Review on Energy Resilience

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Journal of Manufacturing Systems

journal homepage: www.elsevier.com/locate/jmansys

Resilient adaptive control based on renewal particle swarm optimization to improve production system energy efficiency Jing Zoua, Qing Changb,⁎, Xinyan Oua, Jorge Arinezc, Guoxian Xiaoc a Dept of Mechanical Engineering, Stony Brook University, Stony Brook, New York, 11794, USA b Dept of Mechanical and Aerospace, Engineering University of Virginia, Charlottesville, Virginia, 22904, USA c General Motors R&D, General Motors Corporation, Warren, MI, 48090, USA

A R T I C L E I N F O

Keywords: Manufacturing system Real-time diagnosis Energy efficiency System resilience Particle swarm optimization Resilient adaptive production control

A B S T R A C T

Considerable amount of energy may be wasted due to idleness or constraints from the interactions between the machines and buffers. To increase profits, it is desired to quickly identify the energy waste and properly manage machine operations for reducing this energy waste without jeopardizing system production. In this paper, a real- time system performance diagnostic method is developed using both system physical properties and sensor information to identify this energy waste, and evaluate system resilience against random disruption events. Furthermore, by utilizing the real-time system diagnostic results, a real-time resilient adaptive control policy is developed to improve system profit and energy efficiency, and deliver resilient performance against random disruption events. This control policy uses a novel renewal particle swarm optimization (RPSO) algorithm to update its controller parameters, such that the controller is well adapted to the slowly varying system reli- abilities. A case study is given to demonstrate the effectiveness of the proposed control policy.

1. Introduction

Substantial amount of energy is consumed in manufacturing in- dustry. In 2013, manufacturers in U.S. consumed over 19,000 trillion BTUs, and wasted approximately 1/3 of that energy [1]. Large amount of energy consumption is not directly related to the production of parts, which causes a strikingly low energy efficiency. It is strategically im- portant for manufacturers to reduce energy waste and improve energy efficiency.

Among different approaches for manufacturing system improve- ment, control of production operations, which includes machine hold/ release control and working/hibernating control, is often regarded as one of the most cost-effective ways to improve energy efficiency in manufacturing since it usually does not require major capital invest- ment and has a relatively short payback period [2]. However, the ex- isting manufacturing systems control methods are primarily focused on system productivity, production cost and product quality [3,4]. It is desired to develop a control policy on production operations for im- proving energy efficiency.

To achieve higher system profit, the control policy should not jeo- pardize the production performance. In manufacturing systems, random disruption event is arguably the single most significant

contributor to production inefficiency [5]. The ability of an enterprise to withstand potential high-impact disruptive events is known as resi- lience. Resilience is characterized by the redundant or absorbing cap- ability of the system to the event to “dampen” the corresponding impact [6]. Existing studies on resilience manufacturing control are mostly focused on control of resource allocation (e.g., buffer capacity) [7] and reconfiguration policies [8,9]. In comparison, analysis of real-time machine operation control policies for resilience has received less at- tention [6]. Therefore, to mitigate the impact induced by machine disruption events, system resilience against random disruptions should be evaluated and considered in the control policy design.

In addition, the disruption events are inherently associated with uncertainties. A fundamental understanding of the underlying un- certainties is very important for the design of an effective resilient control policy. However, it is hard to calculate the probability model, since modern manufacturing systems are increasingly complex and their parameters and dynamics may also vary as time goes by. For optimization problems of such systems, evolutionary algorithms such as genetic algorithm and particle swarm algorithm are more hopeful and powerful approaches [10]. Therefore, this research investigates the potential of evolutionary algorithms integrated control policy to achieve better control performance in manufacturing system.

https://doi.org/10.1016/j.jmsy.2018.12.007 Received 12 July 2017; Received in revised form 27 September 2018; Accepted 8 December 2018

⁎ Corresponding author. E-mail addresses: [email protected] (J. Zou), [email protected] (Q. Chang), [email protected] (X. Ou), [email protected] (J. Arinez),

[email protected] (G. Xiao).

Journal of Manufacturing Systems 50 (2019) 135–145

Available online 21 December 2018 0278-6125/ © 2018 The Society of Manufacturing Engineers. Published by Elsevier Ltd. All rights reserved.

T

This research is devoted to address the above issues. The unique contributions of this paper are: 1) developing a real-time system per- formance diagnostic method to evaluate the status of the system with respect to productivity, energy efficiency and resilience against random disruption events; 2) establishing a real-time resilient adaptive control policy based on the real-time system diagnostic results to holistically improve system profit and energy efficiency while ensuring resilient performance against random disruption events; and 3) proposing a novel renewal particle swarm optimization (RPSO) algorithm to update the controller parameters for adapting to the slowly varying system reliabilities.

The rest of the paper is organized as follows: literature review is provided in Section 2. Section 3 introduces the notations and assump- tions. A real-time system performance diagnostic method is developed in Section 4. Section 5 describes the resilient feedback production control policy based on the real-time system diagnostic information. In Section 6, a RPSO algorithm based resilient adaptive production control policy is proposed. A case study is shown in Section 7. Section 8 sum- marizes conclusions and future research.

2. Literature review

Extensive research has been devoted to production system design, schedule plan and control to improve system productivity and product quality, and reduce production cost [11–14]. Tajan et al. study the production control of the serial processor by considering the processing time window between the upstream processor and the downstream batch processor [11]. This control policy manages the production and release time of the jobs to reduce rework cost and production cycle time. Wolf et al. establish a network flow model to evaluate multistage recycling system performance and identify optimal system configura- tions under flexible conditions [15]. In [16], a hedging point produc- tion control policy is developed to minimize the average inventory or backlog cost per part. Due to the large dimension of manufacturing systems, evolutionary algorithms, such as genetic algorithm, have also been utilized in production system design and control [17–19]. Zhang et al. develop a hybrid evolutionary algorithm to solve the stochastic multiobjective assembly line balancing problem [18]. A hybrid opti- mization approach based on differential evolutionary algorithm and receptor editing property of immune system for milling operation op- timization is proposed in [19]. However, these control methods are mainly focused on system production improvement and production cost reduction without explicitly considering energy consumption.

There is an increasing interest in manufacturing system energy ef- ficiency optimization and control [2,3,20–29]. Most of the previous studies in this area focus on isolated or mutually independent process or machine [23–26]. Dietmair et al. develop a modeling framework to describe tool machine energy consumption [23]. Machine energy con- sumption prediction and optimization using this model have been de- monstrated. Kiss et al. proposes a novel selection scheme of energy efficient distillation technologies focusing on heat pumps [26]. The type of separation tasks, product flow and specifications, operating pressure, difference in boiling points, reboiler duty and its temperature level are the main selection criteria of the scheme. This scheme will lead to major time and resources savings in the design of eco-efficient processes. However, in manufacturing systems, the operation status of each machine is determined not only by itself, but also by other ma- chines and buffers. Hence, these interactions within manufacturing systems should be considered for effective energy control.

Some effort has been spent to improve energy efficiency at the system level [2,3,20–22,27–29]. Chen et al. evaluate the performance of Bernoulli serial lines with time-dependent machine efficiencies by using system transient performance analysis method, and develop a production scheduling plan through a greedy algorithm-based proce- dure to reduce system energy consumption [2]. Brundage et al. propose a control methodology to improve system profit and reduce energy

consumption by inserting energy opportunity windows at different machines [3]. Discrete event or agented based simulation methods have also been utilized for developing energy control policies at system level [28,29]. Frigerio et al. propose a framework to integrate different control policies for switching on/off machine based on part flow and buffer conditions [28]. Discrete event simulation model of job arrivals and status transitions are built. The policy parameters to minimize the requested machine expected energy are solved analytically based on the model and job arrival time distribution. However, these studies mainly rely on heuristic rules, simulation-based methods or steady state ana- lysis to improve the long-term expected performance.

Existing research on system resilience is primarily focused on re- source allocation control and plans [[7,30–33], and reconfiguration mechanisms [8,9,34]. Battini et al. conduct a simulative study for serial production line storage capacity allocation and provide a new experi- mental cross matrix to determine the optimal buffer size for reliability performance [30]. Bruccoleri et al. develop an object-oriented high- level control structure for real-time error handling [34]. This structure combines the reconfiguration technology for error handling and the existing reactive scheduling system. These studies mostly make optimal plan and design based on steady state analysis and long-term perfor- mance measures, which are not applicable to real-time monitoring and decision-making due to the fundamental differences between system long-term steady-state behavior and real-time behavior [5]. In com- parison, the analysis of real-time machine operation control policies for resilience has received less attention [6,35]. Hu et al. develop the real- time resilient control policy for a simple type of serial network with advance notice of disruptions [6]. By controlling the operation at each machine, the buffer content will be changed to a desired value to reduce the impact by the foreseen disruption. However, these control methods are designed for, and have limited application only to, the systems with foreseen disruptions or systems with Bernoulli machines, and there is a lack of real-time resilient control of machine operations for general serial lines. Moreover, time-variant reliabilities are usually not con- sidered in the design of the existing resilient control methods. Hence, their control performance will be jeopardized since system reliabilities commonly vary with time in reality.

3. Notations and assumptions

In this paper, we adopt continuous flow models because the pro- duction dynamics can be conveniently described by integral or differ- ential equations, and the properties derived from such models can be generally applied to discrete systems [5,36]. Continuous flow models assume the quantity of jobs in the buffer varies continuously from zero to its capacity. A manufacturing system typically consists of a series of machines separated by finite buffers. Consider a serial production line consisting of M machines (represented as rectangles) and M 1 buffers (represented as circles) as shown in Fig. 1, the following notations are adopted:

• Si denotes the ith machine, where i M1 ; • Bi denotes the ith buffer, where i M2 ; • Ti denotes the base cycle time (rated cycle time) of machine Si, where i M1 ; • s t( )i denotes the actual processing speed of machine Si at time t; • b t( )i denotes buffer level of buffer Bi at time t; • Ki denotes the power rating of machine Si; • cp denotes the profit per part produced; • ce denotes the electricity rate;

Fig. 1. General serial production line.

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• ci denotes the inventory cost per part per day; • = = … = …e j t d i n j M( , , ), 1, 2, , 1,2, , ,i i i represents a disruption event that machine Sj is down at time ti for di time period; • E denotes a sequence of disruption events, i.e., = …E e e[ , , ]n1 ; • MTBFi and MTTRi denote mean time between failure and mean time to repair of machine Si, respectively.

We make the following assumptions:

1) Each buffer …B B B, , , M2 3 has a finite capacity. With abuse of no- tation, …B B B, , , M2 3 are also used to denote the maximum capacity of the buffer;

2) Machine = …S i M, 2, ,i , is partially starved if the following con- ditions hold: i) machine Si is up; ii) its immediate upstream buffer Bi is empty; iii) its actual processing speed is smaller than its rated speed, i.e., <s t T( ) 1/i i;

3) Machine = …S i M, 2, ,i , is completely starved if the following conditions hold: i) machine Si is up; ii) its immediate upstream buffer Bi is empty; iii) its actual processing speed reduces to 0, i.e.,

=s t( ) 0i ; 4) Machine = …S i M, 1, , 1i , is partially blocked if the following

conditions hold: i) machine Si is up; ii) its immediate downstream buffer +Bi 1 is full; iii) its actual processing speed is smaller than its rated speed, i.e., <s t T( ) 1/i i;

5) Machine = …S i M, 1, , 1i , is completely blocked if the following conditions hold: i) machine Si is up; ii) its immediate downstream buffer +Bi 1 is full; iii) its actual processing speed reduces to 0, i.e.,

=s t( ) 0i ; 6) A machine will run at its rated speed if it is operational and is

neither (partially) starved nor blocked; 7) The first machine S1 is never (partially) starved and the last ma-

chine SM is never (partially) blocked; 8) Each machine Si will run at its power rate Ki when up and will

consume no power when switched off; 9) Machine warm-up time and cool-down time are not considered for

the ease of math expression; 10) S Mk* denotes the slowest machines, i.e.,

= = …

M T k Marg max ( ), 1k i i M

*

1, , ;

11) S M * denotes the slowest machine that is closest to the end-of-line machine SM, since there might be one or multiple slowest machines in a system as described in 10). It is also denoted as the last slowest machine;

12) Manufacturing system reliability or machine reliabilities vary slowly but continuously over time.

4. System resilience and energy efficiency

In modern control theory (also known as model-based control), the first step is to model the system or identify the system model [37]. A manufacturing system is a stochastic dynamic system, and is usually modeled by state space equation of the form [38]

=X F X U Wt t t( ( ), ( ), ( ) ) (1)

where X t R( ) n is the states, U t R( ) m is the known input or control, and W t( ) is the unknown disturbance or noise at time t.

Usually a measurement equation is also utilized to model the output Y t R( ) l

=Y H X Vt t t( ) ( ( ), ( ) ) (2)

where Y t( ) is the observation or output, and V t( ) is the unknown measurement error or noise.

We do not consider the measurement error or noise in this paper. Hence, Eq. (2) can be reorganized as

=Y H Xt t( ) ( ( ) ) (3)

In the context of a manufacturing system, the corresponding para- meters are defined as

• = …X t X t X t X t( ) [ ( ), ( ), , ( ) ]M1 2 , where X t( )i is the production count of machine Si up to time t; • = …F f f f(*) [ (*), (*), , (*) ]M1 2 , where f (*)i represents the dynamic function for machine Si; • = …W t W t W t W t( ) [ ( ), ( ), , ( ) ]M1 2 , where W t( )i describes whether machine Si suffers from a disruption event at time t. W t( )i is directly related to E. If =Ee s t e i t d, . . ( , , )k k k k and +t t t d[ , ]k k k , then =W t( ) 1i . Otherwise, =W t( ) 0i ; • = …U t u t u t u t( ) [ ( ), ( ), , ( ) ]M1 2 , where u t( )i denotes the input or control at machine Si at time t. u t( )i is denoted by the binary vari- able as

=u t switch off machine S at time t switch on machine S at time t

( ) 0, 1,i

i

i

Let = …t i M( ), 1, ,i , represent the status of machine Si at time t, which is either up ( =t( ) 1i ) or down ( =t( ) 0i ). It is not hard to see that machine Si is up at time t only if =u t( ) 1i and =W t( ) 0i , i.e.,

=t u t W t( ) ( ) (1 ( ) )i i i . However, due to the complex nature of manufacturing systems, it is

hard or even impossible to obtain closed-form solutions for manu- facturing system dynamic behavior. In pursuit of higher production efficiency, resilience, and profit, we develop the following data-driven methods for production system energy efficiency and resilience iden- tification to aid real-time production control.

4.1. Resilience against random disruption events

In manufacturing systems, disruption events at different machines will have different impact on system performance. From our previous studies, we have obtained knowledge on disruption events’ impact. Any stoppage of the last slowest machine S M * contributes to the production loss at all machines in the line. This loss of production at all machines can be interpreted as the production loss of the whole production line [5]. Note that the stoppage includes not only the disruption events at machine S M * due to failure, but also the temporary stoppage due to blockage or starvation. Definition 1 describes the real-time system re- silience against random disruptions.

Definition 1. The resilience of a machine Si at time t, denoted as R t( )i , is the ability of machine Si to withstand a potential disruption event happening on Si without causing permanent production loss at the end- of-line machine based on the current machine and buffer status, i.e.,

= ={ }

R t d s t T d s d s e d T

T d

( ) sup 0: . . ( ), ( ) ( ; ) ,

( )

i T

M T

M *

0 0

*

where s e d( ; )T M0 and s d( ) T

M0 are the production volume of the end-of-line machine SM at time T, with and without disruption event

=e i t d( , , ), respectively. T d( )* signifies the potential dependency of T * on d.

Furthermore, R t( ) is system resilience which includes each ma- chine, and = = …R t R t i M( ) { ( ), 1, , }i .

R t( )i is defined as a system ability to withstand disruptions on machine Si, and is determined by the location of machine Si and levels of buffers between machine Si and S M *. When considering only the next disruption event on machine Si, R t( )i can be evaluated based on system structure.

It is known that machine Si will starve or block the slowest machine S M * when all buffers between machine Si and S M * are empty (for <i M *) or full (for >i M *). In addition, any stoppage of the last slowest ma- chine S M * contributes to system permanent production loss with a rate of T1/ M *. Hence, R t( )i is the longest stoppage at machine Si at time t

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that does not starve or block machine S M *, which can be evaluated as following:

1 For <i M *,

= + > = = + = +

R t d s t b t d T b t( ) sup 0: . . ( ) 0 ( )i k i

M

k M k i

M

k 1

*

* 1

*

2 For =i M *,

=R t( ) 0i

3 For >i M *,

= + <

=

= + = +

= +

R t d s t b t d B

T B b t

( ) sup 0: . . ( )

( ( ) )

i k M

i

k k M

i

k

M k i

M

k k

* 1 * 1

* 1

*

To summarize the above, we have

= <

= >

= +

= +

R t T b t m M

m M T B b t m M

( ) ( ), *

0, * ( ( ) ), *

i

M k m M

k

M k M m

k k

* 1 *

* * 1 (4)

Furthermore, the corresponding system permanent production loss caused by this single disruption event, denoted as PL, can be calculated by [39]

=PL d R t T

max ( ) , 0i M *

where d is the duration of this disruption event. From Eq. (4), we can obtain the maximum value of R t( )i , denoted as

Rimax, which is

= <

= >

= +

= +

R T B m M

m M T B m M

, * 0, *

, * i max

M k m M

k

M k M m

k

* 1 *

* * 1 (5)

4.2. Energy waste due to machine and buffer interactions

This section discusses the energy efficiency of multi-stage manu- facturing systems. Considerable amount of energy is wasted in manu- facturing systems due to idleness or constraints from the interactions between the machines and buffers. The following proposition is in- troduced to identify such deterioration in manufacturing system energy efficiency.

Proposition 1. For a realized production process subject to a sequence of disruption events = …E e e[ , , ]n1 and suppose + <

= … t d Tmax { }

l n l l

1, , ,

there will be energy waste if and only if (partial) starvation or blockage occurs within T[0, ) at any machine Si.

Proof. We first prove the necessity of Proposition 1. According to assumptions 2)-5), and 8), when machine …S i M, {1, , }i , is (partially) starved or blocked, its actual processing speed is smaller than its rated speed T1/ i. On the other hand, the power consumption rate of machine Si is still Ki. Therefore, certain amount of energy is wasted at machine Si due to the interactions between the machines and buffers. Consequently, there will be energy waste if (partial) starvation or blockage occurs within T[0, ) at any machine Si. Necessity is proved.

Now, assume there is no (partial) starvation or blockage within T[0, ) at any machine. In this case, each machine = …S i M, 1, ,i , will

process at its rated speed T1/ i with the power consumption rate of Ki.

Hence, at each machine Si, there is no energy waste due to the inter- actions between the machines and buffers. Thus there will be no energy waste if no (partial) starvation or blockage occurs within T[0, ) at any machine. This is equivalent to the statement that there will be energy waste only if (partial) starvation or blockage occurs within T[0, ) at any machine Si. Sufficiency is proved.

According to Proposition 1, any (partial) starvation or blockage will impact system energy efficiency.

5. Resilient control policy

This section presents the real-time resilient feedback control meth- odology. A control of switching on or off a machine is adopted in this paper, which can be alternatively seen as speeding up or slowing down the machine. This control policy aims at reducing system production cost and energy waste without jeopardizing system resilience and avoiding frequently switching on and off machines. Hence, the control policy will manage operation at each machine to minimize the real-time control cost function:

= + + +C t C t C t C t C t( ) ( ) ( ) ( ) ( )EW PL R SW

where, C t( )EW represents the real-time cost of energy waste, which can be measured by the corresponding cost of energy waste within a unit time based on the current rate of energy waste; C t( )PL is the real-time cost of system production loss, which is calculated as the corresponding cost of system production loss within a unit time with respect to the current rate of system production loss; C t( )R is the real-time cost related to system resilience R t( ); and C t( )SW stands for the status switching cost at time t, which accounts for the potential damage to the machine by switching it on and off, and extra energy cost when ramp up a machine from off to on.

The real-time control cost function utilizes the information of the current rate of system production loss, real-time resilience and the current rate of energy waste. These information are obtained by using the real-time diagnostic methods in Section 4 and real-time sensor data of buffer levels and disruption events.

Due to the complexity in manufacturing systems, no explicit eva- luation method is available to calculate C t( )R . Furthermore, the un- derlying relationship between C t( )EW and C t( )R are also hard to solve. Therefore, the following control policy is proposed to reduce the value of the real-time cost function C t( ).

According to Proposition 1, any (partial) starvation or blockage will cause energy waste (with certain rate) and potentially decrease system energy efficiency. Hence, to minimize C t( )EW , the control policy should strategically switch the machines on and off to avoid (partial) starva- tion and blockage as much as possible. Note that machine

…S i M, {1, , }i , can be (partially) starved or blocked only when its immediate upstream buffer is empty or its immediate downstream buffer is full. Therefore, to avoid (partial) starvation and blockage, machine S i M,i *, will be switched off when its upstream buffer is empty or its downstream buffer is full.

According to the analysis in Section 4.1 any stoppage of the slowest machine S M * will lead to permanent production loss with a rate of T1/ M * [5]. To minimize C t( )PL , the control policy should avoid switching off the slowest machine S M *.

The real-time cost C t( )R is closely related to machine resilience values R t( ). With bigger values in R t( ), a manufacturing system will have higher resilience, and the impact of random disruption events can be mitigated, and thus the value of C t( )R will be smaller. It is clear from Eq. (4) that R t( ) is closely related to the system real time status. However, as mentioned above, no explicit evaluation method is avail- able to calculate C t( )R , and the explicit relationship between C t( )R and C t( )SW is unknown. To derive the resilient control policy and obtain an acceptable tradeoff between C t( )R and C t( )SW , a set of predefined de- sired system resilience threshold values = …r r r r R i{ , , }, ,M i imax1 is determined through the use of intuition and previous experience. To

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achieve the required resilience, the control policy will coordinate the production of each machine so that = …R t r i M( ) , 1, ,i i .

In addition, the control policy should avoid abnormal high value of C t( )SW caused by frequently switching on and off machines. Therefore, a “waiting time window” is selected based on real situation. If ma- chine = …S i M, 1, ,i , is switched off (or on) at time t, then within

+t t[ , ], it should not be switched back on (or off). To summarize the above discussion, a resilient feedback control

policy is formulated to regulate the switching on/off of machines as shown in Fig. 2.

However, these estimated values of …r r, , M1 based on intuition and previous experience are not always reliable, and may not be well adapted to system dynamics. To achieve better control performance, it is necessary to establish a solution methodology for finding the desired values of r. This will be discussed in the next section.

6. RPSO algorithm based resilient adaptive control policy

The search of desired control parameters r is a nonlinear pro- gramming (NP) problem since manufacturing systems are nonlinear dynamic systems. Conventional NP problem solution methods such as gradient descent, Newton's method, subgradient projection methods and interior-point methods require the system to be differentiable so that the convergence to global optimum can be guaranteed. Since manufacturing systems are non-differentiable, these conventional so- lution methods cannot be applied to our production control parameter optimization problem. Heuristic optimization techniques such as ge- netic algorithms, simulated annealing and PSO can be used to solve such problems. Compared to single-point heuristic techniques such as simulated annealing and tabu search, PSO provides higher convergence speed. In addition, PSO has less computational complexity and provides better performance than GA [10]. In our optimization problem, the search space can be very big. Hence, these advantages of PSO can help us find the desired r more efficiently and quickly. In this section, an adaptive production control policy is developed. This control policy uses a novel RPSO algorithm to update the predefined desired system

resilience threshold values r, such that the overall system profit and energy efficiency can be improved, and the performance of the con- troller will not deteriorate as time goes by. We first introduce the RPSO algorithm.

6.1. Renewal particle swarm optimization algorithm

Particle swarm optimization (PSO) algorithm is a population based stochastic optimization algorithm inspired by the simulation of social behavior, specifically bird flocking. In PSO, the potential solutions, called “particles”, fly through the search space by following the current optimum particles [10].

PSO algorithm is initialized with a group of random particles. In every iteration, each particle is updated according to corresponding particle’s experience and the particle’s companions’ experience. The fitness of every particle can be assessed based on the cost function of optimization problem. At each iteration n, the velocity of every particle can be obtained as follows:

+ = + +v v pbest p gbest pn w n c r n n c r n n( 1) ( ) ( ( ) ( ) ) ( ( ) ( ) )i i i i i1 1 2 2 (6)

where p n( )i is the position of the particle i in the nth iteration, pbest n( )i is the best previous position of the particle i, gbest n( ) is the best po- sition among all the particles in nth iteration, w is the inertia weight which determines the impact of the previous velocity on the new ve- locity, r1 and r2 are two random values in the range [0,1], c1 and c2 are the cognitive and social scaling parameters, respectively. Upon acquiring the velocities, the position of every particle is updated by

+ = + +p p vn n n( 1) ( ) ( 1)i i i (7)

The PSO algorithm performs repeated applications of the update Eqs. (6) and (7) until the predefined maximum iterations or minimum error criteria is achieved.

Compared to genetic algorithm (GA), standard PSO (SPSO) is easier to implement since it does not involve many of GA operators such as mutation, crossover, and the selection operator [40]. SPSO as a multi- point technique also has higher convergence speed compared to single- point heuristic techniques such as simulated annealing and tabu search. However, manufacturing systems are characterized by their stochastic and complex dynamics, and time-variant reliabilities. Therefore, when applied to manufacturing systems, SPSO is easy to fall into local op- timum, and the corresponding results may be less effective as time goes by. In addition, the cost function may also be a stochastic function. Motivated by the aforementioned challenges, a novel RPSO algorithm is developed. In the RPSO algorithm, Eqs. (6) and (7) are still utilized to update particle positions at each iteration. Different from SPSO algo- rithm, a renewal rule is added in the RPSO algorithm and will be executed in every m iteration to ensure that the current best position gbest *( ) is saved in a selected particle while other particles start the search at new random initial positions. By applying the renewal rule, the particles will not be trapped to local optimums or global optimum that may have deteriorated performance as time goes by. Details of this RPSO algorithm are shown as following.

1 Particle

In this RPSO algorithm, each particle is a vector consisting of M values. The corresponding particle position p n( )i represents a candi- date solution of = …r r r{ , , }M1 .

2 Cost/Fitness function pf n( ( ) )i

In this paper, the main purpose of production control is to improve the overall system profit. Therefore, we use this profit as the cost function of the RPSO algorithm. To evaluate the cost function and the effectiveness of the proposed control policy, we analyze the profit and

Fig. 2. Flow chart of the resilient control policy.

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energy economics of the manufacturing system.

a) System profit and energy economics analysis

Let ta and tb denote two time instants and <t ta b. To analyze the system profit, we first define the following terms: Under the resilient control policy in Section 5 with a set of predefined system resilience thresholds as =r p n( )i ,

• pProfit n t t( ( ), [ , ) )i a b denotes the corresponding system profit within t t[ , )a b ;

• pTR n t t( ( ), [ , ) )i a b denotes the corresponding total revenue within t t[ , )a b ;

• pTC n t t( ( ), [ , ) )i a b denotes the corresponding total cost within t t[ , )a b ; • pPC n t t( ( ), [ , ) )i a b denotes the corresponding system production count within t t[ , )a b ; • pEC n t t( ( ), [ , ) )i a b denotes the corresponding total cost of energy consumption within t t[ , )a b ; • pIVC n t t( ( ), [ , ) )i a b denotes the corresponding total inventory cost within t t[ , )a b ; • pT n t t( ( ), [ , ) )iju a b denotes the corresponding time machine Sj is up within t t[ , )a b ; • pIL n t( ( ), )i denotes the corresponding total inventory level of the production line at time t; • pb n t( ( ), )il denotes the corresponding buffer level of buffer Bl at time t.

The system profit within t t[ , )a b is formulated as the difference be- tween the total revenue and the total cost.

=

=

p p p

p p

p

Profit n t t TR n t t TC n t t

PC n t t c EC n t t

IVC n t t

( ( ), [ , ) ) ( ( ), [ , ) ) ( ( ), [ , ) )

( ( ( ), [ , ) ) ) ( ) ( ( ), [ , ) )

( ( ), [ , ) )

i i i

i i

i

a b a b a b

a b p a b

a b (8)

where cp is the profit per part produced. The cost of energy consumption in t t[ , )a b is calculated as

= =

p pEC n t t c K T n t t( ( ), [ , ) ) ( ( ), [ , ) ) ($)i ia b e j

M

j j u

a b 1 (9)

where ce is the electricity rate, and Kj is the power consumption rate of machine Sj.

The total inventory level of the production line at time t, i.e., pIL n t( ( ), )i , is evaluated as

= =

p pIL n t b n t( ( ), ) ( ( ), )i i l

M

l 2 (10)

The total inventory cost in t t[ , )a b is then calculated as

=p pIVC n t t c IL n t dt( ( ), [ , ) ) ( ( ), ) ($)i ia b i t t

a

b

(11)

where ci is the inventory cost per part per day. Inserting Eqs. (9)–(11) into Eq. (8) provides

=

=

p p

p

p

Profit n t t PC n t t c

c K T n t t

c IL n t dt

( ( ), [ , ) ) ( ( ( ), [ , ) ) ) ( )

( ( ), [ , ) )

( ( ), ) ($)

i i

i

i

a b a b p

e j

M

j j u

a b

i t

t 1

a

b

(12)

• Using system profit as cost function In the RPSO algorithm, the particle positions are updated every ,

where is a time interval. Then the fitness of each particle in the nth iteration can be evaluated as the system profit within n n[ ( 1) , ).

=p pf n Profit n n n( ( ) ) ( ( ), [ ( 1) , ) )i i (13)

Due to the complex dynamics of manufacturing systems, there is no closed-form expression for pProfit n n n( ( ), [ ( 1) , ) )i . Therefore, it will be evaluated through simulation using the sensor data of buffer levels at time =t n( 1) (referred to as starting buffer levels), and random disruption events within the time interval n n[ ( 1) , ).

For >n n1, > >p p p pP f n f n f n f n( ( ( ) ) ( ( ) ) | ( ( ) ) ( ( ) ) )i j i j1 1 is the conditional probability of >p pf n f n( ( ) ) ( ( ) )i j given

>p pf n f n( ( ) ) ( ( ) )i j1 1 . It is noted that the cost function pf n( ( ) )i is a stochastic function. To address this issue, we first introduce Proposition 2 to describe the relationship between and

> >p p p pP f n f n f n f n( ( ( ) ) ( ( ) ) | ( ( ) ) ( ( ) ) )i j i j1 1 .

Proposition 2. For a realized production process, suppose >n n1, =p pn n( ) ( )i i 1 , and =p pn n( ) ( )j j 1 . In general,

> >p p p pP f n f n f n f n( ( ( ) ) ( ( ) ) | ( ( ) ) ( ( ) ) )i j i j1 1 increases with increase in .

Proof. We divide n n[ ( 1) , )1 1 into K smaller time intervals of length , i.e., = K . And

= + + +

= =

p p

p

f n Profit n n k n k

K n n

( ( ) ) ( ( ), [ ( 1) , ( 1) ( 1) ) )

( ( ), )

i i

i

k

K

1 0

1

1 1 1

1 1 (14)

where

= + + +=p

p n n

Profit n n k n k K

( ( ), ) ( ( ), [( 1) , ( 1) ( 1) ) )

i ik

K

1 1 0 1

1 1 1

is an estimation of the expected value of +pProfit n k k( ( ), [ , ( 1) ) )i 1 , denoted as pµ n( ( ) )i 1 , based on the samples in n n[ ( 1) , ( 1) )1 1 .

It is noted that larger sample size generally leads to increased estimation precision. By increasing , more samples of

+pProfit n k k( ( ), [ , ( 1) ) )i 1 are included, and p n n( ( ), )i 1 1 and p n n( ( ), )j 1 1 as the estimations of pµ n( ( ) )i 1 and pµ n( ( ) )j 1 are normally

more precise. Thus, in general, >p pP µ n µ n( ( ( ) ) ( ( ) )i j1 1 >p pn n n n| ( ( ), ) ( ( ), ) )i j1 1 1 1 increases with the increase in . Similarly,

one can also show that when increases, within the time interval n n[ ( 1) , ), p n n( ( ), )i 1 and p n n( ( ), )j 1 can generally give more

precise estimations of pµ n( ( ) )i 1 and pµ n( ( ) )j 1 . Hence, in general, > >p p p pP n n n n µ n µ n( ( ( ), ) ( ( ), ) | ( ( ) ) ( ( ) ) )i j i j1 1 1 1 increases with in-

crease in . Noted that >p pP n n n n( ( ( ), ) ( ( ), )i j1 1 > = >

> >

>

p p p p

p p p p

p p

n n n n P n n n n

µ n µ n P µ n µ n

n n n n

| ( ( ), ) ( ( ), ) ) ( ( ( ), ) ( ( ), )

| ( ( ) ) ( ( ) ) )* ( ( ( ) ) ( ( ) )

| ( ( ), ) ( ( ), ) )

i j i j

i j i j

i j

1 1 1 1 1 1

1 1 1 1

1 1 1 1 Therefore, the rising of also in general causes

> >p p p pP n n n n n n n n( ( ( ), ) ( ( ), ) | ( ( ), ) ( ( ), ) )i j i j1 1 1 1 1 1 to increase. It is assumed in Proposition 2 that =p pn n( ) ( )i i 1 and =p pn n( ) ( )j j 1 . According to Eq. (14), we have =p pf n K n n( ( ) ) ( ( ), )i i1 1 1 ,

=p pf n K n n( ( ) ) ( ( ), )j j1 1 1 , = =p p pf n K n n K n n( ( ) ) ( ( ), ) ( ( ), )i i i 1 , and = =p p pf n K n n K n n( ( ) ) ( ( ), ) ( ( ), )j j j 1 . Thus, in general,

> > = >p p p p p pP f n f n f n f n P n n( ( ( ) ) ( ( ) ) | ( ( ) ) ( ( ) ) ) ( ( ( ), ) (i j i j i j1 1 1 >p pn n n n n n( ), ) | ( ( ), ) ( ( ), ) )i j1 1 1 1 1 increases with increase in . ■

According to Proposition 2, >n n1, if is large enough, and =p pn n( ) ( )i i 1 and =p pn n( ) ( )j j 1 , then >p pP f n f n( ( ( ) ) ( ( ) )i j

>p pf n f n| ( ( ) ) ( ( ) ) )i j1 1 will be close to 1 in most cases. Therefore, by choosing a large enough and comparing their fitness values, a rela- tively reliable estimation of the rankings of all particles can be ob- tained. However, if is too big, then the particles will update much less frequently. Thus more data is required to obtain the gbest n( ) that can deliver satisfactory production performance.

Remark 1. Assumption 8) in Section 3 assumes that machine Si will run at its power rate Ki when up and will consume no power when switched off. It is noted that our control scheme can adopt more realistic scenarios such as lower power consumption rate for a machine when idled. Parameters in the cost/fitness function can be easily adjusted to

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140

accommodate such scenario. For example, assume that machine Si will run at a lower power rate <K K K,i i i, when it is up and is (partially) starved or blocked. In this case, we only need to modify the calculation equation of pEC n t t( ( ), [ , ) )i a b , i.e., Eq. (9), as follows to reflect this change in machine power rate.

= + =

p p pEC n t t c K T n t t K T n t t( ( ), [ , ) ) { ( ( ), [ , ) ) ( ( ), [ , ) ) }i i ia b e j

M

j j np

a b j j p

a b 1

where pT n t t( ( ), [ , ) )ij np

a b denotes the corresponding time that machine Sj is up and is neither (partially) starved or blocked within t t[ , )a b ; and

pT n t t( ( ), [ , ) )ij p

a b denotes the corresponding time that machine Sj is up and is (partially) starved or blocked within t t[ , )a b .

However, a reasonable value of Ki depends on additional informa- tion or assumptions. For example, one may need to know the re- lationship between machine power rate and processing speed, which may vary based on the power consumption characteristics of each machine. Therefore, assumption 8) is adopted to avoid additional spe- cifications and discussion. If additional information is available, as- sumption 8) can be relaxed to adopted more general and realistic sce- narios.

3 RPSO algorithm

For the ease of math expression and analysis, we introduce Definition 2.

Definition 2. The original manufacturing system with no production control is defined as a special case of the resilient production control system with = + … +r R R{ 1, , 1}max Mmax1 .

Let = + … +p n R R n( ) { 1, , 1},max Mmax1 1 , and >n n. Assume is large enough. Based on Definition 2, pf n( ( ) )1 is the system profit within n n[ ( 1) , ) when there is no production control. It is noted that the positions of other particles are restricted by the range of r, i.e.,

p n R j i0 ( ) , , 1i j

j max , where p n( )i

j is the jth element in p n( )i . According to Proposition 2, we have

gbest p gbest pP f n f n f n f n( ( ( ) ) ( ( ) ) | ( ( ) ) ( ( ) ) )1 1 , where gbest n( ) = gbest n( ), is close to 1 in most cases, i.e., the resilient control policy with =r gbest n( ) will improve system profit most of the time. Moreover, to minimize the possible profit impact in rare cases, the concept of inaccurate estimation of gbest n( ) is introduced as follows.

Definition 3. An estimation of gbest n( ) is defined as “inaccurate estimation” if >n n, such that <gbest pf n f n( ( ) ) ( ( ) )1 , where

=gbest gbestn n( ) ( ) and = = + … +p pn n R R( ) ( ) { 1, , 1}max Mmax1 1 1 .

In other words, an estimation of gbest n( ) is identified as inaccurate estimation when gbestProfit n n n( ( ), [ ( 1) , ) ) is smaller than that of the manufacturing system with no control. Any inaccurate estimations of gbest n( ) can be detected according to Definition 3, and saved to an inaccurate estimation set, denoted by . To minimize the corre- sponding impact on system profit, we avoid any further use of these inaccurate estimations in in the resilient production control system.

Assume the change in manufacturing system reliability is slow but continuous. To avoid falling into local optimum and adapt to the time- variant machine reliabilities, a renewal rule is designed as following.

Renewal rule: in every m iterations, set p n( )1 = + … +R R{ 1, , 1}max Mmax1 and =p gbestn n( ) ( )2 , and randomize the positions and clear pbest n( )i for all other particles.

This renewal rule ensures that = + … +p n R R( ) { 1, , 1}max Mmax1 1 and the current best particle position is sustained while other particles re- start the search at new random initial positions. Therefore, by applying the proposed renewal rule, the particles will not stick to a local op- timum or the global optimum position that may have deteriorated performance as time goes by. Meanwhile, we will still have at least one relatively good position after each renewal.

According to the above analysis, the RPSO algorithm is formulated as shown in Fig. 3.

6.2. Adaptive control using the RPSO algorithm

In this part, we develop a RPSO algorithm based resilient adaptive

Fig. 3. Flow chart of the RPSO algorithm.

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control policy. This control policy utilizes the RPSO algorithm to update the set of controller parameters r. To further improve the system profit, the initial controller parameters …r r, , M1 are obtained through the RPSO algorithm using the historical data of starting buffer levels and dis- ruption events. The structure of the control framework is shown in Fig. 4.

The pseudo procedure is presented to illustrate this control policy. RPSO algorithm based adaptive control policy: 1. Implement the RPSO algorithm by using the historical data of

starting buffer levels and disruptions events, and acquire the set of in- itial controller parameters as =r gbest n( ).

2. At any time t, 2.1) If =t integer/ , then apply the resilient control policy, update

the particle positions using the RPSO algorithm, and denote =n t/ , (2.1a) if <r pProfit n n f n( , [ ( 1) , ) ) ( ( ) )1 , i.e., r takes values

from an inaccurate estimation, then save the current position of r to , and set =r gbest n( );

(2.1b) Otherwise, set = =

r pProfit n narg max { ( , [ ( 1) , ) ) } p gbest rn{ ( ), }

.

2.2) Otherwise, apply the resilient control policy.

Remark 2. Note that the update frequency of the RPSO algorithm is different from the real-time control frequency. The resilient production control policy as shown in Fig. 2 is actually utilized for production control at every time instant. Meanwhile, the RPSO algorithm only needs to update the positions of all particles, and renew the system resilience threshold values r for the resilient control policy at every

based on their fitness values pf n i( ( ) ),i .

As mentioned after Eq. (13), the fitness value of each particle, i.e., =p pf n Profit n n n i( ( ) ) ( ( ), [ ( 1) , ) ),i i , is evaluated through si-

mulation using sensor data of buffer levels at time =t n( 1) and random disruption events only within the time interval n n[ ( 1) , ). Hence, pf n i( ( ) ),i , will be available at the time of the next iteration, i.e., =t n . Per the Renewal rule, the RPSO algorithm only needs to compare and rank these particles based on the obtained results of their fitness values pf n i( ( ) ),i at every . And this can be efficiently ac- complished in a real-time basis.

7. Case study

The effectiveness of the proposed RPSO algorithm based resilient adaptive production control policy is investigated through numerical experiments. A total of 1000 production lines are investigated. In these experiments, the system parameters are randomly generated from the following sets with equal probability:

…M {2, 3, , 100}

= …MTBF min i M[150, 500] , 1, ,i

= …MTTR min i M[10, 50] , 1, ,i

= …T sec i M[10, 600] , 1, ,i

= …B i M[10, 100], 2, ,i

For comparison, we also consider the performance of the same re- silient control policy with SPSO algorithm introduced in Section 6.

In each experiment, the simulation duration is 1 year, i.e., 518,400 min by assuming 24 h a day, 360 working days a year. The historical data of disruption events and buffer levels over the past year is also available. Three scenarios are compared using simulation: 1) baseline scenario with no production control; 2) comparison scenario with the SPSO algorithm based comparison control method; 3) con- trolled scenario with the proposed control policy. The total cost of energy consumption (EC), overall profit (PF), and total inventory cost (IVC) can be calculated by Eqs. (9), (11), and (12). As an illustration, a segment of a real battery production line consisting of 15 machines and 14 buffers is used. The parameters and data are recorded from the real

Fig. 4. RPSO algorithm based resilient adaptive controller.

Table 1 Parameters for the 15 machines.

Parameters S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 S11 S12 S13 S14 S15

Cycle (sec) 40 45 35 60 32 50 42 36 28 55 46 37 40 42 35 Power rate Ki (kW) 50 60 42 58 66 36 48 35 40 68 40 34 54 60 46 MTTRi (min) 13 22 20 18 20 25 15 20 18 30 24 12 28 30 14

Table 2 Parameters for the 14 buffers.

B2 B3 B4 B5 B6 B7 B8 B9 B10 B11 B12 B13 B14 B15

Buffer capacity 30 40 60 60 30 40 30 25 30 40 30 40 25 20 Initial buffer level 7 13 5 14 5 8 10 10 5 15 20 3 10 9

Table 3 Simulation results.

Energy cost ($) Production count Profit ($) Inventory cost ($)

Baseline 2263464 495427 21669979 837907 Comparison Method 1681601 491546 22016699 879000 Proposed Method 1310878 495083 22731808 711464

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production line and mocked for confidential reasons, which are listed in Tables 1 and 2. The machine MTBFi varies slowly but continuous with time and can be described by

The profit per part produced is assumed to be =c part$50/p . The electricity rate is assumed to be =c kWh$0.2/e . The inventory cost is assumed to be =c part day$10/( * )i . In this example, in order to accel- erate the searching process and get a large enough sample size for re- liable estimation, a total of 10 particles are used in the RPSO algorithm, and we choose = min2 , =w 0.5, = =c c 21 2 , = day3 , and =m 10. Moreover, to study the impact of particle updating interval on the performance of the production control system, we further select

= hour3 , day1 , day10 , month1 and compare their corresponding re- sults of EC, production count (PC), PF, and IVC.

For this example, the comparison results of EC, PC, PF, and IVC can be seen in Table 3. System improvements by using the proposed control policy and the comparison control method are shown in Table 4. System profit improvements by choosing different are shown in Table 5.

It is observed from experiment results that, by applying the pro- posed control policy, a 15–40% reduction in energy consumption and a 5%–15% increment in profit are achieved with a minor throughput impact and an acceptable amount of increment in total inventory cost, which does not conflict with the control goal focusing on the actual profit. It is worth mentioning that we can obtain a 15%–30% energy consumption reduction and a 0%–8% profit improvement by using the comparison control method. In addition, the percentage difference in profit improvement between the proposed control policy and the comparison control is usually about 3%–10%. Therefore, our proposed control policy, which uses both production system physical properties and sensor information, can more effectively improve production system profit and performance.

Remark 3. According to Table 5, system performance will be deteriorated when is too small (e.g., when = hours3 ), and we will get less profit improvement when is too large (e.g., when

= month1 ). The corresponding results match the previous discussion of Proposition 2. If is too small, then

> >p p p pP f n f n f n f n( ( ( ) ) ( ( ) ) | ( ( ) ) ( ( ) ) )i j i j1 1 will be closer to 0, and the estimation of the rankings of all particles in the RPSO algorithm will not be reliable. As a result, it is very likely that we choose inappropriate resilience threshold values r, and system performance will be jeopardized. If is too large, then the particles will update much less frequently. Thus the available data may not be enough to find the values of r that can more significantly improve system performance.

Remark 4. The parameters of the proposed RPSO algorithm can determine its behavior and efficiency in searching the desired values of control parameters r. We choose =w 0.5 and = =c c 21 2 to balance

the influence of previous particle velocity, each particle’s own cognitive knowledge and the mutual cooperation between particles on current particle velocity. The number of particles, denoted by N , will be selected based on the size of the search space, which is determined by buffer number M 1 and capacity = …B i M, 1,2, ,i . We must determine N to achieve a desired convergence speed. In our experiments, we have …M {2,3, , 100} and B [10,100]i . In most cases, by choosing =N 10, the RPSO algorithm can find the values of r that will render satisfactory control performance. When the search space gets bigger (M and B80 80i ), we need to tune up N to 12 to increase the convergence speed and find the satisfactory values of r based on the given amount of historical data.

8. Conclusion and future work

In this paper, a real-time diagnostic methodology is proposed to evaluate some key indicators of production system performance, such as energy waste due to machine and buffer interactions, and system resilience against random disruptions, on a real-time basis. This pro- vides useful information for real-time system control and management.

More importantly, a resilient adaptive production control policy is developed by using the real-time diagnostic results. A novel RPSO al- gorithm is proposed to update the controller parameters. This real-time diagnostic method and production control policy utilize both produc- tion system properties and sensor data to ensure resilient operation against random disruption events, and to significantly improve system profit and energy efficiency. In addition, the designed controller is well adapted to the time-variant system reliabilities.

This work focuses on a real-time resilient production control policy. Our control policy utilizes real-time sensor information and real-time system diagnostic results to initiate timely reaction to system disrup- tions and energy inefficiencies. Note that manufacturing systems are constantly in dynamic. Hence, compared to existing control methods focusing on improving long-term steady-state performance, this real- time control action can better improve system production efficiency and profit.

Most resilience manufacturing control methods are concentrated on downtime impact reduction and production improvement through managing system structure or resource allocation. In contrast, the proposed real-time resilient adaptive control policy in this paper holi- stically improve system profit and energy efficiency while ensuring resilient performance against random disruption events. In addition, the proposed policy make decisions on machine operations, which is easy to implement and is cost friendly.

Production control or management methods are commonly de- signed to work with systems with fixed parameters or characteristics.

Table 4 System improvement by the proposed control policy and the comparison control method.

Reduction in EC (%) Reduction in PC (%) Increase in PF (%) Increase in IVC (%)

Comparison Method 25.7% 0.7% 1.6% 4.9% Proposed Method 42.1% 0.07% 4.9% −15.1%

Table 5 System profit improvement by choosing different updating interval.

Updating interval hour3 day1 day3 day10 month1

Increase in PF (%) −42.6% 3.6% 5.2% 4.9% 3.1%

=MTBF min250 t1 6030 , =MTBF min263 t

2 5010 , =MTBF min358 t3 5000 , =MTBF min364

t 4 3820

,

=MTBF min274 t5 5500 , =MTBF min242 t

6 8000 , =MTBF min322 t7 4530 , =MTBF min356

t 8 4240

,

=MTBF min298 t9 6100 , =MTBF min410 t

10 6020 , =MTBF min312 t11 5400 , =MTBF min286

t 12 4750

,

=MTBF min340 t13 4500 , =MTBF min520 t

14 4320 , =MTBF min245 t15 5910 .

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These methods adopt fixed rules or control policies with fixed para- meters. Hence, their control performance will be largely impacted when there are changes in system parameters or behavior. To address this issue, a RPSO algorithm is developed for updating our control para- meters. Through RPSO algorithm, our controller can well adapted to systems with time-variant parameters and patterns.

In the future, machine warm-up and cool-down status will be con- sidered. In addition, we plan to extend our research to the cooperation between the production line and other subsystems in a manufacturing plant including HVAC and power supply systems to further reduce energy consumption. Moreover, we will use the PSO algorithm to identify the hidden properties and characteristics of manufacturing systems.

Acknowledgement

This work was supported by the U.S. National Science Foundation (NSF) Grant No. CMMI 1351160.

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Jing Zou received the B.S. degree from the Huazhong University of Science and Technology, Wuhan, China, in 2012, and the M.S. degree from the University of Florida, Gainesville, FL, USA, in 2014. He is currently pursuing the Ph.D. degree in mechanical engineering with Stony Brook University, Stony Brook, NY, USA, all in mechanical en- gineering. He has participated in different projects related to production system modeling and control. His current research interests include data-driven production system mod- eling, performance diagnosis and prognosis, and distributed control.

Qing Chang received the M.S. degree in mechanical engineering from the University of Wisconsin–Madison, Madison, WI, USA, and the Ph.D. degree in manufacturing from the University of Michigan, Ann Arbor, MI, USA. She is currently an Associate Professor with the Department of Mechanical and Aerospace Engineering, University of Virginia, Charlottesville, VA 22904. Prior to her position at UVA, Dr. Chang was an associate professor of Mechanical Engineering at the Stony Brook University, Stony Brook, NY, USA. She was a Senior Researcher with General Motors Research and Development Center, Warren, MI, USA. Her current research interests include real-time monitoring and control of smart manufacturing systems, energy systems for sustainability, energy effi- ciency management of production processes, and intelligent maintenance systems.

Xinyan Ou received the B.S. degree and M.S. degree in 2011 and 2014 from the Beijing Institute of Technology, Beijing, China. She is currently pursuing the Ph.D. degree in mechanical engineering with Stony Brook University, Stony Brook, NY, USA, all in me- chanical engineering. She has participated in different projects related to production system modeling and control. Her current research interests include gantry production system analysis, data-driven production system modeling and performance diagnosis and control.

Jorge Arinez received the B.A.Sc. degree from the University of Toronto, Toronto, ON, Canada, and the master’s and Ph.D. degrees in mechanical engineering from the Massachusetts Institute of Technology, Cambridge, MA, USA. He is a Laboratory Group Manager with the Manufacturing Systems Research Laboratory, GM Global Research and Development, Warren, MI, USA, where his main responsibilities involve strategically defining and managing portfolios of advanced manufacturing technology projects. He has

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also led the development and implementation of the advanced technology projects throughout GM’s global manufacturing operations. His current research interests include development of analytical tools for real-time production monitoring and control with a focus on energy efficiency and sustainability of manufacturing systems.

Guoxian Xiao received the B.S. degree in mechanical engineering and the M.S. degree in manufacturing engineering from Northeastern University, Shenyang, China, and the

Ph.D. degree in mechanical engineering from the University of Massachusetts, Amherst. He is a Technical Fellow at General Motors (GM) Research and Development Center. With GM since 1997, he leads several projects on the research and development of advanced technologies in machining processes, realtime plant floor systems, and remanufacturing systems. He has six U.S. patents and authored more than 80 technical papers for journals and conferences.

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