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Date of publication xxxx 00, 0000, date of current version xxxx 00, 0000.

Digital Object Identiﬁer 10.1109/ACCESS.2017.DOI

Improving prescriptive maintenance by

incorporating post-prognostic

information through chance constraints

ANTHONY D. CHO1, RODRIGO A. CARRASCO1,2, (Member, IEEE), and GONZALO A.

RUZ1,2,3, (Senior Member, IEEE),

1Faculty of Engineering and Sciences, Universidad Adolfo Ibáñez, Santiago 7941169, Chile

(e-mail: acholo@alumnos.uai.cl, rax@uai.cl, gonzalo.ruz@uai.cl)

2Data Observatory Foundation, Santiago 7941169, Chile

3Center of Applied Ecology and Sustainability (CAPES), Santiago 8331150, Chile

Corresponding author: Gonzalo A. Ruz (e-mail: gonzalo.ruz@uai.cl).

This research was partially funded by ANID FONDECYT 1180706, ANID PIA/BASAL FB0002, and ASTRO20-0058 grants from ANID,

Chile.

ABSTRACT Maintenance is one of the critical areas in operations in which a careful balance between

preventive costs and the effect of failures is required. Thanks to the increasing data availability, decision-

makers can now use models to better estimate, evaluate, and achieve this balance.

This work presents a maintenance scheduling model which considers prognostic information provided by

a predictive system. In particular, we developed a prescriptive maintenance system based on run-to-failure

signal segmentation and a Long Short Term Memory (LSTM) neural network. The LSTM network returns

the prediction of the remaining useful life when a fault is present in a component. We incorporate such

predictions and their inherent errors in a decision support system based on a stochastic optimization model,

incorporating them via chance constraints. These constraints control the number of failed components and

consider the physical distance between them to reduce sparsity and minimize the total maintenance cost.

We show that this approach can compute solutions for relatively large instances in reasonable computational

time through experimental results. Furthermore, the decision-maker can identify the correct operating point

depending on the balance between costs and failure probability.

INDEX TERMS prescriptive maintenance, chance constraints, remaining useful life.

I. INTRODUCTION

Operational areas within organizations are under ever-

increasing pressure to improve their performance. Social,

political, and competitors are just some of the drivers push-

ing companies to be more efﬁcient and effective with their

resources and assets. This pressure, in turn, has added a

tremendous burden to maintenance, an area that must keep

a delicate balance between the effects of failures and the

cost of preventive measures. Furthermore, the increase in

complexity of current production systems makes this balance

even more challenging, making condition-based maintenance

policies hard to deﬁne and implement. To deal with these

difﬁculties, maintenance areas have turned to operational

data to get an answer, taking advantage of many sensors and

telemetry systems that are now available. Here, predictive

analytics tools have helped convert data into information,

transforming the constant ﬂow from sensors and actuators to

detect and even predict changes in the state of the system

[1], [2]. The development of frameworks like the Prognostics

and Health Management (PHM) one [3], [4], have further

increased the need for fault prediction [5]–[8] as well as

estimating the remaining useful life (RUL) of a component

after a fault appears [9]–[12]. However, this is only a partial

solution. As systems grow, so will the number of detections

and diagnoses, and what maintenance areas need is to have

reliable plans that help them balance the cost of preventive

measures with the ones caused by undetected or untreated

failures [13], [14]. In this setting, prescriptive analytics tools

might hold the key to improving the efﬁciency and efﬁcacy

of these complex systems, taking advantage of the plethora

of operational data sources that are now available, if these

systems can handle the uncertainties inherent with prognostic

VOLUME 4, 2016 1

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This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI

10.1109/ACCESS.2022.3177537, IEEE Access

A. D. Cho et al.: Preparation of Papers for IEEE TRANSACTIONS and JOURNALS

FIGURE 1: ALMA radio telescopes. From image gallery of almaobservatory.org by Liam Young, Juan Carlos Rojas, and Sergio Otárola

procedures.

Researchers have recently been dealing with uncertainty

and component connections in maintenance planning from

the decision-making perspective [14]–[16]. Covering both

aspects will be essential for large and complex production

facilities like wind farms [17], solar generators, and even

scientiﬁc instruments such as the ALMA radio telescope

[5]. In this work, we will focus on the last step of PHM

for decision-making in maintenance, which covers the two

aspects mentioned before.

A. OUR CONTRIBUTION

Our work has the following novel contributions:

1) We propose a stochastic model with chance constraints

to handle unexpected failures and address components

with different levels of uncertainty in decision-making

for maintenance to minimize the total cost. In addition,

the model considers the distance between components

in each maintenance period and the total residual RUL.

2) We study and describe the effect of varying of the

chance constraints in the resulting schedule.

II. PROBLEM DESCRIPTION

Let Nbe the set of components distributed over Kmachines,

which might be in different sites, as shown in Figure 1. Ad-

ditionally, each machine has a list of components on which a

predictive system, like the one described in [5], has detected

a degradation fault. Furthermore, each component has a pre-

dicted RUL distribution provided by this predictive system.

The machines are not necessarily identical, and we assume

that their components are independent between machines and

within each machine. If one of the machine’s components

fails, we consider that the machine fails. This type of setting

rises in several applications like manufacturing [18], off-

shore wind farms [17], and scientiﬁc instruments like the

ALMA radio telescope [19], among others.

Our goal is to arrange this set of components to minimize

the maintenance cost considering the distance between ma-

chines and balancing the machines’ availability. We consider

a one-year planning horizon with maintenance decisions per

month in our work.

A. PREDICTIVE SYSTEM

LSTM networks are a type of artiﬁcial recurrent neural

network (RNN) architecture proposed by Hochreiter and

Schmidhuber [20] to deal with the vanishing gradient prob-

lem. One LSTM unit comprises three gates: an input gate,

an output gate, and a forget gate. It also has a memory cell

that remembers values over arbitrary time intervals, while the

three gates regulate the ﬂow of information into and out of the

cell. This type of RNN has been found extremely successful

in many applications [21]. A typical LSTM [22] is illustrated

in Figure 2.

We have developed an RUL prediction system based on

LSTM neural networks .This network was pre-trained us-

ing run-to-failure data with degradation faults as the ones

described in [5]. The data for each component was ana-

lyzed and clustered, with each cluster having a catastrophic

failure threshold. The system is in charge of identifying

which cluster best represents the detected fault, after which

2VOLUME 4, 2016

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10.1109/ACCESS.2022.3177537, IEEE Access

A. D. Cho et al.: Preparation of Papers for IEEE TRANSACTIONS and JOURNALS

FIGURE 2: LSTM unit.

it uses the corresponding analytical model to predict the

RUL’s distribution. As a result, we have available the mean

ˆriand the standard deviation ˆσiof the RUL estimation for

each component i. A general diagram with the developed

prediction system is shown in Figure 3.

III. PROPOSED MAINTENANCE SCHEDULING MODEL

The scheduling model formulation is based on the ideas

developed in [23]. However, unlike that work, instead of

accomplishing the given demands, our approach aims to use

the components as much as possible before the end of their

respective RUL.

A. DYNAMIC MAINTENANCE COST

A dynamic maintenance cost function models the trade-off

between the cost of preventive maintenance Cp(early repair

before failure) and the corrective maintenance cost Ccthat

deals with unexpected failures [24]. Typically, corrective

maintenance costs are higher than preventive maintenance

ones. Therefore, dynamic cost functions are directly related

to the RUL of each component, and it is deﬁned in [23]–[25]

Fault

prediction

Classiﬁer Model

Selection

RUL

prediction

Signal

Cluster 1

Cluster 2

Cluster k

Cluster N

Model 1

Model 2

Model k

Model N

FIGURE 3: Predictive system.

as:

Ci,ti,0(t) = CpPRi,ti,0> t+CcPRi,ti,0≤t

Rt

0PRi,ti,0> zdz +ti,0

(1)

where Ri,ti,0is the residual RUL of component i, which

started at time ti,0.

B. SCHEDULING MODEL

The prescriptive maintenance problem is modeled as the

following optimization problem:

min X

i∈GX

t∈T

Ci,ti,0(t)zi,t −X

i∈GX

t∈T

Vi,tzi,t

+X

t∈T

C+γt

+X

t∈TCd

clDt+Cr+

cl ¯

∆t+Cr−

cl ∆t,(2)

such that, X

t∈T

zi,t = 1,∀i∈G, (3)

P X

i∈GX

t∈T

ζi,tzi,t ≤ρ!≥1−, (4)

X

i∈G

fizi,t ≤¯

M+γt,∀t∈T, (5)

Dt≥ϕi,j (zi,t +zj,t −1) ,∀i, j ∈G, i 6=j;∀t∈T , (6)

¯

∆t=X

i∈G

zi,t max {0, ri−Op·t},∀t∈T, (7)

∆t=X

i∈G

zi,t max {0, Op·t−ri},∀t∈T, (8)

zi,t ∈ {0,1}, γt, Dt,¯

∆t,∆t≥0,∀i∈G, ∀t∈T, (9)

where Ci,ti,0(t)is the dynamic maintenance cost deﬁned

in Section III-A. The parameters and decision variables are

summarized in Table 1.

The objective function, given by equation (2), minimizes

the total maintenance costs of a set of |G|components.

Each component has its dynamic maintenance cost, nominal

functional cost, additional time for the repair cost, the cost of

the distance between components, and cost related to residual

RUL.

Constraints (3) guarantees that each component enters

maintenance only once in the planning horizon. In contrast,

the chance constraint (4) restricts the number of components

that run out of RUL before their scheduled maintenance with

a threshold ρand a probability of 1−. In that constraint,

the Bernoulli random variable ζi,t is 1 if Ri,ti,0< t and

0 otherwise; and ρsets a upper bound on the number of

components with catastrophic failure. The probability of not

achieving the bound set by ρis given by .

Constraints (5) ensures that at most ¯

M+γtwork-hours are

needed for maintenance in each period t. If additional work-

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TABLE 1: Summary of the sets, decision variables and parameters of the

scheduling model.

Sets

GSet of components.

TSet of maintenance periods in the planning horizon.

Decision & State Variables

zi,t 1 if component ienters maintenance in maintenance

period t, and 0 otherwise.

γtAdditional maintenance hour added to maintenance pe-

riod t.

DtMaximum distance between components in mainte-

nance period t.

¯

∆tTotal residual RUL of components in maintenance pe-

riod t.

∆tTotal time after the end of RUL that components enter

to maintenance in maintenance period t.

Parameters

CcPer unit cost of corrective maintenance.

CpPer unit cost of preventive maintenance.

C+Per unit cost of maintenance work-hours added.

Vi,t Nominal functional cost of component iin period t.

HPlanning horizon length of maintenance, i.e, total main-

tenance periods.

¯

MMaximum work-hours for maintenance in each mainte-

nance period.

OpOperational period length.

Cd

cl Per unit cost of distance in each period.

Cr+

cl Per unit cost residuals RUL of components in each

period.

Cr−

cl Per unit cost of time after the end of RUL of compo-

nents in each period.

ϕi,j Distance between components.

fiMean-hours to repair the component i.

riRUL of component i.

hours are needed, then additional costs are added to the total

maintenance cost.

Constraints (6) determine the maximum distance between

components planned for maintenance in period t; this allows

for reducing the dispersion of the components in each main-

tenance period. Finally, constraints (7)-(8) represent the total

number of days before and after the end of the RUL in which

components require maintenance in period t.

C. SAFE APPROXIMATION OF CHANCE CONSTRAINT

The usage of chance constraint (4) in a decision-making

model makes it computationally challenging. In order to

make this constraint tractable, an upper bound can be com-

puted on the left-hand side of this inequality using Markov

and generalized Bernstein inequality as proposed in Proposi-

tion 1 in [25]. Hence, given z∈ {0,1}|T|×|G|satisfying

X

i∈GX

t∈T

E[ζi,t]zi,t

≤max (ρ, max

δ>0"|G|(eδρ )1/|G|−1

eδ−1#)=ρ∗,(10)

FIGURE 4: Safe approximation curve using ρ= 11 and 150 components

it will also satisfy constraint (4).

Figure 4 shows the behavior of the values of ρ∗, for ρ= 11

and 150 components. In this Figure, we can notice that for

very close to 0, the bound is smaller, implying that it

is strengthened more than the number of components with

corrective maintenance, as long as it does not exceed the

amount ρ. As the value of increases, this condition becomes

less strict.

D. STOCHASTIC MIP SCHEDULING MODEL

To deal with non-linear terms, we linearize the chance

constraint and dynamic cost using safe approximation and

approach the stochastic optimization model with a set of

scenarios sampled from the prediction distribution of the

RUL of each component.

1) Chance constraint linearization

Using the safe approximation deﬁned in Section III-C, we

can reformulate chance constraint (4) taking the same strat-

egy proposed in [23] by deﬁning an auxiliary decision vari-

able as follows

Pi,t := E(ζi,t) = P(Ri,ti,0≤t),∀i∈G, ∀t∈T . (11)

Considering ¯

Pi,t as an upper bound of Pi,t and 0≤Pi,t ≤

¯

Pi,t ≤1, we can rewrite

ui,t =Pi,tzi,t ,∀i∈G, ∀t∈T, (12)

in the form of a safe approximation of the chance constraint

as follows: X

t∈TX

i∈G

ui,t ≤ρ∗,(13)

0≤ui,t ≤Pi,t,∀i∈G, ∀t∈T , (14)

Pi,t −(1−zi,t )¯

Pi,t ≤ui,t ≤¯

Pi,tzi,t ,∀i∈G, ∀t∈T. (15)

Analogously, we apply the linearization to the non-linear

term Ci,ti,0(t)zi,t of the objective function by deﬁning

wi,t := θi,tzi,t ,(16)

where, θi,t =Ci,ti,0(t), and 0≤θi,t ≤¯

θi,t ≤Cc. Therefore,

the linearization of wi,t is given as follows:

0≤wi,t ≤θi,t,∀i∈G, ∀t∈T , (17)

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θi,t −(1 −zi,t)¯

θi,t ≤wi,t ≤¯

θi,tzi,t ,∀i∈G, ∀t∈T, (18)

¯

θi,t = max

0≤t0≤ti,0+tCi,ti,0(t0),∀i∈G, ∀t∈T. (19)

2) Scenarios

Since each component has its RUL distribution provided by

the predictive system, we create a set of scenarios, S, such

that each scenario is generated from each component’s RUL

distribution, i.e.,

S={s1, s2, . . . , s|S|}(20)

with

sk= (rsk,1, rsk,2, . . . , rsk,|G|), k ={1, . . . , |S|},(21)

rsk,i ∼ N (ˆri,ˆσ2

i),∀i∈G, (22)

where ˆri,ˆσirepresent the mean and standard deviation of the

RUL estimate of component i, respectively.

3) Optimization model

Considering the information on the distribution of the RUL

of each component and the linearization of the non-linear

terms of both the chance constraint and the dynamic cost

function described in Section III-D1, we can formulate our

prescriptive maintenance problem into a stochastic mixed-

integer model as follows,

min 1

|S|X

s∈S

Φs,(23)

such that,

Φs= X

t∈TX

i∈G

wi,t +X

t∈T

C+γt!

+X

t∈TCd

clDt+Cr+

cl ¯

∆s,t +Cr−

cl ∆s,t

−X

t∈TX

i∈G

Vi,t ·zi,t,∀s∈S, (24)

X

t∈T

zi,t = 1,∀i∈G, (25)

X

i∈G

fizi,t ≤¯

M+γt,∀t∈T, (26)

Dt≥ϕi,j (zi,t +zj,t −1) ,

∀i, j ∈G, i 6=j;∀t∈T , (27)

¯

∆s,t =X

i∈G

zi,t max(0, rs,i −Op·t),∀t∈T, ∀s∈S, (28)

∆s,t =X

i∈G

zi,t max(0, Op·t−rs,i),∀t∈T , ∀s∈S, (29)

X

t∈TX

i∈G

ui,t ≤ρ∗.(30)

0≤ui,t ≤Pi,t,∀i∈G, ∀t∈T , (31)

Pi,t −(1 −zi,t)¯

Pi,t ≤ui,t ≤¯

Pi,tzi,t ,

∀i∈G, ∀t∈T, (32)

0≤wi,t ≤θi,t,∀i∈G, ∀t∈T , (33)

θi,t −(1 −zi,t)¯

θi,t ≤wi,t ≤¯

θi,tzi,t ,

∀i∈G, ∀t∈T, (34)

zi,t ∈ {0,1};wi,t, γt, Dt,¯

∆s,t,∆s,t ≥0;

∀i∈G, ∀t∈T, ∀s∈S, (35)

where, ¯

θi,t = max

0≤t0≤ti,0+tCi,ti,0(t0),(36)

Pi,t =P(Ri,ti,0≤t) = P(ri≤ti,0+t),(37)

and rihas the same distribution as deﬁned in (22). ti,0repre-

sents the days elapsed since the last emission of the predictive

information until the moment the scheduling process is car-

ried out and ρ∗is the safe approximation constant deﬁned in

(10). For simplicity, we consider ¯

Pi,t = 1,∀i∈G, ∀t∈T.

The model aims to minimize the average cost generated

through all the scenarios, which is described by the equations

(23) and (24). The constraints (25)-(29) guarantee that all

components enter maintenance only once during the planning

horizon, and ensure that at most they need ¯

M+γtwork-

hours for maintenance in each period t. These constraints also

reduce the geographical dispersion between the components

attended in each period, considering the distance between

them. The model aims to use each component as much as

possible and reduce the days each enters maintenance after

the end of RUL in each period tin each scenario.

The constraints (30)-(32) represent the linearization of

the chance constraint (4), whereas the linearization of the

dynamic cost is given by the equations (33)-(34).

IV. EXPERIMENTAL SETTINGS

The proposed prescriptive maintenance system was imple-

mented in Python 3.8.10 using Gurobi 9.1.1 as a mixed-

integer optimization solver. The experiments were done on

a computer with an Intel®Core™ Processor i5-3230M of 2.6

GHz x 4 cores, with 8 GB RAM, and Linux Mint 20.1 Ulyssa

(64 bits) as OS.

The model settings were as follows: the planning horizon

for maintenance was set to one year, i.e. H=|T|= 12,

with each month as a period with operational length of 30

days, Op= 30. The preventive and corrective costs were

Cp= 100000 and Cc= 400000, respectively. Other related

costs were: C+= 10000,Cd

cl = 10000,Cr+

cl = 11000,

Cr−

cl = 22000, and Vi,t = 5000. The maximum work-hours

was set to ¯

M= 160, and 100 scenarios were generated.

These cost values were set with the objective of evaluating

both the dynamic cost and the performance of the proposed

model.

A public repository with all the benchmark instances tested

with our methodology can be found at [26].

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(a) Distribution of maintenance costs of all scenarios.

(b) Number of components per machine. (c) Maintenance before or after RUL (ˆri, i ∈G).

(d) Maintenance before or after RUL of all scenarios. (e) Pareto curve: Varying -value.

FIGURE 5: Case study: 150 faulty components distributed in 9 machines.

V. COMPUTATIONAL RESULTS

A simulated problem of |G|= 250 components distributed

over K= 9 machines, as shown in Fig. 5b was used

as one of the instances to test the model’s performance.

Furthermore, we set = 0.1and ρ= 11; this implies that

about 5% of the components enter corrective maintenance

due to a catastrophic failure with a probability of at least

1−. We solved the model using multiple scenarios sampled

from RUL distribution, described in Section III-D2, and we

assumed that the predictive system provided us with the

information on the same day that the scheduling model was

executed; therefore, we set ti,0= 0. The result of the

minimum maintenance cost of each scenario is shown in

Figure 5a, where the red dash line represents the average

maintenance cost over all the scenarios.

In the resulting recommendation, all components enter

maintenance before the end of their RUL, with planned main-

tenance of fewer than 12 days before they fail with respect

to the estimated RUL ˆri∀i∈G, as illustrated in Figure

5c (which presents no After RUL orange bars). Looking at

the cases for all scenarios, 3.41% of cases have some of the

components go into maintenance after the end of the sampled

RUL, rs,i ∀s∈S, ∀i∈G. This study veriﬁes that less

than 5% of the components goes into corrective maintenance,

which we have previously set, and is reﬂected in the orange

bars in Figure 5d.

Constraint (4) introduces a tuning parameter , that helps

the decision-maker balance the different costs. Figure 5e

shows that for smaller values of , a higher maintenance cost

is needed since the model tries to increase the machines’

availability by making earlier maintenance procedures. For

the case study, if ≥0.1, the maintenance cost decreases

almost linearly, showing slight changes in some periods.

Figures 6a to 6b show the effect on the schedule of in-

creasing from 10−8to 0.1. The analysis shows signiﬁcant

changes, showing several grouping modiﬁcations in each pe-

riod. On the other hand, when we increased the from 0.1 to

0.2, there were only small changes in the movement of some

components: one component from period 2 to period 1, two

components from period 9 to period 10, and two components

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from period 10 to the next period. Varying implied some

schedule changes and the effect on the maintenance cost and

computational effort. In the ﬁgures, for each period, the red

box indicates the component with a residual RUL of less than

ten days, the orange box when it is between 11 and 20 days,

and the green one when it is greater than 20 days.

We also tested the performance in instances with 500 and

1000 components distributed over 20 machines, measuring

the time required to solve them. Our instances with 1000

components were solved in around 12 minutes. The results

are summarized in Table 2.

VI. CONCLUSION

The increasing complexity of systems has made it harder

for the operational areas to develop well-balanced policies in

maintenance. The availability of data has helped signiﬁcantly

get better information, but decision support tools are crucial

to help improve efﬁciency and the effective use of resources

and assets. Furthermore, these tools need to embrace the

uncertainty inherent with predictive analytics tools such as

RUL predictions to be helpful.

Our work shows an initial approach to doing this. Our

model presents excellent performance, even when there are

different levels of uncertainty in the predicted RUL. This

approach complements predictive systems, taking advantage

of their information. Furthermore, the scheduling model can

handle a more extensive set of components, reduce process-

ing time, and give robust recommendations to the decision-

makers.

ACKNOWLEDGMENT

This research was partially funded by ANID FONDECYT

1180706, ANID PIA/BASAL FB0002, and ASTRO20-0058

grants from ANID, Chile.

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10.1109/ACCESS.2022.3177537, IEEE Access

A. D. Cho et al.: Preparation of Papers for IEEE TRANSACTIONS and JOURNALS

TABLE 2: Runtime in seconds to load each step.

Components Data-loading [sec] Decision vars. [sec] Constraints [sec] Solver [sec] Total [sec]

150 20.48 0.03 2.75 17.40 40.68

500 64.68 0.08 23.28 97.44 185.53

1000 128.98 0.20 87.39 503.37 719.99

(a) Scheduling (= 10−8).

(b) Scheduling (= 0.1).

(c) Scheduling (= 0.2). The boxes highlight the changes from (b)

FIGURE 6: Effect of scheduling: varying -value in the chance constraint

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ANTHONY D. CHO received the B.S. degree in

mathematics from the Universidad de Carabobo,

Valencia, Venezuela, in 2008. He is currently pur-

suing the Ph.D. degree in Industrial Engineer-

ing and Operations Research at the Universidad

Adolfo Ibáñez, Santiago, Chile.

His research interests include machine learning,

evolutionary algorithms, operation research, pre-

8VOLUME 4, 2016

10.1109/ACCESS.2022.3177537, IEEE Access

A. D. Cho et al.: Preparation of Papers for IEEE TRANSACTIONS and JOURNALS

TABLE 3: Complemtary: sets and parameters.

SSet of scenearios of RULs sampled from RUL

distribution

rs,i RUL sampled from the distribution of the com-

ponent ifor the scenario s.

ˆriEstimated mean RUL of the component i.

ˆσiEstimated standard deviation of RUL of the

component i.

Ri,ti,0Residual RUL of the component istarted at

time ti,0.

TABLE 4: Abbreviations.

RUL Remaining Useful Life

RNN Recurrent Neural Network

ALMA Atacama Large Millimeter Array

PHM Prognostic and Health Management

LSTM Long-Short Term Memory

IFP Intermediate Frecuency Processor

scriptive analytics, and image processing.

RODRIGO A. CARRASCO (M’2002) is a pro-

fessor at the School of Engineering and Sciences

at Universidad Adolfo Ibáñez, and Academic Di-

rector of the Master in Industrial Engineering pro-

gram. He also founded and was the initial director

of the UAI Systems Center, a center dedicated

to technology transfer and solving complex real-

life problems using operations research tools. His

research is focused on the design and development

of decision support tools and algorithms.

Before joining UAI, he was a researcher at Siemens Corporate Research

in Princeton, NJ, developing decision support algorithms for smart grids

and energy management. Prior to this, he worked at Booz Allen Hamilton,

leading operations research projects in Chile, Argentina, Brazil, Peru, and

Canada.

Rodrigo holds an electrical engineering degree and a master of science

in engineering, focused in control systems, from Universidad Católica de

Chile, and an M.Phil. and a Ph.D. from Columbia University in industrial

engineering and operations research.

GONZALO A. RUZ received his B.Sc. (2002),

P.E. and M.Sc. (2003) degrees in Electrical En-

gineering from Universidad de Chile, Santiago,

Chile. He then completed his Ph.D. degree (2008)

at Cardiff University, UK. Currently, he is a Pro-

fessor at the Faculty of Engineering and Sciences,

Universidad Adolfo Ibáñez, Santiago, Chile. His

research interests include machine learning, evolu-

tionary computation, data science, gene regulatory

network modeling, and complex systems.

VOLUME 4, 2016 9