# A Correlation Driven Approach with Edge Services for Predictive Industrial Maintenance

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Related Works

#### 2.1. Predictive Industrial Maintenance

#### 2.2. Edge Computing

#### 2.3. Service Relationship

#### 2.4. Event Relationship

#### 2.4.1. Event Correlation

#### 2.4.2. Event Dependency

## 3. Proactive Data Service Model

#### 3.1. Preliminaries

#### 3.2. Proactive Data Service Model Refinement

**Definition**

**1.**

**Definition**

**2.**

**Definition**

**3.**

**Definition**

**4.**

_{i}= (uri, APIs, input_channels, event_handler, operations, event_definition, output_channel, service_hyperlinks). uri is the unique identifier; APIs is a set of RESTful-like APIs; input_channels represents a set of channels receiving different kinds of inputs; event_handler invokes different operations for different input service events; operations is a set of operations used for processing the inputs; event_definition is responsible for defining out-put service event type and format; output_channel represents the channel for outputting service events generated by operations; service_hyperlinks is essentially a routing table, which can point out the target services of each output service event. Proactive data service can be categorized into two types:

- edge service: the service model for encapsulating sensor data from one sensor, where event_handler = ϕ, and input_channels is used for receiving sensor data.
- cloud service: the service model for encapsulating a fault, where input_channels s used for receiving service events.

## 4. Service Hyperlink Model

_{1}, …, E

_{k}} be k service event sequences, E

^{t}be a set of service event types in E

_{1}, …, E

_{k}, and there exists e

_{i}

^{t}∈ E

^{t}, E

_{-}

^{t}= E

^{t}−{e

_{i}

^{t}}, 〈E

_{-}

^{t}, {e

_{i}

^{t}}〉 becomes a time-constrained frequent co-occurrence pattern, short for TFCP, if the following conditions are satisfied: (1) instances of E

^{t}occur together f(〈E

_{-}

^{t},{ e

_{i}

^{t}}〉) times, f(〈E

_{-}

^{t},{e

_{i}

^{t}}〉)≥δ

_{co}, where δ

_{co}is a times threshold; (2) instance of e

_{i}

^{t}has the largest timestamp in each occurrence of Et. In a TFCP 〈E

_{-}

^{t}, {e

_{i}

^{t}}〉, E

_{-}

^{t}is called as antecedent, and e

_{i}

^{t}is called as consequent. Figure 1 implies an example of a TFCP: 〈{L-CF}, {L-AP}〉.

_{-}

^{t}and e

_{i}

^{t}in a TFCP. Many studies measure the relationship by the conditional probability p(e

_{i}

^{t}|E

_{-}

^{t}) = f(〈E

_{-}

^{t},{e

_{i}

^{t}}〉)/f(E

_{-}

^{t}), where f(〈E

_{-}

^{t},{e

_{i}

^{t}}〉) and f(E

_{-}

^{t}) are the occurrence times of 〈E

_{-}

^{t},{e

_{i}

^{t}}〉 and E

_{-}

^{t}respectively [46].

**Definition**

**5.**

_{-}

^{t}be a set of service event types and e

_{i}

^{t}be another type, there is a service event correlation between E

_{-}

^{t}and e

_{i}

^{t}if and only if 〈E

_{-}

^{t},{e

_{i}

^{t}}〉 is a TFCP. The service event correlation is denoted as γ(E

_{-}

^{t}, e

_{i}

^{t}) = (E

_{-}

^{t}, e

_{i}

^{t}, T

_{int}, p), where E

_{-}

^{t}is the causes, e

_{i}

^{t}is the effect, T

_{int}= [t

_{min}, t

_{max}] is the propagation time interval, and p is the conditional probability.

**Definition**

**6.**

_{-}

^{t}, e

_{i}

^{t}) be a service event correlation, where E

_{-}

^{t}are contained by a set S of proactive data services, e

_{i}

^{t}is contained by a service s

_{i}. Given a probability threshold δ

_{p}, if p ≥ δ

_{p}, there is a service hyperlink L(S, s

_{i}) = (S, s

_{i}, γ(E

_{-}

^{t}, e

_{i}

^{t}), δ

_{p}), where S is a set of source services, s

_{i}is the target service.

## 5. Service Hyperlink Generation

#### 5.1. Problem Analysis

_{-}

^{t}, e

_{i}

^{t}) is measured by a conditional probability. To calculate the probability, we have to count the occurrence times f(〈E

_{-}

^{t},{e

_{i}

^{t}}〉) of 〈E

_{-}

^{t},{e

_{i}

^{t}}〉 in an event sequence set. Besides, the co-occurrence time interval of 〈E

_{-}

^{t},{e

_{i}

^{t}}〉 needs to be recorded as propagation time interval of the service hyperlink. Thus, the task of mining service event correlations is easily transformed into mining TFCPs with recording co-occurrence time interval.

_{-}

^{t},{e

_{i}

^{t}}〉 consists of two event type groups, where intra-group’s instances (instances of E

_{-}

^{t}) are unordered and inter-group’s instances are time-ordered (instances of E

_{-}

^{t}occur earlier than instance of e

_{i}

^{t}). Traditional frequent co-occurrence pattern mining algorithms cannot directly handle the challenge. They only focused on the occurrence frequency of a group of unordered objects [47,48]. But they still give an inspiration to us for developing an effective algorithm to mine TFCPs.

#### 5.2. Service Event Correlation Generating

#### 5.2.1. Frequent Co-Occurrence Pattern Mining

_{1}, o

_{2}, …, o

_{k}} from a sequence E

_{i}is a co-occurrence pattern, if max{T(O)}-min{T(O)}, where T(O) = {t

_{o}

_{1}, t

_{o}

_{2}, …, t

_{ok}}, t

_{oj}is the occurrence time of o

_{j}(j = 1, 2, …, k) in E

_{i}, and ∆t is a predefined time threshold. The co-occurrence pattern O becomes a frequent co-occurrence pattern, if it occurs in no less than δ sequences.

#### 5.2.2. TFCP Mining

_{co}. All TFCPs can be grouped by its consequent, i.e., R = ⋃R(e

^{t}), where R is the complete set of TFCPs, R(e

^{t}) = {〈E

_{-}

^{t},{e

_{i}

^{t}}〉| e

_{i}

^{t}= e

^{t}∧〈E

_{-}

^{t},{e

_{i}

^{t}}〉 is a TFCP}. Each group can be mined separately in the service event sequence set E = {E

_{1}, E

_{2}, …, E

_{k}}. Such divide and conquer strategy has been widely used in frequent pattern mining problem [49].

_{1}, …, E

_{k}} by f(e

^{t}) = ∑

_{i}n

_{i}, where n

_{i}is the occurrence times of e

^{t}in sequence E

_{i}. Service event types whose occurrence times are no less than δ

_{co}are selected as potential consequents, which is denoted as C

_{cq}.

^{t}in C

_{cq}, we generate the corresponding TFCP set R(e

^{t}) separately. Every type e

_{j}

^{t}(e

_{j}

^{t}≠ e

^{t}) in C

_{cq}will be selected to generate a potential TFCP 〈{e

_{j}

^{t}},{e

^{t}}〉. Then we test whether 〈{e

_{j}

^{t}},{e

^{t}}〉 is a TFCP with consequent e

^{t}by judging whether f(〈{e

_{j}

^{t}},{e

^{t}}〉) ≥ δ

_{co}. During this process, we record the co-occurrence time interval. After generating a valid TFCP, we extend it by adding a third type e

_{k}

^{t}∈ C

_{cq}(e

_{k}

^{t}≠ e

_{j}

^{t}, e

_{k}

^{t}≠ e

^{t}) into the antecedent. We test whether 〈{e

_{j}

^{t}, e

_{k}

^{t}},{e

^{t}}〉 is a TFCP with consequent e

^{t}in the same manner. The extension is repeated until there is no new valid TFCP. There is a skill during the extensions to avoid generating repeated TFCPs, i.e., all types are added in lexicographical order. It indicates that we only add a larger service event type to a validated TFCP. Thus, we can easily mine the service event correlations in generated TFCPs.

#### 5.2.3. Service Hyperlink Generating

## 6. Our Predictive Industrial Maintenance Approach

#### 6.1. The Framework of Our Approach

#### 6.2. Proactive Data Service Graph Generating

**Definition**

**7.**

- V = A∪F, F is the complete set of edge proactive data services, and F is the complete set of cloud proactive data services. Each node v ∈ F should be AND type or OR type. AND type implies that the fault represented by v occurs if all anomalies and faults pointing to v occur; OR type implies that the fault represented by v occurs if any anomaly or fault pointing to v occurs.
- E ⊆ V × F is a non-empty edge set. Each edge e ∈ E is labelled with a propagation time interval T
_{int}.

_{i})|e

_{i}

^{t}= α} be all service hyperlinks whose effect event is α. Thus, these service hyperlinks have same target service, which is written s

_{α}. If |SHL(α)| > 1, the cloud service s

_{α}is defined as an OR node. Otherwise, s

_{α}is defined as an AND node.

#### 6.3. Event Routing on Proactive Data Service Graph

_{i}can reach a service s

_{j}, i.e., s

_{j}is reachable from s

_{i}, if there exists a sequence of adjacent services (i.e., a path) which starts from s

_{i}and ends with s

_{j}. Based on the definition of PDSG, all services reachable from a given service s

_{i}are cloud services. Therefore, when a service s

_{i}generates a service event, all reachable services may be the destinations of this service event. However, the number of these destinations may be too large. For example, as Figure 3 shows, an L-CF service event from s

_{1}may be routed to each rest service on the graph. Finding the routing path to all potential destinations are too expensive. Furthermore, it may cause repeat maintenance plans. For instance, an L-IPAV and a CB fault are generated by service s

_{9}and s

_{12}on one path. If people predict that a CB fault is going to happen, they will certainly realize that an L-IPAV will happen before the CB fault. But if the L-IPAV is stopped, the CB will not happen. Therefore, there is no need to plan the maintenance twice for the two faults respectively. Consequently, a candidate destination set is needed to be selected from all potential destinations. Herein, a candidate destination set can be regarded as these reachable services which are not on the path to other reachable services. The formal definition is shown below.

**Definition**

**8.**

_{i}on a PDSG, a reachable service s

_{j}becomes a candidate destination of the service events generated by s

_{i}if there is no reachable service s

_{j}’ (s

_{j}’ ≠ s

_{j}), which s

_{j}is on a path from s

_{i}to s

_{j}’.

_{i}’s candidate destination set is to generate all reachable services of s

_{i}. This can be achieved as follows: Each graph has a reachable matrix to reflect its reachability. A PDSG corresponds to a reachable matrix M

_{n}

_{*n}, where n is the service number on the PDSG, and the element M[i, j] at the ith line jth column is 1, if s

_{i}reaches s

_{j}; otherwise, M[i, j] = 0. The candidate destination set of an arbitrary service s

_{i}can be expressed as CDS(s

_{i}) = {s

_{j}|M[i,j] = 1 ∧ d

_{out}(s

_{j}) = 0}, where d

_{out}(s

_{j}) is the out-degree of s

_{j}.

_{i}may reach a candidate destination via multiple paths. It has to route a service event on the most probable path to this candidate destination. It means, a service should select the target service pointing by its hyperlinks which will most probably route the service event into the candidate destination. We develop a heuristic approach based on A* algorithm to help a service make a selection automatically. Our approach considers the heuristic that estimates the most probable path to each candidate destination, which means to maximize f = g + h, g is the probability from service s

_{i}to an arbitrary service, h is the probability from the arbitrary service to a candidate destination. In this paper, the occurrence of a service event is only related to its casual service events’ occurrence. Under this case, we can calculate h by multiply the probabilities on a path from the arbitrary service to the candidate destination.

_{i}generates a service event, it will compute its candidate destination set CDS(s

_{i}) = {d

_{1}, d

_{2}, …, d

_{n}}. For each candidate destination d

_{j}, service s

_{i}computes the probability from itself to d

_{j}. If the probability is no less than a predefined probability threshold, s

_{i}will make a warning to the staff for making maintenance plan of the related fault. Whether the probability exceeds the threshold or not, service s

_{i}will select the target service for the most probable path from s

_{i}to d

_{j}for routing the generated service event. After this, the process is over. Any service generating a service event will start a new process same with this one.

## 7. Proactive Data Service Graph Validation

^{+}(the set of non-negative real numbers) representing the timestamp of each state, i.e., an assignment to X - {τ}. Thus, a trace π of S is an infinite time-ordered sequence of states denoted as π = s

_{0}, s

_{1}, …, s

_{i}, …, where s

_{0}⊨ I, and ∀k ≥ 0, (s

_{k}, s

_{k}

_{+1}) ⊨ T. ⊨ is the satisfaction relation representing a variable assignment satisfies a formula, i.e., the formula is true under the variable assignment. The kth state of a trace π is written π[k].

_{I}ϕ|φS

_{I}ϕ|♢

_{I}φ|◻

_{I}φ, where ⊥ represents false, ⊤ represents true, and p∈APs. U

_{I}, S

_{I}, ♢

_{I}and ◻

_{I}are temporal operators, in which I is an interval as [a, b], [a, b), (a, b], (a, b), a, b∈R

^{+}∪{+∞}. U

_{I}is a time-constrained until operator, and φU

_{I}ϕ means φ will be true lasting a time interval no longer than I until a time when ϕ is true. S

_{I}is a time-constrained since operator, and φS

_{I}ϕ means φ has been true lasting a time interval no longer than I since a time when ϕ was true. ♢

_{I}is a time-constrained eventually operator, and ♢

_{I}φ means φ will be true at some future time, where the time interval during which φ is not true, is no longer than I. ◻

_{I}is a time-constrained always operator, and ◻

_{I}φ means φ will be true lasting a time interval no longer than I in the future.

- π[k] ⊨ p, if and only if p is an atomic proposition which is true under π[k].
- π[k] ⊨ ¬φ, if and only if not π[k] ⊨ p.
- π[k] ⊨ φ∧ϕ, if and only if π[k] ⊨ φ and π[k] ⊨ ϕ.
- π[k] ⊨ φ∨ϕ, if and only if π[k] ⊨ φ or π[k] ⊨ ϕ.
- π[k] ⊨ φU
_{I}ϕ, if and only if ∃i > k, π[i] ⊨ ϕ, τ_{i}-τ_{k}∈ I, ∀k ≤ j < i, π[j] ⊨ φ. - π[k] ⊨ φS
_{I}ϕ, if and only if ∃i < k, π[i] ⊨ ϕ, τ_{k}-τ_{i}∈ I, ∀i < j ≤ k, π[j] ⊨ φ. - π[k] ⊨ ♢
_{I}φ, if and only if ∃i < k, π[k] ⊨ φ, τ_{k}-τ_{i}∈ I, ∀i ≤ j < k, π[j] ⊨ ¬φ. - π[k] ⊨ ◻
_{I}φ, if and only if ∃i < k, π[i] ⊨ ¬φ, τ_{k}-τ_{i}∈ I, ∀i < j ≤ k, π[j] ⊨ φ.

**Definition**

**9.**

_{G}= 〈X

_{G}, I

_{G}, T

_{G}〉, where X

_{G}= ES∪CS∪{τ}, ∀x

_{g}∈X

_{G}, D(x

_{g}) = {⊥, ⊤}, and ES, CS are the edge and cloud services on the PDSG respectively; I

_{G}= X∧(τ = 0); T

_{G}= ∧

_{(x}

_{g}

_{∈ES}

_{∪CS)}(x

_{g}→x

_{g}’)∧(τ≤τ’)∧((∨

_{(x}

_{g}

_{∈ES}

_{∪CS)}(x

_{g}≠ x

_{g}’))→(τ = τ’)), x

_{g}’ is the next state of x

_{g}.

_{G}reflects the assumption that a state can last for a period but change instantly. To describe system state behaviors, a state variable x

_{g}∈ES of a PDSS will be expressed as a set of predicates. These predicates are generated according to the preset operations in each edge service. For example, BT sensor data can be expressed as {d

_{BT}.value ≤ 20, 20 < d

_{BT}.value < 80, d

_{BT}.value ≥ 80}. It is because the preset operations (Some classification-based outlier detection method will classify the data and consider the classes with small data as outliers.) classify the input sensor data into three classes, in which data d satisfying d.value ≤ 20 and d.value ≥ 80 are outliers. Formally, each state variable x ∈ X in an industrial system model S is mapped into a state variable x

_{g}in a PDSS. It is expressed by a non-empty set p

_{x}of predicates. The mapping function is denoted as M. In this way, an assignment to a state variable can be expressed as a proposition. Therefore, system states and traces of S can be expressed as MTL formulae. Herein, a trace π of S is mapped into a routing path of a PDSS, which is denoted as π’.

_{or}, then a consecutive set of states π’[j], π’[j + 1], …, and π’[k] satisfied f

_{or}, and there is a time interval left adjacent to π’[j], states in which satisfied at least one node v, where (v, f

_{or}) is an edge pointing to f

_{or}; (2) Any node n satisfying condition 1) also satisfies that its corresponding interval does not exceed the propagation time interval T

_{int}labelled on the edge (v, f

_{or}).

_{and}, then a consecutive set of states π’[j], π’[j + 1], …, and π’[k] satisfied f

_{and}, and for each node v pointing to f

_{and}there is a time interval I

^{(v)}left adjacent to π’[j], states in which satisfied v; (2) For any node v satisfying condition (1), its corresponding interval I

^{(v)}does not exceed the propagation time interval T

_{int}labelled on the edge (v, f

_{and}).

## 8. Results

#### 8.1. Experiment Setup

#### 8.2. Effectiveness

#### 8.2.1. Effects of Our Approach

#### Variation of Correlation Number and Hyperlink Number

_{p}= 0.8) into service hyperlinks. We record the results and draw them in Figure 7.

#### Effectiveness of Our Approach

#### 8.2.2. Comparative Effects of Different Approaches

#### 8.3. Efficiency

**Definition**

**10.**

_{i}is the time our algorithm consumes to route the ith output service event. Let N be the current size of all output service events, the average latency of an approach can be defined as t

_{lat}= ∑

_{i}t

_{i}/N.

## 9. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Partial anomaly propagation under correlations among sensors and devices in a coal power plant.

Abbreviation | Explanation | |
---|---|---|

device | CFD | coal feeder |

CM | coal mill | |

PAF | primary air fan | |

sensor/service | AP | active power |

BT | bear temperature | |

CAVD | cold air valve degree | |

CF | coal feed | |

DPGB | differential pressure of grinding bowl | |

DPSF | differential pressure of strainer filter | |

E | electricity | |

HAVD | hot air valve degree | |

IAP | inlet air pressure | |

IPAP | inlet primary air pressure | |

IPAT | inlet primary air temperature | |

IPAV | inlet primary air volume | |

OTT | oil tank temperature | |

UL | unit load | |

V | vibration | |

anomaly/fault/event type | CB | coal blockage |

CI | coal interruption | |

H-CAVD | over high cold air valve degree | |

H-DPSF | over high differential pressure of strainer filter | |

H-HAVD | over high hot air valve degree | |

H-IPAT | over high inlet primary air temperature | |

H-V | over high vibration | |

L-AP | over low active power | |

L-BT | over low bear temperature | |

L-CF | over low coal feed | |

L-DPGB | over low differential pressure of grinding bowl | |

L-E | over low electricity | |

L-HAVD | over low hot air valve degree | |

L-IAP | over low inlet air pressure | |

L-IPAP | over low inlet primary air pressure | |

L-IPAT | over low inlet primary air temperature | |

L-IPAV | over low inlet primary air volume | |

L-OTT | over low oil tank temperature | |

L-UL | over low unit load |

Fault Type | Associated Anomalies | Conf ^{1} | |
---|---|---|---|

L-IPAV fault on a PAF device | AE_{1}^{2} | L-IPAT, L-HAVD, L-IPAP. | 100.00% |

AE_{2} | L-E on CM. | 100.00% | |

AE_{3} | L-IPAT, L-IPAP. | 80.00% | |

L-IPAP fault on a PAF device | AE_{1} | H-CAVD, L-OTT. | 86.96% |

CB fault on a CM device | AE_{1} | H-HAVD, L-IAP. | 100.00% |

AE_{2} | L-IPAT. | 88.89% | |

H-DPSF fault on a CM device | AE_{1} | L-BT on PAF. | 100.00% |

^{1}‘Conf’ is the confidence of an association rule;

^{2}‘AE

_{i}’ is the ith set of associated events of a fault.

Fault Type | L-IPAV | L-IPAP | CB | L-DPSF | ||||
---|---|---|---|---|---|---|---|---|

Approaches | AE_{1} | AE_{2} | AE_{3} | AE_{1} | AE_{1} | AE_{2} | AE_{1} | |

Our Approach | 70 | 58 | 82 | 152 | 63 | 96 | 132 | |

Range-based Approach | - ^{1} | 12 | 9 | - | 15 | 2 | - | |

Outlier Detection Approach | 18 | 21 | - | 31 | 23 | 19 | 33 | |

Discord Discovery Approach | - | 21 | 19 | 31 | 35 | 26 | 34 |

^{1}‘-’ represents this approach cannot make a warning.

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Zhu, M.; Liu, C. A Correlation Driven Approach with Edge Services for Predictive Industrial Maintenance. *Sensors* **2018**, *18*, 1844.
https://doi.org/10.3390/s18061844

**AMA Style**

Zhu M, Liu C. A Correlation Driven Approach with Edge Services for Predictive Industrial Maintenance. *Sensors*. 2018; 18(6):1844.
https://doi.org/10.3390/s18061844

**Chicago/Turabian Style**

Zhu, Meiling, and Chen Liu. 2018. "A Correlation Driven Approach with Edge Services for Predictive Industrial Maintenance" *Sensors* 18, no. 6: 1844.
https://doi.org/10.3390/s18061844