YIN Leilei，ZHU Haihua，SUN Hongwei，LIAO Liangchuang

1.School of Automation，Nanjing Institute of Technology，Nanjing 211167，P.R.China；2.College of Mechanical and Electrical Engineering，Nanjing University of Aeronautics and Astronautics，Nanjing 210016，P.R.China；3.Jiangsu Automation Research Institute，Lianyungang 222006，P.R.China

Abstract: Engineering change management is a special form of problem solving where many rules must be followed to satisfy the requirements of product changes. As engineering change has great influence on the cycle and the cost of product development，it is necessary to anticipate design changes（DCs）in advance and estimate the influence effectively. A process simulation-based method for engineering change management is proposed incorporating multiple assessment parameters. First，the change propagation model is established，which includes the formulation of change propagation influence，assessment score of DC solution. Then the optimization process of DC solution is introduced based on ant colony optimization（ACO），and an optimization algorithm is detailed to acquire the optimal DC solution automatically. Finally，a case study of belt conveyor platform is implemented to validate the proposed method. The results show that changed requirement of product can be satisfied by multiple DC solutions and the optimal one can be acquired according to the unique characteristics of each solution.

Key words：change propagation；simulation；ant colony algorithm；design change solution

0 Introduction

Engineering change management is a special form of problem solving where many rules must be followed to satisfy the requirements of product changes. Triggers of design change（DC）can be in?correct assumption about market conditions，future customer needs and available technology［1-3］. It has been suggested that DCs can consume one-third of the engineering design capacity［4］. The later product changes are detected，the more cost it takes to im?plement them［5］. Thus，it is necessary to anticipate DCs in advance and estimate the risk effectively.De?signers mostly have limited choices of DC solutions with manual forecasting. Available choices may be referring to similar cases or DC solutions with the in?corporation of personal or co-workers’experiences.However，traversing all the solutions and acquiring the optimal one are difficult for unaided designers or design teams.

To address the challenge，researches in the aca?demic can be classified into three areas：DC object，DC relation and change propagation analysis. DCs can be modifications of dimensions，performance in?dices，materials and so on，which are dependent on the specific DC cases. Cohen et al.［6］proposed a change favorable representation（C-FAR）method from the perspective of product entity and its attri?butes. Griffin et al.［7］studied 41 500 changed re?quirements and introduced three types of node mo?tifs of requirements. Yin et al.［8］applied the topolo?gy faces to model geometrical change propagation.Koh et al.［9］drawn on the individual components to estimate the system changeability. However，the de?tailed process of change propagation is not given when an initial change is triggered.

Multiple forms are applied to describe the DC relation，e. g.，design structure matrix，network.Chen et al.［10］constructed the module relations in the form of matrix to analyze the change propaga?tion. Hamraz et al.［11］recorded the relations among multiple entities（i.e.，function，behavior and struc?ture）in the matrices. Network is widely used to rep?resent the design data. Smith et al.［12］organized the relations among function，attribute and structure in the network. Li et al.［13］applied the network to re?cord the mutual relations among components. Refer?ring to the research of Li et al.［13］，the network is in?corporated to demonstrate the product DC relations in the paper.

As change propagation can enlarge the scope and influence，the prediction is the core of engineer?ing change management. Based on the DC rela?tions，computational tools have emerged to aid de?signers to explore possible DC solutions and acquire the optimal one. Koh et al.［14］proposed a prediction method to model the effects of potential change propagation brought by different change options quantitatively. Clarkson et al.［15］developed mathe?matical models to predict the risk of change propaga?tion in terms of change likelihood and impact. Wynn et al.［16］introduced a simulation model to predict re?source requirements and schedule change process risk. Li et al.［17］applied the resource constraint in the prediction of change propagation. Tang and Yin［18］proposed a collaborative change method to analyze the changeability of aircraft assembly tool?ing. Zheng et al.［19］assessed the impact of configura?tion changes in complex product. However，multi?ple indices for the risk analysis of change propaga?tion are rarely studied.

Considering the above problems，this paper proposes a process simulation-based method to pre?dict and acquire the optimal DC solution. Network is applied to detail the product relations. The change propagation model is proposed to predict the possi?ble DC solutions. The improved ant colony optimi?zation（ACO）incorporating the DC characteristics of iteration，change propagation，and learning factor is developed to obtain the assessment scores of DC solutions. And DC solution of the largest score can be regarded as the optimal one for designers’deci?sion-making. A case study is conducted to verify that the proposed method can effectively help de?signers manage the engineering change.

1 Change Propagation Model

1.1 Change propagation influence

In product DC，the initial change is triggered and it can be propagated due to complex product re?lations.The relations are recorded in the form of net?work as shown in Fig.1. In Fig.1，R（Fk，Cn）and R（Ci，Cj）represent the funtion-component and com?ponent-component relatives， respectively. These two types of relations，i.e.，R（Fk，Cn）and R（Ci，Cj），are introduced by

Fig.1 Product change relations

where Fkrepresents the function，and Ci，Cnand Cjrepresent the components. The change likelihood and impact between function and component are de?picted withandwhich implies the possibili?ty and impact of changed component on the func?tion. The component relations are depicted with change likelihoodand change impact

During the change propagation， initiating changed component is modified to satisfy the func?tional requirement. Changed components can further affect other coupled ones. Meanwhile，the affected component can cause related functions to deviate from the optimal status，which implies that more work is required to maintain the performance of af?fected functions. On this basis，the propagation in?fluence of Cion Cjis calculated by

where z is the quantity of influence iteration of Cion Cj，h the quantity of influence iteration of Cjon func?tion Fk，and k the serial number of functions affected by Cj.

1.2 Assessment score of DC solution

Satisfaction of functional change is the target of product DC. A functional change can be realized by different solutions，and each solution is different from others. According to the unique characteristics of each solution，the optimal one can be identified.The changed function can be satisfied by multiple components and the DC of component can be evalu?ated with multiple parameters. For example，the component DC can be assessed with cost，duration，or environment factor. Corresponding to a function，the weightingsof one type of parameter are val?ued and the summation is 1. Besides，the assess?ment valueis introduced to assess the compo?nent influence in the DC process. For example，as?sessment value of motor’s cost is larger than that of blade in terms of duration，then the blade can be giv?en priority in the DC process to cause lower risk.The weightings and values are estimated according to engineer’s experiences，which reflect the product characteristics and engineer’s creativity. On this ba?sis，the assessment score（AS）of components for a DC solution can be formulated as

where DCnis the design change of component Cn，p the serial number of assessment parameter，n the se?rial number of component. For a change propagation path（i.e.，DC solution），the assessment scores of changed components for the corresponding functions are summed. With the proposed assessment score model，all the DC solutions can be assessed for the decision-making of engineers.

2 Optimization of DC Solution

A functional change can be realized by multiple DC solutions.Each DC solution is composed of mul?tiple affected components and requirements. It is necessary to optimize the DC solutions to acquire the least risky one. In this paper，the ACO is ap?plied to optimize the DC solutions. The optimiza?tion process can be vividly demonstrated as shown in Fig.2. A virtual initial node is added in the begin?ning of each change propagation path. With the ACO，the paths are traversed from node C0by all the ants according to the rules of pheromone update and selection probability. Each column represents a DC solution，and the element（Fk，Ci）represents the affected component and function in a propaga?tion step.

Fig.2 Optimization process with ACO

According to Section 1.2， the assessment score with ACO can be formulated by

where ASais the assessment score with the im?proved ACO，and i，j are the components of DC so?lution. The reachability of ant between components can be demonstrated by the change propagation in?fluence. The assessment score for the path travelled by an ant is calculated withwhere wijis the reciprocal of PI(Ci，Cj)，and ? a coefficient ad?justing AS andin the same order of magni?tude.

In order to guide the ant colony to traverse the components，the rules of pheromone update and se?lection probability are introduced and improved，which are formulated by

where ?ρij(c) is the variation of pheromone caused by all the ants in the cth cycle and ρij(c) the amount of pheromone after the cth cycle. μ and τ are the con?centration and volatilization coefficients of phero?mone， respectively. Based on the assessment score，the pheromone is updated iteratively.

The ant’s selection of each step path，i.e.，（Ci，Cj），is dependent on the amount of residual pheromone and change propagation influence，which is formulated by

where α and β are the pheromone and reachability simulation factors，respectively，and G is the collec?tion of next components through which ant a can pass.

As there are many DC solutions，a termination condition is proposed to improve the efficiency of op?timization as shown in Eq.（9）.

where ASH(c) and ASH(c-1) are the highest as?sessment scores with ACO in the cth and the（c-1）th cycles，respectively，and ε is the termination co?efficient.

To automatically acquire the optimal DC solu?tion，an algorithm is proposed to evaluate the DC solutions as shown in Fig.3，which is detailed as fol?lows.

Step 1Initialize parameters and acquire the product relations.

The quantity of ant and travelling cycle are set as n and 0. The first component for the ant to pass is C0. Other parameters are set as follows：?=1，μ=1，τ=0.75，?ρ0j(c)=0，ρ0j(0)=1，α=1，β=1，ASH(0)=0，which implies that the components in the first change propagation step are randomly se?lected.

Step 2Ant（or another ant）selects the next affected component，and the amount of pheromone and selection possibility are updated.

Based on the function-component and compo?nent-component relations，the ith ant selects the next component according to the selection possibili?ty. And the change propagation influence is calculat?ed according to Eq.（3）. Then the amount of phero?mone and selection possibility are updated on the ba?sis of Eqs.（6—8）.

Step 3Judge the optimization process based on the propagation influence.

If the change propagation influence is less than 0.01［9］，go to Step 4；Otherwise go to Step 2.

Step 4Calculate the ASiof the path travelled by ant i.

Calculate the ASiaccording to Eq.（5）. If all the ants have finished passing the change propaga?tion paths，go to Step 5；otherwise，go to Step 2.

Step 5Judge the optimization process based on the termination condition.

If|ASH(c)-ASH(c-1)| ≤ε，go to Step 6；otherwise all the ants start travelling the compo?nents another time and go to Step 2.

Fig.3 Flowchart of the optimization algorithm

Step 6Acquire the optimal DC solution cor?responding to the highest score.

Step 7End of program.

With the proposed method，the change propa?gation paths can be acquired. Meanwhile，DC solu?tions are evaluated comprehensively with the param?eters of cost，duration，etc. In other words，the op?timal DC solution incorporates the balance of multi?ple indices. The DC risk is evaluated in terms of as?sessment score. The higher the score is，the lower the risk is. The DC solution with the highest score is regarded as the basic one for the designers to de?cide and implement the design change process.

3 Case Study

A case study of a belt conveyor platform is car?ried out to demonstrate how the proposed method can assist designers during the early phases of engi?neering change. The belt conveyor platform is sim?plified and the weightings of functions are shown in Table 1. Weightings of components along with the couplings between main functions and components are shown in Table 2. The conversion of electrical energy into rotational energy，the adjustment of force and speed transmission，and the conversion of rotational energy into translational energy are the elicited functions of the platform. Three types of pa?rameters，which are cost，duration and resource consumption，are applied to analyze the DC solu?tions comprehensively. The components are listed according to the functions. Besides，componentcomponent relations（change likelihood and impact）are extracted as shown in Fig.4. Values below the arrow represent the influence relations from the left component to the right one. Values above the arrow represent the opposite relations. Values on the left of the arrow represent the influence relations from the upper component to the lower one. Values on the right of the arrow represent the opposite rela?tions.All the values are evaluated by the senior engi?neers，who have participated in the similar product design. To guarantee the accuracy as far as possi?ble，these engineers are interviewed separately and the results are discussed in a round-table conference.Different opinions must be unified before the next topic.

As the transmission force is not large enough to carry heavy objects，it is necessary to improve the transmission capacity. The transmission module to adjust the force and speed is required to be changed.That is，the changed function is adjustment of force and speed transmission. After that，the affectedcomponents in the first change propagation step are passed by an ant with the same probability. Next，the iteration process of component selection is imple?mented，and the pheromone and selection possibili?ty are updated. Finally，the component chains con?stitute the possible change propagation paths and the corresponding assessment scores are acquired with the proposed algorithm.

Table 1 Parameter weightings of functions

Table 2 Parameter weightings of function components

Fig.4 Component-component relations of conveyor platform

As shown in Fig.5，the assessment results are plotted. It can be seen that the score of the 36th DC solution is the highest and the change propagation path（i.e.，Gear 2→Shaft 2→Coupling 2→Shaft 2→Coupling 2→Roller→Transmission belt）can be acquired，implying that it is the optimal DC solu?tion. It can be a catalytic idea triggering designers to further analyze and decide the actual implementation plan. To the contrary，the 9th DC solution is the riskiest one，which should be avoided as far as possi?ble. Besides，designers should be alert about the DC solutions in the yellow rectangular box，which are the medium risky options.

Compared with the simulation-based method proposed in the research of Ref.［13］，this method combines multiple parameters to comprehensively analyze the DC solution. Besides，the characteris?tics of iteration，learning factor and change propaga?tion are incorporated with the improved ACO.

Fig.5 Assessment results of the belt conveyor platform

4 Conclusions

A process simulation-based method for DC so?lutions is introduced. The purpose is to utilize the existing design information of product to rapidly gen?erate a number of DC solutions and screen out the optimal one in the early DC process. The change propagation model incorporating the iteration influ?ence between functions and components is devel?oped. Multiple product parameters are applied in the assessment score model to rank the DC solutions comprehensively. The solutions can be listed accord?ing to the descending order of the scores and the op?timal one with the highest score can be acquired. An algorithm of scheduling the DC solutions based on the improved ACO is proposed to schedule DCs in advance and estimate the influence effectively.

Next，more complex products will be tested for the proposed method. Considering the concurren?cy of tasks，logic relations of product design should be incorporated in the change propagation process.Furthermore，the efficiency of algorithm execution can be improved with respect to the enormous prod?uct data.Further research is currently underway.