states to achieve different required functions. In this work, suppose that F F where Φ In this work, robustness is used to evaluate the quality of design considering both the performance measures and the variations of these performance measures due to uncertainties. Many measures, such as the SNR and the variance of functional performance, can be used to evaluate the robustness of a product design (Taguchi 1993). Since both functional performance and variation of the performance are considered in the SNR, the SNR has been selected in this research as the robustness evaluation measure. Robustness of the s-th operation configuration state for the i-th design configuration candidate considering the parameters X n k=1 where μ The overall robustness of the i-th design configuration candidate considering all the n operation configuration states with the un-adaptable design parameters X n R s=1 where P From Equation (8), the optimal parameters of X R ## 3.2.2.Robustness with unknown add-on modulesFor an unknown add-on module, since values of the interface input/output parameters can be varied as continuous values and discrete values, the product performance measures are also influenced by the changes of these interface input/output parameters. In this work, suppose that I F where Robustness of the s-th operation configuration state for the i-th design configuration candidate considering the parameters X R(si)(XD,IU,OU) ,(11) where μ Since the values of the interface input/output parameters for the unknown add-on modules are varied as continuous and discrete parameters, the influence of the different values of interface input/output parameters for the unknown add-on modules on product performance measures has to be considered. In this research, a statistical method and a worst-case method are developed considering possible changes of interface parameter values for the unknown add-on modules. The statistical method for calculation of robustness Changes of input/output interface parameters can be continuous and discrete. If I U U RP(X U LL If I R(X The worst-case method for calculation of robustness In this method, the worst-case robustness considering changes of input/output interface parameters is calculated. The robustness of the s-th operation configuration state for the i-th design configuration candidate considering the un-adaptable design parameters X R(X The best robustness for the i-th design configuration candidate, R ## 3.3.A multi-level optimisation model to identify the optimal design of OAPA multi-level optimisation model is developed in this work to identify the best design configuration candidate and its un-adaptable design parameter values considering robustness. In this optimisation model, first the optimal un-adaptable design parameter values for the i-th design configuration candidate are achieved through parameter optimisation. Find : theun-adaptabledesignparametersX n ## Maximise : R(15) Subjectto : X |

No. | Modules in an operation configuration state | Probability (time percentage) |

1 2 3 4 5 6 7 | S S S S S S S | P P P _{3 }= 10 P_{4 }= 10P _{5 }= 10P _{6 }= 10P _{7 }= 20 |

are summarised in Table 3. The non-design parameters associated with the different configurations are summarised in Table 4. The variations of parameters caused by uncertainties are summarised in Table 5.

The interactions between the platform and the unknown add-on modules are described in Figure 9. For the open architecture labelling machine, the input and output parameters of unknown add-on modules, M_{1}^{U }andM_{2}^{U}, are summarised in Table 6. The input parameters, N_{1}^{U }andN_{2}^{U}, are subjected to the following relations:

NI_{a},(17)

N.(18)

In this work, for operation configuration states 1, 3, and 5, the labelling machine is used as a vertical one and the target values of speeds for the applicator and pressing unit, V_{a}^{T}^{ }and V_{p}^{T}, were set to 20,000 mm/min. For operation configuration states 2, 4, and 6, the labelling machine is used as a horizontal one and the target values of speeds for the applicator and pressing unit, V_{a}^{T}^{ }and V_{p}^{T}, were set to 10,000 mm/min. For the operation configuration state 7, the unknown applicator and unknown pressing unit are connected with the platform. In this work, only horizontal labelling machine is considered under operation configuration state 7, and the target values of functional performance, V_{a}^{T}^{ }and V_{p}^{T}, were set to 10,000 mm/min.

Figure 7.Modelling of different design configurations of the platform.

Figure 8.Modelling of design configurations of add-on modules.

Table 3.Design parameters.

Type of parameters | Name | Symbol | Boundary | Unit |

Un-adaptable design parameters | Belt transmission ratio for the applicator | Ia | [0.1, 10] | – |

| Belt transmission ratio for the pressing unit | Ip | [0.1, 10] | – |

Adaptable design parameters | Rotation speed of the motor for the applicator | N _{a} | [0, 1500] | rpm |

| Rotation speed of the motor for the pressing unit | N _{p} | [0, 1500] | rpm |

When the open interfaces are connected with specific add-on modules, the labelling speed V_{a}_{ }and the pressing speed V_{p}_{ }can be calculated by

V _{a}_{ }= π · N_{a }· R_{a }· I_{a}_{ }· I_{1 }· D_{1}, | (19) |

V _{p}_{ }= π · N_{p }· R_{p}_{ }· I_{p}_{ }· I_{2 }· D_{2}, | (20) |

Table 4.Non-design parameters.

Name | Symbol | Value | Unit |

Transmission ratio of a gearbox for the specific applicator | R _{a} | TBD | – |

Transmission ratio of a gearbox for the specific pressing unit | R _{p} | TBD | – |

Transmission ratio of a bevel gear pair for the specific applicator | I11 | TBD | – |

Transmission ratio of a bevel gear pair for the specific pressing unit | I21 | TBD | – |

Transmission ratio of a spur gear pair for the specific applicator | I12 | 1 | – |

Transmission ratio of a spur gear pair for the specific pressing unit | I22 | 1 | – |

Diameter of the driving roller for the specific applicator | D _{1} | 60 | mm |

Diameter of the driving roller for the specific pressing unit | D _{2} | 60 | mm |

Note: TBD: To be determined depending on the selected configuration.

Table 5.Parameter variations caused by uncertainties.

Name | Symbol | Standard deviation | Unit |

Variation of rotation speed of motor for the applicator | N _{a} | 0.5 | rpm |

Variation of rotation speed of motor for the pressing unit | N _{p} | 0.3 | rpm |

Variation of gearbox ratio for the applicator Variation of gearbox ratio for the pressing unit Variation of transmission ratio of flat belt for the applicator | R _{a }R_{p}Ia(1) | 22 ×× 1010−−66 0.03 | – – – |

Variation of transmission ratio of V-belt for the applicator | Ia(2) | 0.02 | – |

Variation of transmission ratio of synchronous belt for the applicator Variation of transmission ratio of flat belt for the pressing unit | Ia(3) Ip(1) | 3 × 10− ^{6}0.02 | – – |

Variation of transmission ratio of V-belt for the pressing unit | Ip(2) | 0.01 | – |

Variation of transmission ratio of synchronous belt for the pressing unit Variation of transmission ratio of a bevel gear pair for the applicator Variation of transmission ratio of a bevel gear pair for the pressing unit Variation of transmission ratio of a spur gear pair for the applicator Variation of transmission ratio of a spur gear pair for the pressing unit Variation of diameter of the driving roller for the applicator Variation of diameter of the driving roller for the pressing unit | Ip(3) I11 I21 I12 I22 D _{1}D _{2} | 2 × 10−−36 222288 ×××××× 101010101010−−−−−66633 | – – – – – mm mm |

where I_{1 }is selected either as I_{11 }or I_{12 }and I_{2 }is selected either as I_{21 }or I_{22}.

When the open interfaces are connected with unknown add-on modules, the labelling speed V_{a}_{ }and the pressing speed V_{p}_{ }can be calculated by

V_{a}_{ },(21)

V_{p}_{ }.(22)

By considering the importance factors of the labelling speed V_{a}_{ }and the pressing speed V_{p}, the weighting factors of the robustness measures for the labelling speed V_{a}_{ }and the pressing speed V_{p}_{ }at each operation configuration state were selected as 0.5 and 0.5, respectively. The overall robustness of the i-th design configuration candidate for the s-th operation configuration state considering the un-adaptable design parameters, I_{a}_{ }and I_{p}, and the interface parameters,

Figure 9.Interactions between platform and add-on modules under operation configuration 7.

Table 6.Input and output parameters of add-on modules M_{1}^{U }andM_{2}^{U}.

Add-on module | Input/output parameter | Symbol | Scope | Unit |

M _{1}U | Rotation speed of the pulley | N _{1}U | [0, 1500] | rpm |

| Diameter of the driving roller | DU _{1} | [30, 150] | mm |

| Gear ratio of the gear pair | I1U | [2, 1, 2/3, 0.5, 0.4] | – |

M _{2}U | Rotation speed of the pulley | N _{2}U | [0, 1500] | rpm |

| Diameter of the driving roller | DU _{2} | [30, 150] | mm |

| Gear ratio of the gear pair | I2U | [2, 1, 2/3, 0.5, 0.4] | – |

I_{1}^{U},D^{U}_{1 },I_{2}^{U }andD^{U}_{2 }, can be calculated by

,(23)

where μ_{a}_{ }and μ_{p}_{ }are the nominal values of V_{a}_{ }and V_{p}, respectively. In this work, μ_{a}_{ }= V_{a}^{T},μ_{p}_{ }= V_{p}^{T}, and σ _{a }and σ _{p }are the standard deviations of V_{a}_{ }and V_{p}, respectively.

In this case study, the overall robustness of the i-th design configuration candidate, R^{(}^{i}^{)}, can be calculated using Equation (9).

In order to improve the robustness of the OAP, the overall performance of labelling machine under seven different operation configuration states should be insensitive to the parameter variations caused by uncertainties. The optimal product design configuration and its associated product/operating parameter values need to be identified to achieve the best overall robustness. Optimisation was employed to identify the best product design configuration candidate and its un-adaptable design parameter values.

In this case study, the configuration optimisation was formulated as

Find : thei-thdesignconfigurationcandidate

Maximise : R = R^{(}^{i}^{)}^{}(24)

where i represents the i-th design configuration candidate and 18,225 is the number of all feasible design configuration candidates.

Parameter optimisation to obtain the un-adaptable design parameters was formulated a:

Find : theun-adaptabledesignparametervaluesI_{a}, andI_{p}

n

Maximise : R(I_{a},I_{p})](25)

Subjectto : 0.1 I_{a}_{ } 10; 0.1 I_{p}_{ } 10

In this work, both the statistical method and the worst-case method were used to calculate the robustness by considering the changes of input/output interface parameters of unknown add-on modules.

In the statistical method, the probabilities of changes of interface parameters are required. In this work, it was assumed that the values of interface parameters D^{U}_{1 }andD^{U}_{2 }follow even distribution between 30 and 150 mm for the s-th operation configuration state, that is, P

P 120. It was also assumed that the values of interface parameter I_{1}^{U }andI_{2}^{U }are discrete ones defined by [2, 1, 2/3, 0.5, 0.4] and follow probabilities of P(2) = P(0.4) = 15%, P(1) = P(0.5) = 20%, and P(2/3) = 30% for the s-th operation configuration state. The robustness R can be calculated using Equations (12) and (13). For the design configuration candidate optimisation, the population size and the maximal generation were selected as 12 and 80, respectively. The predefined threshold crossover probability and mutation probability were selected as 0.65 and 0.7, respectively. The stopping criterion of the genetic programming was predefined as the maximum change of the average overall robustness of the last five generations be less than 1 × 10^{−}^{6}.

In this case study, 26 generations of individuals were generated to achieve the optimal product configuration and its parameter values. The average overall robustness measures of these 26 generations are shown in Figure 10. The un-adaptable design parameter optimisation is also shown in Figure 10. The optimal configuration, the optimal parameter values for this configuration, and the overall robustness measure were obtained as shown in Table 7. In this work, the ratio of the belt transmission for the applicator, I_{a}, was optimised as 2.5 (i.e. the numbers of teeth of the two pulleys for belt transmission mechanism were selected as 25 and 10, and the diameters of the two pulleys were selected as 100 and 40 mm). The ratio of the belt transmission for the pressing unit, I_{p}, was optimised as 4 (i.e. the numbers of teeth of the two pulleys for the belt transmission mechanism were selected as 40 and 10, and the diameters of the two pulleys were selected as 160 and 40 mm).

Figure 10. Optimisation results by using the statistical method. (a) Configuration optimisation based on generic programming. (b) Un-adaptable design parameter optimisation.

Table 7.The optimal design results based on the statistical method.

Item | The optimal configuration, parameters, and robustness |

Configuration | Gearbox for the applicator: type F; belt transmission for the applicator: synchronous belt; gearbox for the pressing unit: type e; belt transmission for the pressing unit: synchronous belt; bevel gear pair in the applicator: type IV; bevel gear pair in the pressing unit: type 1 |

Parameters Robustness | Belt transmission ratio for the applicator, I _{a}_{ }= 2.5 (–)Belt transmission ratio for the pressing unit, I _{p}_{ }= 4.0 (–) The overall robustness, R = 58.0 (–) |

In the worst-case method, optimisation models for different operation configuration states can be established separately according to Table 2. In this case study, 47 generations of individuals were generated to achieve the optimal product configuration and its parameter values. The average overall robustness measures of these 47 generations are shown in Figure 11. The unadaptable design parameter optimisation is also shown in Figure 11. The optimal configurations, the optimal parameter values associated with the configurations, and the overall robustness measures were obtained as shown in Table 8. In this work, the ratio of the belt transmission for the applicator, I_{a}, was optimised as 2 (i.e. the numbers of teeth of the pulleys for belt transmission were selected as 20 and 10, and the diameters of the pulleys for belt transmission were selected as 120 and 60 mm). The ratio of the belt transmission for the applicator, I_{p}, was optimised as 3.6 (i.e. the numbers of teeth of the pulleys for belt transmission were selected as 36 and 10, and the diameters of the pulleys for belt transmission were selected as 180 mm and 50 mm).

Compared with the design results using the worst-case method and the statistical method, we can see that the overall robustness with the worst-case method can maximise the minimal robustness considering all possible values of the input/output interface parameters. The average overall robustness obtained using the worst-case method, however, is lower than the overall robustness achieved through the statistical method.

In the traditional design of a reconfigurable or an adaptable product with closed architecture, only platform and specific add-on modules are considered. Since the different possible values of the

Figure 11. Optimisation results by using the worst-case method. (a) Configuration optimisation based on generic programming. (b) Un-adaptable design parameter optimisation.

Table 8. The optimal design for the open architecture labelling machine with the worst-case method.

Item | The optimal configuration, parameters, and robustness |

Configuration | Gearbox for the applicator: type C; belt transmission for the applicator: synchronous belt; gearbox for the pressing unit: type g; belt transmission for the pressing unit: synchronous belt; bevel gear pair in the applicator: type II; bevel gear pair in the pressing unit: type 3 |

Parameter Robustness | Belt transmission ratio for the applicator, I _{a}_{ }= 2.0 (–)Belt transmission ratio for the pressing unit, I _{p}_{ }= 3.6 (–) The overall robustness, R = 56.0 (–) |

Table 9.The optimal design results obtained using the traditional design method.

Item | The optimal configuration, parameters, and robustness |

Configuration | Gearbox for the applicator: type H; belt transmission for the applicator: synchronous belt; gearbox for the pressing unit: type g; belt transmission for the pressing unit: synchronous belt; bevel gear pair in the applicator: type IV; bevel gear pair in the pressing unit: type 3 |

Parameter Robustness | Belt transmission ratio for the applicator, I _{a}_{ }= 6.0 (–)Belt transmission ratio for the pressing unit, I _{p}_{ }= 5.4 (–)R = 63.3 (–) |

input/output interface parameters for unknown add-on modules are not considered at the product design stage, when new add-on modules are designed and added in the product operation stage, the original design created using the traditional design method is no longer optimal considering both the add-on modules created at the product design stage and the add-on modules created later on at the product operation stage.

Among all product operation configuration states shown in Table 2, only the operation configuration states 1 and 2 are not composed of any unknown add-on modules. In other words, the traditional design can be used to identify the optimal design with the best robustness considering the operation configuration states 1 and 2. The optimal design is shown in Table 9.

In this work, suppose that a new horizontal applicator add-on module and a new horizontal pressing unit add-on module need to be added and the labelling machine will be operated with

Table 10.Input and output interface parameters of new add-on modules M_{13 }and M_{23}.

Add-on module | Input/output parameter | Symbol | Value | Unit |

M13 | Rotation speed of the pulley | N13 | 26.5 | rpm |

| Diameter of the driving roller | D13 | 120 | mm |

| Gear ratio of the spur gear pair | I13 | 1 | – |

M23 | Rotation speed of the pulley | N23 | 26.5 | rpm |

| Diameter of the driving roller | D23 | 120 | mm |

| Gear ratio of the spur gear pair | I23 | 1 | – |

Table 11.Results in the comparative study.

Design method | Robustness of product for operation configuration states 1 and 2 | Robustness of product for operation configuration states 1, 2 and N |

The traditional design The statistical method The worst-case method | R _{T }= 63.3 (σ_{T}_{ }= 10.2 mm/min)R _{S }= 59.0 (σ_{S}_{ }= 16.8 mm/min)R _{W }= 58.1 (σ_{W}_{ }= 18.6 mm/min) | R _{T }= 58.2 (σ_{T}_{ }= 16.4 mm/min)R _{S}_{}14.3 mm/min)R _{W}_{}15.6 mm/min) |

a new operation configuration state, the robustness of the design considering all three operation configuration states is no longer optimal. In this case study, this new operation configuration state is called operation configuration state N. Interface parameters of the two new add-on modules are shown in Table 10. In this table, the values of D_{13}, D_{23}, I_{13}, and I_{23 }were selected based on design experience, and values of N_{13 }and N_{23 }were calculated from the parameters of the platform and add-on modules.

When the two new add-on modules were added, the overall robustness considering all three operation configuration states was lowered. In this work, the same probability values (i.e. 33.33%) were assigned to the three operation configuration states 1, 2, and N for the ease of explanation. The overall robustness is changed from 63.3 to 58.2 as shown in Table 11. To better demonstrate the physical meaning of robustness, the average values of the standard deviations of the labelling speed V_{a}_{ }and the pressing speed V_{p}_{ }for the different designs were also calculated and summarised in Table 11.

The newly developed statistical method and worst-case method were also employed in this comparative study. First, the statistical method and worst-case method were used to obtain the optimal designs as shown in Tables 7 and 8. Then the overall robustness measures considering only operation configuration states 1 and 2 were calculated as shown in Table 11. From this table, we can see that the robustness measures, 59.0 and 58.1, using the statistical method and the worst-case method are lower than the robustness obtained using the tradition method. When the new operation configuration state N with the two new add-on modules is considered, the robustness measures, 59.4 and 58.6, using the statistical method and the worst-case method are higher than the robustness obtained using the tradition design method.

Adaptable design is a new design paradigm that aims to create adaptable products. Among various adaptable products, the OAPs allow new add-on modules with new functions to be designed by third-party vendors and added to the existing products. In this research, an adaptable design method is introduced to design the OAP with robust performance. An OAP is modelled by a platform, add-on modules and interfaces to connect the platform with different add-on modules.

In this work, in addition to the specific add-on modules that need to be designed at the product development stage, the unknown add-on modules that could be added in the future are also considered. The optimal design with the best robustness is achieved through optimisation. Characteristics of this research are summarised as follows:

Open architecture is a good architecture to design adaptable products. The method to use a

platform, add-on modules and open interfaces is effective to model OAPs.

Robustness is a good measure to evaluate the quality of an OAP considering both functional performance measures and their variations.

By considering both specific add-on modules that need to be designed at the product development stage and unknown add-on modules that could be added in the future, the overall robustness of OAP can be improved. In addition, the statistical method and the worst-case method are effective to identify the optimal design.

The multi-level optimisation method is effective to identify the optimal design configuration and its parameter values of an open architecture adaptable product.

Despite the progress, a number of issues need to be further addressed to improve the currently developed method. In this research, only aleatory uncertainties in parameters (i.e. parameter variations caused by uncertainties) are considered. New design methods considering other types of uncertainties such as epistemic uncertainties modelled by fuzzy membership functions need to be developed. In addition, only embodiment design stage is considered in the newly developed method. Since product robustness can also be influenced by selection of design concepts, an integrated approach to design OAPs considering both conceptual design and embodiment design stages needs to be developed.

Disclosure statement

No potential conflict of interest was reported by the authors.

The authors wish to thank the Leading Talent Project of Guangdong Province, China, the Natural Sciences and Engineering Research Council (NSERC) of Canada, and the National Natural Science Foundation of China [grant number 51375287] for providing financial supports to this research.

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