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Modeling technologies can provide strong support to existing emission management systems, by means of what is known as a Predictive Emission Monitoring System (PEMS). These systems do not measure emissions through any hardware device, but use computer models to predict emission concentrations on the ground of process data (e


Introduction
The increasing attention devoted to air quality by legislative, scientific, industrial and public sectors has led to the development and enforcement of different emission monitoring strategies.
The traditional solution employed by the industry to comply with the legislation is to monitor the emissions via hardware based CEMS; such systems normally comprise analysers (to sample and identify the compositions of released flue gas) and an IT infrastructure to manage, record and store the emissions values (Arioni et al., 2013;Paira et al., 2017). PEMS are an innovative technology able to exploit advanced mathematical models in order to estimate emission values with an accuracy comparable with that of CEMS at a fraction of the cost.
Several techniques are actually available for model building, however, a broad categorization into two groups can be made:


Empirical or data-driven modelling, wherein available data are used to train "black-box" models;  First principle modelling, wherein a theoretical model derived from the physics of the problem is adopted.
Indipendently from the approach, PEMS need to be fed with real-time process data, such as fuel flow, load, operating pressure and temperature.
On the ground of more than 15 years of successful field applications (Eisemann et al., 2014) and because of the inherent lower life-cycle costs and reduced footprint (Roth & Lawrence, 2010), PEMS have gained and keep gaining acceptance and popularity in a growing number of industries and countries. According to several environmental regulations (EPA, 2009;Netherlands Technical Agreement, 2014), plants are allowed to lease a portable CEMS to gather emissions data, which, combined with simultaneous process data, will be used to build and validate mathematical models.

Figure 1. Inferential Modeling For Emission Monitoring
Once the models have been certified, the temporary CEMS is removed and replaced by the inferential http://www.scholink.org/ojs/index.php/se Sustainability in Environment Vol. 3, No. 4, 2018 331 Published by SCHOLINK INC. system.
This approach is particularly suited when applied to combustion processes where fuel nature and composition are reasonably stable or measurable: for the same reason it is not advisable to use PEMS on urban incinerators where feed composition is "by design" highly variable and uncontrolled. Some countries have already released specific guidelines about where PEMS should be applied instead of CEMS and where the hardware-based solution will be maintained as the only allowed option (Ciarlo & Bonavita, 2016).
PEMS can also be used as a back-up if a CEMS is in place, and irrespective of which role it plays, it provides numerous benefits in different applications (Samdami, 1994 (Chui et al., 2018).

PEMS and Sensor Validation
While PEMS show a number of specific advantages over CEMS (reduced maintenance, no consumables, no energy consumption, etc.), because of their data-driven nature, they require distinctive attentions.
Great care has to be paid on the quality assurance of PEMS output; building an effective and reliable model is not enough as the ongoing accuracy of the model strictly relies on the quality of the input variables used by the model itself.
This means that each process parameter fed into the model shall be routinely verified to confirm that related instrumentation is performing according to expectations. In the case any anomalous behaviour is detected, a proper alarm shall be raised, warning about PEMS prediction quality.
Presently, some of the best commercial solutions exploit simple data range checks to verify, in real-time, if a sensor reading stays within predefined limits. Although reasonable, these checks are pretty relaxed and not very effective in identifying all possible failures (sensor freezing to a constant value is for example not discoverable through such a basic control). Additionally if sensor j is found out-of-range the typical action is to replace its value with the last useful sample at time t* (see Figure 2). Obviously this emergency gimmick becomes quickly less and less acceptable.

Figure 2. Basic Sensor Fault Detection in Present PEMS
Notwithstanding the above approach is actually accepted by most of the regulations, additional requirements will be increasingly present in legislation and in end-user specifications. The development and deployment of robust SV routines will become a relevant requirement for PEMS applications (Ciarlo et al., 2017): this additional software module will be responsible not only to identify possible sensors malfunctions, but also to provide reconstructed values to be temporarily used as input values.
In fact, reconciled data-under proper conditions-could be automatically selected as a replacement of the affected sensor, maintaining PEMS accuracy and performances well within legislation limits.
Machine Learning techniques are now available and promise to greatly enahance data-driven application robustness and reliability. Authors have developed an approach that, starting from a very general sensor classification, is able to help end-users and practitioners in automatically:

a)
Detect when a PEMS output should be labelled as "bad quality" because one of the related model input is faulty; b) Identify which is the sensor to be blamed as faulty (in order to promptly alert maintenance department); c) Whenever possible, substituting the faulty sensor reading with a reconciled value with the objective of preserving PEMS acceptable performances (Angelosante et al., 2018).
The final scope is to provide a resilient version of PEMS, able to properly manage model input failures. This Robust PEMS (or R-PEMS) could contribute to reassure Environmental and Health Authorities and public opinion at large about the reliability and effectiveness of software-based emission monitoring systems facilitating their adoption and operation.

R-PEMS: Concept and Procedure
At the beginning of each project, PEMS engineer have to select the most relevant process data showing good correlation with the emission variables.
The acquired parameters are normally chosen after a deep analysis and investigation on the P&IDs and other process documentation. As modern industrial plants are equipped with an extensive set of devices for control and monitoring purposes, the initial data-collection phase involves a very large number of signals (much more than those actually used as input variables for PEMS) that are then reduced during the engineering phases. During a PEMS project, it is quite common to acquire up to 80-100 different process variables and to progressively reduce the number up to use less than a dozen inputs for each model.
Under normal operations, the abundance of sensors naturally provides a frame rich of multiple correlations among instrument values. When a sensor encounters a fault (e.g., drifiting, freezing), the correlation of its values with other variables tends to change: this peculiar behaviour can be used to identify a faulty sensor.
This scenario paves the way for sensor validation techniques based on analytical redundancy: this approach consists in continuously comparing the actual readings from sensors with estimated values obtained through data-driven models exploiting the relationships with other plant parameters.
Unfortunately analytical redundancy is not always present among sensors. It is the case of variables that cannot be estimated by the readings of surrounding devices (e.g., the sulfur content in gas in combustion processes).
In thoses cases a different approach must be adopted: this is generally referred as hardware redundancy sensor validation, and requires the presence of multiple devices (usually at least three in order to allow "voting" mechanisms) so that it is possible to promptly identify failures and resort to reliable back-ups.
Clearly, hardware redundancy, requiring additional instrumentation, is expensive and it is typical of critical processes (nuclear power plants, aerospace…) while it is limited to highly crucial variables in most industrial processes.
The present paper focuses only on the analytical redundancy methods and how these solutions can help in maintaining PEMS accuracy within the regulatory-enforced limits: the normal target is to keep model relative accuracy within 10% limit even in case of input failures (different values can be applicable depending on actual pollutant concentrations).
From an operative point of view, the first step will be understanding if and where analytical redundancy among model inputs exists and how it can be used for SV purposes: in the following section an overview on how to classify the different sensors will be provided and eventually which SV strategy should be applied to each category.

Establishing a SV Procedure: The Sensor Taxonomy Classification
Building a PEMS always starts with identifying quantitative relationships among a number of sensors.  sensor measurements and the constraint relations among them (Chow & Willsky, 1984;Lee & Park, 2005). Its principle is generally based on consistency checking between the observed behavior of the process provided by the sensors and the expected behavior given by a mathematical representation of the process.
The basic concept of R-PEMS is to add a number of computational functions to the standard PEMS and perform on-line checks in order to make the system as much robust as possible through advanced machine learning algorithms (see Table 1).  implementation, each devoted to one specific function and producing a specific action.
In the following the three steps will be briefly discussed. All the following discussions are based on the assumption of a single sensor fault hypothesis. That is, we are assuming that persistent sensor failure are so sporadic that the probability that two sensors fails contemporaneously or in a short time difference is negligible. Therefore, our approach relies upon the fact that we can detect, isolate and reconcile a sensor before another one fails.

Figure 4. R-PEMS Concept
Step 1: Sensor Fault Detection (SFD) The input of the SFD algorithm is the process vector x t containing the values of the N process tags at time t, and the output of the SFD is a binary variable SFD t which states whether the point x t is faulty (SFD t = 1) or not faulty (SFD t = 0). In case the point x t is not faulty, x t is fed to the existing PEMS and the emission at time t corresponding to the process vector x t is evaluated. If SFD t = 1, we keep observing the evolution of SFD τ for t < τ < t + t SFD , where t SFD is an SFD activation length. If SFD τ = 1 for t < τ < t + t SFD , we declare that the process vector has one or more persistent faults, and we activate the SFI block.
Step 2: Sensor Fault Isolation (SFI) Once the fault has been declared, the SFI aims at isolating the faulty sensor. The input of the SFI is a set of consecutive process vectors. Clearly, our rationale is to feed the SFI with points having a sensor fault. Therefore, we want to make sure that only the points after the sensor fault detection are fed to the SFI block are fed to the SFI block. The output of the SFI is an index i SFI of the faulty sensor.
Step 3: Sensor Reconciliation (SR) Once the faulty sensor index i SFI has been identified, the last step of the R-PEMS pre-processing is the data reconciliation that is the substitution of the measurement of the faulty sensor with a reconciled value which is calculated from the non-faulty sensors. Several Machine Learning algorithms may be applied for such tasks, trying to exploit the wealth of information which is hidden in historical process data. Next section will provide some further details on the algorithms used for reaching the scope of building fault resilient PEMS.

Operating Envelope Estimation
As mentioned in the previous sections, the idea of data validation and reconciliation is to detect sensor failures based on multiple (redundant) sensor measurements and the constraint relations among them.
The mathematical representation of the process, that intrinsically contains the analytical redundancy of the system, can be derived from first principle equations, i.e., mass/energy conservation laws, Ohm/Kirchoff laws in electric networks, etc. However, in many situations, physics-based equations may be difficult to obtain due to the complexity of the process and high process dimensionality and therefore a data-driven approach has to be preferred.
In this section, we advocate a method for learning an approximate form of balance equations. It is worth pointing out here that we do not assume any process knowledge for performing this task. Any prior knowledge can be embedded in this formalism to improve the learning process.
To be specific, given the training data drawn from the process tags time series, we aim at discovering the operating envelope of the process, that is, the regions where the process tags must lie during normal operations. For the sake of simplicity, if we assume the process to be defined by N = 3 process tags, an example of the training data drawn from the process tags time series is depicted in Figure 5. sensor 3

Figure 5. Training Set Example for N=3 Sensors
Given these training data, machine learning algorithms for density estimation can provide an estimate of the operating envelope. Figure 6 depicts the operating envelope of the training data an example of   LWR have been adopted in the final implementation of the algorithm. Although a complete description of the algorithm is outside the scope of this work-the interested reader can refer to (Angelosante et al, 2018) for a more rigorous treatment of the sensor fault isolation, detection and reconciliation problem-in the next section a short introduction to LWR is given.

Locally Weighted Regression (LWR)
LWR is a nonparametric regression method wherein regression of a data input is performed by a linear (or quadratic) regression around a local subset of the training set around the point of interest (Cleveland, 1979).
An important parameter to be designed (typically via cross validation) is the bandwidth τ, that is, the The major advantage of LWR is the insensitivity to training set imbalance, that is, the non-uniformity of the sample in the operating envelope. While classical parametric regression methods are biased by training set imbalance and require pre-processing, LWR are natively insensitive to this effect.
Additionally LWR, as a memory-based method, entails favourable features which reduce the amount of engineering work and skills required to properly configure them. For these reasons, they have been chosen for the final implementation of the Robust PEMS.

Practical Implementation of SFD
Once the operating envelope has been estimated, SFD can be performed. In fact, abnormal situations that occur due to sensor faults, induce changes in sensor measurements that can drive the process data outside the operating envelope.
The crux of the SFD is to monitor the distance between the process sensor data x and the operating envelope: a fault is declared in case the process data lies outside the operating envelope.
An example of a detected faulty case is depicted in Figure 8, which shows the operating envelope (green volume) and an anomalous process data point (red circle), which lies outside the estimated operating envelope. In such a case, the SFD will detect a sensor fault.

Practical Implementation of SFI
The goal of SFI is to identify which sensor out of N has failed. In principle, the fault can occour in any of the N sensors. Isolating faulty sensors amounts to a combinatorial problem as all the possible combinations of sensors must be checked for consistency to find the anomalous sensors. Assuming that only one sensor at time can fail simplifies the search.
Referring to the example in Figure 8, it is clear that the faulty sensor is sensor 2. In fact, if we eliminate sensor 2 from the problem, so creating operating envelope without sensor 2, the process tag data will lie inside this reduced operating envelope (Figure 9). This procedure also shows a pratical manner for identifying sensor anomalies, that is, if the fault is caused by the i-th sensor, it is expected that all but the i-th projection are still outside the projected operating envelope.

Practical Implementation of the Reconciliation Algorithm
The output of the SFI will return the index i SFI of the most likely faulty sensor. The goal of the recovery algorithm is to reconstruct this sensor reading, using the rest of the healthy data. For this task, we advocate the usage of non-linear regression methods (e.g., LWR) that, using training data, create a soft-sensor of the faulty tag, using the rest of the healthy tags, as sketched in Figure 10.

Tests and Results
In this section, we empirically verify the performances of the SFD/SFI algorithms that have been introduced in the previous sections. We are considering a data set collected during a real PEMS project in Europe. The raw dataset consists in more than 100 sensor data. Out of these tags, only 29 are used for the development of PEMS application. In this document, we are focusing only in one particular gas for the sake of brevity, the O 2 , and we will be dealing only with the 8 tags in input to the O 2 PEMS, that is, N = 8.
The dataset consists of 4160 time ordered observations from 8 different sensors tags. The dataset is split into a training set, validation set and testing set. The training, validation and testing datasets will have the size of 2774, 693 and 693 observations, respectively. The training set is used to develop both the PEMS and the SFD/SFI and Recovery algorithm. The Validation set is used for fine tuning the models. The test set is used for performance evaluation purpose. In this study we focus our attention on the permanent faults characterized by continuity of the fault signature occurrence leading to a mismatch that we can observe over time. Within the class of permanent faults we restrict our study to the following fault types:

Sensor Fault Simulation Setting
While large biases and drifts may be discovered from simple range check, the sensor freeze will be never discovered by a range check. Therefore, for the sake of brevity, we highlight the performance of the proposed SFD/SFI and Recovery algorithm for sensor freeze. In this paper, we want to analyze how "general purpose" SFD/SFI methods would perform on sensor freeze. In this respect, the proposed algorithm has shown also good performance against sensor biases and drifts.
In our sensor fault simulation setting, we retain the unchanged training set used for the evaluation of the PEMS and the SFD, SFI, and Recovery algorithm and we simulate freeze in the test set. This assumption is not limited since any fault or anomalous data in the training set can be manually or automatically removed by the PEMS designer.
We have simulated a deterministic sensor freeze in each of the sensor. From the original test set, we have created 8 test sets wherein in the i-th test set, the i-th sensor is frozen at its value at time 300 (we have performed test for various freezing time but they will not be reported in this paper). Figure 11 shows the case Sensor 1 freezes at time 300 vs the original sensor value. The other input sensor to the PEMS, i.e., Sensor 2 -Sensor 8 are unchanged.

Figure 12. PEMS vs R-PEMS Performance Comparison
The dotted ellipses denotes a point around freeze time 300 wherein there is a significant discrepancy between the true O 2 concentration and the performance of the original PEMS and R-PEMS with freeze.
At this point, the SFD/SFI has not decided about the fault. The dash ellipses show a significant discrepancy between the true O 2 concentration and the performance of the original PEMS, but the R-PEMS output is in line with the target performance. To show this, Figure 12 depicts the absolute relative error of the original PEMS with no freeze, the original PEMS with freeze, and the R-PEMS with freeze. Out of the 693 test points, we have created 9 block of 70 consucutive point and the last of 63 points, and we have calculated the relative absolute error (i.e., the relative accuracy).

Figure 13. PEMS vs R-PEMS Relative Accuracy Comparison
As already pointed out, the target is to keep this relative accuracy within 10% limit. While the original PEMS with no fault is well below this limit, when Sensor 1 freezes, the relative accuracy of the original PEMS exceed the 10% limit. On the other hand, the R-PEMS, after a transient phase required for detecting the fault, recovers the performance to an acceptable limit.

Conclusions
Predictive Emission Monitoring Systems have shown the capability to provide a valuable alternative to traditional HW-based analysers, offering comparable level of performances and reliability at reduced life-cycle cost and with additional benefits.
Such paybacks are making plant owners more and more aware of PEMS potential and are largely expanding the interest around this technology.
However some additional features are expected to be required to remove any residual concern from Authorities which would jeopardize their complete acceptance. Other than a problem in the integrity of the model-which can be assessed on a regular basis-PEMS performances may degrade only for input values reliability issues.
Focus of this paper has been to introduce a possible systematic approach to sensor validation for environmental monitoring and to outline what a modern software tool should be able to provide.
Starting from a detailed classification of sensor types and roles it is possible to classify sensors whose readings can be reconstructed through analytical redundancy from the ones which have little or no correlation with other measured variables. While the latter can be validated only by hardware redundancy, sensor belonging to the first category are usually the largest majority and are the typical target variables used for advanced data-driven algorithms.
The paper shows how Machine Learning techniques can effectively contribute to solve the tasks of Fault Detetction, Fault Isolation and Sensor Reconciliation. Extensive tests on real plant data showed how a careful application of several algorithms is able to properly manage the problem of single-sensor fault, driving back the PEMS prediction inside the acceptance limits and largely increasing the reliability of the system even in presence of a sensor malfunction. Among several alternative algorithms, Local Weighted Regression was selected as the most appropriate because of the smaller amount of engineering requested and the easiness of implementation.